Abstract
We study the entanglement entropy as a probe of the proximity effect of a superconducting system by using the gauge/gravity duality in a fully back-reacted gravity system. While the entanglement entropy in the superconducting phase is less than the entanglement entropy in the normal phase, we find that near the contact interface of the superconducting to normal phase the entanglement entropy has a different behavior due to the leakage of Cooper pairs to the normal phase. We verify this behavior by calculating the conductivity near the boundary interface.
Highlights
It was proposed [13] that this low temperature regime can be probed by the entanglement entropy [14, 15]
While the entanglement entropy in the superconducting phase is less than the entanglement entropy in the normal phase, we find that near the contact interface of the superconducting to normal phase the entanglement entropy has a different behavior due to the leakage of Cooper pairs to the normal phase
We have found that the entanglement entropy is less than the entanglement entropy of the normal phase
Summary
The Maxwell equations ∇μ F μν + √η−g ∂μ √−g(DκΨ)(DλΨ)∗ gκν F μλ − gκμF νλ + gνλF μκ − gμλF νκ = iq Ψ∗(Dν Ψ) − Ψ(Dν Ψ)∗ + iqηgμρF ρν F μκΨ∗(DκΨ) − F μλΨ(DλΨ)∗ , (2.3). − iqηgκλF κν F λμAμ ∂ν Ψ − iqAν Ψ. We will set L = 1, 8πG = 1, q = 1. We note that the presence of the coupling constant η adds new terms in the field equations which makes the system of the differential equations highly non-trivial. We have to find numerical solutions of the fully back-reacted system
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