Higher-bands topological superconductors and superfluids

Among all superconductors, the chiral px+ipy ones are particularly interesting. We have shown recently that chiral 2D superconductors spontaneously develop a magnetic field when their surface is curved[1] (see figure). This unique signature may allow us to identify these long-sought materials, conjectured to provide the ideal qubits for building quantum computers. In the case of high-Tc cuprates, which consist of a 2D Lieb lattice with d-electrons on the corners (copper sites) and p-electrons on the sides (oxygen sites), physics beyond Dirac can be accessed due to the tripartite nature of the lattice. We have shown that within a fully relativistic description, based on the Duffin-Kemmer-Petiau algebra, an atypical quantum Hall effect emerges when a magnetic field is applied perpendicularly to the plane: the Hall conductivity is then quantized, but with non-integer (quarter) values even in the absence of interactions [2]. These results can be simulated in an artificial anisotropic Lieb lattice. One of the challenging goals in the studies of many-body physics with ultracold atoms is the creation of a topological px + ipy superfluid for identical fermions in 2D. Recently, we have considered a scenario in which a single-component degenerate gas of fermions in 2D is paired via phonon-mediated interactions provided by a 3D BEC. We found that the critical temperature Tc for the fermionic pair formation is significantly boosted by higher-order diagrammatic terms, such as phonon dressing and vertex corrections. The proposed experimental scheme to implement our findings indicates that the long-sought p-wave superfluid should be at reach with state-of-the-art setups [3]. In the case of bosonic lattices, very interesting states of matter occur when the BEC is driven into higher bands. For an alternating s- and p-band Lieb lattice, on-site interactions may drive an anomalous Hall effect for the excitations, carrying a non-zero Chern number (see figure), although the system is neither topological at the single-particle level nor for the interacting ground state [4]. For a bipartite square lattice, with intercalated s- and p-bands, interactions may drive a chiral px+ipy phase, with spontaneously generated staggered currents [5] (see figure).

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