Abstrakti
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.
Alkuperäiskieli  Englanti 

Artikkeli  245149 
Sivut  117 
Julkaisu  Physical Review B (Condensed Matter and Materials Physics) 
Vuosikerta  94 
Numero  24 
DOI  pysyväislinkit  
Tila  Julkaistu  30 jouluk. 2016 
OKMjulkaisutyyppi  A1 Julkaistu artikkeli, soviteltu 
Sormenjälki
Sukella tutkimusaiheisiin 'Effective theory and emergent SU(2) symmetry in the flat bands of attractive Hubbard models'. Ne muodostavat yhdessä ainutlaatuisen sormenjäljen.Palkinnot

Marie SkłodowskaCurie Action (Individual Fellowship)
Peotta, Sebastiano (Recipient), 1 huhtik. 2016
Palkinto: Sijoittuminen kilpailussa tai osallistuminen kutsukilpailuun