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A standard perturbative expansion around the mean-field solution is used to derive the low-energy effective action for superconductors at T=0. Taking into account the density fluctuations at the outset we get the effective action where the…
We discuss the derivation of a low-energy effective field theory of phase (Goldstone) and amplitude (Higgs) modes of the pairing field from a microscopic theory of attractive fermions. The coupled equations for Goldstone and Higgs fields…
We study high quality-factor (high Q) resonances supported by periodic arrays of Mie resonators from the perspectives of both Bloch wave theory and multiple scattering theory. We reveal that, unlike a common belief, the bound states in the…
In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of the superfluid weight $D_s$, does not draw from the curvature of the band but has a purely band-geometric origin. In a…
Based on the relativistic Hartree-Bogoliubov theory, the influence of the pairing interaction strength on the di-neutron correlations and the crossover from superfluidity of neutron Cooper pairs in the $^{1}S_{0}$ channel to Bose-Einstein…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
The superfluid stiffness fundamentally constrains the transition temperature of superconductors, especially in the strongly coupled regime. However, accurately determining this inherently quantum many-body property in microscopic models…
We analyze the phase diagram of superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) limit as a function of scattering parameter, population imbalance and mass…
We derive simplified Faddeev type equations for the three particle T-matrix which are valid in the Hubbard model where only electrons with opposite spins interact. Using the approximation of dynamical mean field theory these equations are…
Electrons, holes, and photons in semiconductors are interacting fermions and bosons. In this system, a variety of ordered coherent phases can be formed through the spontaneous phase symmetry breaking because of their interactions. The…
Motivated by recent experiments on Al nanoparticles, we have studied the effects of fixed electron number and small size in nanoscale superconductors, by applying the canonical BCS theory for the attractive Hubbard model in two and three…
We study dynamics of a superconducting condensate in the presence of a domain wall defect in the order parameter. We find that broken translation and reflection symmetries result in new collective excitations, bound to the domain wall…
Strongly correlated quantum matter -- such as interacting electron systems or interacting quantum fluids -- possesses properties that cannot be understood in terms of linear fluctuations and free quasi-particles. Quantum fluctuations in…
We derive the shape of the high-energy features due to a weakly coupled boson in cuprate superconductors, as seen experimentally in Bi_2 Sr_2 Ca_1 Cu_2 O_8+x (BSCCO) by Lee et al. [Nature (London) 442, 546 (2006)]. A simplified model is…
The Bogoliubov-de Gennes (BdG) equations are solved in the strong-coupling limit, where real-space (preformed) pairs bose-condense with finite center-of-mass momenta. There are two energy scales in this regime, a temperature independent…
Through the Higgs mechanism, the long-range Coulomb interaction eliminates the low-energy Goldstone phase mode in superconductors and transfers spectral weight all the way up to the plasma frequency. Here we show that the Higgs mechanism…
We investigate the extended hard-core Bose-Hubbard model on the triangular lattice as a function of spatial anisotropy with respect to both tunneling and nearest-neighbor interaction strength. At half-filling the system can be tuned from…
The Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein condensation (BEC) crossover in the two-dimensional attractive Hubbard model under the magnetic field is discussed at the half-filling at T=0 K on the basis of the formalism of Eagles and…
We explore the universal properties of interacting fermionic lattice systems, mostly focusing on the development of pairing correlations from attractive interactions. Using renormalization group we identify a large number of fixed points…
Different realizations of the Hubbard operators in different Hilbert spaces give rise to various microscopic lattice electron models driven by strong correlations. In terms of the Gutzwiller projected operators, the most familiar examples…