Superconducting transitions in flat-band systems

Abstract

The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes that the ground state of the repulsive Hubbard model on a bipartite lattice with unequal number of sites in each sublattice must have nonzero spin S at half-filling. Recently, there has been interest in Lieb geometries due to the possibility of novel topological insulator, nematic, and Bose-Einstein condensed (BEC) phases. In this paper, we extend the understanding of the attractive Hubbard model on the Lieb lattice by using Determinant Quantum Monte Carlo to study real space charge and pair correlation functions not addressed by the Lieb theorems. Specifically, our results show unusual charge and charge transfer signatures within the flat band, and a reduction in pairing order at ρ = 2/3 and ρ = 4/3, the points at which the flat band is first occupied and then completely filled. We compare our results to the case of flat bands in the Kagome lattice and demonstrate that the behavior observed in the two cases is rather different.

Epitaxial thin films of Dirac semimetal antiperovskite Cu3PdN

“…2(a), we show a 2θ scan around the SrTiO 3 (002) peak, where it is seen that post-annealing in NH 3 results in a shift of the Cu 3 PdN (002) peak toward the 2θ value previously reported for bulk Cu 3 Pd 0.989 N single crystals. 19 This result is in agreement with X-ray reciprocal space mapping (RSM) measurements taken around the (113) reciprocal lattice point [ Fig. 2(d)], which shows that post-annealing in NH 3 drives the Cu 3 PdN (113) peak towards a nearly relaxed, bulk-like, state.…”

“…In the NLS phase, "drumhead" surface states are predicted, which have been proposed as a platform for achieving high-temperature superconductivity. [16][17][18][19] Additionally, if the C 4 crystal symmetry of Cu 3 PdN is broken, the Dirac nodes in the 3D-DSM phase are gapped and Cu 3 PdN becomes a strong topological insulator. 14,15 Despite its intriguing predicted physical properties, the experimental realization of bulk Cu 3 PdN and its consequent electronic and transport characterization has been hindered due to the difficulty of synthesizing this material.…”

Magnetism in the three-dimensional layered Lieb lattice: Enhanced transition temperature via flat-band and Van Hove singularities

“…In particular, successful creations of twodimensional (2D) optical lattices with singular DOSs, the Kagome [6] and Lieb (line-centered-square) [7] lattices, have activated theoretical studies on phenomena related to the FBS [8][9][10][11][12][13][14][15][16][17][18][19]. In general, in these 2D lattices, the Mermin-Wagner theorem states that no phase transitions occur at finite temperatures [20].…”

Geometric Origin of Superfluidity in the Lieb-Lattice Flat Band

“…Recent studies on models defined on the Lieb lattice focus on the ferromagnetic and topological properties [25][26][27][28][29][30][31], while superconductivity has been studied in Refs. [28,32]. On the experimental side, a highly tunable Lieb lattice has been realized with ultracold gases [33].…”

“…The Hartree term of Eq. (2) is needed for preserving the SUð2Þ symmetry that allows us to calculate D s for arbitrary flat band fillings [32]. This symmetry corresponds, under the particle-hole transformation, to the spin rotational symmetry of the repulsive Hubbard model.…”