Research blogging: Magnetism in layered materials

Following on from graphene, there has been enormous interest in other layered materials for the last few years, such as transition metal dichalcogenides (TMDs) like MoS₂.   Depending on the constituents and particular structure, these materials can be semiconductors, superconductors, charge density wave compounds, etc., and can have properties that vary strongly as the number of layers in the material is reduced toward one.  You can expand the palette further by substitutionally doping different elements into the chalcogenide layers, or you can intercalate other atoms between the layers.  There are a huge number of possible compounds and variations.  (Fun note:  TMDs have been studied intensely before.  See here for a review from almost 50 years ago!  And magnetism in intercalated TMDs was examined by people like Stuart Parkin and Richard Friend almost 40 years ago.   The resurgence now is due to a combination of improved growth and characterization techniques, interest in low-dimensionality materials, and theoretical appreciation for the richness of possible states in these systems.)

Recently, collaborating with my colleague Jun Lou, we had some fun examining a related material, V₅S₈, which you can also think of as (V_0.25)VS₂.  There are vanadium disulfide layers, and intercalated between them are additional vanadium atoms in an ordered pattern.  The bulk version of this material was found in the 1970s to be an antiferromagnet - below the Neel temperature T_N ~ 32 K, the spins of the unpaired electrons on the intercalated vanadium atoms spontaneously order into the arrangement shown in the upper panel at right.   If an external magnetic field bigger than about 4 T is applied perpendicular to the planes of the material, the spins flop over into the arrangement shown in the bottom panel - this is called a spin flop transition. 

Prof. Lou's group has figured out how to grow V₅S₈ by chemical vapor deposition, so that we were able to make measurements on single crystals of a variety of thicknesses, down to about 10 nm.  We found a couple of cool things, as reported here.   

First, we found a previously unreported first-order (in the thicker crystals) phase transition as a function of externally applied magnetic field.   The signature of this is hysteresis in the electrical resistance of the material as a function of the magnetic field, H.  Just below T_N, the hysteresis appears near zero magnetic field.  As T is lowered, the magnetic field where the hysteresis takes place increases dramatically - in a thick crystal, it can go from basically 0 T to taking place at 9 T when the temperature is lowered by only three Kelvin!  Indeed, that's probably one reason why the transition was missed by previous investigators:  If you take data at only select temperatures, you could easily miss the whole thing.   This kind of a transition is called metamagnetic, and we think that large applied fields kill the antiferromagnetism (AFM), driving the material into a paramagnetic (PM) state.  We suggest a phase diagram shown in the table-of-contents figure shown here.  The transition extrapolates to a finite value of H at zero temperature.  That implies that it ends up as a quantum phase transition.

Second, we found that there are systematic changes in the magnetic properties as a function of the thickness of the crystals.  In thinner crystals, the antiferromagnetism appears to be weaker, with T_N falling.  Moreover, the hysteresis in the field-driven transition vanishes in thinner crystals, suggesting that the metamagnetic transition goes from first-order to second order in the thin limit.   

This work was a lot of fun.  As far as I know, it's the first example of a systematic study of magnetic properties in one of these layered materials as a function of material thickness.  I think we've just scratched the surface in terms of what could be possible in terms of magnetism in this layered material platform. 

Interacting Quantum Systems Driven Out of Equilibrium - day 2

Continuing into day 2 of our workshop:

