Session M42: New Developments in Disordered Quantum Materials

From disorder to order and back again

One surprising phenomenon in frustrated magnets is the order-by-disorder mechanism: thermal and/or quantum fluctuations lift a macroscopic accidental degeneracy of the classical ground state of frustrated magnets. The resulting magnetically ordered-by-(thermal/quantum)disorder state often breaks a real-space symmetry of the crystal lattice. In this talk, we use symmetry arguments and Monte Carlo simulations to investigate the effects of impurities (vacancies, chemical doping, etc.). Because inhomogeneities generically break real-space symmetries, it couples to the order-parameter as a conjugate field. As a consequence, inhomogeneities are responsible for non-perturbative effects that destabilize an ordered-by-disorder state at sufficiently low dimensions. As an example, we apply our theory to the J1-J2 Heisenberg model on a square lattice and to the easy-plane pyrochlores.   

Interplay of disorder and superconductivity at quantum critical points

We study the superconducting instability of a two-dimensional disordered Fermi liquid weakly coupled to the soft fluctuations associated with proximity to an Ising-ferromagnetic quantum critical point. We derive interaction-induced corrections to the Usadel equation governing the superconducting gap function, and show that diffusion and localization effects drastically modify the interplay between fermionic incoherence and strong pairing interactions. In particular, we obtain the phase diagram, and demonstrate that (i) there is an intermediate range of disorder strength where superconductivity is enhanced, eventually followed by a tendency towards the superconductor-insulator transition at stronger disorder; and (ii) diffusive particle-particle modes (so-called "Cooperons") acquire anomalous dynamical scaling z=4, indicating strong non-Fermi liquid behavior.   

Anomalous successes and a surprising failure: The Dirac equation and topological materials

The Dirac equation was formulated nearly a century ago, with the goal of combining quantum mechanics and special relativity. The elegance and simplicity of its construction infused the entire project of quantum physics, through the idea that a minimal combination of relativistic and quantum principles should define the basic building blocks of physical theories. This philosophy produced the most-tested, successful theories of physics, such as quantum electrodynamics (QED). In condensed matter physics, the Dirac equation has become a source of fascination in more recent times. Versions of the Dirac equation describe chiral edge states of quantum Hall droplets, "ultrarelativistic" carriers in graphene, Weyl semimetals, and moire materials, and surface states of 3D topological phases.

In this talk, after reviewing some of these successes, I will discuss a very surprising recent development wherein the emergent Dirac equation that is supposed to describe surface states of most "strong" 3D topological phases fails to determine even the most basic properties of the surface. One such question is whether surface particles can conduct energy in the presence of impurities. This development implies that 2+1-D quantum field theories meant to describe surface states of topological matter are fundamentally incomplete. This is analogous to requiring an understanding of physics at the Planck scale in order to predict properties of ordinary 3+1-D quantum matter. The "missing" information turns out to be a type of symmetry-preserving, hidden surface Berry curvature that resides outside the minimal Dirac description. We show that surface Berry curvature can interupt bulk-boundary spectral flow and Anderson localize most surface states. Our work reveals that three-dimensional phases in the periodic table have a much richer boundary phenomenology than previously believed, where the extreme cases correspond to (1) spectrum-wide quantum-critical surface delocalization, with a bulk "bridge" connecting boundary states at different surfaces, vs. (2) bulk-disconnected surface states that avoid localization only at zero energy.   

Electronic nematicity in disordered crystals: the impact of random strain

Besides superconductivity, magnetism, and charge order, electronic interactions can also promote unusual types of electronic order analogous to liquid-crystalline phases. Indeed, electronic nematicity has been observed in a diverse set of systems, from unconventional superconductors to doped topological insulators to twisted moiré devices. In all cases, the presence of the underlying lattice (or superlattice) significantly influences the critical properties associated with the nematic phase by restricting the allowed directions of the nematic director, mediating long-range nematic interactions, and introducing random strain. The latter is ubiquitously generated in crystals by several sources, such as chemical substitution, vacancies, interstitials, and dislocations. In this talk, I will explore different aspects of the impact of random strain on electronic nematicity. First, I will discuss how surface defects can trigger a modulated nematic phase, which is the analogue of the smectic phase in liquid crystals. Then, I will show that important qualitative effects are not captured by descriptions based solely on the random-field Ising model, such as the long-range correlated nature of the random strain and the disorder-induced correlations with phases intertwined with nematicity. I will propose and explore the properties of different types of models that incorporate these effects, such as a random Baxter-field model and a transverse-field Ising model with correlated random longitudinal and transverse fields. I will conclude by arguing that the interplay between random strain and electronic nematicity leads to a unique landscape of phenomena with no counterparts in clean systems, which could explain puzzling experimental data in different materials.   

Nonequilibrium transport and thermalization in strongly disordered 2D electron systems

Understanding the dynamics of isolated disordered systems and its dependence on the range of interactions has been attracting a lot of research attention in recent years, but many questions remain open, especially in two spatial dimensions.  At the same time, experiments have been limited mostly to those on synthetic quantum matter, such as ultracold atoms in optical lattices and superconducting qubits.  However, observing the absence of thermalization and signatures of many-body localization (MBL) in real, solid-state materials has been a challenge.  

This talk will describe experimental studies of nonequilibrium dynamics in strongly disordered, 2D electron systems with weak thermal coupling to the environment.  We find that, while reducing the range of the Coulomb interaction has practically no effect on the dc transport, there is a striking difference in the dynamics.  In the case of a long-range Coulomb interaction (~1/r), the system thermalizes, although the dynamics is glassy.  In contrast, in the case of a screened or dipolar Coulomb interaction (~1/r³), the thermalization is anomalously slow and strongly sensitive to coupling to the thermal bath, consistent with the proximity to a MBL phase. This direct observation of the MBL-like, prethermal regime in an electronic system thus clarifies the effects of the interaction range on the fate of glassy dynamics and MBL in 2D.  These are important insights for theory, especially since the results have been obtained on systems that are much closer to a thermodynamic limit than synthetic ensembles of interacting, disordered particles employed in previous studies of MBL.  By establishing a new, versatile solid-state platform for the study of MBL, our work also opens new possibilities for further investigations, such as noise measurements as a probe of ergodicity breaking and many-body entanglement.