Holographic superconductors in Born-Infeld electrodynamics and external magnetic field

In this paper, we analytically investigate the effect of adding an external magnetic field in presence of Born-Infeld corrections to a holographic superconductor in the probe limit. The technique employed is based on the matching of the solutions to the field equations near the horizon and the asymptotic AdS region. We obtain expressions for the critical temperature and the condensation values explicitly to all orders in the Born-Infeld parameter. The value of the critical magnetic field is finally obtained and is found to get affected by the Born-Infeld parameter. The formulation of the BCS theory of superconductivity over five decades ago still remains the most successful microscopic theory describing the phenomenology of super-conductivity exhibited by a large number of metals and alloys [1]. However, there is a class of materials which exhibit superconductivity at high temperatures, namely the high Tc cuprates. The theoretical understanding of the pairing mechanism leading to a charged condensate remains a mystery for these materials. It is by now clear that these materials are strongly coupled and hence a new theoretical breakthrough is required to understand them. The gauge/gravity correspondence discovered first in string theory has proved to be an important tool to deal with strongly coupled systems [2]-[5]. Recently, it has provided some excellent theoretical insights to understand the physics of high Tc superconductors. The dual gravitational description of a superconductor observed in [6]-[11] involved the mechanism of spontaneous breaking of a local U(1) symmetry near the event horizon of the black hole resulting in the formation of a scalar hair condensate at a temperature T less than a certain critical value Tc. A major aspect of superconductors is their response to magnetic field. They exhibit perfect diamagnetism as the temperature is lowered below Tc in the presence of an external magnetic field and the phenomenon is known as Meissner effect [12]. Till date a numbe