Researchers investigate mechanics of lithium sulfides, which show promise as solid electrolytes.


MIT Lithium Sulfide Press Web
Using specialized equipment, the MIT team did tests in which they used a pyramidal-tipped probe to indent the surface of a piece of the sulfide-based material. Surrounding the resulting indentation (seen at center), cracks were seen forming in the material (indicated by arrows), revealing details of its mechanical properties. Courtesy of the researchers

Most batteries are composed of two solid, electrochemically active layers called electrodes, separated by a polymer membrane infused with a liquid or gel electrolyte. But recent research has explored the possibility of all-solid-state batteries, in which the liquid (and potentially flammable) electrolyte would be replaced by a solid electrolyte, which could enhance the batteries’ energy density and safety.

Now, for the first time, a team at MIT has probed the mechanical properties of a sulfide-based solid electrolyte material, to determine its mechanical performance when incorporated into batteries.

The new findings were published this week in the journal Advanced Energy Materials, in a paper by Frank McGrogan and Tushar Swamy, both MIT graduate students; Krystyn Van Vliet, the Michael (1949) and Sonja Koerner Professor of Materials Science and Engineering; Yet-Ming Chiang, the Kyocera Professor of Materials Science and Engineering; and four others including an undergraduate participant in the National Science Foundation Research Experience for Undergraduate (REU) program administered by MIT’s Center for Materials Science and Engineering and its Materials Processing Center.

“Batteries with components that are all solid are attractive options for performance and safety, but several challenges remain,” Van Vliet says.

Read more at the MIT News Office.

David L. Chandler | MIT News Office
February 2, 2017


Analyzing lithium ion battery fatigue

2016 Materials Day Poster Session Winners

Faculty highlight: Krystyn Van Vliet


McGrogan Eggleton 6517 Web
Graduate student Frank McGrogan, left, supervised the work of 2016 Summer Scholar Erica Eggleton on lithium manganese oxide [LMO] electrodes for lithium ion batteries in the Van Vliet Lab. Photo, Denis Paiste, Materials Processing Center.
Published in Daily News
Once fabricated, objects can be altered by adding new polymers.
MIT 3D Printing 1 press Web
MIT chemists have now developed a 3-D printing technique that allows them to print objects and then go back and add new polymers that alter the materials’ chemical composition and mechanical properties. These new polymers can be reactivated by light. Image, Demin Liu and Jeremiah Johnson

Three-dimensional printing technology makes it possible to rapidly manufacture objects by depositing layer upon layer of polymers in a precisely determined pattern. Once these objects are completed, the polymers that form the material are “dead” — that is, they cannot be extended to form new polymer chains.

MIT chemists have now developed a technique that allows them to print objects and then go back and add new polymers that alter the materials’ chemical composition and mechanical properties. The researchers can also fuse two or more printed objects together to form more complex structures.

“The idea is that you could print a material and subsequently take that material and, using light, morph the material into something else, or grow the material further,” says Jeremiah Johnson, the Firmenich Career Development Associate Professor of Chemistry at MIT.

This technique could greatly expand the complexity of objects that can be created with 3-D printing, says Johnson, the senior author of a paper describing the approach in the Jan. 13 issue of ACS Central Science. The paper’s lead authors are former MIT postdoc Mao Chen and graduate student Yuwei Gu.

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Read more at the MIT News Office.

Anne Trafton | MIT News Office
January 13, 2017

Published in Newsletter Articles
Porous, 3-D forms of graphene developed at MIT can be 10 times as strong as steel but much lighter.

A team of researchers at MIT has designed one of the strongest lightweight materials known, by compressing and fusing flakes of graphene, a two-dimensional form of carbon. The new material, a sponge-like configuration with a density of just 5 percent, can have a strength 10 times that of steel.

In its two-dimensional form, graphene is thought to be the strongest of all known materials. But researchers until now have had a hard time translating that two-dimensional strength into useful three-dimensional materials.

The new findings show that the crucial aspect of the new 3-D forms has more to do with their unusual geometrical configuration than with the material itself, which suggests that similar strong, lightweight materials could be made from a variety of materials by creating similar geometric features.

Read more at the MIT News Office.back to newsletter

David L. Chandler | MIT News Office
January 6, 2017

Published in Newsletter Articles
MIT engineer’s research on surfaces is improving everything from power plants to ketchup bottles.
MIT Varanasi 01 Press Web
“If you really understand the phenomena, you can reduce it to a few nondimensional parameters,” MIT mechanical engineer Kripa Varanasi says. That collapses the complexity into manageable formulas and phase diagrams, “and then we can design new processes, new products, and zero-tradeoff solutions.” That approach, he says, has been “at the heart of the companies we’ve started.”
Photo, Bryce Vickmark.

Ketchup’s sluggish pace as it oozes out of its bottle is a longstanding nuisance — but one that is about to be upended by a new product coming to market. The brainchild of MIT mechanical engineer Kripa Varanasi and his students, a new coating called LiquiGlide is set to make the transition from the laboratory to consumer and industrial markets.

