Superconductivity in semiconductor structures: The excitonic mechanism

Abstract

We study theoretically the effect of the fermion and boson densities on the superconductivity transition critical temperature (Tc) of a two dimensional electron gas (2DEG), where superconductivity is mediated by a Bose-Einstein condensate of exciton-polaritons. The critical temperature is found to increase with the boson density, but surprisingly it decreases with the 2DEG density increase. This makes doped semiconductor structures with shallow Fermi energies better adapted for observation of the exciton-induced superconductivity than metallic layers. For the realistic GaAsbased microcavities containing-doped and neutral quantum wells we estimate Tc as close to 50K. Superconductivity is suppressed by magnetic fields of the order of 4T due to the Fermi surface renormalisation.PACS numbers: 71.36.+c, 74.78.Fk, 71.35.Gg High temperature superconductivity (HTSC) has been desperately searched for during decades since the appearance of the seminal work of Bardeen-Cooper-Schrieffer (BCS) [1] in the early 50s. Among many different paths physicist have tried to achieve it, the excitonic mechanism of superconductivity (SC) deserves a particular attention [2][3][4]. According to Ginsburg [5,6], excitons are expected to be suitable for realization of HTSC because the characteristic energy above which the electron attraction mediated by excitons vanishes is several orders of magnitude larger than the Debye energy limiting the attraction mediated by phonons.Despite optimistic expectations, to the best of our knowledge, the exciton mechanism of SC has never worked until now, most likely due the reduced retardation effect [4,7]. Phonons in the BCS model are very slow compared to electrons on the Fermi surface. Hence there is a strong retardation effect in phonon-mediated electronelectron attraction, so that the size of a Cooper pair is very large (of the order of 100nm), and the Coulomb repulsion can be neglected at such distances. In contrast, an exciton is a very fast quasi-particle once it is accelerated to the wave-vectors comparable with the Fermi wave-vector in a metal. Therefore the replacement of phonons by excitons leads to the loss of retardation and the smaller sizes of Cooper pairs, that is why the Coulomb repulsion starts playing an important role. In realistic multilayer structures the Coulomb repulsion appears to be stronger than the exciton-mediated attraction so that Cooper pairs cannot be formed. In literature [8, 9] one find reports on layered metal-insulator structures where SC at 50K in layered metal-insulator structures, nevertheless there is still no evidence that the excitonic mechanism is responsible for this effect.Recently, the novel mechanism to achieve superconductivity mediated by exciton-polaritons has been proposed in references [10,11]. Exciton-polaritons are quasiparticles that arise due to the strong coupling of excitons with light. Particularly interesting exciton-polariton related phenomena have been observed in semiconductor quantum wells (QW) embedded in microcavity [12,13]. Bose-Einste...

Superconductivity and other collective phenomena in a hybrid Bose-Fermi mixture formed by a polariton condensate and an electron system in two dimensions

“…As mentioned above, as we reach the strong coupling regime the 2DES can become superconducting. Contrary to previous assertions [3][4][5] we find that polariton mediated superconductivity is not possible in the presence of electronic screening without taking into account the softening of the polaritons. As the polaritons soften and the polariton BEC approaches the supersolid transition, the electron-polariton interaction greatly increases and the system enters the strong coupling regime.…”

“…This prior work however, did not take into account the effect of the exciton BEC on the 2DES. Concurrently, the effect of a polariton condensate on a 2DES has been investigated without considering the back-action of electrons on the polaritons and it has been * ocotlet@phys.ethz.ch predicted that the 2DES can undergo a superconducting phase transition [3][4][5]. Our work unifies and extends the above mentioned prior work and shows that the predicted phase transitions are closely intertwined.…”

“…In Section III A we investigate quantitatively the superconducting transition in the 2DES. This transition has been previously investigated [3][4][5] without taking into account either the screening effects due to the 2DES or the polariton softening, which we find to be crucial for reaching the strong coupling regime. Moreover, we show in Appendix B that the Fröhlich [17] type potential is not suitable for a reliable calculation of the critical temperature.…”

“…We notice that the strong interactions can lead to instabilities both in the condensate and in the 2DES. We investigate quantitatively the instability of the 2DES towards superconductivity [3][4][5] while also taking into account the effect of the 2DES on the BEC. We also comment briefly on the instability of the 2DES towards the formation of an unconventional CDW ordered state as a con-sequence of the renormalized electron-polariton interaction becoming strongly peaked at wavevector q r .…”

Interplay of Phonon and Exciton-Mediated Superconductivity in Hybrid Semiconductor-Superconductor Structures

“…Dashed curve represents the result derived by formula 18. Solid curve shows the result derived from numerical simulation of gap equation with two types of interaction potentials taken into account: electron-phonon, electron-polariton and Coulomb interaction in line with[9,11].…”