We study the complexity of holographic superconductors (Einstein-Maxwell-complex scalar actions in $d+1$ dimension) by the `complexity = volume' (CV) conjecture. First, it seems that there is a universal property: the superconducting phase always has a smaller complexity than the unstable normal phase below the critical temperature, which is similar to a free energy. We investigate the temperature dependence of the complexity. In the low temperature limit, the complexity (of formation) scales as $T^α$, where $α$ is a function of the complex scalar mass $m^2$, the $U(1)$ charge $q$, and dimension $d$. In particular, for $m^2=0$, we find $α=d-1$, independent of $q$, which can be explained by the near horizon geometry of the low temperature holographic superconductor. Next, we develop a general numerical method to compute the time-dependent complexity by the CV conjecture. By this method, we compute the time-dependent complexity of holographic superconductors. In both normal and superconducting phase, the complexity increases as time goes on and the growth rate saturates to a temperature dependent constant. The higher the temperature is, the bigger the growth rate is. However, the growth rates do not violate the Lloyd's bound in all cases and saturate the Lloyd's bound in the high temperature limit at a late time.
We do more discussions of holographic s-wave superconductors in the background of AdS3 spacetime. We analytically compute the holographic superconductor model with the motion equation has two different characteristic root on the framework of Maxwell electrodynamics field. We study superconductor models on the framework of Born-Infeld electrodynamics field and on the framework of the Stückelberg form in the background of AdS3 spacetime.
The holographic superconductors, as one of the most important application of gauge/gravity duality, promote the study of strongly coupled superconductors via classical general relativity living in one higher dimension. One of the interesting properties in holographic superconductor is the appearance of first and second order phase transitions. Recently, another active studies in holographic framework is the holographic entanglement entropy and complexity evaluated from gravity side. In this note, we study the properties of the holographic entanglement entropy and complexity crossing both first…
We construct a type-II holographic superconductor from an anisotropic rotating background metric. We study the effects of the magnetic field on the vortex structure, including continuous deformations both from triangular to square lattices or vice versa. Our holographic model reproduces known experimental vortex lattice deformations and the increment of the vortex population by increasing the external magnetic field.
In this article we have analytically deduced the frequency dependent expression of conductivity and the band gap energy in $AdS_{4}$ Schwarzschild background for p-wave holographic superconductors considering Einstein-Yang-Mills theory. We also used the self consistent approach to obtain the expressions of conductivity for different frequency ranges at low temperature. We then compared the imaginary part of conductivity at low frequency region. The band gap energy obtained from these two methods seem to agree very well.
We study the dynamics of the holographic $s$-wave superconductors described by the Einstein-Maxwell-complex scalar field theory with a negative cosmological constant. If the eigenfunction of the linearized equation of motion of the scalar field in the planar RNAdS black hole background is chosen as the initial data, the bulk system will evolve to the intermediate state that corresponds to the excited state superconductor on the boundary. The process can be regarded as the non-equilibrium condensation process of the excited state of holographic superconductor. When the linear superposition of t…
Using a noncommutative inspired anti-de Sitter-Einstein-Born-Infeld black hole with both non-commutative mass and charge distributions, we analyse a holographic superconductor in the context of the AdS/CFT correspondence. We show that the coupling of the Born-Infeld parameter and the noncommutative perturbations provides an enhancing mechanism for higher values of the expectation value of the condensate and that noncommutativity counter-balances nonlinearity of the electrodynamics to keep the ratio $ω_g/T_c \approx 8$.
In a recent paper, Kiritsis and Li presented a holographic model to study the competition between different orders at finite doping in holographic superconductors. In the present work, we introduce fermions into such model and study the fermionic spectral functions in the normal phase at zero and finite temperatures. Combining analytic and numerical methods, we found that there is a crossover from a strange metal with short lived excitations at small doping, into a Fermi liquid with well defined quasiparticles at large doping. The critical doping at which excitations becomes long lived increas…
By employing the gauge/gravity duality, we disclose the effects of the non-minimal coupling between the scalar and Maxwell fields on the holographic superconductors in the probe limit. As the background spacetime, we consider a five dimensional Gauss-Bonnet (GB) black hole with a flat horizon. We find out that the critical temperature decreases for larger values of GB coupling constant or smaller values of non-minimal coupling constant, which means that the condensation is harder to form. In addition, we study the electrical conductivity in the holographic setup. We show that at low frequency …
