Exciton-Polariton Mediated Superconductivity

We revisit the exciton mechanism of superconductivity in the framework of microcavity physics, replacing virtual excitons as a binding agent of Cooper pairs by excitations of an exciton-polariton Bose-Einstein condensate. We consider a model microcavity where a quantum well with a two-dimensional electron gas is sandwiched between two undoped quantum wells, where a polariton condensate is formed. We show that the critical temperature for superconductivity dramatically increases with the condensate population, opening a new route towards high-temperature superconductivity.

Figure 1

The polariton dispersion, on the scale of interest for mediating Cooper pairing at $k_F=5\times {10}^6{\mathrm{cm}}^{-1}$. The photon (electron/hole) effective mass has been taken as ${10}^{-5}{m}_0$ ($0.22/1.25m_0$), $m_0$ being the electron mass in vacuum, the vacuum Rabi splitting as $\Omega =45\mathrm{meV}$, $X^2=1/2$, and $UA\approx 0.6\mu \mathrm{eV}\times \mu {\mathrm{m}}^2$. Other parameters are $L=50\AA$, $a_B=25\AA$, $R_y=32\mathrm{meV}$, $ϵ\approx 7{ϵ}_0$. The peculiar polariton dispersion allows for the coexistence of a BEC at low $k$ that mediates the interaction and of slow excitonlike states at large $k$ providing the retarded electron-electron attraction. In the inset, the scheme of the model microcavity structure with an $n$-doped QW sandwiched between two undoped QWs where the polariton condensate is formed.

Figure 2

The effective electron-electron interaction potential $U_0$ [cf. Equation (7)] for different values of the condensate density $N_0$ (in ${\mathrm{cm}}^{-2}$). Direct Coulomb repulsion is included (horizontal red dashed line) which fights the fragile retardation effect of excitons. Attraction is restored when the density of the condensate is high enough to overcome Coulomb repulsion, leading to Cooper pairing in the 2DEG.

Figure 3

Critical temperature of superconductivity as a function of the exciton-polariton condensate density $N_0$. Inset: Closing of the gap at the energy of the Fermi sea for $N_0=6\times {10}^{11}{\mathrm{cm}}^{-2}$.