Frustrating a correlated superconductor: the 2D Attractive Hubbard Model in an external magnetic field

Grzegorz Pawłowski, S. Robaszkiewicz

We examine the phase separation effects in a class of models developed for description of superconductors with local electron pairing: (i) the extended attractive Hubbard model, (ii) the model of hard-core charged bosons on a lattice.We analyse the behaviour of various superfluid characteristics as well as the evolution of the phase diagrams with increasing external magnetic field.

S. S. Kancharla, Massimo Capone, Marcello Civelli +3 more

Min-Chul Cha, S. M. Girvin

The universal conductivity at the zero-temperature superconductor-insulator transition of the two-dimensional boson Hubbard model is studied for cases both with and without magnetic field by Monte Carlo simulations of the (2+1)-dimensional classical XY model with disorder represented by random bonds correlated along the imaginary time dimension. The effect of the magnetic field is characterized by the frustration f. From the scaling behavior of the stiffness, we determine the quantum dynamical exponent z, the correlation length exponent \ensuremath{\nu}, and the universal conductivity ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$. For the disorder-free model with f=1/2, we obtain z\ensuremath{\approxeq}1, 1/\ensuremath{\nu}\ensuremath{\approxeq}1.5, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.52\ifmmode\pm\else\textpm\fi{}0.03, where ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$ is the quantum conductance. We also study the case with f=1/3, in which we find ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.83\ifmmode\pm\else\textpm\fi{}0.06. The value of ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$ is consistent with a theoretical estimate based on the Gaussian model. For the model with random interactions, we find z=1.07\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{\nu}\ensuremath{\approxeq}1, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.27\ifmmode\pm\else\textpm\fi{}0.04 for the case f=0, and z=1.14\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{\nu}\ensuremath{\approxeq}1, and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathrm{\ensuremath{\sigma}}}_{\mathit{Q}}$=0.49\ifmmode\pm\else\textpm\fi{}0.04 for the case f=1/2.

E.S. Caixeiro, A. Troper

M. H. Pedersen, José Jesús Rodríguez-Núñez, H. Beck +2 more

Nazim Boudjada, Finn Lasse Buessen, Arun Paramekanti

The rise and fall of the superconducting transition temperature $T_c$ upon tuning carrier density or external parameters, such as pressure or magnetic field, is ubiquitously observed in a wide range of quantum materials. In order to investigate such domes of $T_c$, we go beyond the prototypical Hubbard model, and consider a lattice model of electrons coupled via instantaneous, spatially extended, attractive interactions. Using mean-field theory and functional renormalization group (FRG) methods, we find that for a characteristic interaction range $\ell$, there exists a dome in $T_c$ around $k_F \ell \sim \mathcal{O}(1)$. This result can intuitively be understood from the geometric relation between the Fermi surface and the interaction range. We show that our results generally hold for single-band as well as multi-band superconductors, in both two and three dimensions. Our model may be relevant for domes of $T_c$ in dilute weakly coupled superconductors or in engineered cold atom systems.