In this paper, we have investigated the effect of magnetic field numerically as well as analytically for holographic insulator/superconductor phase transition in higher dimensional Gauss-Bonnet gravity. First we have analysed the critical phenomena with magnetic field using two different numerical methods, namely, quasinormal modes method and the shooting method. Then we have carried out our calculation analytically using the Stürm-Liouville eigenvalue method. The methods show that marginally stable modes emerge at critical values of the chemical potential and the magnetic field satisfying the relation Λ 2 ≡ µ 2 − B. We observe that the value of the chemical potential and hence the value of Λ increases with higher values of the Gauss-Bonnet parameter and dimension of spacetime for a fixed mass of the scalar field. This clearly indicates that the phase transition from insulator to superconductor becomes difficult in the presence of the magnetic field for higher values of the Gauss-Bonnet parameter and dimension of spacetime. Our analytic results are in very good agreement with our numerical results. *

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In this paper, we analytically investigate the noncommutative effects of a charged black hole on holographic superconductors. The effects of charge of the black hole is investigated in our study. Employing the Sturm-Liouville eigenvalue method, the relation between the critical temperature and charge density is analytically investigated. The condensation operator is then computed. It is observed that condensate gets harder to form for large values of charge of the black hole. *

This paper employs two analytical techniques, namely, the matching method and the thermodynamic geometry approach to investigate the insulator/superconductor phase transition holographically in the presence of a five-dimensional AdS soliton background. This is a sequel of our earlier work [D. Parai, S. Gangopadhyay and D. Ghorai, Ann. Phys. 403, 59 (2019)] where we carried out a similar analysis using the Sturm–Liouville eigenvalue approach. We have first used the matching method to obtain the critical chemical potential, condensation operator and the charge density. Next, we investigate the free energy and thermodynamic geometry of this model. This investigation of the thermodynamic geometry leads to the critical chemical potential of the system from the condition of the divergence of the scalar curvature. We have then compared the value of the critical chemical potential [Formula: see text] obtained from these two different methods. The findings are then compared with the numerical and analytical results obtained from the Sturm–Liouville technique.

Analytical investigation of the properties of s-wave holographic superconductors in the background of a massive gravity theory in the probe limit has been carried out employing the Sturm-Liouville eigenvalue method . We obtain the analytical expression for the relation between the critical temperature and the charge density. We also obtain the expression for the condensation operator and value of the critical exponent. Our findings show that as we increase the massive gravity couplings the critical temperature increases and the condensate decreases. More precisely we observe that the presence of massive graviton increases the critical temperature compared to the superconductors in Einstein gravity at some point if we keep on increasing the coupling constants. We also obtain the frequency dependence of conductivity by solving analytically the wave equation for electromagnetic perturbations. From the real part of the conductivity, we finally estimate the energy band gap.