One-dimensional backreacting holographic p-wave superconductors

Mahya Mohammadi; Ahmad Sheykhi; Mahdi Kord Zangeneh

doi:10.1140/epjc/s10052-018-6473-x

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2018) 78: 984
https://doi.org/10.1140/epjc/s10052-018-6473-x

Regular Article - Theoretical Physics

One-dimensional backreacting holographic p-wave superconductors

Mahya Mohammadi¹, Ahmad Sheykhi¹^,2^* and Mahdi Kord Zangeneh³

¹ Physics Department and Biruni Observatory, Shiraz University, Shiraz, 71454, Iran
² Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P. O. Box: 55134-441, Maragha, Iran
³ Physics Department, Faculty of Science, Shahid Chamran University of Ahvaz, Ahvaz, 61357-43135, Iran

^* e-mail: asheykhi@shirazu.ac.ir

Received: 14 November 2018
Accepted: 20 November 2018
Published online: 29 November 2018

Abstract

We analytically and numerically study the properties of one-dimensional holographic p-wave superconductors in the presence of backreaction. We employ the Sturm–Liouville eigenvalue problem for the analytical calculation and the shooting method for the numerical investigations. We apply the $\hbox {AdS}_{{3}}$ / $\hbox {CFT}_{{2}}$ correspondence and determine the relation between the critical temperature $T_{c}$ and the chemical potential $\mu$ for different values of the mass m of a charged spin-1 field $\rho _{\mu }$ and backreacting parameters. We observe that the data of both analytical and numerical studies are in good agreement. We find that increasing the backreaction and the mass parameter causes the greater values for ${T_{c}}/{\mu }$ . Thus, it makes the condensation harder to form. In addition, the analytical and numerical approaches show that the value of the critical exponent $\beta$ is 1 / 2, which is the same as in the mean field theory. Moreover, both methods confirm the existence of a second order phase transition.