Friday, September 17, 2021

Moiré materials and the Mott transition

There are back-to-back papers in Nature this week, one out of Columbia and one out of Cornell, using bilayers of transition metal dichalcogenides to examine the Mott transition.  (Sorry for the brevity - I'm pressed for time right now, but I wanted to write something....)

As I described ages ago in here, imagine a lattice of sites, each containing one electron.  While quantum statistics would allow each site to be doubly occupied (thanks to spin), if the on-site electron-electron repulsion \(U\) is sufficiently strong (large compared to the kinetic energy scale \(t\) associated with hopping between neighboring sites), then the interacting system will be an insulator even though the non-interacting version would be a metal.  Moving away from this half-filling condition, you can get conduction, just as having an empty site allows those sliding tile puzzles to work.

As discussed here, in bilayers of 2D materials can lead to the formation of a moiré lattice, where the interlayer interactions result in an effective periodic array of potential wells.  The Columbia folks got a moiré pattern by using a 4-5 degree twisted bilayer of WSe2, while the Cornell folks instead used an aligned bilayer of MoTe2 and WSe2 (where the moiré comes from the differing lattice constants).  In both cases, you end up with a triangular moiré lattice (encapsulated in hBN to provide a clean charge environment and protection from the air).  

The investigators are able to tune the systems in multiple ways.  With overall gate voltage, they can capacitively tune the "filling", the ratio of number of "free" charges to number of moiré lattice sites.  By adjusting top gate vs. back gate, they can tune the vertical electric field across the bilayer, and that is a way of tuning interactions by pushing around localized wavefunctions for the lattice sites.  

Both groups find that they can tune in/out of a Mott insulating phase when they're at one carrier per moiré lattice site.  Interestingly, both groups see that the Mott transition is continuous (second-order) - there is no sudden onset of insulating response as a function of tuning either knob.  Instead, there appears to be quantum critical scaling, and regions of linear-in-\(T\) temperature dependence of the resistivity (a possible indicator of a strange metal) on either side of the insulating region.  The Cornell folks are able to do magnetic circular dichroism measurements to confirm that the transition does not involve obvious magnetic ordering. 

This is very pretty work, and it shows the promise of the moiré lattice approach for studying fundamental issues (like whether or not the Mott transition in a triangular lattice is continuous).  I'm sure that there will be much more to come in these and related systems.

Monday, September 06, 2021

What is the spin Hall effect?

The Hall Effect is an old (1879) story, told in first-year undergraduate physics classes for decades. Once students are told about the Lorentz force law, it's easy to make a handwave classical argument that something like the Hall Effect has to exist:  Drive a current in a conductor in the presence of a magnetic induction \(\mathbf{B}\).  Charged particles undergo a \(q \mathbf{v} \times \mathbf{B}\) force that pushes them transverse to their original \(\mathbf{v}\) direction.  In a finite slab of material with current perpendicular to \(\mathbf{B}\), the particles have to pile up at the transverse edge, leading to the development of a (Hall) voltage perpendicular to the direction of current flow and the magnetic induction.  You can measure the Hall voltage readily, and it's used for sensing magnetic fields, as well as figuring out charge carrier densities in materials.

The spin Hall effect, in contrast, is a much newer idea.  It was first proposed by Dyakonov and Perel in 1971 as an extrinsic effect (that is, induced by scattering from impurities in a material), and this was revisited in 1999 by Hirsch and others.  It's also possible to have an intrinsic spin Hall effect (proposed here and here) due just to the electronic structure of a material itself, not involving impurities.

Adapted from here.

So what is the SHE?  In some non-magnetic conductors, in the absence of any external magnetic field, a charge current (say in the \(+x\) direction) results in a build-up of electrons with spin polarized up (down) along the \(z\) direction along the positive (negative) \(y\) edge of the material, as shown in the bottom left drawing of the figure.  Note that there is no net charge imbalance or transverse voltage - just a net spin imbalance. 

