Excitonic insulators and Gross-Neveu models

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.

arXiv comment12 pages and 17 figures

References in corpus (28)

• Many-Body Physics with Ultracold Gases
• Bose-Einstein Condensation of Excitons in Bilayer Electron Systems
• Strongly correlated excitonic insulator in atomic double layers
• Orthorhombic-to-Monoclinic Phase Transition of Ta2NiSe5 Induced by the Bose-Einstein Condensation of Excitons
• Gate-Tuned Spontaneous Exciton Insulator in Double-Quantum Wells
• From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram
• On the possibility of an excitonic insulator at the semiconductor-semimetal transition
• Nature of symmetry breaking at the excitonic insulator transition: Ta${}_2$NiSe${}_5$
• Emergence of Skyrme crystal in Gross-Neveu and 't Hooft models at finite density
• Electron-hole pair condensation at the semimetal-semiconductor transition: a BCS-BEC crossover scenario
• Strong Coupling Nature of the Excitonic Insulator State in Ta${}_2$NiSe${}_5$
• Direct observation of excitonic instability in Ta2NiSe5
• Thermodynamics of the Massive Gross-Neveu Model
• Band hybridisation at the semimetal-semiconductor transition of Ta${}_2$NiSe${}_5$ enabled by mirror-symmetry breaking
• Emergence of Tricritical Point and Liquid-Gas Phase in the Massless 2+1 Dimensional Gross-Neveu Model
• Heterobilayers of 2D materials as a platform for excitonic superfluidity
• Fate of the excitonic insulator in the presence of phonons
• Critical charge fluctuations and emergent coherence in a strongly correlated excitonic insulator
• Strongly Interacting Fermions and Phases of the Casimir Effect
• Many-flavor Phase Diagram of the (2+1)d Gross-Neveu Model at Finite Temperature
• Asymmetrically Doped Polyacetylene
• Large N solution of generalized Gross-Neveu model with two coupling constants
• Dynamics of the chiral phase transition in the 2+1 dimensional Gross-Neveu model
• The 2d Gross-Neveu Model at Finite Temperature and Density with Finite Corrections
• Finite temperature effects in quantum systems with competing scalar orders
• Excitonic insulators as a model of $d-d$ and Mott transitions in strongly correlated materials
• Phase diagram of the excitonic insulator
• Quantum corrections for the phase diagram of systems with competing order

Cited by in corpus (2)

• Unconventional Gross-Neveu quantum criticality: Interaction-induced SO(3)-biadjoint insulator and emergent SU(3) symmetry
• Generalized Beth-Uhlenbeck Approach to the 2+1D Gross-Neveu Model