Theoretical Possibilities for Flat Band Superconductivity

Abstract

One novel arena for designing superconductors with high T C is the flat-band systems. A basic idea is that flat bands, arising from quantum mechanical interference, give unique opportunities for enhancing T C with (i) many pair-scattering channels between the dispersive and flat bands, and (ii) an even more interesting situation when the flat band is topological and highly entangled. Here we compare two routes, which comprise a multi-band system with a flat band coexisting with dispersive ones, and a one-band case with a portion of the band being flat. Superconductivity can be induced in both cases when the flat band or portion is "incipient" (close to, but away from, the Fermi energy). Differences are, for the multi-band case, we can exploit large entanglement associated with topological states, while for the one-band case a transition between different (d and p) wave pairings can arise. These hint at some future directions.

Superconducting mechanism for the cuprate Ba2CuO3+δ based on a multiorbital Lieb lattice model

“…We show that s-wave and d-wave pairings closely compete with each other, where we find a peculiar case of coexisting intraorbital and interorbital pairings. We further show that superconductivity is strongly enhanced if we increase the energy of the d 3z 2 −r 2 band (from its original position obtained by first-principles calculation for Ba 2 CuO 3 ) to make it "incipient" [23,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44], where the lower band edge comes close to the Fermi level within a realistic band filling regime. In an even wider scope, we reveal that the Lieb model has an intimate relation with the two-orbital model of the K 2 NiF 4 structure where a close competition between s-wave and d-wave pairings is known to occur [9].…”

“…Recently, such a band lying just above or below the Fermi level is referred to as an "incipient band" and has received attention, especially in the context of the iron-based superconductors [27][28][29][30][31][32][33][34][35]38], where hole bands lying just below the Fermi level are observed in some materials [30,31,[68][69][70][71][72][73][74][75]. In a wider context, the possibility of the occurrence or strong enhancement of superconductivity due to an incipient band has long been proposed for multiband Hubbard models on various types of lattices [23,26,36,37,[39][40][41][42][43][44][76][77][78][79][80][81][82]. A salient feature in these cases is that the gap function typically exhibits nodeless "s±-wave" symmetry.…”

Optical imprinting of superlattices in two-dimensional materials

“…By considering Coulomb interaction in our nearly flat and topologically nontrivial bands, one could potentially induce strongly correlated phases such as fractional Chern insulators [3,[61][62][63], superconductors [7,13,[17][18][19]64,65], or magnetic phases [9,[14][15][16]. Moreover, by irradiating with frequencies comparable to the bare tunneling strength instead of the highfrequency regime considered here, higher-order terms become relevant [47] and, therefore, one can induce a wider class of structures.…”

Singular flat bands

“…Due to the suppressed kinetic energy, flat band systems have been considered intriguing in various research areas [1][2][3][4][5][6]. In condensed matter physics, flat bands are considered ideal to study many-body phenomena such as the ferromagnetism [7][8][9][10][11], superconductivity [12][13][14][15][16], and Wigner crystal formation [17][18][19] because the kinetic energy of the carriers in the flat band is quenched and dominated by the electron-electron interaction.…”