Abstract The superconductors can have a Fermi surface even below the transition temperature, which is known as the Bogoliubov Fermi surface. Focusing on the degrees of freedom at low energies, which are described by the spinless Bogoliubov particles for the case without time-reversal symmetry, we consider the self-energy from the impurity scattering on the Bogoliubov Fermi surfaces. The physical quantities such as the density of states are evaluated based on the single-particle Green’s functions. We systematically compare these results with those of the conventional s-wave spin-singlet pairing state, to illuminate the characteristic features of the Bogoliubov particles located at the Fermi level.
Abstract The superconductors can have a Fermi surface even below the transition temperature, which is known as the Bogoliubov Fermi surface. Focusing on the degrees of freedom at low energies, which are described by the spinless Bogoliubov particles for the case without time-reversal symmetry, we consider the self-energy from the impurity scattering on the Bogoliubov Fermi surfaces. The physical quantities such as the density of states are evaluated based on the single-particle Green’s functions. We systematically compare these results with those of the conventional s-wave spin-singlet pairing state, to illuminate the characteristic features of the Bogoliubov particles located at the Fermi level.
We present a systematic investigation of the effects of ``nonmagnetic'' impurities on the s-wave BCS-BEC crossover in atomic Fermi gases within a pairing fluctuation theory. Both pairing and impurity scattering T matrices are treated self-consistently at the same time. While the system is less sensitive to impurity scattering in the Born limit, for strong impurity scatterers, both the frequency and the gap function are highly renormalized, leading to significant suppression of the superfluid Tc, the order parameter, and the superfluid density. We also find the formation of impurity bands and smearing of coherence peak in the fermion density of states, leading to a spectrum weight transfer and finite lifetime of Bogoliubov quasiparticles. In the BCS regime, the superfluidity may be readily destroyed by the impurity of high density, leading to a superfluid-insulator quantum phase transition at zero temperature. In comparison, the superfluidity in unitary and BEC regimes is relatively more robust.
It has recently been realized that the gap nodes of multiband superconductors that break time-reversal symmetry generically take the form of Fermi surfaces of Bogoliubov quasiparticles. However, these Fermi surfaces lead to a nonzero density of states (DOS) at the Fermi energy, which typically disfavors such superconducting states. It has thus not been clear whether they can be stable for reasonable pairing interactions or are in practice preempted by time-reversal-symmetric states with vanishing DOS. In this Letter, we show within BCS theory applied to a paradigmatic model that the time-reversal-symmetry-breaking states are indeed stabilized over broad parameter ranges at weak coupling. Moreover, we introduce a fast method that involves solving the inverse BCS gap equation, does not require iteration, does not suffer from convergence problems, and can handle metastable solutions.
Abstract By considering transition-metal (Shiba-Rusinov model) and rare-earth metal impurities (Abrikosov-Gorkov theory) effect on a many-body system, i.e., a BCS s-wave superconductor, quantum bipartite entanglement of two electrons of the Cooper pairs in terms of the exchange interaction, J, the potential scattering, V(playing an important role, unexpectedly), and the distance of two electron spins of the Cooper pair is calculated at zero temperature by using two-electron spin-space density matrix (Werner state). In transition-metal case, we find new quantum phase transitions (QPTs). The changes of J, which causes to have localized excited state, V and the pairing interaction (via energy gap) lead to the displacement of the QPTs (interactions act in the same direction, however sometimes the pairing interaction causes the competition with other interactions), regardless of their effects on the value of concurrence. Determining the allowable values of all interactions by itself is not possible, due to the smallness of the perturbed Green’s functions (appearing in the density matrix). For non-magnetic and magnetic (rare-earth) impurity cases, concurrence versus the distance and collision times is discussed for all finite and infinite Debye frequency. The quantum correlation, instability of the system and what's more important QPT can be tuned by the impurity.
We discuss the dynamics of magnetic moments in d-wave superconductors. In particular, we focus on moments induced by doping nonmagnetic impurities into cuprates. The interaction of such moments with the Bogoliubov quasiparticles of the superconductors can be described by variants of the pseudogap Kondo model, characterized by a power-law density of states at the Fermi level. The numerical renormalization-group technique is employed to investigate this Kondo problem for realistic band structures and particle-hole asymmetries, both at zero and finite temperatures. In particular, we study the boundary quantum phase transition between the local-moment and asymmetric strong-coupling phases, and argue that this transition has been observed in recent nuclear magnetic resonance experiments. We determine the spectral properties of both phases and the location of the critical point as a function of Kondo coupling and doping, and discuss quantum-critical crossovers near this phase transition. In addition, changes in the local density of states around the impurity are calculated as functions of temperature, being relevant to scanning tunneling microscopy experiments.
We study a short coherence length d-wave superconductor with finite density of unitary scatterers using the Bogoliubov-deGennes technique. We find that the low-energy density of states is reduced, the superfluid stiffness is significantly larger and off-diagonal long range order is more robust than the self-consistent T-matrix prediction. These results are a consequence of the inhomogeneous pairing amplitude in the ground state and of the low-lying excitations formed by hybridized impurity resonances. These features, with their nontrivial spatial structure, cannot be adequately described within the conventional T-matrix approach.
Superconductivity results from an instability of the Fermi surface---contour of poles of the single-particle propagator---to an infinitesimally small attraction between electrons. Here, we instead discuss the analogous problem on a model Luttinger surface, or contour of zeros of the Green function. At zero temperature $(\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\infty})$ and a critical interaction strength $({u}_{c\ensuremath{\infty}})$ characterized by the residue of self-energy pole, we find that the pair susceptibility diverges leading to a superconducting instability. We evaluate the pair fluctuation partition function and find that the spectral density in the normal state has an interaction-driven, power-law $\frac{1}{\sqrt{\ensuremath{\omega}}}$ type, van-Hove singularity (vHS), indicating non-Fermi liquid (NFL) physics. Crucially, in the strong coupling limit $(\ensuremath{\beta}u\ensuremath{\gg}1)$, the leading-order fluctuation free-energy terms in the normal state of this NFL-SC transition resembles the equivalent [O(1)] terms of the Sachdev-Ye-Kitaev (SYK) model. This free-energy contribution takes a simple form $\ensuremath{-}\ensuremath{\beta}F=\ensuremath{\beta}{u}_{c\ensuremath{\infty}}\ensuremath{-}\ensuremath{\gamma}\phantom{\rule{0.16em}{0ex}}\text{ln}\left(\ensuremath{\beta}{u}_{c\ensuremath{\infty}}\right),$ where $\ensuremath{\gamma}$ is a constant equal to 21. Weak impurity scattering $(\ensuremath{\tau}\ensuremath{\gg}{\ensuremath{\beta}}^{\ensuremath{-}1})$ leaves the low-energy spectral density unaffected but leads to an interaction-driven enhancement of superconductivity. Our results shed light on the role played by order-parameter fluctuations in providing the key missing link between Mott physics and strongly coupled toy models exhibiting gravity duals.