Kohn–Luttinger superconductivity

Since Kohn–Luttinger mechanism does not require any additional interactions beyond Coulomb interactions, it can lead to superconductivity in any electronic system. However, the estimated critical temperature, ${\displaystyle T_{\mathrm{c}}}$, for Kohn–Luttinger superconductor is exponential in ${\displaystyle -{\ell }^4}$ and thus is extremely small. For example, for metals the critical temperature is given by

$${\displaystyle \frac{k_{\mathrm{B}}{T}_{\mathrm{c}}}{E_{\mathrm{F}}}=\exp (-(2\ell {)}^4),}$$

where ${\displaystyle k_{\mathrm{B}}}$ is Boltzmann constant and ${\displaystyle E_{\mathrm{F}}}$ is Fermi energy. However, Kohn and Luttinger conjectured that nonspherical Fermi surfaces and variation of parameters may enhance the effect. Indeed, it is proposed that Kohn–Luttinger mechanism is responsible for superconductivity in rhombohedral graphene, which has an annular Fermi surface.