LiquiGlide renders a surface highly slippery and allows every last drop of ketchup — or almost any other viscous product, from paint, to glue, to cosmetics — to flow from its container without sticking, saving billions of gallons of product from going waste.

“Viscous products sticking to the inside of containers leads to huge losses across industries,” Varanasi says. “For example, in paint manufacturing alone, paint sticking to the inside of mixing and holding tanks costs the industry more than 100 million gallons of lost product and billions of dollars per year in associated waste costs. Using the LiquiGlide platform, we are on a mission to eliminate waste generated across manufacturing applications, in areas ranging from food and agrochemical production to health care and energy, to usher in a new era of sustainable manufacturing.”

Read more at the MIT News Office.

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David L. Chandler | MIT News Office
January 19, 2017

Published in Newsletter Articles
Itamar Kimchi studies the physics underlying unusual behavior of electrons in compounds such as transition metal oxides.
Itamar Kimchi 8067 DP Web
MIT Pappalardo Fellow in Physics Itamar Kimchi studies unusual behavior of electrons in transition metal oxides. Frustration of electrons in some materials at extremely low temperatures can force them to abandon their preference for classical magnetic states and instead enter unusual states of collective quantum superposition. Photo, Denis Paiste, Materials Processing Center.

There are many kinds of frustration. There’s the kind of frustration of electrons in some materials at extremely low temperatures that forces them to abandon their preference for classical states such as spin up or spin down and instead enter unusual states of quantum superposition, which is what MIT Pappalardo Fellow in Physics Itamar Kimchi studies. Then there is the kind of scientific frustration when a research path down which Kimchi travels trying to explain these phenomena turns into a dead end.

“Especially in the kind of work I do, you don’t know what the research problem is until you’ve solved it, because you are exploring with a flashlight in the dark things that you only understand once you’ve finished exploring them, that you didn’t even know were there until you’ve understood them,” says Kimchi, who works closely as a postdoctoral associate with Professor of Physics Senthil Todadri.

“One of the things people don’t talk about that much, but I think is helpful to recognize for young people who may go into science, is this emotional roller coaster of scientific research, especially of this basic science, where you’re in the dark even when you try to define the research problem, you don’t know what’s going on, you run into a dead end, but then when you do discover something new that nobody discovered before, it is this high when things make sense, and it’s really something new. That’s beautiful. It’s an emotionally intensive exploration,” Kimchi, 30, says.

Kimchi [SB, ’08] double majored in mathematics and physics at MIT before obtaining his doctorate at the University of California-Berkeley. He returned to MIT as a Pappaladro Fellow in 2015.

Early interest in physics

Interest in math and physics came early to Kimchi, who was born in Jerusalem, Israel, but attended high school in the United States. “I knew I liked math and logic and understanding things. Popular science books that I was exposed to a little bit, like about relativity or the universe, were kind of fun. It felt like there was something neat about there being mysteries that you could uncover and then maybe part of that seems to combine nicely with thinking logically and mathematical reasoning,” he recalls.

Coming to MIT as an undergraduate, Kimchi was hooked from his first physics class. “I immediately could tell that what teachers in physics here wanted me to learn really fit what I wanted to learn as well, much better than any other class or department,” Kimchi says. “I felt like it was a good fit for the kind of problem sets I wanted to work on. The way that the class was taught, I think, really brought me into physics. That’s what cemented it.” He graduated Phi Beta Kappa.

It wasn’t until graduate school that Kimchi specialized in condensed matter physics. “It’s neat when you can use sophisticated math to try to understand real experimental results. That’s the draw of hard condensed matter physics theory, the correlated electron systems, for me. You have these really complicated quantum systems, and you see strange experimental results. And it’s always fun to try to understand them, and sometimes also it turns out that you need some powerful mathematics to make sense of the behavior, and that’s a kind of neat synergy or combination,” Kimchi explains.

In his graduate work, Kimchi discovered he liked the richness in the field of condensed matter physics and that he could accomplish projects on a short time scale. He notes that it overlaps with materials science, chemistry, theoretical mathematics and computer science. “My main project was on a series of magnetic insulator compounds where the magnetic atom is iridium, which is very heavy, far down in the periodic table. The nucleus is big, with a big charge,” Kimchi explains. “So the electrons move around it very fast, and that means that special relativity has some effect on the electronic properties of the material, in particular spin-orbit coupling.” His work on possible quantum spin liquid phases in lithium iridium oxide was published in a Physical Review B paper in 2014. Iridium is a transition metal, making this compound a transition metal oxide. “It turns out that it’s only when the electrons move very fast that their orbital motion can interact with this internal relativistic spin. The effects on the material properties, you don’t need to know special relativity for that, you just see the effects when you measure the magnetic properties of the iridium oxide.” These interactions can also lead to strange quantum entangled states of these electrons, that cannot be described by electronic band theory.

