Eur. Phys. J. B (2021) 94: 84
https://doi.org/10.1140/epjb/s10051-021-00086-y

Regular Article - Solid State and Materials

Pair-correlation functions and density-modulated states in electron–hole bilayer: thermal and mass-asymmetry effects

Department of Physics, Kurukshetra University, 136 119, Kurukshetra, Haryana, India

^b rkmoudgil13@gmail.com

Received: 2 December 2020
Accepted: 19 March 2021
Published online: 13 April 2021

Abstract

We have studied the effect of temperature and electron–hole mass-asymmetry on pair-correlation functions (PCFs) of a coupled electron–hole bilayer, treating correlations dynamically using the dynamical self-consistent mean-field approach of Singwi, Tosi, Land, and Sjölander. Taking a fixed electron–hole effective mass ratio $m_h^{\ast }/m_e^{\ast }=5$, both intra- and interlayer static PCFs are calculated for their dependence on carrier density $r_{\mathit{se}}$, temperature ${\tau }_e$, and interlayer spacing d. Besides, the static wavevector-dependent density susceptibility is obtained to probe the role of these effects on the hitherto existence of density-modulated phases in the bilayer. We find that thermal effects in overall make correlations weaker, but the mass-asymmetry results in stronger correlations both within and across the layers, with the effect being most pronounced in the holes layer. In the strong coupling regime (i.e., large $r_{\mathit{se}}/{\tau }_{e}d$), the intra- and interlayer PCFs show pronounced in-phase periodic oscillations, typical of a spatially localized phase in the bilayer. Correspondingly, the in-phase component of static density susceptibility is seen to exhibit in the close approach of two layers an apparently diverging peak at a wavevector coincident with the location of sharp peak in the static structure factor, implying the emergence of a density-modulated phase in the bilayer. Parallel to the zero-temperature study, the charge-density-wave (CDW) phase is found to dominate at higher densities, with a cross-over to the Wigner crystal (WC) phase below a critical density. As an interesting result, we find that while thermal effects tend to oppose the formation of density-modulated phase, the electron–hole mass-asymmetry boosted correlations favour it, with the two effects almost cancelling out at ${\tau }_e=0.125$, thus resulting in the CDW-WC cross-over at nearly the same critical density as for a zero-temperature mass-symmetric electron–hole bilayer. Our prediction of coupled WC phase is found to be in qualitative agreement with path-integral Monte Carlo simulations.