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).

[1] Proposed Spontaneous Generation of Magnetic Fields by Curved Layers of a Chiral Superconductor,
T. Kvorning, T. H. Hansson, A. Quelle, C. Morais Smith,
Phys. Rev. Lett. 120, 217002 (2018). Editor choice

[2] Chern-Simons theory and atypical Hall conductivity in the Varma phase,
N. Menezes, C. Morais Smith, Giandomenico Palumbo,
Phys. Rev. B 97, 075135 (2018).

[3] Fermi-Bose mixture in mixed dimensions,
M. A. Caracanhas, F. Schreck, C. Morais Smith,
New J. Phys. 19, 115011 (2017).

[4] Topological Varma superfluid in optical lattices,
M. Di Liberto, A. Hemmerich, C. Morais Smith,
Phys. Rev. Lett. 117, 163001 (2016).

[5] Interaction-induced chiral p_x \pm i p_y superfluid order of bosons in an optical lattice,
M. Ölschläger, T. Kock, G. Wirth, A. Ewerbeck, C. Morais Smith, A. Hemmerich,
New Journal of Physics 15, 083041 (2013).