The nontrivial role of interfacial or film-thickness in a magnetic field at a one-electron and a one-Composite Fermion level

TL;DR

This paper develops an exact analytical approach to study the effects of finite quantum well thickness on the magnetic properties of electron systems in magnetic fields, revealing internal phase transitions and corrections to classical oscillation periods.

Contribution

It introduces a systematic, exact Landau Level-based method that captures nontrivial thickness effects and phase transitions, extending to composite fermion and topological insulator systems.

Findings

Discovery of internal phase transitions at partial LL filling

Nontrivial corrections to de Haas-van Alphen periods

Predictions of thickness-dependent magnetic responses in topological insulators

Abstract

By developing a canonical approach that is exact, physically transparent and subtly different from standard methods, we present a systematic study with exact analytical calculations based on a Landau Level (LL) picture of the energetics of a many-electron system in an interface (or film) and in the presence of a uniform and perpendicular magnetic field, by seriously taking into account the finite thickness of the Quantum Well (QW) along the field. We find internal phase transitions (i.e. at partial LL filling) for the global magnetization and magnetic susceptibility that are not captured by other approaches, and that give rise to nontrivial corrections to the standard de Haas-van Alphen periods (but in a manner that reproduces the exact quantal deviations from the semiclassical periodicity in the limit of the full 3D space, a problem mostly discussed in astrophysical applications and which we independently solve analytically as well for comparison). Additional features upon inclusion of Zeeman splitting are also found (such as certain energy minima that originate from the interplay of QW, Zeeman and LL Physics in the full 3D problem), while a corresponding calculation in a Composite Fermion picture (with Lambda-Levels) leads to new predictions on magnetic response properties of a fully-interacting electron liquid in a finite-thickness interface; these exhibit a richer and more delicate structure than the mere monotonic reduction of gaps with thickness reported long ago, a structure possibly detectable with present day technology. Finally, by pursuing the same line of reasoning for a topologically nontrivial system (with a relativistic spectrum, spin-orbit interactions and strong coupling between thickness and planar motion) we find evidence that similar effects may be operative in the dimensionality crossover of 3D strong topological insulators to 2D topological insulator quantum wells