We investigate the development of superconductivity in graphene when the Fermi level becomes close to one of the Van Hove singularities of the electron system. The origin of the pairing instability lies in the strong anisotropy of the e-e scattering at the Van Hove filling, which leads to a channel with attractive coupling when making the projection of the BCS vertex on the symmetry modes with nontrivial angular dependence along the Fermi line. We show that the scale of the superconducting instability may be pushed up to temperatures larger than 10 K, depending on the ability to tune the system to the proximity of the Van Hove singularity.
The effect of Coulomb interaction in an ensemble of Dirac fermions on the formation of superconducting pairing in monolayer and bilayer doped graphene is studied using the Kohn-Luttinger mechanism disregarding the Van der Waals potential of the substrate and impurities. The electronic structure of graphene is described using the Shubin-Vonsovsky model taking into account the intratomic, interatomic, and interlayer (in the case of bilayer graphene) Coulomb interactions between electrons. The Cooper instability is determined by solving the Bethe-Saltpeter integral equation. The renormalized scat…
We show that the recently observed superconductivity in twisted bilayer graphene (TBG) can be explained as a consequence of the Kohn-Luttinger (KL) instability which leads to an effective attraction between electrons with originally repulsive interaction. Usually, the KL instability takes place at extremely low energy scales, but in TBG, a doubling and subsequent strong coupling of the van Hove singularities (vHS) in the electronic spectrum occurs as the magic angle is approached, leading to extended saddle points in the highest valence band (VB) with almost perfect nesting between states belo…
Kohn--Luttinger Superconductivity in Flat Chern Bands
University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；University of Nevada, Reno（内华达大学里诺分校）；Min H. Kao Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校闵浩高电气与计算机工程系）
Motivated by experiments on twisted bilayer graphene, we study the emergence of superconductivity from $\textit{weak}$ repulsive interactions in the Hubbard model on a honeycomb lattice, with both spin and orbital degeneracies, and with the filling treated as a tunable control parameter. The attraction is generated through the Kohn-Luttinger mechanism. We find, similar to old studies of single layer graphene, that the leading superconducting instability is in a $d$-wave pairing channel close to Van Hove filling, and is in an $f$-wave pairing channel away from Van Hove filling. The $d$-wave pai…
We study the emergence of superconductivity in rhombohedral trilayer graphene due purely to the long-range Coulomb repulsion. This repulsive-interaction-driven phase in rhombohedral trilayer graphene is significantly different from those found in twisted bilayer and trilayer graphenes. In the latter case, the nontrivial momentum-space geometry of the Bloch wavefunctions leads to an effective attractive electron-electron interaction; this allows for less modulated order parameters and for spin-singlet pairing. In rhombohedral trilayer graphene, we instead find spin-triplet superconductivity wit…
We study how the Rashba spin-orbit interaction influences unconventional superconductivity in a two dimensional electron gas partially spin-polarized by a magnetic field. Somewhat surprisingly, we find that for all field orientations, only the larger Fermi surface is superconducting. When the magnetic field is oriented out-of-plane the system realizes a topological $p+ip$ pairing state. When the field is rotated in-plane the order parameter develops nodes along the field direction and finite center-of-mass-momentum pairing is realized. We demonstrate that the pairing symmetry of the system can…
Motivated by recent experiments on ABC-stacked rhombohedral trilayer graphene (RTG) which observed spin-valley symmetry-breaking and superconductivity, we study instabilities of the RTG metallic state to symmetry breaking orders. We find that interactions select the inter-valley coherent order (IVC) as the preferred ordering channel over a wide range, whose theoretically determined phase boundaries agree well with experiments on both the hole and electron doped sides. The Fermi surfaces near van Hove singularities admit partial nesting between valleys, which promotes both inter-valley supercon…
We investigate the many-body instabilities of electrons interacting near Van Hove singularities arising in monolayer and twisted bilayer graphene. We show that a pairing instability must be dominant over the tendency to magnetic order as the Fermi level is tuned to the Van Hove singularity in the conduction band of graphene. As a result of the extended character of the saddle points in the dispersion, we find that the pairing of the electrons takes place preferentially in a channel of f-wave symmetry, with an order parameter vanishing at the position of the saddle points along the Fermi line. …
We investigate topological Cooper pairing, including gapless Weyl and fully gapped class DIII superconductivity, in a three-dimensional doped Luttinger semimetal. The latter describes effective spin-3/2 carriers near a quadratic band touching and captures the normal-state properties of the 227 pyrochlore iridates and half-Heusler alloys. Electron-electron interactions may favor non-$s$-wave pairing in such systems, including even-parity $d$-wave pairing. We argue that the lowest energy $d$-wave pairings are always of complex (e.g., $d + i d$) type, with nodal Weyl quasiparticles. This implies …
We show that in a two-dimensional electron gas with an annular Fermi surface, long-range Coulomb interactions can lead to unconventional superconductivity by the Kohn-Luttinger mechanism. Superconductivity is strongly enhanced when the inner and outer Fermi surfaces are close to each other. The most prevalent state has chiral $p$-wave symmetry, but $d$-wave and extended $s$-wave pairing are also possible. We discuss these results in the context of rhombohedral trilayer graphene, where superconductivity was recently discovered in regimes where the normal state has an annular Fermi surface. Usin…
We study a model of strongly-correlated systems that incorporates phases such as Fermi liquids, non-Fermi liquids, and superconductivity, in addition to potential intertwined orders. The model describes Fermi surfaces of spinful electron gas or electron liquid coupled to bosons via an intermediate gauge field. Effectively, the coupling imposes constraints and interactions between the fermion spin and the local boson density. This grants the bosons the meaning as the Schwinger boson of the magnetic order and allows us to probe a larger phase space, rather than around the quantum critical point.…
An appropriate combination of the scattering theory and the transfer matrix formalism, for the solution of a (4 x 4) Kohn-Luttinger model, allow us to study the multichannel-multiband transmission process of heavy and light holes through a (GaAs/AlAs) superlattice. Appealing effects and interesting channel coupling phenomena, mediated by quasi-bond states, are clearly foreseen.
Motivated by the recent discoveries of superconductivity in bilayer and trilayer graphene, we theoretically investigate superconductivity and other interaction-driven phases in multilayer graphene stacks. To this end, we study the density of states of multilayer graphene with up to four layers at the single-particle band structure level in the presence of a transverse electric field. Among the considered structures, tetralayer graphene with rhombohedral (ABCA) stacking reaches the highest density of states. We study the phases that can arise in ABCA graphene by tuning the carrier density and t…
The density of states of graphene has Van Hove singularities that can be reached by chemical doping and have already been explored in photoemission experiments. We show that in the presence of Coulomb interactions the system at the Van Hove filling is likely to undergo a Pomeranchuk instability breaking the lattice point group symmetry. In the presence of an on--site Hubbard interaction the system is also unstable towards ferromagnetism. We explore the competition of the two instabilities and build the phase diagram. We also suggest that, for doping levels where the trigonal warping is noticea…
