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Register a new userPreformed pairs in flat Bloch bands
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In a flat Bloch band the kinetic energy is quenched and single particles cannot propagate since they are localized due to destructive interference. Whether this remains true in the presence of interactions is a challenging question because a flat dispersion usually leads to highly correlated ground states. Here we compute numerically the ground state energy of lattice models with completely flat band structure in a ring geometry. We find that the energy as a function of the magnetic flux threading the ring has a half-flux quantum $Phi_0/2 = hc/(2e)$ period, indicating that only bound pairs of particles with charge $2e$ are propagating, while single quasiparticles with charge $e$ remain localized. We show analytically in one dimension that in fact the whole many-body spectrum has the same periodicity. Our analytical arguments are valid for both bosons and fermions, for generic interactions respecting some symmetries of the lattice and at arbitrary temperatures. Moreover we construct an extensive number of exact conserved quantities for the one dimensional lattice models. These conserved quantities are associated to the occupation of localized single quasiparticle states. Our results imply that in lattice models with flat bands preformed pairs dominate transport even above the critical temperature of the transition to a superfluid state.
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In a partially filled flat Bloch band electrons do not have a well defined Fermi surface and hence the low-energy theory is not a Fermi liquid. Neverethless, under the influence of an attractive interaction, a superconductor well described by the Bardeen-Cooper-Schrieffer (BCS) wave function can arise. Here we study the low-energy 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 Schrieffer-Wolff 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 one-dimensional ladder with two perfectly flat bands. These results motivate a further approximation leading to an effective ferromagnetic Heisenberg model. The gauge-invariant 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 Marzari-Vanderbilt sense are used. Finally, we prove an important inequality $D geq mathcal{W}^2$ between the Drude weight $D$ and the winding number $mathcal{W}$, which guarantees ballistic transport for topologically nontrivial flat bands in one dimension.
We study conditions for the emergence of the preformed Cooper pairs in materials hosting flat bands. As a particular example, we consider time-reversal symmetric pseudospin-1 semimetal, with a pair of three-band crossing points at which a flat band intersects with a Dirac cone, and focus on the s-wave inter-node pairing channel. The nearly dispersionless nature of the flat band promotes local Cooper pair formation so that the system can be considered as an array of superconducting grains. Due to dispersive bands, Andreev scattering between the grains gives rise to the global phase-coherent superconductivity at low temperatures. We develop a theory to calculate transition temperature between the preformed Cooper pair state and the phase-coherent state for different interaction strengths in the Cooper channel.
We introduce a non-Abelian kagome lattice model that has both time-reversal and inversion symmetries and study the flat band physics and topological phases of this model. Due to the coexistence of both time-reversal and inversion symmetries, the energy bands consist of three doubly degenerate bands whose energy and conditions for the presence of flat bands could be obtained analytically, allowing us to tune the flat band with respect to the other two dispersive bands from the top to the middle and then to the bottom of the three bands. We further study the gapped phases of the model and show that they belong to the same phase as the band gaps only close at discrete points of the parameter space, making any two gapped phases adiabatically connected to each other without closing the band gap. Using the Pfaffian approach based on the time-reversal symmetry and parity characterization from the inversion symmetry, we calculate the bulk topological invariants and demonstrate that the unique gapped phases belong to the $Z_2$ quantum spin Hall phase, which is further confirmed by the edge state calculations.
We investigate the unitary evolution following a quantum quench in quantum spin models possessing a (nearly) flat band in the linear excitation spectrum. Inspired by the perspective offered by ensembles of individually trapped Rydberg atoms, we focus on the paradigmatic trasverse-field Ising model on two dimensional lattices featuring a flat band as a result of destructive interference effects (Lieb and Kagome lattice); or a nearly flat band due to a strong energy mismatch among sublattices (triangular lattice). Making use of linear spin-wave theory, we show that quantum quenches, equipped with single-spin imaging, can directly reveal the spatially localized nature of the dispersionless excitations, and their slow propagation or lack of propagation altogether. Moreover we show that Fourier analysis applied to the post-quench time evolution of wavevector-dependent quantities allows for the spectroscopic reconstruction of the flat bands. Our results pave the way for future experiments with Rydberg quantum simulators, which can extend our linear spin-wave study to the fully nonlinear regime, characterized by the appearance of dense, strongly interacting gases of dispersionless excitations.
Variational wavefunctions that introduce zeros (vortices) to screen repulsive interactions are typically difficult to verify in unbiased microscopic calculations. An approach is constructed to insert vortices into ansatz wavefunctions using a matrix product representation. This approach opens the door to validation of a broad class of Jastrow-based wavefunctions. The formalism is applied to a model motivated by experiments on ultracold atomic gases in the presence of synthetic spin-orbit coupling. Validated wavefunctions show that vortices in atomic Fermi gases with flat Rashba spin-orbit bands cluster near the system center and should therefore be directly visible in time-of-flight imaging.
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