Looking back on the work, Kimchi says when he began making theoretical predictions about this particular interplay of spin-orbit coupling and lattice crystal structure in iridium oxides, it wasn’t clear that the crystal structures that he envisioned could be made. But when experimentalist James Analytis moved to Berkeley as a professor, he was able to grow crystals that turned out to form these crystal structures very closely related to the ones Kimchi was studying theoretically. “Then we could understand their magnetic properties, which are very unusual. People are still working on understanding them. The framework for understanding these properties that I and other people are using still comes from the initial theoretical work I did when I didn’t even know if these crystal theoretical structures could be made,” Kimchi says.

“We developed a model for this family of materials that involved frustration and spin-orbit coupling and crystal structure, all three tied up together. The model has some unusual predictions, one about the possibility of a spin liquid type of entangled state,” Kimchi explains. He is continuing work on other predictions from the model proposed in the paper about unusual spiral states, in which spins point in a very unusual spiral configuration. More recently, Kimchi co-authored work on these spiral states with Radu Coldea at Oxford University. “In this recent paper, I discuss what makes them unusual. It’s a little bit technical but turns out to be a very striking qualitative difference from usual spirals, this one is the first of its kind actually, and it comes from these ingredients of frustration and spin-orbit coupling and crystal structure that are in this model,” Kimchi says.

Dance of the electrons

Kimchi likens these mysterious behaviors of electrons to a quantum mechanical dance. “It can mean a lot for how the material behaves because the electrons are doing something completely different,” he says. He tries to develop theories that point to new experimental directions. “The role I see for myself is as a theorist who works with experimentalists. That’s been my role in my PhD as well,” he says.

“All the kinds of work that I do are understanding things that nobody has thought of before. It’s really thinking about the possibilities for how electrons can collectively act with quantum mechanics. So what are possibilities that people haven’t even considered?” Kimchi says.

“Before you can talk about technological applications, you need to understand it quantitatively, but before you can understand things quantitatively, you need to understand them qualitatively, when there is something completely new that you can’t even understand qualitatively. For example, this qualitatively new type of spiral, where you’re just understanding, what is this thing seen in the material? What’s different about it from everything that came before, but how can we use what we know about what came before to understand it?” he explains.

Frustration at triangles

In a very light atom, two properties of the electron, its momentum and its spin, are to a good approximation independent of each other. But in the heavy-element-based materials that Kimchi sometimes studies, relativistic effects couple the spin to the electron motion. At low temperatures, there may sometimes be just a few or one electron per atom [the outermost electron, i.e. a valence electron] involved in the low-temperature behavior, and its various states have low energy. Repulsive interactions between the electrons might lead a compound that should be metallic to instead become an insulator, with the electrons “stuck,” as in a traffic jam, on each atom. In such a so-called Mott insulator, an essential question is what happens to the electron spin. In many cases, the electrons on successive atoms form an alternating line of spin up and spin down electrons, preferring to alternate the spin on every site. In the context of his work, Kimchi says, magnetic frustration refers to cases where the electron doesn’t know whether it wants to be spin up or spin down. For example, this happens in crystals with structures where there are triangles in the lattice of the magnetic atom. In materials with this triangular type of arrangement, the crystal structure doesn’t allow a checkerboard pattern of alternating up/down spins. “This kind of frustration from the triangles is a way to amplify the effects of quantum mechanics,” Kimchi says. Electrons may be spin up at the first point of the triangle and spin down at the second, but the frustration at the third point can force the electron into a quantum superposition of both spin up and spin down. [This type of quantum superposition from coupling of spin up and spin has been shown in nitrogen-vacancy center diamond.] Spin-orbit coupling can have frustration effects similar to the triangles, again amplifying the collective quantum effects in the material.

He is currently working on quantum magnetic insulators that have both magnetic frustration and some disorder, which means there are irregularities in the arrangement of atoms. “There is some really interesting interplay between this quantum frustration and disorder, such as from impurities or other material randomness, and I am exploring how they combine. They can actually enhance each other’s effects, it turns out,” Kimchi says.

At Berkeley, Kimchi was advised by Prof. Ashvin Vishwanath, who also was a Pappalardo Fellow in Physics at MIT from 2001 to 2004. Like Kimchi, Vishwanath [who is now at Harvard] also worked closely with Physics Professor Senthil Todadri. During his PhD work, among other projects, Kimchi analyzed the role of spin-orbit coupling in quantum spin liquids, in which all of the spin moments of the electron are thought to be in a quantum superposition across the material. “Because they are quantum mechanical, one of the fundamental issues is there is no general direct way to see this quantum superposition,” he says. “One of my goals is to try to understand what are other experiments that one could do on other materials to try to understand this elusive behavior better.”

“There is a set of experiments that collectively form sufficient evidence that some kinds of spin liquids do occur in these certain materials, but what they are exactly, there is still some key understanding that’s lacking,” he suggests. “It’s a very hard problem, but it’s very interesting because what you have is a chunk of material where the electrons are in a quantum superposition state of the magnetic moments of their spins involving a subtle dance across the entire chunk of material.”

