Two dimensional electron gas in a non-Euclidean space

TL;DR

This paper investigates a two-dimensional electron gas in a non-Euclidean space, revealing how curvature affects quantum states, degeneracy, and energy levels, with solutions related to the Morse oscillator and implications for electronic properties.

Contribution

It introduces a novel approach to modeling 2DEG in curved space using position-dependent operators, connecting anharmonicity to relativistic corrections and analyzing energy modifications.

Findings

Degeneracy of spin levels is lifted in non-Euclidean space

Fermi energy and ground state energy are modified by curvature

Solution involves Morse oscillator-like equations

Abstract

A charged particle in the presence of a magnetic field is studied in the position dependent operator formalism. Instead of a quantum harmonic oscillator, the solution of the resulting Schr\"odinger-like equation is the one for the Morse oscillator. The anharmonicity that shows up naturally from the theory is analogous to the corrections introduced by relativistic ones.The degeneracy of the spin up and down levels is lifted due to the non-Euclidean space. It is shown that the Fermi energy and the total ground state energy of the 2DEG is also modified.