Anomalous superconductivity and superfluidity in repulsive fermion systems

Abstract

We discuss the mechanisms of unconventional superconductivity and superfluidity in 3D and 2D fermionic systems with purely repulsive interaction at low densities. We construct phase diagrams of these systems and find the areas of the superconducting state in free space, as well as on the lattice in the framework of the Fermi-gas model with hard-core repulsion, the Hubbard model, the Shubin-Vonsovsky model, and the t − J model. We demonstrate that the critical superconducting temperature can be greatly increased in the spin-polarized case or in a two-band situation already at low densities. The proposed theory is based on the Kohn-Luttinger mechanism or its generalizations and explains or predicts anomalous p-, d-, and f -wave pairing in various materials, such as high-temperature superconductors, the idealized monolayer and bilayer of doped graphene, heavy-fermion systems, layered organic superconductors, superfluid 3 He, spin-polarized 3 He mixtures in 4 He, ultracold quantum gases in magnetic traps, and optical lattices.

Fermi-Bose Mixtures and BCS-BEC Crossover in High-Tc Superconductors

“…In conclusion let us stress that recently discovered superconductivity in bilayer twisted graphene possibly also corresponds to the regime of BCS-BEC crossover between local and extended pairs in the d-wave channel (similarly to underdoped cuprates) but with anomalous chiral superconductivity of d+id type [177] which is in agreement with the phase diagram for idealized bilayer graphene in AB modification at low doping levels [20,22,23]. The discovery of superconductivity in graphene with many properties resembling the cuprates helps us to build the bridge between low temperature topological superconductors based on graphene [177] and bismuth [178][179][180] and vanadium oxides [181][182][183][184] which are very promising for superconducting nanoelectronics and quantum calculations (for creation of topologically protected qubits).…”

“…Phase diagram of superconducting state in the AB structure of the bilayer graphene [20] shown as a function of the variables 1 n V -, where 1 1.25 n < < is the carriers density, 1 2 , t t and 1 2 , g g are intralayer and interlayer hoppings, U is onsite Hubbard repulsion, 1 2 , V V and 1 3 4 , , G G G are intralayer and interlayer Soon after the discovery of Müller, Anderson and Schrieffer advanced different unconventional mechanisms for high temperature superconductivity (see e. g. [3,4,5]). Many fruitful ideas were introduced in the first years of HTSC by the leading theorists in USA, Europe, Japan and worldwide (see e. g. [6,7,8,9,10,11,12,13,14,15,16]).…”

“…Many fruitful ideas were introduced in the first years of HTSC by the leading theorists in USA, Europe, Japan and worldwide (see e. g. [6,7,8,9,10,11,12,13,14,15,16]). One of the authors of the present review was very active in unconventional mechanisms focusing on the low density electron systems [17,18,19,20,21,22,23,24] based on the generalization of Kohn-Luttinger ideas [25,26] in purely repulsive Fermi systems. In the framework of the Fermi gas model with hard-core repulsion [27], repulsive-U Hubbard model [28] and the Shubin-Vonsovsky model [29,30] on different type of 3D and 2D lattices during last 30 years of intensive research we predicted p-, d-, f-and anomalous s-wave pairing in various materials such as the idealized and bilayer graphene (see Fig.…”

“…The phase-diagram of this model presented in Fig. 2 shows regions of superconducting phases with different pairing symmetry: p-wave, s-wave and [20,21,24] on the 2D square lattice.…”

Rashba versus Kohn-Luttinger: Evolution ofp-wave superconductivity in magnetized two-dimensional Fermi gases subject to spin-orbit interactions

“…The idea that a superconducting state can arise from direct repulsive interactions between electrons was first introduced in a celebrated paper by Kohn and Luttinger 1 (see 2,3 for recent reviews on this topic). Even though the bare interaction U between electrons is repulsive, an effective attraction arises at O(U 2 ) which forms a p-wave superconducting state in three dimensions.…”