Multicultural realm

Although he was born in Israel, Kimchi considers himself to be more American, but he cherishes the multicultural research environment at MIT. “One of the fun things about science is getting to know people from across the world, how international it is,” he says.

Kimchi is married to Mollie Kimchi-Schwartz, who also is a physicist and a staff scientist at Lincoln Labs, where she works on quantum information and quantum computing. He enjoys traveling, hiking and being outdoors.

– Denis Paiste, Materials Processing Center 
back to newsletterJanuary 26, 2017

PAPER: Three-dimensional quantum spin liquids in models of harmonic-honeycomb iridates and phase diagram in an infinite-D approximation
PAPER: Spin dynamics of counterrotating Kitaev spirals via duality




Published in Newsletter Articles

A new chapter in magnetism

Quest to understand superconductivity leads MIT theoretical physicist Senthil Todadri to discoveries about new magnetic materials called quantum spin liquids. 
Senthil Todadri CloseUp 8100 DP Web
MIT Professor of Physics Senthil Todadri seeks to understand unusual metals that defy the textbook description. “We’ve been making slow but steady progress, not just I, myself, but the community as a whole, but I would really like that progress to accelerate,” he says. Photo, Denis Paiste, Materials Processing Center

Mother nature is like a restless child who fidgets even when at rest, because electrons are never completely at rest, even at the coldest temperatures, MIT Physics Professor Senthil Todadri says. Imagine pushing a pendulum hanging from a clock. It will swing back and forth, but eventually it will come to a complete stop so that it has a velocity of zero, but we also can see that it has a definite position in space. In the quantum world of electrons, knowing both of these properties, velocity and position, with ultimate precision is forbidden by the Heisenberg uncertainty principle, Senthil explains. “Quantum mechanically, there is still some motion even in the default state, what we call the ground state,” he says. “It’s unavoidable motion that’s there, even in the default state, the lowest energy state that a quantum system can find itself in. There is still some motion.” And this basic fact of nature underlies a variety of unusual behaviors of electrons in materials. Explaining these hard-to-observe physical conditions such as new forms of magnetism is Senthil’s life’s work. Although his legal name is Senthil Todadri, he publishes under the name T. Senthil.

Unraveling magnetism

Everyday permanent magnetism in materials such as iron, where opposite poles attract and like poles repel, has been known for some 2,600 years, Senthil notes, and these are called ferromagnets, derived from the Latin word for iron. “A ferromagnet is something in which the electrons inside the material, they have tiny magnetic moments, and those tiny magnetic moments all line up together to form a giant magnet, and that’s what we see in the ordinary world as a ferromagnet,” he says.

Less than 100 years ago, physicists identified a new kind of emergent magnetism in materials that are called antiferromagnets. In an antiferromagnet, these tiny magnetic moments of individual electrons are frozen in space, but the pattern, or direction, of these tiny moments, oscillates in space on an atomic length scale. “From a macroscopic point of view, if you take an antiferromagnet, it’s very hard to know it has any kind of magnetism at all,” he says. That’s because this magnetism varies on a scale of one angstrom to a few angstroms, which is the size of just a few atoms, and technology to detect it didn’t become available until the 20th century.

“But now we know that antiferromagnetism is by far the most common form of magnetism. If you look around in magnetic materials, there are many, many more antiferromagnets than there are ferromagnets. It’s just that they are much harder to detect,” Senthil explains.

While it can be studied by itself, magnetism is intimately related to electricity, since every electron, including a magnetic one, carries an electric charge. A different class of materials, called superconductors, lose their resistance to electricity at very cold temperatures and there textbook analysis breaks down, says Senthil, 46, who is a theoretical physicist. As they are being chilled to a temperature of about 100 kelvins (minus -279.67 degrees Fahrenheit), these materials first show unusual metallic behavior, then become superconducting. Among materials that have been discovered to superconduct, many don’t do so until they reach a range from about 4 kelvins down to a fraction of 1 kelvin, or nearly absolute zero, the coldest possible temperature. So in the world of physics, superconducting at 100 kelvins is spoken of as high-temperature. 

“From a fundamental science point of view what makes them remarkable is they seem to violate almost all of our textbook understanding of how electrons behave inside a solid,” Senthil explains. “Before they become superconducting, when the material is so hot that it’s not a superconductor yet, it’s a metal, but it’s a really unusual metal, and it’s out of this unusual metal that the superconductor is born.”

“Many of us think that understanding this unusual metal will give us a clue as to why the system is superconducting,” he says. “One of the hopes is that once we understand that clue, we can then have sensible ideas on what kinds of other materials might superconduct at relatively high temperatures and eventually maybe the field will discover room temperature superconductivity.”

