Self-Consistent Pair Potential in an Inhomogeneous Superconductor

Bar-Sagi, J.; Kuper, C.G.

doi:10.1103/physrevlett.28.1556

Cited by 51 publications

(26 citation statements)

References 2 publications

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“…This is the form in which this periodic kink solution is presented in the work of Thies et al [7] on the crystalline phase of the Gross-Neveu model, while the form (3.6) was used in the condensed matter literature in [22][23][24][25][26][27]. The spectrum of the associated BdG equation (1.8) has positive and negative energy continua starting at E ¼ AEm, together with a single bound band in the middle of the gap, with band edges at E ¼ AEð 1À ffiffi ffi p 1þ ffiffi ffi p Þm.…”

Section: Mmentioning

confidence: 98%

“…Interestingly, some hints of a problem with the homogeneous condensate assumption were found already in an early lattice study [21]. This discrete-chiral GN 2 model (with vanishing bare fermion mass) turns out to be mathematically equivalent to several models in condensed matter physics [7]: the real periodic condensate may be identified with a polaron crystal in conducting polymers [11,22,23], with a periodic pair potential in quasi-1D superconductors [24][25][26], and with the real order parameter for superconductors in a ferromagnetic field [27]. The Gross-Neveu models also serve as paradigms of the phenomenon of fermion number fractionalization [28][29][30][31].…”

Section: Introductionmentioning

confidence: 98%

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Twisted kink crystal in the chiral Gross-Neveu model

2008

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We present the detailed properties of a self-consistent crystalline chiral condensate in the massless chiral Gross-Neveu model. We show that a suitable ansatz for the Gorkov resolvent reduces the functional gap equation, for the inhomogeneous condensate, to a nonlinear Schrödinger equation, which is exactly soluble. The general crystalline solution includes as special cases all previously known real and complex condensate solutions to the gap equation. Furthermore, the associated Bogoliubov-de Gennes equation is also soluble with this inhomogeneous chiral condensate, and the exact spectral properties are derived. We find an all-orders expansion of the Ginzburg-Landau effective Lagrangian and show how the gap equation is solved order by order.

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Section: Mmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

Twisted kink crystal in the chiral Gross-Neveu model

2008

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“…As a result, for all three choices of the grading operator for the nonperiodic supersymmetric systemĤ , we have consistently jÁ W j ¼ 1. 16 On the other hand, the first-order matrix operatorŝ 1 is identified here as a limit of the BdG Hamiltonian H BdG ¼ S 1 . As may be checked directly, operator R 3 commutes withŝ 1 in accordance with Table I if to take into account the correspondence between nonlocal integrals discussed above.…”

Section: Infinite Period Limitmentioning

confidence: 99%

Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit

2011

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Some time ago, Thies et al. showed that the Gross-Neveu model with a bare mass term possesses a kink-antikink crystalline phase. Corresponding self-consistent solutions, known earlier in polymer physics, are described by a self-isospectral pair of one-gap periodic Lamé potentials with a Darboux displacement depending on the bare mass. We study an unusual supersymmetry of such a second-order Lamé system, and show that the associated first-order Bogoliubov-de Gennes Hamiltonian possesses its own nonlinear supersymmetry. The Witten index is ascertained to be zero for both of the related exotic supersymmetric structures, each of which admits several alternatives for the choice of a grading operator. A restoration of the discrete chiral symmetry at zero value of the bare mass, when the kink-antikink crystalline condensate transforms into the kink crystal, is shown to be accompanied by structural changes in both of the supersymmetries. We find that the infinite period limit may or may not change the index. We also explain the origin of the Darboux-dressing phenomenon recently observed in a nonperiodic self-isospectral one-gap Pöschl-Teller system, which describes the Dashen, Hasslacher, and Neveu kink-antikink baryons.

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“…37 As a result of these research efforts it has been found that apart from the vortex problem anomalous terms in the free energy density also appear in other problems involving inhomogeneous superconducting systems, such as the healinglength problem, 38,39 the N-S proximity junction problem, 40 etc. Soon after the original work of Bar-Sagi and Kuper, 41 who managed to find analytically a self-consistent solution of the BdG equations in the Andreev approximation ͑i.e., the Andreev equations͒ by using a model pair potential ⌬(z) ϰtanh(␣z), an intense search has been started to discover other, practically more useful pair potentials which are selfconsistent solutions of the corresponding Andreev equations. [42][43][44] In fact the existence of these self-consistent pair potentials are related to the supersymmetric property of the properly transformed Andreev Hamiltonian ͑see Sec.…”

Section: Introductionmentioning

confidence: 99%

Free energy of an inhomogeneous superconductor: A wave-function approach

et al. 1998

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A method for calculating the free energy of an inhomogeneous superconductor is presented. This method is based on the quasiclassical limit ͑or Andreev approximation͒ of the Bogoliubov-de Gennes ͑or wave function͒ formulation of the theory of weakly coupled superconductors. The method is applicable to any pure bulk superconductor described by a pair potential with arbitrary spatial dependence, in the presence of supercurrents and external magnetic field. We find that both the local density of states and the free energy density of an inhomogeneous superconductor can be expressed in terms of the diagonal resolvent of the corresponding Andreev Hamiltonian, which obeys the so-called Gelfand-Dikii equation. Also, the connection between the well known Eilenberger equation for the quasiclassical Green's function and the less known Gelfand-Dikii equation for the diagonal resolvent of the Andreev Hamiltonian is established. These results are used to construct a general algorithm for calculating the ͑gauge invariant͒ gradient expansion of the free energy density of an inhomogeneous superconductor at arbitrary temperatures.

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Self-Consistent Pair Potential in an Inhomogeneous Superconductor

Cited by 51 publications

References 2 publications

Twisted kink crystal in the chiral Gross-Neveu model

Twisted kink crystal in the chiral Gross-Neveu model

Exotic supersymmetry of the kink-antikink crystal, and the infinite period limit

Free energy of an inhomogeneous superconductor: A wave-function approach

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