Universal Scaling near Band-Tuned Metal-Insulator Phase Transitions.

We present a theory for band-tuned metal-insulator transitions based on the Kubo formalism. Such a transition exhibits scaling of the resistivity curves in the regime where Tτ>1 or µτ>1, where τ is the scattering time and µ the chemical potential. At the critical value of the chemical potential, the resistivity diverges as a power law, R_{c}∼1/T. Consequently, on the metallic side there is a regime with negative dR/dT, which is often misinterpreted as insulating. We show that scaling and this "fake insulator" regime are observed in a wide range of experimental systems. In particular, we show that Mooij correlations in high-temperature metals with negative dR/dT can be quantitatively understood with our scaling theory in the presence of T-linear scattering.

Determining spin-orbit coupling in graphene by quasiparticle interference imaging.

Inducing and controlling spin-orbit coupling (SOC) in graphene is key to create topological states of matter, and for the realization of spintronic devices. Placing graphene onto a transition metal dichalcogenide is currently the most successful strategy to achieve this goal, but there is no consensus as to the nature and the magnitude of the induced SOC. Here, we show that the presence of backscattering in graphene-on-WSe2 heterostructures can be used to probe SOC and to determine its strength quantitatively, by imaging quasiparticle interference with a scanning tunneling microscope. A detailed theoretical analysis of the Fourier transform of quasiparticle interference images reveals that the induced SOC consists of a valley-Zeeman (λvZ ≈ 2 meV) and a Rashba (λR ≈ 15 meV) term, one order of magnitude larger than what theory predicts, but in excellent agreement with earlier transport experiments. The validity of our analysis is confirmed by measurements on a 30 degree twist angle heterostructure that exhibits no backscattering, as expected from symmetry considerations. Our results demonstrate a viable strategy to determine SOC quantitatively by imaging quasiparticle interference.

Slow Nonthermalizing Dynamics in a Quantum Spin Glass.

Spin glasses and many-body localization (MBL) are prime examples of ergodicity breaking, yet their physical origin is quite different: the former phase arises due to rugged classical energy landscape, while the latter is a quantum-interference effect. Here, we study quantum dynamics of an isolated 1D spin glass under application of a transverse field. At high energy densities, the system is ergodic, relaxing via a resonance avalanche mechanism, that is also responsible for the destruction of MBL in nonglassy systems with power-law interactions. At low energy densities, the interaction-induced fields obtain a power-law soft gap, making the resonance avalanche mechanism inefficient. This leads to the persistence of the spin-glass order, as demonstrated by resonance analysis and by numerical studies. A small fraction of resonant spins forms a thermalizing system with long-range entanglement, making this regime distinct from the conventional MBL. The model considered can be realized in systems of trapped ions, opening the door to investigating slow quantum dynamics induced by glassiness.

Quantum Thermalization and the Expansion of Atomic Clouds.

The ultimate consequence of quantum many-body physics is that even the air we breathe is governed by strictly unitary time evolution. The reason that we perceive it nonetheless as a completely classical high temperature gas is due to the incapacity of our measurement machines to keep track of the dense many-body entanglement of the gas molecules. The question thus arises whether there are instances where the quantum time evolution of a macroscopic system is qualitatively different from the equivalent classical system? Here we study this question through the expansion of noninteracting atomic clouds. While in many cases the full quantum dynamics is indeed indistinguishable from classical ballistic motion, we do find a notable exception. The subtle quantum correlations in a Bose gas approaching the condensation temperature appear to affect the expansion of the cloud, as if the system has turned into a diffusive collision-full classical system.

Universality and critical behavior of the dynamical Mott transition in a system with long-range interactions.

We study numerically the voltage-induced breakdown of a Mott insulating phase in a system of charged classical particles with long-range interactions. At half-filling on a square lattice this system exhibits Mott localization in the form of a checkerboard pattern. We find universal scaling behavior of the current at the dynamic Mott insulator-metal transition and calculate scaling exponents corresponding to the transition. Our results are in agreement, up to a difference in universality class, with recent experimental evidence of a dynamic Mott transition in a system of interacting superconducting vortices.

Explicit Local Integrals of Motion for the Many-Body Localized State.

Recently, it has been suggested that the many-body localized phase can be characterized by local integrals of motion. Here we introduce a Hilbert-space-preserving renormalization scheme that iteratively finds such integrals of motion exactly. Our method is based on the consecutive action of a similarity transformation using displacement operators. We show, as a proof of principle, localization and the delocalization transition in interacting fermion chains with random on-site potentials. Our scheme of consecutive displacement transformations can be used to study many-body localization in any dimension, as well as disorder-free Hamiltonians.

Glassy Dynamics in Geometrically Frustrated Coulomb Liquids without Disorder.

We show that introducing long-range Coulomb interactions immediately lifts the massive ground state degeneracy induced by geometric frustration for electrons on quarter-filled triangular lattices in the classical limit. Important consequences include the stabilization of a stripe-ordered crystalline (global) ground state, but also the emergence of very many low-lying metastable states with amorphous "stripe-glass" spatial structures. Melting of the stripe order thus leads to a frustrated Coulomb liquid at intermediate temperatures, showing remarkably slow (viscous) dynamics, with very long relaxation times growing in Arrhenius fashion upon cooling, as typical of strong glass formers. On shorter time scales, the system falls out of equilibrium and displays the aging phenomena characteristic of supercooled liquids above the glass transition. Our results show remarkable similarity with the recent observations of charge-glass behavior in ultraclean triangular organic materials of the θ-(BEDT-TTF)(2) family.

Influence of long-range interactions on charge ordering phenomena on a square lattice.

Usually complex charge ordering phenomena arise due to competing interactions. We have studied how such ordered patterns emerge from the frustration of a long-ranged interaction on a lattice. Using the lattice gas model on a square lattice with fixed particle density, we have identified several interesting phases, such as a generalization of Wigner crystals at low particle densities and stripe phases at densities between ρ=1/3 and 1/2. These stripes act as domain walls in the checkerboard phase present at half-filling. The phases are characterized at zero temperatures using numerical simulations, and mean field theory is used to construct a finite temperature phase diagram.