Physics Letters B 785 (2018) 238–246
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Optical properties of Born–Infeld-dilaton-Lifshitz holographic
superconductors
M. Kord Zangeneh
a,b,c,∗
, S.S. Hashemi
d,e
, A. Dehyadegari
f
, A. Sheykhi
f,b
, B. Wang
e,g
a
Physics Department, Faculty of Science, Shahid Chamran University of Ahvaz, Ahvaz 61357-43135, Iran
b
Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), P. O. Box: 55134-441, Maragha, Iran
c
Center for Research on Laser and Plasma, Shahid Chamran University of Ahvaz, Ahvaz, Iran
d
Physics Department, Shahid Beheshti University, Evin, Tehran 19839, Iran
e
Center of Astronomy and Astrophysics, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
f
Physics Department and Biruni Observatory, Shiraz University, Shiraz 71454, Iran
g
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
10 April 2018
Received
in revised form 9 August 2018
Accepted
12 August 2018
Available
online 31 August 2018
Editor:
N. Lambert
In this letter, we first study the Lifshitz-dilaton holographic superconductors with nonlinear Born–
Infeld
(BI) gauge field and obtain the critical temperature of the system for different values of Lifshitz
dynamical exponent, z, and nonlinear parameter b. We find that for fixed value of b, the critical
temperature decreases with increasing z. This indicates that the increase of anisotropy between space
and time (encoded in Lifshitz exponent z) prevents the phase transition. Also, for fixed value of z,
the critical temperature decrease with increasing b. Then, we investigate the optical properties of
(2 + 1) and (3 + 1)-dimensional BI-Lifshitz holographic superconductors in the presence of dilaton
field. We explore the refractive index of the system. This is an important study, since it discloses
the effects of anisotropy between space and time as well as nonlinearity of electrodynamics model
and dimension on strange metamaterial behavior of the holographic superconductor. For z = 1and
(2 +1)-dimensional holographic superconductor, we observe negative real part for permittivity Re[] as
frequency ω decreases. Thus, in low frequency region our superconductor exhibit metamaterial property.
This behavior is independent of the nonlinear parameter and can be seen for either linear (b = 0)
and nonlinear (b = 0) electrodynamics. Interestingly, for (3 +1)-dimensional Lifshitz-dilaton holographic
superconductors, we observe metamaterial behavior neither in the presence of linear nor nonlinear
electrodynamics.
© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
The correspondence between gauge fields living on the bound-
ary
of a spacetime and the gravity in the bulk, called gauge/gravity
duality, provides a powerful tool for studying the strongly cou-
pled
systems in quantum field theory [1,2]. According to this dic-
tionary,
one can effectively calculate correlation functions in a
strongly interacting field theory by using a dual classical gravity
description. A new application of this duality, called holographic
superconductor, was recently proposed in order to shed light on
*
Corresponding author.
E-mail
addresses: mkzangeneh@scu.ac.ir (M. Kord Zangeneh),
adehyadegari@shirazu.ac.ir (A. Dehyadegari), asheykhi@shirazu.ac.ir (A. Sheykhi),
wang_b@sjtu.edu.cn (B. Wang).
the understanding the mechanism governing the high-temperature
superconductors in condensed-matter physics [3]. In [3–5], by in-
cluding
the Abelian Higgs model within the AdS black hole space-
time,
holographic superconductors have been built. Decreasing the
Hawking temperature to a critical value, the black hole exhibits
unstability against small perturbations and by condensing some
field, grows hair to make the system stable. This process can be
adjudged as the holographic description of the superconducting
phase transition. The (asymptotically) AdS black hole spacetime
is taken as the starting point for this kind of building for holo-
graphic
superconductors. The studies on the holographic supercon-
ductor
have got a lot of attentions (see for example [6–31] and
references therein). Holographic superconductors with dynamical
(electro)magnetic gauge fields have been studied in [32–35]. When
the gauge field is in the form of nonlinear BI electrodynamics, the
https://doi.org/10.1016/j.physletb.2018.08.059
0370-2693/
© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.