Hall Drag in Correlated Double Layer Quantum Hall Systems

TL;DR

This paper demonstrates that in double layer quantum Hall systems at zero temperature, a current in one layer induces a perpendicular voltage in the other, with a quantized Hall resistivity tensor linked to the system's topological order.

Contribution

It introduces the concept of Hall drag in double layer quantum Hall systems and relates the quantized Hall resistivity tensor to the topological ${f K}$ matrix, even with zero eigenvalues.

Findings

Hall drag occurs in double layer quantum Hall systems at zero temperature.

The Hall resistivity tensor is quantized and proportional to the ${f K}$ matrix.

Quantization persists even when the ${f K}$ matrix has zero eigenvalues.

Abstract

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 driving current. The two-by-two Hall resistivity tensor is quantized and proportional to the ${\bf K}$ matrix that describes the topological order of the quantum Hall state, even when the ${\bf K}$ matrix contains a zero eigenvalue, in which case the Hall conductivity tensor does not exist. Relation between the present work and previous ones is also discussed.