These magnetic and superconducting behaviors appear to be intimately connected. One such material, lanthanum copper oxide, becomes an antiferromagnet at about 27 degrees Celsius (80 degrees Fahrenheit). “Certainly above room temperature in Boston right now,” Senthil says on a chilly winter day. “This is a very famous material. It’s famous because if you take this material and you remove electrons from this material, using chemical methods, it’s precisely this material that becomes one of those superconductors that I mentioned before. If you remove electrons, it losses its magnetism, but it becomes something else, it becomes a superconductor. Of course, it’s superconducting only at temperatures much colder than room temperature.”

“The thing I would really like to understand – that’s been a goal for more than 10 years now – is to understand these metals that defy the textbook description of a metal. In some sense, to me that’s the most outstanding challenge in this entire field, and over the years, we’ve been making slow but steady progress, not just I, myself, but the community as a whole, but I would really like that progress to accelerate. That’s my home base; that’s the problem I am always thinking about. Everything else almost feels like I am doing on the side, but that’s hard. There has been progress, enough to keep me encouraged, but not enough for me to jump up and down. So that’s my pet project. That’s what I see as the main thing I feel like I want to have done by the time I’m ready to retire,” Senthil reveals. 

Random tumbling

Yet another form of magnetism in solid materials is the quantum spin liquid, a name for magnetism drawn by analogy from fluid materials. In a spin liquid, Senthil says, individual electrons still have magnetic moments but they are randomly tumbling around all the time. “If you took a snapshot of what the magnetic moments are doing, different electrons with spins will be pointing in different directions, and if you took a different snapshot, the pattern would be completely different. So as a function of time, it’s moving all over the place, so there is no net magnetic moment. It’s neither a ferromagnet nor an antiferromagnet. We describe that by saying there is no magnetic ordering. ... That’s what’s called a spin liquid,” Senthil says.

Senthil Fractional Electron Mross
At extremely low temperatures in certain materials something unusual happens when an electron splits into fractional pieces. In the top image (which describes a metal), the orange balls represent positively charged metal ions and the smaller green objects are negatively charged electrons swimming freely. The bottom image represents a change from metallic behavior to an electrically insulating quantum spin liquid, in which the electrons split into fractional pieces. Here, the negative charge of the electron has attached itself to the positively charged ion. The remaining part of the electron continues to swim freely. Illustration, David Mross. Reproduced with permission, Physical Review B.

Although there is no magnetic ordering, electrons in these spin liquids possess a property that no other form of magnetism has, that is, their magnetic moments are entangled quantum mechanically with the magnetic moments of other electrons far away from them. Quantum entanglement is one of the most counterintuitive concepts in physics. Its essence is that quantum mechanical systems that are separated from each other spatially still have some sort of contact with each other, what Einstein called “spooky action at a distance.” “The presence of quantum entanglement between distant parts of my sample, that is unusual, and it’s unprecedented in magnetism. So this is a new chapter in the study of magnetism. It leads to all kinds of unusual, bizarre phenomena that can potentially happen inside a solid,” Senthil explains.

An example of something unusual that can happen in these materials is that the electron may split into fractional pieces. How can that be when an electron is supposed to one of the fundamental particles of the universe? “An electron is supposed to be a fundamental particle in the vacuum of the universe, but inside a solid, the presence of long-distance quantum entanglement, enables the system to behave as some soup in which there are particle-like objects that move, but these objects are fractions of the electron,” he says. “What makes all these phenomena possible inside a system that looks very simple – it’s a collection of magnetic moments? What makes it possible is the long distance quantum mechanical entanglement that’s present between the localized magnetic moments. So I’ve been studying these kinds of magnetic matter. Not only is it fascinating by itself as a phenomenon, it turns out that studying these kinds of matter leads to all kinds of insights into other problems in condensed matter physics.”

In a February 2016 Physical Review B paper with Chong Wang [PhD ’15], who now is a postdoctoral associate at the Society of Fellows at Harvard, Senthil explored three-dimensional quantum spin liquids. Thinking about these unusual states of magnetism helped them map the connections between topological insulators, superconductors and quantum spin liquids. “There are some deep connections between many different phenomena in the field in many different kinds of systems that we realized only recently just in 2015, 2016, which ended up in some cases solving, in some cases showing the way forward, on questions that have been open for more than 20 years in the field. So there is enormous progress that has come about in theoretical physics as a whole because of thinking about these kinds of novel states of magnetism,” he says.

