Wigner crystallization in quasi-one-dimensional quantum wire

Abstract

Abstract We study the ground-state properties of quasi-one-dimensional paramagnetic electron fluid using variational quantum Monte Carlo method. The electrons are transversally confined using the harmonically regularized Coulomb potential with long range order. In this work we have investigated the crossover from liquid to crystalline phase in the finite width paramagnetic quantum wire. The calculated pair correlation function shows the oscillations of period $$2r_\text {s} a_0$$ 2 r s a 0 , where $$a_0$$ a 0 is the Bohr’s radius and $$r_\text {s}$$ r s is Wigner Seitz radius or electron-density parameter which corresponds to a $$k=4k_\text {F}$$ k = 4 k F peak with $$k_\text {F}$$ k F being Fermi wave vector in the static structure factor at finite electron density. It is a signature of the onset of Wigner crystallization. It is found that the cross-over from liquid to a quasi-Wigner phase is due to enhancement of the electron correlation effects as $$r_\text {s}$$ r s increases or as the wire width b decreases.

Keywords

• Quantum wire
• Correlations
• One-dimension
• Wigner Crystal