Dynamic correlations in coupled electron-electron and electron-hole quantum wire systems

Abstract

We investigate theoretically the ground-state behavior of the coupled electron-electron and electron-hole quantum wire systems by incorporating dynamic correlation effects within the quantum version of Singwi, Tosi, Land, and Sj\"olander theory. The numerical results are presented for the pair-correlation function, the ground-state energy, the static density susceptibility, and the static and dynamic local-field correction factors over a wide range of system parameters, viz., linear particle number density ${r}_{s}$, wire size $b$, and interwire spacing $d$. The results reveal that the inclusion of the dynamical nature of particle correlations brings in quantitative as well as qualitative changes in the ground-state behavior of both the electron-electron and electron-hole wire systems. In particular, it is found that these (dynamic) correlations can cause the (homogeneous) liquid phase, in these quantum wire systems, to become unstable against a phase transition into a(n) (inhomogeneous) coupled Wigner crystal ground state at sufficiently low particle density and/or narrow wire size in the close approach of two wires. The interwire correlations are found to reduce the critical ${r}_{s}$ for the onset of Wigner crystallization with respect to an isolated quantum wire system, and at $b∕{a}_{0}^{*}=1$ the reduction in ${r}_{s}$ is about $15%$ and $4%$ in the electron-hole and electron-electron wire systems, respectively; ${a}_{0}^{*}$ is the effective Bohr atomic radius. Our prediction of Wigner crystallization for the electron-electron wire system agrees qualitatively with the recent results of Tanatar et al., which they have obtained on the basis of an approximate density functional theory calculation.