Exciton insulator states for particle-hole pair in ZnO / (Zn, Mg) O quantum wells and for Dirac cone

International Journal of Material Science and Engineering

© 2015 by SSRG - IJMSE Journal

Volume 1 Issue 2

Year of Publication : 2015

Authors : Lyubov E. Lokot

10.14445/23948884/IJMSE-V1I2P101

How to Cite?

Lyubov E. Lokot, "Exciton insulator states for particle-hole pair in ZnO / (Zn, Mg) O quantum wells and for Dirac cone," SSRG International Journal of Material Science and Engineering, vol. 1,  no. 2, pp. 1-22, 2015. Crossref, https://doi.org/10.14445/23948884/IJMSE-V1I2P101

Abstract:

In this paper a theoretical studies of the space separation of electron and hole wave functions in the quantum well ZnO/Mg0.27Zn0.73O are presented. For this aim the self-consistent solution of the Schrödinger equations for electrons and holes and the Poisson equations at the presence of spatially varying quantum well potential due to the piezoelectric effect and local exchange-correlation potential is found. The one-dimensional Poisson equation contains the Hartree potential which includes the one-dimensional charge density for electrons and holes along the polarization field distribution. The three-dimensional Poisson equation contains besides the onedimensional charge density for electrons and holes the exchange-correlation potential which is built on convolutions of a plane-wave part of wave functions in addition. In ZnO/(Zn,Mg)O quantum well the electron-hole pairing leads to the exciton insulator states. An exciton insulator states with a gap 3.4 eV are predicted. If the electron and hole are separated, their energy is higher on 0.2 meV than if they are paired. The particle-hole pairing leads to the Cooper instability. In the paper a theoretical study the both the quantized energies of excitonic states and their wave functions in graphene is presented. An integral two-dimensional Schrödinger equation of the electronhole pairing for a particles with electron-hole symmetry of reflection is exactly solved. The solutions of Schrödinger equation in momentum space in graphene by projection the two-dimensional space of momentum on the three-dimensional sphere are found exactly. We analytically solve an integral twodimensional Schrödinger equation of the electron-hole pairing for particles with electron-hole symmetry of reflection. In single-layer graphene (SLG) the electron-hole pairing leads to the exciton insulator states. Quantized spectral series and light absorption rates of the excitonic states which distribute in valence cone are found exactly. If the electron and hole are separated, their energy is higher than if they are paired. The particle-hole symmetry of Dirac equation of layered materials allows perfect pairing between electron Fermi sphere and hole Fermi sphere in the valence cone and conduction cone and hence driving the Cooper instability.

Keywords:

quantum well, graphene, Cooper instability, Dirac cone, exciton.

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