Exchange-correlation effects in coupled quantum wire systems at finite temperature

Abstract

We investigate the exchange-correlation effects in coupled quantum wire systems at finite-temperature within the self-consistent mean-field approximation of Singwi et al by assuming the charge carriers to be electrons in one wire and electrons or heavier holes in the other. Numerical results are presented for the intra- and inter-wire static structure factors, pair-correlation functions and the static charge density susceptibility over a wide range of system parameters (viz. temperature T, particle number density and inter-wire spacing) at equal and fixed transverse width of boththe wires. We find for the first time that the coupled electron-hole (e-h) quantum wire system may favor a charge-density-wave (CDW) instability at sufficiently low T and carrier density in the close proximity of the wires, where as no such phase transition is observed in the electron-electron (e-e) quantum wire system at any non-zero T. The intra-wire contact pair-correlation functions of both the systems show a non-monotonous behavior with increasing (decreasing) T (carrier number density), and increase consistently with decrease in inter-wire spacing. On the other hand, the corresponding inter-wire contact pair-correlation functions show a non-monotonous T - dependence and consistent increase with decrease in carrier number density and/or inter-wire separation. Results of free exchange-correlation energy for both the e-h and e-e coupled systems are also reported which are found to have a noticeable dependence upon T. To highlight the effect of exchange-correlations, our results have been compared with the predictions of the random-phase approximation (RPA).

On some structural phase transitions in coupled quantum wires at finite temperature

“…In figure 2, we show the corresponding PCF's g r; reaffirming CDW instability in the coupled e-h system [22].…”

“…The carriers (electrons or holes) in each wire are assumed to have uniform number density and occupy only the lowest energy sub-band along the confinement directions, without any tunneling occurring between the wires. Ignoring the finite extension of carrier's probability density in the lateral direction, the Fourier transform of intra-and inter-wire Coulomb interaction potential in wires l and l¢ is given as [20,22,23,25,36] V q e K q b d 2 1 , 1…”

“…It is worth noting that the convergence of m-sum for the calculation of S ll (q; τ e ) in equation ( 8) is very slow, typically occurring around m ≈ 3000. To achieve faster convergence, we rewrite the intra-wire components of SSF's as [3,22,[47][48][49] S q S q q z q z q z q z q z ; ; 4 , ; ,…”

“…Later, the CDW instability was also predicted in the e-e [20] and e-h [21] system at absolute zero, though, different confinement model potentials were used in references [19] and [21]. Very recently, Akariti and co-workers [22] theoretically studied e-h and e-e quantum wire systems to explore the CDW instability at finite-T. Interestingly, the formation of a CDW phase was predicted in the e-h system whereas no such phase transition was observed in the e-e system. The STLS theory and near proximity of two wires served as the basis for CDW instability in the above investigations [19][20][21][22].…”

Induced Wigner crystallization in a coupled electron-hole quantum wire system at finite-temperature

“…[1][2][3] have predicted the charge-density-wave (CDW) instability in coupled quantum wire systems by including both the intra-and inter-wire particle correlations through the Singwi, Tosi, Land and Sjolander (STLS) approximation [9] at absolute zero. Very recently, Sharma et al [4] observed the CDW instability in a coupled e-h quantum wire system at sufficiently low temperature and particle number density using the STLS theory. On the other hand, no such instability was found in the coupled e-e quantum wire system at any non-zero T.…”