Some studies on holographic superconductor

Parai, Diganta (2022) Some studies on holographic superconductor. PhD thesis, Indian Institute of Science Education and Research Kolkata India.

Text (PhD thesis of Diganta Parai (16RS028)) 16RS028.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

In this thesis we have discussed two different type of phase transitions holographically, namely metal/superconductor transition and insulator/superconductor transition. First we study metal/superconductor transition in noncommutative Reissner-Nordstrom background with Born-Infeld electrodynamics and in massive gravity background (with usual Maxwell electrodynamics). Both the analysis has been done analytically using Sturm- Liouville eigenvalue method. We find that noncommutative parameter, Born-Infeld parameter and charge of the black hole make condensate harder to form whereas massive gravity background is more favorable than Einstein gravity background if we choose coupling parameters suitably. For massive gravity background we also derive the expression for band gap energy and we observe that bang gap has increased than Einstein gravity background. Then we investigate insulator/superconductor transition by three different analytical method, namely Sturm-Liouville eigenvalue method, matching method and thermodynamic geometry approach. We deduce critical chemical potential and relation between condensation operator and chemical potential around critical chemical potential using these three independent method, and observe that they agree with each other. We also study the effect of magnetic field on insulator/superconductor transition in d-dimensional Gauss-Bonnet AdS soliton background spacetime. We describe it numerically by quasinormal mode method and shooting method. We also have done the calculation analytically using Sturm-Liouville eigenvalue method and observed results are in good agreement with numerical results. We find that in the presence of magnetic field transition from insulator to superconductor becomes more difficult.

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