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Following recent experiments, we consider current flow in two dimensional electronic systems in the quantum Hall regime where a gradient in the electron density induces a spatial variation in the Hall resistivity. Describing the system in…

We study the fractional quantum Hall effect in three dimensional systems consisting of infinitely many stacked two dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics…

It is commonly believed that the current response of an electron fluid to a mechanical force (such as an electric field) or to a ``statistical force" (e.g., a gradient of chemical potential) are governed by a single linear transport…

We show that in the limit of zero temperature, double layer quantum Hall systems exhibit a novel phenomena called Hall drag, namely a current driven in one layer induces a voltage drop in the other layer, in the direction perpendicular to…

The integer quantum Hall effect (QHE) belongs to the most fundamental phenomena of solid state physics and has an important application as resistance standard. It serves as a basis to understand the fractional, anomalous or spin QHEs,…

The thermal Hall conductance is a universal and topological property which characterizes the fractional quantum Hall (FQH) state. The quantized value of the thermal Hall conductance has only recently been measured experimentally in integer…

In some recent experiments [A. J. Bestwick, et. al., Phys. Rev. Lett. 114, 187201 (2015), Cui-Zu Chang, et. al., Nat. Materials. 14, 473-477 (2015)] it has been shown that in observations of the quantum anomalous Hall (QAH) effect the…

The response of particle density to a dilation of a periodic potential in an insulator, with or without a fixed background potential or a magnetic field, is shown to be quantized. A similar phenomenon occurs in a quantum Hall system, where…

Correlated quantum systems can exhibit thermodynamic behaviors that defy classical expectations, with anomalous energy flow (AEF) against temperature gradients serving as a paradigmatic example. While AEF has been shown to arise from the…

We propose a new formula that extracts the quantum Hall conductance from a single (2+1)D gapped wavefunction. The formula applies to general many-body systems that conserve particle number, and is based on the concept of modular flow: i.e.,…

Non-equilibrium thermodynamics can provide strong advantages when compared to more standard equilibrium situations. Here, we present a general framework to study its application to concrete problems, which is valid also beyond the…

A quantum anomalous Hall (QAH) insulator is characterized by quantized Hall and vanishing longitudinal resistances at zero magnetic field that are protected against local perturbations and independent of sample details. This insensitivity…

We theoretically investigate quantum transport properties of quantum anomalous Hall bilayers, with arbitrary ratio of lattice constants, i.e., with lattice mismatch. In the simplest case of ratio 1 (but with different model parameters in…

Recent experiments have studied the tunneling current between the edges of a fractional quantum Hall liquid as a function of temperature and voltage. The results of the experiment are puzzling because at "high" temperature (600-900 mK) the…

We study the effect of correlation on the direction of particle exchange between local thermal sub-systems where the total system is isolated. Our focus is the situation where both sub-systems have the same temperature but different…

Quantized Hall conductance is a generic feature of two dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is…

Using recently developed tools from space-adiabatic perturbation theory, in particular the construction of a non-equilibrium almost stationary state, we give a new proof that the Kubo formula for the Hall conductivity remains valid beyond…

The discovery of the quantum Hall (QH) effect led to the realization of a topological electronic state with dissipationless currents circulating in one direction along the edge of a two dimensional electron layer under a strong magnetic…

A key step towards dissipationless transport devices is the quantum anomalous Hall effect, which is characterized by an integer quantized Hall conductance in a ferromagnetic insulator with strong spin-orbit coupling. In this work, the…

We study two-dimensional systems with Galilean invariance gapped under magnetic fields. When such quantum Hall systems are coupled with external sources for charge, energy, and momentum currents, they exhibit invariance under the Milne…