A holographic model of d-wave superconductor vortices with Lifshitz scaling

Abstract

We study analytically the d-wave holographic superconductors with Lifshitz scaling in the presence of external magnetic field. The vortex lattice solutions of the model have also been obtained with different Lifshitz scaling. Our results imply that holographic d-wave superconductor is indeed a type II one even for different Lifshitz scaling. This is the same as the conventional d-wave superconductors in the Ginzburg-Landau theory. Our results also indicate that the dynamical exponent z has no effect to the shape of the vortex lattice even after higher order corrections (away from the phase transition point B c ) are included. However, it has effects on the upper critical magnetic field B c 2 through the fact that a larger z results in a smaller B c 2 and therefore influences the size (characterized by r 0 ≡ 1/ B c 2 ) of the vortex lattices. Furthermore, close comparisons between our results and those of the Ginzburg-Landau theory reveal the fact that the upper critical magnetic field B c 2 is inversely proportional to the square of the superconducting coherence length ξ, regardless of the anisotropy between space and time.

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“…Along this line, besides the current study, more interesting outcomes in curved acoustic black holes deserve further investigations, for instances, i) Further consider the electromagnetic and gravitational perturbations and test its (in)stability; ii) It is natural to extend the curved acoustic black hole into a rotating case and study the properties of curved acoustic rotating black hole; iii) Other attempt is to discuss the curved acoustic black hole in the wormhole background; iv) It was addressed in [65] that the acoustic black hole can also be realized by the holographic approach. This gives more interest to relate the curved acoustic black hole with the holographic principle [66] and holographic vortex [67,68]; v) Next but not the last interesting issue is how to mimic the charge in the experiment since in the current theoretical setup, the fluid is not charged and the 'charge' is introduced in its velocity.…”

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“…(23) and (24) and therefore has not yet been taken into account. Although it is complicated, it is possible to do that, following what we have done in a recent paper on vortex lattice formation of a d−wave superconductor [51]. We leave this calculation for future work.…”

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