Excitonic insulators and Gross-Neveu models

TL;DR

This paper models excitonic insulator phases in semi-metals and semi-conductors using a generalized Gross-Neveu approach, analyzing phase diagrams, transition orders, and thermodynamic signatures in 2D and 3D systems.

Contribution

It introduces a solvable GN model framework for excitonic instabilities, providing detailed phase diagrams and thermodynamic behavior analysis for different regimes.

Findings

Identification of excitonic order parameter and phase diagrams.

Discovery of first- and second-order thermal transitions.

Analysis of specific heat behavior near quantum critical points.

Abstract

We introduce a generalized Gross-Neveu (GN) model to describe the excitonic instabilities in two different systems: a small overlap semi-metal (SM) and a small gap semi-conductor (SMC), both in two (2d) and three-dimensions (3d). We identify the excitonic order parameter (EOP) and obtain the effective potential within the Large $N$ limit approach where the GN model can be exactly solved. We obtain the excitonic insulator (EI) phase diagrams as a function of temperature, chemical potential, overlap between bands and gaps of the system. We show that the EI may undergo first- or second-order thermal transitions depending on the regime whereupon this phase is approached. We also investigate the expected thermodynamic signatures for the specific heat above the fine-tuned excitonic quantum critical point (EQCP), in both 2d and 3d, in the SMC regime. We show that the EQCP is a different kind of critical point since although the EOP vanishes at the EQCP, there is always a finite gap in the SMC regime. We find that for high temperatures, the specific heat might exhibit a scaling behavior in the form $C_V/T \propto T^{(d-z)/z}$, where $d$ is the dimension of the system and $z$ is the dynamical critical exponent. The very low temperature behavior has a dominant exponential thermally activated term due to the presence of a gap that does not vanish at the excitonic transition.