Magnetic phase transitions in two-dimensional two-valley semiconductors with in-plane magnetic field

TL;DR

This paper investigates the magnetic phase transitions in two-dimensional two-valley semiconductors under in-plane magnetic fields, revealing a complex phase diagram with multiple magnetic phases and quantum critical points influenced by electron interactions and spin-orbit coupling.

Contribution

It provides a detailed analysis of the zero-temperature magnetic instabilities and phase transitions in two-valley semiconductors, highlighting the role of non-analytic free energy corrections and external tuning parameters.

Findings

Identification of four non-trivial magnetic phases.

Discovery of first and second order phase transitions driven by interactions.

Presence of two quantum critical tri-critical points.

Abstract

A two-dimensional electron gas (2DEG) in two-valley semiconductors has two discrete degrees of freedom given by the spin and valley quantum numbers. We analyze the zero-temperature magnetic instabilities of two-valley semiconductors with SOI, in-plane magnetic field, and electron-electron interaction. The interplay of an applied in-plane magnetic field and the SOI results in non-collinear spin quantization in different valleys. Together with the exchange intervalley interaction this results in a rich phase diagram containing four non-trivial magnetic phases. The negative non-analytic cubic correction to the free energy, which is always present in an interacting 2DEG, is responsible for first order phase transitions. Here, we show that non-zero ground state values of the order parameters can cut this cubic non-analyticity and drive certain magnetic phase transitions second order. We also find two tri-critical points at zero temperature which together with the line of second order phase transitions constitute the quantum critical sector of the phase diagram. The phase transitions can be tuned externally by electrostatic gates or by the in-plane magnetic field.