The SHE is a result of spin-orbit coupling - it's fundamentally a relativistic effect (!).  While we static observers see only electric fields in the material, the moving charge carriers in their frame of reference see effective magnetic fields, and that affects carrier motion.  In the extrinsic SHE, scattering of carriers from impurities ends up having a systematic spin dependence, so that spin-up carriers are preferentially scattered one way and spin-down carriers are scattered the other.  In the intrinsic SHE, there ends up being a spin-dependent term in the semiclassical velocity that one would get from the band structure, because of spin-orbit effects.  (The anomalous Hall effect, when one observes a Hall voltage correlated with the magnetization of a magnetic conductor, is closely related.  The net charge imbalance shows up because the populations of different spins are not equal in a ferromagnet.)  The result is a spin current density \(\mathbf{J}_{\mathrm{s}}\) that is perpendicular to the charge current density \(\mathbf{J}_{\mathrm{c}}\), and is characterized by a (material-dependent) spin Hall angle, \(\theta_{\mathrm{SH}}\), so that \(J_{\mathrm{s}} = (\hbar/2e)\theta_{\mathrm{SH}}J_{\mathrm{c}}\).

There is also an inverse SHE:  if (appropriately oriented) spin polarized charge carriers are injected into a strong spin-orbit coupled non-magnetic metal (say along \(+x\) as in the bottom right panel of the figure), the result is a transverse (\(y\)-directed) charge current and transverse voltage build-up.  (It's this inverse SHE that is used to detect spin currents in spin Seebeck effect experiments.)

The SHE and ISHE have attracted a lot of interest for technological applications.  Generating a spin current via the SHE and using that to push around the magnetization of some magnetic material is called spin orbit torque, and here is a recent review discussing device ideas.

Wednesday, September 01, 2021

Rice University physics faculty search in experimental quantum science and technology

The Department of Physics and Astronomy at Rice University invites applications for tenure-track faculty positions in the broad area of experimental quantum science and technology. This encompasses quantum information processing, quantum sensing, quantum communication, quantum opto-mechanics, and quantum simulation in photonic, atomic/ionic, quantum-material, and other solid-state platforms. We seek outstanding scientists whose research will complement and extend existing activities in these areas within the Department and across the University. In addition to developing an independent and vigorous research program, the successful applicants will be expected to teach, on average, one undergraduate or graduate course each semester, and contribute to the service missions of the Department and University. The Department anticipates making appointments at the assistant professor level. A Ph.D. in physics or related field is required.

Beginning September 1, 2021, applications for this position must be submitted electronically at .

Applications for this position must be submitted electronically. Applicants will be required to submit the following: (1) cover letter; (2) curriculum vitae; (3) statement of research; (4) statement on teaching; (5) statement on diversity, mentoring, and outreach; (6) PDF copies of up to three publications; and (7) the names, affiliations, and email addresses of three professional references. Rice University, and the Department of Physics and Astronomy, are strongly committed to a culturally diverse intellectual community. In this spirit, we particularly welcome applications from all genders and members of historically underrepresented groups who exemplify diverse cultural experiences and who are especially qualified to mentor and advise all members of our diverse student population.We will begin reviewing applications November 15, 2021. To receive full consideration, all application materials must be received by January 1, 2022. The expected appointment date is July, 2022.  

Rice University is an Equal Opportunity Employer with commitment to diversity at all levels, and considers for employment qualified applicants without regard to race, color, religion, age, sex, sexual orientation, gender identity, national or ethnic origin, genetic information, disability or protected veteran status.

Saturday, August 28, 2021

What is the spin Seebeck effect?