• Bryce Gadway of the University of Illinois spoke about using cold atoms in an optical lattice to simulate topological and disordered systems.  His group has implemented an optical lattice constructed not by interference of retroreflected lasers, but by interference between a laser and counterpropagating beams frequency shifted by precise, controlled amounts.  As a non-atomic physics person I'm a bit fuzzy on the details, but the point is that this allows his group to put in place precise control of the on-site potential of each lattice site and to dial in designer phase shifts associated with tunneling between adjacent sites, on demand.  This means it is possible to study transport problems (like Bloch oscillations) as well as introducing designer, time-varying, site-specific disorder if desired.  
• I spoke about my group's work on heating and dissipation in atomic- and molecular-scale junctions driven out of equilibrium (and into a steady state) by electronic bias.  I framed the discussion in terms of how hard it is to obtain truly local information about vibrational and electronic distributions in such driven systems.  On the vibration side, if you're interested, I suggest looking here, here, and here, with a recent related result here.  On the electronic front, I talked about published (here and here) and some unpublished data looking at electronic shot noise at high biases in atomic-scale metal junctions.  
• Eugene Demler from Harvard (my grad school classmate) gave a nice talk that addressed nonequilibrium aspects of both cold atoms and electrons.   For example, he and collaborators have developed some theoretical machinery for looking at a cold atom version of the orthogonality catastrophe - what happens if you suddenly "turn on" interactions between a cold Fermi gas and a single impurity, and watch the dynamics.  These same theoretical techniques can be applied to solid state systems as well.  (This is just a subset of what was presented.)
• Ryo Shimano from Tokyo University gave a very pretty talk about optical manipulation and driving of the Higgs mode inside superconductors.  You can hit a superconductor with THz radiation as a pump, and then probe at some delay with additional THz radiation.  If the pump is at the right frequency (energy half the superconducting gap, in the s-wave case), you can excite collective sloshing of the condensate (see here and scroll down to the first example).  As you might imagine, things get more rich and complicated with more exotic superconductors (multiband or unconventional).
• Emil Yuzbashyan from Rutgers presented a look at the fundamental issues involved in non-thermal steady states of ensembles of quantum particles at long times after a quench (a sudden change in some parameter).  As I wrote in the first-day discussion, the interesting question here is when does the system evolve seemingly coherently (i.e., the particles slosh around in recurring patterns, just as a Newton's cradle ticks back and forth), and when does the system instead tend toward a long-time state that looks like a randomized, thermalized condition?   To see how this relates to classical mechanics, see these articles (here and here) that I need to find time to read.  
• Lastly, my colleague Matt Foster from Rice spoke about quenched BCS superfluids, topology, spectral probes, and gapless (topological) superconductivity under intense THz pumping.  This was a neat pedagogical talk about this work.  It touches some of the same issues as the Shimano talk above.  One aspect that I found interesting to consider:  You can have a system where a quench drives some collective oscillations, and those collective oscillations act as a Floquet perturbation, changing the effective band structure and giving rise to nonlinearities that continue the oscillations.  Wild stuff - here are the slides.  

We then had a lunch that segued smoothly into a relaxed poster session for students and postdocs.  Overall, it was a great workshop and a good chance to get people from diverse areas of CM and AMO physics together over common interests in nonequilibrium response of quantum systems.  Thanks to everyone who was able to come, to our staff organizer who made everything actually come together, and of course to our sponsors (NSF DMR, ICAM-I2CAM, the Gordon and Betty Moore Foundation, Lakeshore, Advantest, and Coherent)!

Interacting Quantum Systems Driven Out of Equilibrium - day 1 (updated - complete)

Our workshop was fun and interesting.   There are multiple ways to drive physical systems out of equilibrium - you can take some system and push on it with some force, for example.  In the case of a condensed matter system (whether solid state or trapped cold atoms), you can apply a bias - some difference in population (or chemical potential or pressure) that drives the system, either by adding kinetic energy to it or encouraging the flow of matter and/or charge.  You can apply a temperature difference across the system, driving some average flow of energy through the system's degrees of freedom.  You can shine light on the system, adding energy and momentum either at a steady rate or in a sudden pulse.  One favorite piece of vocabulary these days is a quench - suddenly (compared with relaxation rates of the system) changing some condition like the potential energy of the particles, and then watching the response of the system's degrees of freedom.  Does the system "thermalize"?  That is, do the microscopic pieces of the system interact with each other and redistribute energy so that there seems to be some effective temperature?  Or does the system fail to thermalize, and instead slosh around in some non-thermal configuration for a long time?  There are many open issues.

We had 13 talks on the first day, and I don't want to write exhaustive summaries of all of them.  We will eventually be posting pdf files of the relevant slides.  That being said, I will give a super-brief description of each, and link to a relevant paper or two so that you can see what was discussed.  Here are the 13 talks we had on the first day.

