Holographic Superconductor/Insulator Transition at Zero Temperature

TL;DR

This paper constructs a five-dimensional Einstein-Maxwell-scalar holographic model on an $AdS$ soliton background to realize a zero-temperature insulator-to-superconductor transition in a $(2+1)$-dimensional dual as the chemical potential $bmu$ is varied.It analyzes both the confining soliton and the deconfined $AdS_5$ black hole backgrounds, computes scalar condensates and conductivities, and derives the phase boundaries between geometries as well as the superconducting transitions, revealing second-order behavior in the soliton sector and a confinement/deconfinement first-order transition overall.The authors interpret the phase structure in the spirit of RVB theory, mapping the confined AdS soliton to a gapped phase with emergent gauge dynamics and the soliton superconductor to the RVB superconducting state, while the black-hole region corresponds to pseudo-gap/strange-metal behavior at higher temperatures.String-theory embeddings (e.g., $AdS_5 imes T^{1,1}$) and connections to the $t$-$J$ model with slave-boson approaches are discussed, suggesting qualitative parallels and future extensions that include backreaction, fermionic sectors, and entanglement entropy analyses.

Abstract

We analyze the five-dimensional AdS gravity coupled to a gauge field and a charged scalar field. Under a Scherk-Schwarz compactification, we show that the system undergoes a superconductor/insulator transition at zero temperature in 2+1 dimensions as we change the chemical potential. By taking into account a confinement/deconfinement transition, the phase diagram turns out to have a rich structure. We will observe that it has a similarity with the RVB (resonating valence bond) approach to high-Tc superconductors via an emergent gauge symmetry.

Figures (14)

• Figure 1: The condensations of the scalar operators $\langle {\cal O}_1 \rangle$ (left) and $\langle {\cal O}_2 \rangle$ (right).
• Figure 2: The charge density $\rho$ plotted as a function of $\mu$ when $\langle {\cal O}_1\rangle\neq 0$ (left) and $\langle {\cal O}_2\rangle\neq 0$ (right). Its derivative jumps at the phase transition point.
• Figure 3: The imaginary part of the conductivity for the AdS soliton without a scalar condensation $\langle {\cal O}_{1,2}\rangle=0$ (left) and with a scalar condensation $\langle {\cal O}_1\rangle\neq 0$. We employed the background with $\rho=0.0094$ and $\mu=0.84$ in the right graph.
• Figure 4: The real and imaginary parts of the conductivity in AdS$_5$ charged black hole. Three curves correspond to $b=0,\ 0.5$ and $b=1$, respectively in the unit $r_+=L=1$. When we fixed $\omega/T$, the real part of the conductivity decreases as $b$ becomes large, while the imaginary part increases.
• Figure 5: The scalar condense for ${\cal O}_1$ (left) and ${\cal O}_2$ (right).