Superconductivity from repulsive interactions in the two-dimensional electron gas

We present a well-controlled perturbative renormalization-group treatment of superconductivity from short-ranged repulsive interactions in a variety of model two-dimensional electronic systems. Our analysis applies in the limit where the repulsive interactions between the electrons are small compared to their kinetic energy.

Figure 1

Phase diagram of a 2DEG having two subbands. (a) Phase diagram for fixed $\eta \equiv k_{F1}/k_{F2}=0.5$ as a function of the dimensionless couplings $\rho V$ and $\rho J$. $U$ does not enter the problem except in that it is responsible for the suppression of $s$-wave pairing. (b) Phase diagram for fixed $\rho V=0.1$ as a function of $\eta$ and $\rho J$. (c) The dimensionless strength of the pairing interaction in the $p$-wave (solid line) and $d$-wave (dashed line) channels for fixed $J=0$. (d) Same as (c), but for $J=0.2\text{V}$.

Figure 2

Diagrams which contribute to $V(\mathit{k},\mathit{q})$, shown to quadratic order in the interactions. Each of the incoming quasiparticles has momentum $\pm \mathit{k}$ and band index $a$. The outgoing electrons have momentum $\pm q$, and are in band $b$ (with the exception of the first diagram, the momenta and band indices of each diagram are not shown). Both intraband and interband scattering processes contribute to the effective interaction.

Figure 3

The scaling function $\Phi (\eta )$ which determines the effective interband interaction ${\mathrm{g̃}}_{1,2}^{s,2}$.