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Register a new userStatistics, Condensation and the Anderson-Higgs Mechanism: The Worldline Path Integral View
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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. The exchange statistics are encoded via the inclusion of additional Grassmann coordinates in a manner that leads to a manifest worldline supersymmetry. This extra symmetry is key in demonstrating the absence of the effect for charged fermions.
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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.
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When quantum flavor Hall insulator phases of itinerant fermions are disordered by strong quantum fluctuations, the condensation of skyrmion textures of order parameter fields can lead to superconductivity. In this work, we address the mechanism of skyrmion condensation by considering the scattering between (2+1)-dimensional, Weyl fermions and hedgehog type tunneling configurations of order parameters that violate the skyrmion-number conservation law. We show the quantized, flavor Hall conductivity ($sigma^f_{xy}$) controls the degeneracy of topologically protected, fermion zero-modes, localized on hedgehogs, and the overlap between zero-mode eigenfunctions or t Hooft vertex determines the nature of pairing. We demonstrate the quantum-disordered, flavor Hall insulators with $sigma^f_{xy}= 2 N$ lead to different types of charge $2 N e^-$ superconductivity. Some implications for the competition among flavor Hall insulators, the charge $2e^-$ paired states in BCS and pair-density-wave channels, and the composite, charge $4e^-$ superconductors for twisted bilayer graphene are outlined.
The phase-integral and worldline-instanton methods are two widely used methods to calculate Schwinger pair-production densities in electric fields of fixed direction that depend on just one time or space coordinate in the same fixed plane of the electromagnetic field tensor. We show that for charged spinless bosons the leading results of the phase-integral method integrated up through quadratic momenta are equivalent to those of the worldline-instanton method including prefactors. We further apply the phase-integral method to fermion production and time-dependent electric fields parallel to a constant magnetic field.
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