Semiconducting Cylindrical Quantum – wire for Wigner Crystal of Electron Gas System with Density Functional Theory

Abstract

We have studied the Density Functional Theory (DFT) for Wigner crystal of electron gas in semiconducting cylindrical quantum wire (q-wire). The Wigner crystals are of single & double q-wire electron gas system. The electrons move freely in quasi one dimension as in semiconductor q-wire structure of infinite length in the direction of z-axis of cylinder. For lower density the solid-liquid phase transition is investigated in quasi one dimension and found Wigner transition at zero value temperature in crystalline phase and at critical densities if kinetic energy is lesser than Coulomb potential energy. The DFT of quantum-freezing for quantum-liquid describes the transition properties and the quantum-freezing transition is observed in one dimensional electron gas system that gives the hetero-structures of semiconductor q-wire. We have to calculate the ground state energy and energy difference per particle with electron density function, exchange and correlation energy and approximation of Thomas-Fermi & Weizsӓcker and Coulomb potential. The distribution of inhomogeneous electron density in straight line gives Wigner transition in the two-dimension but in this work we have focused on one dimensional structure for quantum freezing density. The calculation of critical density parameter and q-wire width phase transition at zero temperature and Wigner crystal that observed in double layer electron gas system under the highest magnetic field and Wigner transition in quasi one dimension. By DFT as increasing the Wigner transition, decreasing the separation between double electron wire system and if more q-wire is available, the crystal density slightly decreases. This calculation for quasi one dimensional electron gas model with Wigner crystal by DFT is true for other types of models and found the energy of ground state. Our results were found with good agreement comparable to others.