Quantization of entropy in a quasi-two-dimensional electron gas

Abstract

We demonstrate that the partial entropy of a two-dimensional electron gas (2DEG) exhibits quantized peaks at resonances between the chemical potential and electron levels of size quantization. In the limit of no scattering, the peaks depend only on the subband quantization number and are independent on material parameters, shape of the confining potential, electron effective mass and temperature. The quantization of partial entropy is a signature of a topological phase transition in a 2DEG. In the presence of stationary disorder, the magnitude of peaks decreases. Its deviation from the quantized values is a direct measure of the disorder induced smearing of the electronic density of states. Introduction. -Low-dimensional electronic devices are important building blocks for quantum electronics. This is one of the reasons of great interest to these systems. Another reason is that size quantization of the electronic states in low-dimensional systems leads to quantization of their thermal and transport properties. The most famous are the integer [1] and fractional [2] quantum Hall effect in two-dimensional electron gas (2DEG) and conductance quantization of quasi-one-dimensional channels [3].In this Letter, we address the major thermodynamic quantity -entropy -of a quasi-two-dimensional electron gas. An elegant way to measure directly the entropy per electron, s ≡ (∂S/∂n) T , was recently demonstrated [4]. Here T is temperature. We will show that the quantization of the energy spectrum of quasi-2DEG into subbands leads to a very specific quantization of the entropy: s exhibits sharp maxima as the chemical potential µ passes through the bottoms of size quantization subbands (E i ). The value of the entropy in the N -th maximum depends only on the number of the maximum, N :

Ferromagnetism in the vicinity of Lifshitz topological transitions

“…This transition is a particular case of the Lifshitz topological transition [13]. It has been recently demonstrated that such transformations are accompanied by the spikes in the entropy per particle as well as by the spikes in the temperature derivative of the chemical potential of the electron or hole gas [14]. Below we show that the magnetic susceptibility of the system experiences similar spikes in the vicinity of the Lifshitz transition points.…”

“…Before presenting the numerical results, let us focus on the simplified analytical model which takes into account only one type of holes but provides a clear physical picture of the effect of topological Lifshitz transitions on the hole spin susceptibility and the ferromagnetic order of Mn spins. Let us represent the density of heavy-hole states as g(E) = (m * /π 2 ) ν Θ(E − E hhν ), where m * is the heavy-hole effective mass, E hhν are the energies of the size-quantized subbands, and Θ(E) is the Heaviside step function [14,15]. Furthermore, let us assume that relevant temperatures are low enough so that the thermal broadening in Eq.…”

Entropy Signatures of Topological Phase Transitions

“…Near the Lifshitz transition points, µ = ±∆, we observe that the dependences s(µ) are monotonic functions, so that these points are not marked by spikes. This is typical for any system where DOS has just one discontinuity [17]. Nevertheless, the entropy per particle quantization rule for graphene s(µ = ±∆) = ±2 ln 2 ЖЭТФ is fulfilled.…”

Entropy per particle spikes in the transition metal dichalcogenides

“…It was theoretically predicted [4] that in a quasi-twodimensional electron gas (2DEG) with parabolic dispersion, the entropy per electron exhibits quantized peaks when the chemical potential crosses the size quantized levels. The amplitude of such peaks in the absence of scattering depends only on the subband quantization number and is independent of material parameters, shape of the confining potential, electron effective mass, and temperature.…”