Contradictory behavior

In particular, Senthil and Wang clarified how a particular metallic system chilled to very low temperatures in the presence of a large magnetic field can display the seemingly contradictory behavior of having both an overall current running at a right angles to an applied voltage while at the same time carrying charged particles that were shown in experiment to move in a straight line with the voltage. A long-standing theory from the early ’90s by co-authors Patrick A. Lee at MIT, Bertrand I. Halperin at Harvard and Nicholas Read at Yale proposed that this phenomenon could be explained by thinking of each charge carrier as having an electron that attaches to itself a bit of magnetic flux, so that even though each such composite particle moves in a straight line, it carries both an electrical charge and a magnetic flux. This movement of magnetic flux produces an electric field in the perpendicular [or transverse] direction. But the Lee-Halperin-Read theory couldn’t explain a kind of physical symmetry in this system known as particle-hole symmetry, Senthil says. A hole, perhaps most familiar in the context of semiconducting materials, is the absence of an electron in an atom where one is expected. Symmetry means that whether you view the system as a collection of electrons or view it as a collection of holes, the system is the same. “These are just two different viewpoints on what’s really the same system,” Senthil says. In experiments, replacing electrons with holes in this system didn’t make a physical difference, so it is considered to be in electron-hole symmetry, Senthil explains. Physicists model electrons mathematically through a complicated formula known as a wave function, which incorporates the electrons’ properties such as spin and momentum. Senthil says he and Wang were motivated by an idea proposed by Dam T. Son at the University of Chicago that this could be explained by thinking of the composite particle as carrying a “spin” that is locked into some definite angle to its momentum. A peculiar occurrence in quantum physics is that when spin of this composite particle, just like the electron spin itself, is rotated in a full circle, the particle’s quantum mechanical wave function turns from a positive number to a negative number. By coupling spin to momentum in this system, Senthil explains, “What we now understand in this story is that these objects that move in straight lines inside this medium, inside this two-dimensional collection of electrons in a strong field, that they have this feature that if you rotate their momentum on a full circle, the wave function changes sign, so that’s a different theory from the older theory.”

The technical term for these spin-momentum coupled particles is Dirac particles, from the Dirac equation that quantifies their quantum state. “Going from electrons to holes it turns out, flips the direction of the momentum of these Dirac particles, and it also has the effect of flipping, therefore, the direction of the spin, because the spin of this particle is tied to the momentum. So the momentum changes sign, the spin changes sign, so that’s all that happens,” he says. But importantly it explains how the electron-hole symmetry acts in this system. Wang and Senthil derived this solution from their understanding of other phenomena in condensed matter physics, such as topological insulators and quantum spin liquids. “In the process, we ended up learning a lot about all of these different systems,” Senthil says.

Senthil notes that these ideas also were pursued independently by Max Metlitski, who recently joined the MIT Physics faculty as Assistant Professor in the Condensed Matter Theory group, and Harvard Professor of Physics Ashvin Vishwanath. “These are friends of mine who it turns out were working on the same thing at the same time independently,” Senthil says. Vishwanath previously was a Pappalardo Fellow at MIT, serving as a postdoctoral associate in physics with Senthil.

Research group

Senthil supervises a small group of graduate students, Michael Pretko and Liujun Zou, who are working on quantum spin liquids, and Yahui Zhang, who is working on unconventional metallic states of matter through numerical calculations. “In experimental groups, the PI [principal investigator] tells the group what to work on. In theory groups, there is a lot more freedom. If a student comes to me and says, look, I have this idea, I encourage them to work on it, even if I am not working on it myself. ... It’s a great thing for students to come up with their own ideas,” Senthil says. Senthil also works with Pappalardo Fellows Inti Sodemann and Itamar Kimchi and Moore Fellow Sam Lederer and advises them on their work on magnetism, unconventional metals, and superconductivity.

This spring, Senthil will teach an advanced graduate course on Many Body Quantum Mechanics. Over the past four years, he taught quantum mechanics for first-year graduate students.

Senthil is married and has two daughters, ages 7 and 14. “Whenever I find time, which is getting harder and harder, I try to read,” he says.back to newsletter

Denis Paiste, Materials Processing Center
January 26, 2017

Senthil Todadri
Condensed Matter Theory Group
Theorists predict new forms of exotic insulating materials
PAPER: Symmetry-Protected Topological Phases of Quantum Matter
Published in Newsletter Articles

New observations confirm an 80-year-old quantum theory.

MIT QuantumMelt Web
MIT researchers believe they have finally captured the process of quantum melting — a phase transition in quantum mechanics, in which electrons that have formed a crystalline structure purely through their quantum interactions melt into a more disordered fluid, in response to quantum fluctuations to their density.
Illustration, Jose-Luis Olivares, MIT (Wigner crystal image courtesy of Arunas.rv, CC BY-SA 3.0)

For the first time, MIT physicists have observed a highly ordered crystal of electrons in a semiconducting material and documented its melting, much like ice thawing into water. The observations confirm a fundamental phase transition in quantum mechanics that was theoretically proposed more than 80 years ago but not experimentally documented until now.

The team, led by MIT professor of physics Raymond Ashoori and his postdoc Joonho Jang, used a spectroscopy technique developed in Ashoori’s group. The method relies on electron “tunneling,” a quantum mechanical process that allows researchers to inject electrons at precise energies into a system of interest — in this case, a system of electrons trapped in two dimensions. The method uses hundreds of thousands of short electrical pulses to probe a sheet of electrons in a semiconducting material cooled to extremely low temperatures, just above absolute zero.

With their tunneling technique, the researchers shot electrons into the supercooled material to measure the energy states of electrons within the semiconducting sheet. Against a background blur, they detected a sharp spike in the data. After much analysis, they determined that the spike was the precise signal that would be given off from a highly ordered crystal of electrons vibrating in unison.