Thermoelectricity is an old story, and I've also discussed it here.  Take a length of some conductor, and hold one end of that conductor at temperature \(T_{\mathrm{hot}}\), and hold the other end of that conductor at temperature \(T_{\mathrm{cold}}\).  The charge carriers in the conductor will tend to diffuse from the hot end toward the cold end.  However, if the conductor is electrically isolated, that can't continue, and a voltage will build up between the ends of the conductor, so that in the steady state there is no net flow of charge.  The ratio of the voltage to the temperature difference is given by \(S\), the Seebeck coefficient.  

It turns out that spin, the angular momentum carried by electrons, can also lead to the generation of voltages in the presence of temperature differences, even when the material is an insulator and the electrons don't move.  

Let me describe an experiment for you.  Two parallel platinum wires are patterned next to each other on the surface of an insulator.  An oscillating current at angular frequency \(\omega\) is run through wire A,  while wire B is attached to a voltage amplifier feeding into a lock-in amplifier.  From everything we teach in first-year undergrad physics, you might expect some signal on the lock-in at frequency \(\omega\) because the two wires are capacitively coupled to each other - the oscillating voltage on wire A leads to the electrons on wire B moving back and forth because they are influenced by the electric field from wire A.  You would not expect any kind of signal on wire B at frequency \(2 \omega\), though, at least not if the insulator is ideal.

However, if that insulator is magnetically interesting (e.g., a ferrimagnet, an antiferromagnet, some kinds of paramagnet), it is possible to see a \(2 \omega\) signal on wire B.  

In the spin Seebeck effect, a temperature gradient leads to a build-up of a net spin density across the magnetic insulator.  This is analogous to the conventional Seebeck effect - in a magnetically ordered system, there is a flow of magnons from the hot side to the cold side, transporting angular momentum along.  This builds up a net spin polarization of the electrons in the magnetic insulator.  Those electrons can undergo exchange processes with the electrons in the platinum wire B, and if the spins are properly oriented, this causes a voltage to build up across wire B due to the inverse spin Hall effect.  

So, in the would-be experiment, the ac current in wire A generates a temperature gradient between wire A and wire B that oscillates at frequency \(2 \omega\).  An external magnetic field is used to orient the spins in the magnetic insulator, and if the transported angular momentum points the right direction, there is a \(2 \omega \) voltage signal on wire B.   

I think this is pretty neat - an effect that is purely due to the quantum properties of electrons and would just not exist in the classical electricity and magnetism that we teach in intro undergrad courses.

(On writing this, I realized that I've never written a post defining the spin Hall and related effects. I'll have to work on that....  Sorry for the long delay between postings.  The beginning of the semester has been unusually demanding of my time.)

Thursday, August 12, 2021

More amazingly good harmonic oscillators

 Harmonic oscillators are key elements of the physicist's toolkit for modeling the world.  Back at the end of March I wrote about some recent results using silicon nitride membranes to make incredibly high quality (which is to say, low damping) harmonic oscillators.  (Remember, the ideal harmonic oscillator that gets introduced in undergrad intro physics is a mass on a spring, with no friction or dissipation at all.  An ideal oscillator would have a \(Q\) factor that is infinite, and it would keep ringing forever once started.) This past week, two papers appeared on the arxiv showing that it's possible to design networks of (again) silicon nitride beams that have resonances at room temperature (in vacuum) with \(Q > 10^{9}\).  

(a) A perimeter mode of oscillation. (b) a false-
color electron micrograph of such a device.
One of these papers takes a specific motif, a suspended polygon made from beams, supported by anchoring beams coming from its vertices, as shown in the figure.  The resonant modes with the really high \(Q\) factors are modes of the perimeter, with nodes at the vertices.  This minimizes "clamping losses", damping that occurs at anchoring points (where the strain tends to be large, and where phonons can leak vibrational energy out of the resonator and into whatever is holding it).  

The other paper gets to a very similar design, through a process that combines biological inspiration (spiderwebs), physics insight, and machine learning/optimization to really maximize \(Q\).  

