The effect of mass-asymmetry on the ground-state of coupled electron-hole quantum wire system is investigated within the quantum version of the self-consistent mean-field approximation of Singwi, Tosi, Land, and Sj¨olander. The pair-correlation functions, static density susceptibility, and correlation energy are calculated over a range of wire parameters. We find that the mass-asymmetry affects appreciably both the intra- and inter-wire correlations, which in turn bring in a marked change in the e-h ground-state. Below a critical density, the e-h correlations now favor the liquid-Wigner crystal phase transition at a sufficiently large wire spacing. This result is in striking difference with the corresponding study on the mass-symmetric e-h wire model since here transition to the Wigner crystal phase occurs in the adequately close proximity of two wires at a much lower density, and there also occurs a crossover from Wigner to a charge-density-wave phase at relatively higher densities. We find that for a GaAs based e-h wire the critical density for Wigner crystallization is enhanced by a factor of about 2.6. As an important result, our theory captures nicely the recent experimental observation of Wigner crystallization in an un-equal density GaAs based e-h wire by Steinberg et al. [Phys. Rev. B 73, 113307 (2006)].
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