Read more at the MIT News Office.

Jennifer Chu | MIT News Office
December 20, 2016

Published in Daily News

MIT biophysicists apply evolutionary dynamics and game theory to understand personal relations and come up with some surprising results.

Payoffs Decision Tree APE MPC Web
Decision points for the first player in an “envelope game” are graphed like the branches of a tree. In a game with two players, each has a potential payoff, but the first one’s actions determine the second one’s payoff in each round. Choices whether to gather more information by looking in an envelope that contains either a high or a low temptation and whether to cooperate or defect from the game mimic choices in life such as how to respond to a friend’s request to stay with you or a romantic partner’s flirtation with someone else. Illustration, Alfonso Pérez-Escudero.

When we ask friends if we can stay at their place, we prefer them to say yes without asking details such as for how long. Yet, if the answer is going to be no, then we often prefer them to seek more information from us first. At first glance, this situation seems very different from how we react when we are in an exclusive relationship and our boyfriend or girlfriend flirts with someone else. However, a probability-based analysis with Bayesian game theory shows that each involves differing degrees of manipulation and preferential interaction, MIT researchers report in a new paper.

MIT Postdoctoral Associate Alfonso Pérez-Escudero and colleagues analyzed how these manipulation and preferential interaction mechanisms play out in “the envelope game,” a framework developed by Martin Nowak, Erez Yoeli and Moshe Hoffman at Harvard. “These are two situations that, in principle, I wouldn’t put together, and thanks to the framework that these researchers developed, we realized that they belong to the same family of situations,” Pérez-Escudero says. The original framework contained the manipulative mechanism but not the preferential interaction mechanism. “Our contribution is to realize that this family has two sub-families that can be mixed. We developed a generalization, creating a model that can describe both of these mechanisms at the same time and that contains the original model as a particular case,” he says.

The paper, co-authored by Pérez-Escudero, Postdoctoral Associate Jonathan Friedman and Latham Family Career Development Associate Professor of Physics Jeff Gore, was published in the Proceedings of the National Academy of Sciences (PNAS), Dec. 6, 2016. The Gore Laboratory, in the Physics of Living Systems group at MIT, more often uses game theory to explain evolutionary dynamics such as cooperation among microbes. “Here we use the same math that you can use to describe evolution in biology to describe human behavior and human psychology, building a unifying framework between biological problems and human ones,” Professor Gore says.

An unequal game

In the envelope game, each player has a potential payoff, but the first player’s actions determine the second player’s payoff, so their roles are unequal, or asymmetric. The envelope contains a bonus prize, which is sometimes of low value and sometimes of high value, and Player 1 can choose whether to look in the envelope. After either looking in the envelope or choosing not to look, Player 1 will decide next whether to “cooperate,” in which case both players get a payoff, or to “defect,” in which case only Player 1 gets a payoff and Player 2 takes a loss. Player 2’s only choice is whether to continue the game or to quit.

“The player who can cooperate or defect has power over payoffs in the current round, while the other player has the power to continue the game for more rounds or stop,” Pérez-Escudero explains. “It’s unsurprising that Player 2 ends the game in retaliation if Player 1 defects. The surprising part is that Player 2 may also end the game if Player 1 cooperates – just because he looked in the envelope – even though looking has no effect on Player 2’s payoffs.”

Strategic choice, open signal

Each player is assigned a strategy profile, which is a set of rules that tells each player what to do in each situation. Since both players stand to win more by continuing the game, Player 2’s choice whether to continue or to end the game will influence Player 1’s strategy. Players who always cooperate are said to be “reliable,” whereas players who sometimes, or always, defect are “unreliable.” When a set of strategies for Player 1 and Player 2 reaches a balanced state where neither player will benefit by following a different strategy, it is said to be in “equilibrium,” in mathematical terms, either a Nash equilibrium or a sequential equilibrium.

The player who looks in the envelope is sending a signal to the other player. “By opening the envelope, she is telling us something,” Pérez-Escudero says. “This means that her decision wasn’t very clear. She wasn’t 100 percent sure she was going to cooperate, nor 100 percent sure she was going to defect. She needed this piece of information to make her decision. So the price of learning the contents of the envelope is giving away some information about herself.” The intuition, then, is that the other player will prefer not to interact with someone who was not sure from the beginning, because she might change her mind if the conditions change slightly. “But this is what piqued our curiosity,” he says. “In the original paper, both players know each other perfectly – the only uncertainty is about the content of the envelope. And if I already know that you are an unreliable cooperator, I will not learn anything when I see that you look in the envelope; looking should play no role. But the results were there: the envelope game does have a Nash equilibrium in which looking plays a fundamental role.” Something was missing.