With tools like this, it's possible to do quantum mechanics experiments  (that is, mechanics experiments where quantum effects are dominant) at or near room temperature with these.  Amazing.

Monday, August 09, 2021

Brief items

 It's been a busy week, so my apologies for the brevity, but here are a couple of interesting papers and sites that I stumbled upon:

  • Back when I first started teaching about nanoscience, I said that you'd really know that semiconductor quantum dots had hit the big time when you occasionally saw tanker trucks full of them going down the highway.  I think we're basically there.  Here is a great review article that summarizes the present state of the art.
  • Reaching back a month, I thought that this is an impressive piece of work.  They combine scanning tunneling microscopy, photoluminescence with a tunable optical source, and having the molecule sitting on a layer of NaCl to isolate it from the electronic continuum of the substrate.  The result is amazingly (to me) sharp spectral features in the emission, spatially resolved to the atomic scale.
  • The emergence of python and the ability to embed it in web pages through notebooks has transformative educational potential, but it definitely requires a serious investment of time and effort.  Here is a fluid dynamics course from eight years ago that I found the other day - hey, it was new to me.
  • For a more up-to-the-minute example, here is a new course about topology and condensed matter.  Now if I only had time to go through this.  The impending start of the new semester. 
  • This preprint is also an important one.  There have been some major reports in the literature about quantum oscillations (e.g., resistivity or magnetization vs. magnetic field ) being observed in insulators.  This paper shows that one must be very careful, since the use of graphite gates can lead to a confounding effect that comes from those gates rather than the material under examination.
  • This PNAS paper is a neat one.  It can be hard to grow epitaxial films of some "stubborn" materials, ones involving refractory metals (high melting points, very low vapor pressures, often vulnerable to oxidation).  This paper shows that instead one can use solid forms of precursor compounds containing those metals.  The compounds sublime with reasonably high vapor pressures, and if one can work out their decomposition properly, it's possible to grow nice films and multilayers of otherwise tough materials.  (I'd need to be convinced that the purity achieved from this comparatively low temperature approach is really good.)

Monday, August 02, 2021

Metallic water!

What does it take to have a material behave as a metal, from the physicist's perspective?  I've written about this before (wow, I've been blogging for a long time).  Fundamentally, there have to be "gapless" charge-carrying excitations, so that the application of even a tiny electric field allows those charge carriers to transition into states with (barely) higher kinetic energies and momenta.  

Top: a droplet of NaK 
alloy.  Bottom: That 
droplet coated with 
adsorbed water that 
has become a metal. 
From here.
In conventional band insulators, the electronic states are filled right up to the brim in an energy band.  Apply an electric field, and an electron has no states available into which it can go without somehow grabbing enough energy to make it all the way to the bottom of the next (conduction) band.  Since that band gap can be large (5.5 eV for diamond, 8.5 eV for NaCl), no current flows, and you have an insulator.

This is, broadly speaking, the situation in liquid water. (Even though it's a liquid, the basic concept of bands of energy levels is still helpful, though of course there are no Bloch waves as in crystalline solids.)  According to calculations and experiments, the band gap in ordinary water is about 7 eV.  You can dissolve ions in water and have those carry a current - that's the whole deal with electrolytes - but ordinarily water is not a conductor based on electrons.  It is possible to inject some electrons into water, and these end up "hydrated" or "solvated" thanks to interactions with the surrounding polar water molecules and the hydronium and hydroxyl ions floating around, but historically this does not result in a metal.  To achieve metallicity, you'd have to inject or borrow so many electrons that they could get up into that next band.

This paper from late last week seems to have done just that.  A few molecular layers of water adsorbed on the outside of a droplet of liquid sodium-potassium metal apparently ends up taking in enough electrons (\( \sim 5 \times 10^{21}\) per cc) to become metallic, as detected through optical measurements of its conductivity (including a plasmon resonance).   It's rather transient, since chemistry continues and the whole thing oxidizes, but the result is quite neat!