• Nadya Mason from UIUC spoke about her group's work on engineered superconducting/normal metal structures in magnetic fields.  These devices allow studies of current-driven motion of trapped magnetic flux.  In some sense this is an old, established problem, but traditional models actually do a poor job of reproducing the experimental data.  The experiments are here, and it looks like it's important to include some "delayed friction" to understand vortex motion.
• Jonathan Bird from Buffalo spoke about his group's studies of quantum point contacts in semiconductors, where it's long been known how to measure electronic conduction down to the limit of discrete quantum channels, where the devices act like waveguides for the electrons.   His group has developed some high speed techniques for making sub-ns electronic measurements, and what really gets interesting is when systems are driven hard, so that the electronic bias is the largest energy scale in the problem - you have to worry quite a bit about exciting phonons and what they do.  A key result is the apparent formation of a specific, somewhat heating-immune transport mode when such a point contact is driven really hard.
• David Goldhaber-Gordon from Stanford spoke about his group's recent experiments looking at quantum dots, some building on work looking at the so-called two-channel Kondo effect.  An unpaired electron is placed in the position of trying to couple to two (carefully tuned to be) independent baths of electrons.  Some of the not-yet-published results look at interesting scaling as one tunes through the accessible regimes, and involved some stunningly pretty device fabrication done at the Weizmann Institute.  Other experiments looked at the apparent emergence of symmetry in systems comprising two quantum dots.
• Tilman Esslinger of ETH presented his group's great work on using cold atoms to look at systems rather analogous to the ones Prof. Bird had mentioned.  They can create blobs of fermionic cold atom fluids of unequal populations, and link them by a carefully controlled constriction, and then they can image transport.  If they squeeze the contact to be effectively one dimensional, they can see quantized conductance of atoms (just as solid state folks can do with charge in a quantum point contact).  They can use atomic physics methods to dial around the interactions between the particles, and can then look at how this affects dissipation in the out of equilibrium situation.  Gorgeous stuff.
• Takashi Oka of the Max Planck Institutes in Dresden talked about Floquet theory and using lasers to control the topology of the band structure of materials.  There was a lot to this talk, and it's not easy to summarize.  In Floquet theory, you apply a periodic driving potential to a quantum system.  Just like a spatially periodic potential energy picks out certain spatial periodicities and gives you a compact way of looking at band structure, temporal periodicity creates what you could call replicas of the band structure but shifted in energy by multiples of \( \hbar \omega\), where \(\omega\) is the driving frequency.  If you do this right, the driven system can have topological edge states.  You can also use periodic driving to reorient the magnetization of materials as if you had a whopping huge effective magnetic field.
• Andrew Millis of Columbia University has worked on many relevant topics, and in this case chose to speak about theory he and collaborators have done regarding a recent experiment looking at vanadium dioxide.  That material has a structural phase transition at 65 C that separates a low temperature, monoclinic, insulating state from a high temperature, tetragonal, metallic state.  In the experiment, optical excitation puts the material into a metallic state without actually leaving the monoclinic crystal structure.  The theory suggests that this is a correlation effect - scoop electrons out of the lower Hubbard band and drop them into the upper band, and interorbital interaction effects can stabilize a new, metastable electronic structure that's a metal.
• Alessandra Lanzara of Berkeley gave a really nice talk about her group's work on time-resolved angle-resolved photoemission.  You hit a material of interest with an ultrafast, time-resolved pump pulse of near-infrared light (1.5 eV photons), and then at some known delay you smack the system with a 6 eV probe pulse at a particular polarization and orientation, and measure the energy and momentum distribution of the electrons that get kicked out.  This lets you measure the transient electronic structure.  They've been able to use this approach to study the dynamics of quasiparticles in cuprate superconductors, how Cooper pairs respond to such pumping, etc.
