Kohn–Luttinger superconductivity

Kohn–Luttinger superconductivity is a theoretical mechanism for unconventional superconductivity proposed by Walter Kohn and Joaquin Mazdak Luttinger based on Friedel oscillations. In contrast to BCS theory, in which Cooper pairs are formed due to electron–phonon interaction, Kohn–Luttinger mechanism is based on fact that screened Coulomb interaction oscillates as $$\cos(2k_F r + \phi)/r^3$$ and can create Cooper instability for non-zero angular momentum $$\ell$$.

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, $$T_{\rm c}$$, for Kohn–Luttinger superconductor is exponential in $$-\ell^4$$ and thus is extremely small. For example, for metals the critical temperature is given by

$$\frac{k_{\rm B} T_{\rm c}}{E_{\rm F}} = \exp(-(2 \ell )^4),$$

where $$k_{\rm B}$$ is Boltzmann constant and $$E_{\rm F}$$ 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.