Sachdev-Ye-Kitaev Non-Fermi-Liquid Correlations in Nanoscopic Quantum Transport.

Electronic transport in nanostructures, such as long molecules or 2D exfoliated flakes, often goes through a nearly degenerate set of single-particle orbitals. Here we show that in such cases a conspiracy of the narrow band and strong e-e interactions may stabilize a non-Fermi-liquid phase in the universality class of the complex Sachdev-Ye-Kitaev (SYK) model. Focusing on signatures in quantum transport, we demonstrate the existence of anomalous power laws in the temperature dependent conductance, including algebraic scaling T^{3/2} in the inelastic cotunneling channel, separated from the conventional Fermi liquid T^{2} scaling via a quantum phase transition. The relatively robust conditions under which these results are obtained indicate that the SYK non-Fermi-liquid universality class might not be as exotic as previously thought.

Quantum Criticality of Granular Sachdev-Ye-Kitaev Matter.

We consider granular quantum matter defined by Sachdev-Ye-Kitaev dots coupled via random one-body hopping. Within the framework of Schwarzian field theory, we identify a zero-temperature quantum phase transition between an insulating phase at weak and a metallic phase at strong hopping. The critical hopping strength scales inversely with the number of degrees of freedom on the dots. The increase of temperature out of either phase induces a crossover into a regime of strange metallic behavior.

Sinai Diffusion at Quasi-1D Topological Phase Transitions.

We consider critical quantum transport in disordered topological quantum wires at the transition between phases with different topological indices. Focusing on the example of thermal transport in class D ("Majorana") quantum wires, we identify a transport universality class distinguished for anomalous retardation in the propagation of excitations-a quantum generalization of Sinai diffusion. We discuss the expected manifestations of this transport mechanism for heat propagation in topological superconductors near criticality and provide a microscopic theory explaining the phenomenon.

Effective Field Theory of the Disordered Weyl Semimetal.

In disordered Weyl semimetals, mechanisms of topological origin lead to the protection against Anderson localization, and at the same time to different types of transverse electromagnetic response-the anomalous Hall and the chiral magnetic effect. We here apply field theory methods to discuss the manifestation of these phenomena at length scales that are beyond the scope of diagrammatic perturbation theory. Specifically, we show how an interplay of symmetry breaking and the chiral anomaly leads to a field theory containing two types of topological terms. Generating the unconventional response coefficients of the system, these terms remain largely unaffected by disorder, i.e., information on the chirality of the system remains visible even at large length scales.

Class D spectral peak in Majorana quantum wires.

Proximity coupled spin-orbit quantum wires purportedly support midgap Majorana states at critical points. We show that, in the presence of disorder, these systems generate a second band center anomaly, which is of different physical origin but shares key characteristics with the Majorana state: it is narrow in width, insensitive to magnetic fields, carries unit spectral weight, and is rigidly tied to the band center. Depending on the parity of the number of subgap quasiparticle states, a Majorana mode does or does not coexist with the impurity peak. The strong "entanglement" between the two phenomena may hinder an unambiguous detection of the Majorana by spectroscopic techniques.

Full counting statistics in the self-dual interacting resonant level model.

We present a general technique to obtain the zero temperature cumulant generating function of the full counting statistics of charge transfer in interacting impurity models out of equilibrium from time-dependent simulations on a lattice. We demonstrate the technique with application to the self-dual interacting resonant level model, where very good agreement between numerical simulations using the density matrix renormalization group and those obtained analytically from the thermodynamic Bethe ansatz is found. We show from the exact form of counting statistics that the quasiparticles involved in transport carry charge 2e in the low bias regime and e/2 in the high bias regime.

Full current statistics of incoherent "cold electrons".

We evaluate the full current statistics (FCS) in the low-dimensional (1D and 2D) diffusive conductors in the incoherent regime eV>>E(Th)=D/L(2), E(Th) being the Thouless energy. It is shown that the Coulomb interaction substantially enhances the probability of big current fluctuations for short conductors with E(Th)>>1/tau(E), tau(E) being the energy relaxation time, leading to the exponential tails in the current distribution. The current fluctuations are most strong for low temperatures, provided E(Th) approximately [(eV)(2)/Dnu(2)(1)](1/3) for 1D and E(Th) approximately (eV/g)ln(g for 2D, where g is a dimensionless conductance and nu(1) is a 1D density of states. The FCS in the "hot electron" regime is also discussed.