The Superconducting Transition due to the spontaneous Interlayer Loop Current fluctuations

TL;DR

This work investigates whether interlayer loop current (ILC) fluctuations can mediate superconductivity by simulating an unbiased bilayer $t$-$J_{ot}$-$V$ model with sign-problem-free projector quantum Monte Carlo. It shows that interlayer repulsion $V$ stabilizes spontaneous ILC near half-filling, while hole doping suppresses ILC and enhances interlayer s-wave superconductivity (IS-SC) with an optimal doping. A phase diagram reveals a superconducting transition driven by ILC fluctuations, including a narrow coexistence region near a quantum critical point where ILC fluctuations accompany IS-SC. The findings offer insights into bilayer nickelates and ultracold-atom platforms, illustrating a concrete mechanism by which orbital magnetism fluctuations can promote superconductivity, with IS-SC favored over competing intralayer pairings.

Abstract

Loop currents, as an orbital magnetism, have been proposed as a possible fluctuation mechanism for superconducting pairing, which always remains elusive. Here, we investigate the role of an interlayer loop current fluctuation in mediating superconductivity using an unbiased bilayer $t-J_{\perp}-V$ model via sign-problem-free projector quantum Monte Carlo simulations. The model spontaneously generates the interlayer loop current by breaking time-reversal and translational symmetries, favored by interlayer Coulomb repusion. With hole doping, the loop current is rapidly suppressed, while its fluctuations give rise to an interlayer $s$-wave superconductivity. Our results establish a phase diagram to demonstrate a superconducting transition due to the interlayer loop current fluctuations. It also provides possible insights into some physics related to bilayer nickelates, with which it shares a similar structure and a large interlayer spin exchange.

Figures (9)

• Figure 1: (a) A sketch of the bilayer model with intralayer hopping $t_{\parallel}$, interlayer hopping $t_{\perp}$, interlayer AFM spin-exchange interaction $J_{\perp}$ and interlayer Coulomb repulsive interaction $V$. (b) The phase diagram containing an interlayer loop current (ILC), an interlayer $s$-wave SC (IS-SC) and their coexisting phase, dependent on hole doping $x$ and interlayer repulsion $V$ at $J_{\perp}=2$. The green and blue solid lines are the phase boundaries of ILC and IS-SC respectively. An inset is attached to intuitively exhibit physical illustrations of ILC and IS-SC. Those critical points are extracted by the finite-size scaling analysis.
• Figure 2: The structure factor $O_{\mathrm{ILC}}$/$O_{\mathrm{IS-SC}}$ as a function of doping $x$ with different interlayer repulsion $V$ for (a) ILC and (b) IS-SC. $O_{\mathrm{ILC}}$ is greatly promoted by $V$ near half-filling while $O_{\mathrm{IS-SC}}$ is decreased by $V$ with an optimal doping behavior.
• Figure 3: The structure factor $O_{\mathrm{ILC}}$/$O_{\mathrm{IS-SC}}$ as a function of doping $x$ with different lattice size $L$ at (a) $V=0$ and (b) $V=0.3$ for ILC, and at (c) $V=0$ and (d) $V=0.3$ for IS-SC. The $L$-dependence of structure factor is showed in this figure, where a growth with increasing $L$ indicates a trend for ordering.
• Figure 4: The structure factor $O/L^{2}$ as a function of the reciprocal of lattice size $1/L$ for ILC, IS-SC and AFM. The data with different sizes are extrapolated to the thermodynamic limit at different doping $x=0$, $x=1/32$ and $x=1/16$ for the interlayer repulsion (a)-(c) $V=0$ and (d)-(f) $V=0.3$ respectively. The finite-size scaling is performed by the polynomial fittings to the data of $L=4, 6, 8, 12$ denoted by dashed lines. A special instruction is that a additional $L=10$ for ILC is added at (d) and the red flat dashed line of (d) is a guide for eyes.
• Figure 5: The correlation length $\xi$ as a function of doping $x$ for ILC, AFM and IS-SC with different interlayer repulsion (a) $V=0.0$, (b) $V=0.1$, (c) $V=0.3$ and (d) $V=0.5$ at $L=8$. The crossover where the dominant order changes is marked by a black dashed line. The pink records the region of coexisting phase as shown in Fig. \ref{['Fig_1']}.