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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
We have investigated whether the electron-phonon interaction can support a d-wave gap-anisotropy. On the basis of models derived from LDA calculations, as well as LDA linear-response calculations we argue that this is the case, for materials with buc
We discuss a new mechanism of microwave absorption in s- and d-wave superconductors, which arises in the presence of a dc supercurrent in the system. It produces a contribution to the ac conductivity that is proportional to the inelastic quasiparticl
We study suppression of superconductivity by disorder in d-wave superconductors, and predict the existence of (at least) two sequential low temperature transitions as a function of increasing disorder: a d -wave to -wave, and then an s-wave to metal
We study the effect of dissipation on quantum phase fluctuations in d-wave superconductors. Dissipation, arising from a nonzero low frequency optical conductivity which has been measured in experiments below $T_c$, has two effects: (1) a reduction of