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Register a new userQuasiparticle Hall Transport of d-wave Superconductors in Vortex State
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We present a theory of quasiparticle Hall transport in strongly type-II superconductors within their vortex state. We establish the existence of integer quantum spin Hall effect in clean unconventional $d_{x^2-y^2}$ superconductors in the vortex state from a general analysis of the Bogoliubov-de Gennes equation. The spin Hall conductivity $sigma^s_{xy}$ is shown to be quantized in units of $frac{hbar}{8pi}$. This result does not rest on linearization of the BdG equations around Dirac nodes and therefore includes inter-nodal physics in its entirety. In addition, this result holds for a generic inversion-symmetric lattice of vortices as long as the magnetic field $B$ satisfies $H_{c1} ll B ll H_{c2}$. We then derive the Wiedemann-Franz law for the spin and thermal Hall conductivity in the vortex state. In the limit of $T to 0$, the thermal Hall conductivity satisfies $kappa_{x y}=frac{4pi^2}{3}(frac{k_B}{hbar})^2 T sigma^s_{xy}$. The transitions between different quantized values of $sigma^s_{xy}$ as well as relation to conventional superconductors are discussed.
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We calculate the density of states of a disordered inhomogeneous d-wave superconductor in a magnetic field. The field-induced vortices are assumed to be pinned at random positions and the effects of the scattering of the quasi-particles off the vortices are taken into account using the singular gauge transformation of Franz and Tesanovic. We find two regimes for the density of states: at very low energies the density of states follows a law rho(epsilon) sim rho_0 + |epsilon|^{alpha} where the exponent is close to 1. A good fit of the density of states is obtained at higher energies, excluding a narrow region around the origin, with a similar power law energy dependence but with alpha close to 2. Both at low and at higher energies rho_0 scales with the inverse of the magnetic length (sqrt{B}).
The effect of vortices on quasiparticle transport in cuprate superconductors was investigated by measuring the low temperature thermal conductivity of YBa_2Cu_3O_6.9 in magnetic fields up to 8 T. The residual linear term (as T to 0) is found to increase with field, directly reflecting the occupation of extended quasiparticle states. A study for different Zn impurity concentrations reveals a good agreement with recent calculations for a d-wave superconductor, thereby shedding light on the nature of scattering by both impurities and vortices. It also provides a quantitative measure of the gap near the nodes.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is an unconventional superconducting state found under the influence of strong Zeeman field. This phase is identified by finite center-of-mass momenta in the Cooper pairs, causing the pairing amplitude to oscillate in real space. Repulsive correlations, on the other hand, smear out spatial inhomogeneities in d-wave superconductors. We investigate the FFLO state in a strongly correlated d-wave superconductor within a consolidated framework of Hartree-Fock-Bogoliubov theory and Gutzwiller approximation. We find that the profound effects of strong correlations lie in shifting the BCS-FFLO phase boundary towards a lower Zeeman field and thereby enlarging the window of the FFLO phase. In the FFLO state, our calculation features a sharp mid-gap peak in the density of states, indicating the formation of strongly localized Andreev bound states. We also find that the signatures of the FFLO phase survive even in the presence of an additional translational symmetry breaking competing order in the ground state. This is demonstrated by considering a broken symmetry ground state with a simultaneous presence of the d-wave superconducting order and a spin-density wave order, often found in unconventional superconductors.
The concept of broken symmetry, that the symmetry of the vacuum may be lower than the Hamiltonian of a quantum theory, plays an important role in modern physics. A manifestation of this phenomena is the Higgs boson in particle physics whose long awaited discovery is imminent. An equivalent mode in superconductors is implicit in the early theories of their collective fluctuations. Spurred by some mysterious experimental results, the theory of the oscillation of the amplitude of superconductivity order parameter, which is the equivalent to the Higgs modes in s-wave superconductors and its identification in the experiments, was explicitly provided. It was also shown that a necessary condition for this to occur is the emergent Lorentz invariance in the superconducting state while the metallic state and the region just below $T_c$ is manifestly non-Lorentz invariant. Here we show that d-wave superconductors, such as the high temperature Cuprate superconductors, should have a rich assortment of Higgs bosons, each in a different irreducible representation of the point-group symmetries of the lattice. We also show that these modes have a characteristic singular spectral structure which can be discovered in Raman scattering experiments.
In the theoretical analyses of impurity effects in superconductors the assumption is usually made that all quantities, except for the Green functions, are slowly varying functions of energy. When this so-called Fermi Surface Restricted Approximation is combined with the assumption that impurities can be represented by delta-function potentials of arbitrary strength, many reasonable looking results can be obtained. The agreement with experiments is not entirely satisfactory and one reason for this might be the assumption that the impurity potential has zero range. The generalization to finite range potentials appears to be straightforward, independent of the strength of the potential. However, the selfenergy resulting from scattering off finite range impurities of infinite strength such as hard spheres, diverges in this approximation at frequencies much larger than the gap amplitude! To track down the source of this unacceptable result we consider the normal state. The elementary results for scattering off a hard sphere, including the result that even an infinitely strong delta-function potential does not lead to scattering at all in systems of two and more dimensions, are recovered only when the energy dependencies of all quantities involved are properly taken into account. To obtain resonant scattering, believed to be important for the creation of mid-gap states, the range of the potential is almost as important as its strength.
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