Abstract
In a partially filled flat Bloch band electrons do not have a well defined Fermi surface and hence the lowenergy theory is not a Fermi liquid. Neverethless, under the influence of an attractive interaction, a superconductor well described by the BardeenCooperSchrieffer (BCS) wave function can arise. Here we study the lowenergy effective Hamiltonian of a generic Hubbard model with a flat band. We obtain an effective Hamiltonian for the flat band physics by eliminating higher lying bands via perturbative SchriefferWolff transformation. At first order in the interaction energy we recover the usual procedure of projecting the interaction term onto the flat band Wannier functions. We show that the BCS wave function is the exact ground state of the projected interaction Hamiltonian and that the compressibility is diverging as a consequence of an emergent SU(2) symmetry. This symmetry is broken by second order interband transitions resulting in a finite compressibility, which we illustrate for a onedimensional ladder with two perfectly flat bands. These results motivate a further approximation leading to an effective ferromagnetic Heisenberg model. The gaugeinvariant result for the superfluid weight of a flat band can be obtained from the ferromagnetic Heisenberg model only if the maximally localized Wannier functions in the MarzariVanderbilt sense are used. Finally, we prove an important inequality D≥W^{2} between the Drude weight D and the winding number W, which guarantees ballistic transport for topologically nontrivial flat bands in one dimension.
Original language  English 

Article number  245149 
Pages (fromto)  117 
Journal  Physical Review B (Condensed Matter and Materials Physics) 
Volume  94 
Issue number  24 
DOIs  
Publication status  Published  30 Dec 2016 
MoE publication type  A1 Journal articlerefereed 
Keywords
 Flat band
 SUPERCONDUCTIVITY
 Hubbard model
 Superfluidity
 Quantum gases
 Topological matter
 critical temperature
 Wannier functions
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Marie SkłodowskaCurie Action (Individual Fellowship)
Peotta, Sebastiano (Recipient), 1 Apr 2016
Prize: Invitation or ranking in competition