By analyzing the game more closely, the MIT researchers realized that a different mechanism was driving the results: by threatening to end the game if Player 1 looks, Player 2 can force her to make a blind decision. This manipulative mechanism makes looking a key element of the game’s Nash equilibrium, even if both players know each other perfectly. “But this is not what happens in real life. Uncertainty is everywhere, and even if we know a person, we are never sure of their true feelings and thoughts. So we implemented this uncertainty into the model, turning it into a Bayesian game,” Pérez-Escudero says. [In everyday life, applying Bayesian rules is how email programs filter out spam.]

Computer simulations

Using computer simulations, Pérez-Escudero modeled how different strategies play out over several thousand rounds, which yields data for about 100,000 to 1 million possible combinations. The model runs a mathematical formula to simulate the repeated games and differing strategies. What he found is that when Player 1 always acts in the same way, only manipulation can make looking matter in the game. Player 2 accomplishes this manipulation by ending the game if Player 1 looks, which effectively punishes Player 1 by denying her any future gains and also protects Player 2 against any further losses. But where the game introduces two varieties of Player 1 with different payoffs and strategies, Player 2 will see “favorable” and “unfavorable” types, and pay attention to looking as a cue to tell them apart. In this scenario, no punishment is required.

The mathematical formula, which is called a replicator equation, comes from evolutionary biology. “Imagine you have a population with 1,000 people that are playing slightly different strategies; those with more successful strategies are going to have more children, and they are going in the end to take over the population. The replicator equation was designed to describe this kind of situation, but it was found later that it can also describe cultural evolution, where a given idea (or behavior) can be learned and copied, making it a powerful tool to analyze human behavior. But to use it properly, one needs to enumerate all the possible strategies that can exist in the game. If I enumerate all these strategies, then the replicator equation can tell me who wins,” Pérez-Escudero explains.

But simulations alone would not be enough. The envelope game has infinite possible strategies, so it’s just not possible to enumerate them all. Simulations were therefore complemented by a different tool from game theory called the one-shot deviation principle, which acts to put a limit on what otherwise would be infinite calculations in order to draw meaningful conclusions. “Thanks to this principle, we can prove that a strategy is optimal even if we don’t know what other strategies are out there. You start from your strategy and test every decision you make, one by one. If you cannot benefit by deviating from the strategy in any single decision, then it is a best response and potentially part of a Nash equilibrium, or in our game, a refinement called sequential equilibrium,” he says. “Simulations, even if they cannot prove the equilibrium, were still useful to check that the equilibriums we were finding were also stable.”

Manipulation versus preference

These mathematical models neatly simulate personal interactions, where both manipulation and preferential interactions play a role – often together. “Take for example an exclusive couple relationship. If I have an exclusive relationship with my girlfriend and I flirt with other people, I can expect my girlfriend to punish me. She can get very angry; she can leave me. In this case, there is true leverage from one person to the other, and then it’s very likely that the manipulative mechanism is playing a role.” The preferential interaction mechanism can also play a role here because one partner’s decision to flirt also informs the other that her partner is perhaps not very invested in the relationship. “Maybe she would prefer another person who is more invested in the relationship,” he says. “Here there are these two mechanisms. On the one hand, she is learning something about me and maybe she prefers not to interact more with me because of what she learns. On the other hand, she has the power to punish me if I do something she doesn’t want me to do,” Pérez-Escudero says.

Another key finding of the study is that the preferential interactions mechanism can give rise to the opposite effect: preference for looking. The defining characteristic is whether Player 1 ends up cooperating or defecting. “If Player 1 cooperates, I prefer her to cooperate without looking, because she’s a reliable cooperator. If player 1 defects, I prefer her to look, because then she could be an unreliable defector, and I can still hope she will cooperate in the future,” Pérez-Escudero explains. “I think this connects with real-life situations. If you ask ‘Can you do me a favor?’ it would be very rude that I just say no. Instead, even if I’m confident I will not grant the favor, I will first ask what favor is it, and then present an excuse. My asking here would be a false signal that prevents you from realizing that I’m such a bad person that I would not grant you even the smallest favor.”

Commenting on the new MIT findings, Moshe Hoffman, a research scientist and lecturer at Harvard's Program for Evolutionary Dynamics, says, “The model helps us understand why we trust more those who don't look at the costs and benefits before deciding whether to cooperate, and more generally why we value principled behavior above strategic calculated behavior.”

“This model is a solid contribution to our understanding of principles of behavior, cooperation, and morality, and more generally fits within a wider literature that is important and insightful which uses game theoretic models and models of learning and evolutionary processes to understand puzzling aspects of human social behavior,” Hoffman says. “How else can we understand our social species if we don't try and uncover the hidden function behind what they do think and believe? And what better tools to do that than models of game theory, learning and evolutionary processes?”

This work was supported by EMBO Postdoctoral Fellowship [Grant ALTF 818-2014], Human Frontier Science Foundation Postdoctoral Fellowship [Grant LT000537/2015], and the Paul Allen Family Foundation.

back to newsletterDenis Paiste, Materials Processing Center,
December 19, 2016

Related Paper: Preferential interactions promote blind cooperation and informed defection


Published in Newsletter Articles

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