Quantum Hall effect on the Lobachevsky plane

TL;DR

This paper investigates how negative curvature of the Lobachevsky plane affects the quantum Hall effect, revealing modifications in conductivity plateaus and temperature-induced smearing.

Contribution

It provides a novel analysis of the quantum Hall effect on negatively curved surfaces, highlighting curvature-induced changes in Hall conductivity features.

Findings

Curvature alters break points and plateau widths in Hall conductivity.

Temperature increases cause smearing of quantum Hall steps.

Surface curvature impacts quantum Hall effect characteristics.

Abstract

The Hall conductivity of an electron gas on the surface of constant negative curvature (the Lobachevsky plane) in the presence of an orthogonal magnetic field is investigated. It is shown that the effect of the surface curvature is to change the break locations and the plateau widths in the Hall conductivity. An increase of temperature results in smearing of the steps.