• N. Peter Armitage at Johns Hopkins articulated nicely three reasons to "go nonequilibrium":  to learn about elementary excitations of an equilibrium phase; to access "phases" not possible in equilibrium material configurations; and to look for new "phases" that have no equilibrium analog.  He then gave a fun talk about using optical spectroscopy techniques to look at many-body relaxations (older paper here) in the Coulomb glass phase of lightly doped semiconductors - when there are strongly interacting, localized electrons in a disordered configuration so that screening is poor.  Interestingly, these systems relax more slowly when the carrier densities get higher, in physics related to the orthogonality catastrophe. 
• My faculty colleague Jun Kono from Rice spoke about so-called Dicke phenomena (such as superradiance, superfluorescence) in semiconductors.  These effects are great examples of nonequilibrium physics, when a driven system (say a semiconductor in a magnetic field illuminated by THz radiation that spans the energy scale of the cyclotron resonance, \(\omega_{\mathrm{c}} = e B/m^{*}\)) spontaneously develops coherence among the many electron-hole excitations in the system.  You can put such a system in a clever kind of 1d optical cavity, and approach the "strong coupling" regime so that the energetic coupling between the charge carriers and the photons in the cavity is comparable to the cyclotron energy.
• Christof Weitenberg from Hamburg then spoke about exciting results in simulating condensed matter systems using cold atoms in optical lattices.  One piece of physics that's very in vogue right now because of the rise of topology and various 2d materials is Berry curvature.  It's hard to explain this in brief - if you look at how the energy bands of a material as a function of crystal momentum \(E(\mathbf{k})\) are curved, the wavefunction of a particle traversing some closed trajectory in \(\mathbf{k}\)-space can pick up a phase factor related to that curvature.  In Weitenberg's experiments, cleverly arranged laser beams can create designer lattices.  Shaking the lasers periodically as a function of time can lead to the same Floquet physics discussed above, changing the effective band structure for atoms confined in those lattices, and through cool imaging techniques the experimentalists can reconstruct the Berry curvature that they have designed into that effective band structure.
• Another colleague Kaden Hazzard from Rice gave a nice theoretical talk about different nonequilibrium collective phenomena in ultracold atomic matter.  One aspect involved dilute molecules with electric dipoles (KBr) trapped in an optical lattice.  Because of their dipole moments, the molecules interact with each other over long ranges (dipole-dipole interactions scale like \(1/r^{3}\)), and their relaxation after getting dinged is governed by many-body interaction effects.  Another system is trapped Rydberg atoms, where dipolar interactions scale like the principal quantum number to the eleventh power (!).  
• Andrea Cavalleri from the Max Planck in Hamburg (and also spending time at Oxford) spoke about his group's very high profile work that I've already described here.  The central question here is really can driving a quantum material stabilize collective states like superconductivity that have coherence, correlations, and remarkable physical properties that would be absent without the drive.  Both Cavalleri and Oka made reference to this video, which shows how driving a classical pendulum can render the inverted position of the pendulum stable.  The experiments themselves are truly remarkable.
• In the last talk of Day 1, Sarang Gopalakrishnan of Cal Tech gave a theory talk again examining the response of driven many-body quantum systems, focusing particularly on the issue of many-body localization.  That is, when do the quantum dynamics of a many-body system lead to a real breakdown of quantum ergodicity, so that the degrees of freedom get "stuck", having large variability of local observables (instead of things being smoothed out and looking thermally smeared) and comparatively weak entanglement (which grows more slowly with system size than in the effectively thermal case).  He pointed out experimental challenges, that experiments probe dynamics rather than quantum eigenstates and that everything really is coupled (however weakly) to some thermal "bath", but argued that these issues aren't fatal to the interesting physics.

Updates coming - Interacting Quantum Systems Driven Out of Equilibrium

As I'd advertised, the Rice Center for Quantum Materials is hosting a two-day workshop on interacting quantum systems driven out of equilibrium.  This event brings together people from roughly three different perspectives:  people who worry about (solid state) systems driven out of equilibrium by electrical bias; people who worry about quantum systems driven out of equilibrium by light (often ultrafast and/or very intense); and people who leverage the amazing cleanliness and tunability of cold atom systems to examine driven quantum many-body systems.   I've been taking notes, and after the workshop wraps up today I'll post some highlights.