Quantum Hall effect on the Lobachevsky plane

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.

Aharonov-Bohm effect on the Poincaré disk

“…Combining these formulas with the relations (2.14), (2.11), one can rewrite the Green function (4.1) in the following way: 6) where the functions G…”

“…Analyzed examples include, for instance, the free motion under the action of constant magnetic fields [8,9,23], the Kepler problem [25], the scattering by the Aharonov-Bohm (AB) [24,26] and Aharonov-Bohm-Coulomb [29] potentials, the study of point interactions [3,5] and quantum Hall effect [6].…”

Coupling curvature to a uniform magnetic field: An analytic and numerical study

“…Nanostructures with novel geometries have become the subject of a large body of experimental and theoretical work [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. Many of the fabricated structures exhibit curvature on the nanoscale making once purely theoretical investigations of quantum mechanics on curved and reduced dimensionality surfaces relevant to device modelling.…”

Inertial and topological effects on a 2D electron gas

“…This leads to a plethora of phenomena, among them, the integer quantum Hall effect (IQHE) [2], which may be affected by geometric and inertial factors. For instance, curvature is known to affect the IQHE [3][4][5]. In fact, curvature may be used as a tool to manipulate the electronic structure of charge carriers confined to a surface [6][7][8].…”