Intrinsic Perturbation of the Landau Levels in Metals and Semiconductors at Low Temperatures

TL;DR

This paper investigates how a perturbative correction to Landau levels affects magnetic oscillations and electronic specific heat in metals and semiconductors at ultra-low temperatures and high magnetic fields, revealing anomalous behaviors.

Contribution

It introduces a perturbative term in the Landau equation that modifies Landau levels and predicts observable effects on magnetic oscillations and specific heat at ultra-low temperatures.

Findings

Frequency correction depends on Fermi energy and electron g-factor.

Electronic specific heat approaches zero as temperature nears absolute zero.

Proposes experimental detection via magneto optical absorption measurements.

Abstract

It is shown that the frequency of the de Haas van Alphen effect in nonsuperconducting metals at very low temperatures is significantly corrected by a perturbative term which appears in the Landau equation sequel to an extension of the Pauli equation. The correction to the frequency of the de Haas van Alphen oscillations is found to depend on the Fermi energy and the measurable anomalous part of the electron gyro-magnetic factor. Furthermore, it is shown that as a consequence of the perturbing term the electronic specific heat Cv of a dilute, degenerate Fermi gas, under high magnetic field induction greater that 25 Tesla and at ultra-low temperatures of the order of one milli Kelvin shows an anomalous behavior, and at a finite temperature becomes vanishingly small, i.e Cv is approximately zero, as the temperature approaches absolute zero. Precision measurement at low temperatures and high magnetic fields of the magneto optical absorption in simple band semiconductors is suggested as an immediate way of detecting the modification of the Landau levels due to the weak perturbation term which corrects in a magnetic field, the kinetic energy of the electrons.