Particle-hole pair states of layered materials

TL;DR

This paper provides an analytical solution to the electron-hole pairing Schrödinger equation in layered materials like gapped graphene and MoS2, predicting exciton insulator states and their energies.

Contribution

It introduces an exact analytical approach to solving the electron-hole pairing problem in layered materials with strong spin-orbit coupling.

Findings

Analytical solutions for excitonic states in gapped graphene and MoS2.

Prediction of exciton insulator states with specific energy gaps.

Identification of perfect electron-hole pairing leading to potential Cooper instability.

Abstract

In the paper a theoretical study the both the quantized energies of excitonic states and their wave functions in gapped graphene and in monolayer of MoS2 is presented. An integral two-dimensional Schr\"odinger equation of the electron-hole pairing for a particles with electron-hole symmetry of reflection is analytically solved. The solutions of Schr\"odinger equation in momentum space in gapped graphene and in the direct band monolayer of MoS2 by projection the two-dimensional space of momentum on the three-dimensional sphere are found. We analytically solve an integral two-dimensional Schr\"odinger equation of the electron-hole pairing for particles with electron-hole symmetry of reflection and with strong spin-orbit coupling. In monolayer of MoS2 as well as in single-layer graphene (SLG) the electron-hole pairing leads to the exciton insulator states. Calculating an integral two-dimensional Schr\"odinger equation of the electron-hole pairing for bilayer graphene, an exciton insulator states with a gap 3 meV are predicted. The particle-hole symmetry of Dirac equation of layered materials allows perfect pairing between electron Fermi sphere and hole Fermi sphere in the valence band and conduction band and hence driving the Cooper instability.