Kohn–Luttinger superconductivity explained

Kohn–Luttinger superconductivity is a theoretical mechanism for unconventional superconductivity proposed by Walter Kohn and Joaquin Mazdak Luttinger^[1] based onFriedel 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( 2 k _{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} , for Kohn–Luttinger superconductor is exponential in - \ell ^{4} and thus is extremely small. For example, for metals the critical temperature is given by

$$\backslash frac\; =\; \backslash exp(-(2\; \backslash ell)^4),$$

where

k _{\rm} is Boltzmann constant and E _{\rm} 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,^{[2] [3]} which has an annular Fermi surface.

Further reading

Gor'kov . L. P. . Melik-Barkhudarov . T. K. . Contribution to the theory of superfluidity in an imperfect Fermi gas . 13 . 5 . 1018–1022 . Soviet Physics JETP . November 1961 .

Chubukov . Andrey V. . Kohn-Luttinger effect and the instability of a two-dimensional repulsive Fermi liquid at T=0 . 48 . 2 . 1097–1104 . American Physical Society . Physical Review B . 15 July 1993 . 10.1103/PhysRevB.48.1097. 10007968 . 1993PhRvB..48.1097C .

Book: Maiti . S. . Chubukov . A. V. . November 2014 . Bennemann . Karl-Heinz . Ketterson . John B. . Novel Superfluids: Volume 2 . Oxford . Superconductivity from repulsive interaction . 89–158 . 10.1093/acprof:oso/9780198719267.003.0004. 978-0198719267 .

Notes and References

1. Kohn . Walter . Luttinger, Joaquin M. . New mechanism for superconductivity . 15 . 12 . 524–526 . American Physical Society . Physical Review Letters . 1 July 1955 . 10.1103/PhysRevLett.15.524.
2. Ghazaryan . Areg . Holder . Tobias . Serbyn . Maksym . Berg . Erez . Unconventional Superconductivity in Systems with Annular Fermi Surfaces: Application to Rhombohedral Trilayer Graphene . 127 . 24 . 247001 . 9 December 2021 . American Physical Society . Physical Review Letters . 10.1103/PhysRevLett.127.247001. 34951779 . 2109.00011 . 2021PhRvL.127x7001G . 237372021 .
3. Cea . Tommaso . Pantaleón . Pierre A. . Phong . Võ Tiến . Guinea . Francisco . Superconductivity from repulsive interactions in rhombohedral trilayer graphene: A Kohn-Luttinger-like mechanism . 105 . 7 . 075432 . 1 February 2022 . American Physical Society . Physical Review B . 10.1103/PhysRevB.105.075432. 2109.04345 . 2022PhRvB.105g5432C . 237452263 .