Decoherence of Josephson coupling and thermal quenching of the Josephson diode effect in bilayer superconductors

Abstract

Motivated by recent studies on superconducting (SC) diode nonreciprocity, we uncover an unexpected hierarchy of SC-phase decoherence in bilayer superconductors hosting both interlayer Josephson coupling and a Josephson diode effect. Contrary to the conventional single-energy-scale paradigm where Josephson coherence and diode nonreciprocity vanish simultaneously at the SC gap-closing temperature, we demonstrate, using a self-consistent microscopic theory incorporating phase fluctuations, that the system undergoes a sequence of distinct thermal crossovers upon heating: the diode effect disappears first at $T_η$, Josephson coherence is subsequently lost at $T_c$, and the SC gap collapses only at a higher temperature $T_s$. Rather than a direct SC-normal transition, the system thus evolves through successive nonreciprocal, reciprocal, and incoherent Josephson regimes before entering the normal state. Counterintuitively, the separation between these regimes is governed not only by interlayer coupling, but also sensitively by in-plane disorder and carrier density. These findings point to a generic hierarchy of SC decoherence in low-dimensional Josephson systems, and suggest broader relevance to layered superconductors, including cuprates and recently discovered nickelates, as well as to SC qubits.

Figures (3)

• Figure 1: ( a) Schematic illustration of a bilayer superconductor with interlayer Josephson coupling. ( b) The CPR given by Eq. (\ref{['CPR']}). Inset: Temperature dependence of the critical-current strength (normalized) in the forward and backward directions from Eq. (\ref{['CPR']}) based on the mean-field BCS theory to calculate the SC gap. For simplicity and without loss of generality, we set $\alpha=0.2\pi$ and $|J_1|=4|J_2||\Delta_1||\Delta_2|$.
• Figure 2: Temperature dependence of the Josephson critical current, the diode efficiency and the SC gap self-consistently calculated by ( a) mean-field and ( b) phase-fluctuation theories. We set $\tau|\Delta_{\rm MF}(0)|=0.2$, $v_F=10^5~$m/s and $|\Delta_{\rm MF}(0)|=2~$meV, where $|\Delta_{\rm MF}(0)|$ is the zero-temperature gap from mean-field theory.
• Figure 3: ( a) Schematic illustration of phase diagram upon heating. ( b) Temperature dependence of the critical-current strength in the forward and backward directions. The distinct temperatures $T_{\eta}$, $T_c$, and $T_s$ under reducing phase stiffness by ( c) increasing disorder at $v_F=v_0$ and ( d) reducing the Fermi velocity at $\tau|\Delta_{\rm MF}(0)|=0.1$. Here, $v_0=10^5~$m/s and $|\Delta_{\rm MF}(0)|=2~$meV, where $|\Delta_{\rm MF}(0)|$ is the zero-temperature gap calculated from mean-field theory.