Thickness-induced violation of de Haas-van Alphen effect through exact analytical solutions at a one-electron and a one-Composite Fermion level

TL;DR

This paper presents exact analytical solutions for electron energetics in magnetic fields considering finite quantum well thickness, revealing phase transitions and violations of de Haas-van Alphen periodicity, with implications for topological insulators.

Contribution

It introduces a transparent analytical approach that captures internal phase transitions and de Haas-van Alphen violations, extending to composite fermions and topological systems.

Findings

Discovery of internal phase transitions at partial Landau level filling.

Identification of violations of standard de Haas-van Alphen periods.

Prediction of similar effects in topological insulator crossover.

Abstract

A systematic study of the energetics of electrons in an interface in a magnetic field is reported with exact analytical calculations based on a Landau Level (LL) picture, by serious consideration of the finite thickness of the Quantum Well (QW). The approach is physically transparent and subtly different in its line of reasoning from standard methods avoiding any semi-classical approximation. We find "internal" phase transitions (at partial LL filling) for magnetisation and susceptibility that are not captured by other approaches and that give rise to nontrivial violations of the standard de Haas-van Alphen periods, in a manner that reproduces the exact quantal astrophysical behaviours in the limit of full three-dimensional (3D) space. Upon inclusion of Zeeman splitting, additional features are also found, such as global energy minima originating from the interplay of QW, Zeeman and LL Physics, while a corresponding calculation in a Composite Fermion picture with {\Lambda}-Levels, leads to new predictions on magnetic properties of an interacting electron liquid. By pursuing the same line of reasoning for a topologically nontrivial system with a relativistic spectrum, we find evidence that similar effects might be operative in the dimensionality crossover of 3D strong topological insulators to 2D topological insulator quantum wells.