Lifshitz scaling effects on the holographic p -wave superconductors coupled to nonlinear electrodynamics
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Regular Article - Theoretical Physics
Lifshitz scaling effects on the holographic p-wave superconductors coupled to nonlinear electrodynamics Mahya Mohammadi1,a , Ahmad Sheykhi1,2,3,b 1
Physics Department and Biruni Observatory, Shiraz University, Shiraz 71454, Iran Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P.O. Box 55134-441, Maragha, Iran 3 Institut für Physik, Universität Oldenburg, Postfach 2503, 26111 Oldenburg, Germany
2
Received: 12 December 2019 / Accepted: 18 September 2020 © The Author(s) 2020
Abstract We employ gauge/gravity duality to study the effects of Lifshitz scaling on the holographic p-wave superconductors in the presence of Born–Infeld nonlinear electrodynamics. By using the shooting method in the probe limit, we calculate the relation between critical temperature Tc and ρ z/d numerically for different values of mass, nonlinear parameter b and Lifshitz critical exponent z in various dimensions. We observe that critical temperature decreases by increasing b, z or the mass parameter m which makes conductor/superconductor phase transition harder to form. In addition, we analyze the electrical conductivity and find the behavior of the real and the imaginary parts as a function of frequency, which depend on the model parameters. However, some universal behaviors are seen. For instance at low frequencies, the real part of conductivity shows a delta function behavior, while the imaginary part has a pole, which means that these two parts are connected to each other through the Kramers–Kronig relation. The behavior of the real part of the conductivity in the large frequency regime can be achieved by Re[σ ] = ω D−4 . Furthermore, with increasing the Lifshitz scaling z, the energy gap and the minimum values of the real and imaginary parts become unclear.
1 Introduction After the discovery of superconductivity, considerable attempts have been done to understand the different aspects of this phenomenon [1]. The most successful way to describe the superconductivity within a microscopic theory was proposed by Bardeen, Cooper and Schrieffer (BCS), who could address the superconductivity as a microscopic effect that originates from the condensation of Cooper pairs into a boson-like a e-mail:
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b e-mail:
[email protected] (corresponding author)
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state [2]. However, it was not suitable to declare this effect completely. More specifically, it is only practical for s-wave superconductors, while there are other types of superconductors such as p-waves and d-waves [3,4]. Besides, the BCS theory cannot explain the mechanism of high temperature superconductors, because the Cooper pairs are decoupled and no longer exist when the temperature of the system becomes high [4]. By applying the AdS/CFT correspondence, which relates the strong coupling conformal field theory on the boundary in d-dimensions to a weak coupling gravity in (d +1)-dimensional bulk, the novel idea of holographic superconductors was proposed by Hartnoll et al. [5
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