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We develop a microscopic and gauge-invariant theory for collective modes resulting from the phase of the superconducting order parameter in non-centrosymmetric superconductors. Considering various crystal symmetries we derive the corresponding gauge mode $omega_{rm G}({bf q})$ and find, in particular, new Leggett modes $omega_{rm L}({bf q})$ with characteristic properties that are unique to non-centrosymmetric superconductors. We calculate their mass and dispersion that reflect the underlying spin-orbit coupling and thus the balance between triplet and singlet superconductivity occurring simultaneously. Finally, we demonstrate the role of the Anderson-Higgs mechanism: while the long-range Coulomb interaction shifts $omega_{rm G}({bf q})$ to the condensate plasma mode $omega_{rm P}({bf q})$, it leaves the mass $Lambda_0$ of the new Leggett mode unaffected and only slightly modifies its dispersion.
In materials without spatial inversion symmetry the spin degeneracy of the conduction electrons can be lifted by an antisymmetric spin-orbit coupling. We discuss the influence of this spin-orbit coupling on the spin susceptibility of such superconduc
In materials without an inversion center of symmetry the spin degeneracy of the conducting band is lifted by an antisymmetric spin orbit coupling (ASOC). Under such circumstances, spin and parity cannot be separately used to classify the Cooper pairi
We explain, in the first quantized path integral formalism, the mechanism behind the Anderson-Higgs effect for a gas of charged bosons in a background magnetic field, and then use the method to prove the absence of the effect for a gas of fermions. T
Third-harmonic generation (THG) experiments on superconductors can be used to investigate collective excitations like the amplitude mode of the order parameter known as Higgs mode. These modes are visible due to resonances in the THG signal if the dr
I review theoretical ideas and implications of experiments for the gap structure and symmetry of the Fe-based superconductors. Unlike any other class of unconventional superconductors, one has in these systems the possibility to tune the interactions