Landau levels, self-adjoint extensions and Hall conductivity on a cone

Abstract

In this work we obtain the Landau levels and the Hall conductivity at zero temperature of a two-dimensional electron gas on a conical surface. We investigate the integer quantum Hall effect considering two different approaches. The first one is an extrinsic approach which employs an effective scalar potential that contains both the Gaussian and the mean curvature of the surface. The second one, an intrinsic approach where the Gaussian curvature is the sole term in the scalar curvature potential. From a theoretical point of view, the singular Gaussian curvature of the cone may affect the wave functions and the respective Landau levels. Since this problem requests {\it self-adjoint extensions}, we investigate how the conical tip could influence the integer quantum Hall effect, comparing with the case were the coupling between the wave functions and the conical tip is ignored. This last case corresponds to the so-called {\it Friedrichs extension}. In all cases, the Hall conductivity is enhanced by the conical geometry depending on the opening angle. There are a considerable number of theoretical papers concerned with the self-adjoint extensions on a cone and now we hope the work addressed here inspires experimental investigation on these questions about quantum dynamics on a cone.

arXiv commentFig. 2b at the end

References in corpus (27)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Supersymmetry and Quantum Mechanics
• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Geometric Theory of Defects
• Hidden supersymmetry in quantum bosonic systems
• Tuning electronic properties of corrugated graphene: confinement, curvature and band gap opening
• Giant asymmetry of the longitudinal magnetoresistance in high-mobility two-dimensional electron gas on a cylindrical surface
• Physical regularization for the spin-1/2 Aharonov-Bohm problem in conical space
• Cylindrical Two-Dimensional Electron Gas in a Transverse Magnetic Field
• Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem
• Geometry induced potential on a 2D-section of a wormhole: catenoid
• On the quantum dynamics of a point particle in conical space
• Bound states of massive fermions in the Aharonov--Bohm-like fields
• Quantum mechanics of a free particle on a pointed plane revisited
• Bilayer graphene Origami: curvature-induced p-n junctions
• Self-adjoint Extension Approach to the spin-1/2 Aharonov-Bohm-Coulomb Problem
• On the dynamics of a particle on a cone
• Quantum Hall effect on the Lobachevsky plane
• Dipole binding in a cosmic string background due to quantum anomalies
• Comment on "Relativistic Aharonov-Bohm effect in the presence of planar Coulomb potentials"
• Hidden superconformal symmetry of spinless Aharonov-Bohm system
• Supersymmetries of the spin-1/2 particle in the field of magnetic vortex, and anyons
• Runge-Lenz Vector, Accidental SU(2) Symmetry, and Unusual Multiplets for Motion on a Cone
• Magnetic moment of an electron gas on the surface of constant negative curvature
• Specific heat of a particle on the cone
• Path Integration in Conical Space

Cited by in corpus (8)

• Emergent Conformal Symmetry of Quantum Hall States on Singular surfaces
• Lowest Landau level on a cone and zeta determinants
• Study on the effects of anisotropic effective mass on electronic properties, magnetization and persistent current in semiconductor quantum ring with conical geometry
• The centripetal force law and the equation of motion for a particle on a curved hypersurface
• Curved non-interacting two-dimensional electron gas with anisotropic mass
• Generalized Centripetal Force Law and Quantization of Motion Constrained on 2D Surfaces
• Inertial and topological effects on a 2D electron gas
• Effects of curvature on the electronic states of a two-dimensional mesoscopic ring