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arXiv:1401.5485 · Physical Review B

Superconductivity from weak repulsion in hexagonal lattice systems

Rahul Nandkishore, Ronny Thomale, Andrey V. Chubukov

Published Apr 7, 2014• 98 citations
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Abstract

The authors examine thoroughly the general cases in which superconductivity can arise on a hexagonal lattice with purely repulsive bare interactions, and find superconducting phases with unusual symmetries: $f$- and chiral $d+i\phantom{\rule{0}{0ex}}d$-wave.

DOI
10.1103/physrevb.89.144501

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The authors examine thoroughly the general cases in which superconductivity can arise on a hexagonal lattice with purely repulsive bare interactions, and find superconducting phases with unusual symmetries: fff- and chiral d+i\phantom{\rule{0}{0ex}}d-wave.
In superconducting phases, repulsive interactions between the electrons usually lead to higher-angular momentum Cooper pairing. Here, the authors employ the weak-coupling renormalization group approach to study unconventional superconducting phases emerging in the extended, repulsive Hubbard model on paradigmatic two-dimensional lattices. Among their findings are extended regions of chiral topological superconductivity on the square, triangular, and honeycomb lattices. They provide detailed superconducting phase diagrams as well as the coupling strengths that quantify the corresponding critical temperatures depending on the band-structure parameters, band filling, and interaction parameters. The importance of the resolution and accuracy of the numerical integration for the method is discussed and a way to higher numerical efficiency provided.
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−Jt-Jt−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 ppp-, ddd-, and fff-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 3^33He, spin-polarized 3^33He mixtures in 4^44He, ultracold quantum gases in magnetic traps, and optical lattices.
Can superconductivity arise from strong repulsive interactions between electrons in a lattice model with topological bands? Here, the authors answer this question in the affirmative via DMRG numerical simulations of an interacting spinful bilayer Hofstadter model featuring low-lying bands of opposite Chern number. Furthermore, by developing a new technique to probe the pairing symmetry in number-conserving DMRG, the authors demonstrate that superconductivity is ppp-wave, tantalizingly reminiscent of nodal pairing recently observed in twisted bilayer graphene, which shares many structural similarities with their model. This work thus showcases the possibility of an all-electronic pairing mechanism in the strong coupling limit in two dimensions, which can be tested directly with cold fermions in an optical lattice.
Motivation With few exceptions [131] it is widely accepted that the conventional Bardeen–Cooper–Schrieffer (BCS) theory [12] and its intermediate-coupling Eliashberg extension [14] do not suffice to explain high-temperature superconductivity. As shown in the preceding chapters the true origin of high-temperature superconductivity could be found in a proper combination of the bare Coulomb repulsion with the bare electron–phonon interaction in the framework of the many-body polaron theory [51] beyond the BCS–Eliashberg approximation. Nevertheless some researchers have maintained that the repulsive electron–electron interaction alone should provide pairing at high temperatures without phonons despite substantial experimental evidence that the EPI is an important player and needs to be included in the successful theory of high- T c superconductivity. Following the original proposal by P. W. Anderson, many authors [22, 74] argued that the electron–electron interaction in high-temperature superconductors was strong but repulsive providing high T c without phonons via superexchange and/or spin fluctuations in the d -wave pairing channel ( l = 2). A motivation for this concept can be found in the earlier works by Kohn and Luttinger (KL) [132, 133] who showed that the Cooper pairing of fermions with any weak repulsion was possible since the two-particle interaction induced by many-body effects is attractive for pairs with large orbital momenta, l ≫ 1.
With the discovery of strong-coupling physics and superconductivity in moir\'e superlattices, it is essential to have an understanding of strong-coupling driven superconductivity in systems with trigonal symmetry. The simplest lattice model with trigonal symmetry is the triangular lattice Hubbard model. Although the triangular lattice spin model is a heavily studied model in the context of frustration, studies of the hole-doped triangular lattice Hubbard model are rare. Here, we use density matrix renormalization group to investigate the dominant superconducting channels in the hole-doped triangular lattice Hubbard model over a range of repulsive interaction strengths. We find a clear transition from ppp-wave superconductivity at a moderate on-site repulsion strength (U/t=2U/t=2U/t=2) at filling above 1/4 ($n\ensuremath{\sim}0.65$) to ddd-wave superconductivity at a strong on-site repulsion strength (U/t=10U/t=10U/t=10) at filling below 1/4 ($n\ensuremath{\sim}0.4$). The unusual tunability that moir\'e superlattices offer in controlling U/tU/tU/t would open up the opportunity to realize this transition between ddd-wave and ppp-wave superconductivity.
For any purely fermionic system on a lattice in arbitrary space dimension we prove that there is a different but well-defined system on the same lattice, consisting of both bona fide fermions and bosons with an interaction depending on a parameter \ensuremath{\lambda}, which characterizes a same-site repulsion between particles. The energy spectrum and the scattering matrix of the former are identical to those in the finite energy sector of the latter, in the limit \ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty} (i.e., hard-core repulsion). This general theorem is applied to a resonance-boson model in a lattice fermion system, whose solution may have relevance to high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductivity.