Current Induced Switching of Superconducting Order and Enhancement of Superconducting Diode Efficiency

Abstract

We propose that the superconducting diode (SD) efficiency can be significantly enhanced near the transition between two superconducting states by choosing parameters where, before the system goes normal with increasing supercurrent, it switches into a different superconducting order for one direction of the current but not for the other. This mechanism for producing high SD efficiency relies on the expectation that the critical current depends sensitively on the superconducting order. We demonstrate this explicitly by performing detailed calculations for a bilayer superconductor with an in-plane magnetic field, which admits the standard Bardeen-Cooper-Schrieffer (BCS) and the orbital Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) orders as a function of the strength of the magnetic field. We predict a sharp peak in the SD efficiency in the FFLO state close to the transition, which arises from a complex interplay between the two superconducting orders. An implication of our study is that the measurement of the SD efficiency can provide fundamental insight into the nature of the BCS-FFLO transition both as a function of the magnetic field and the supercurrent.

Figures (3)

• Figure 1: Upper panels: Ground state energy $E_{\rm con}$ versus momentum $q$. The results are shown for a bilayer with asymmetry parameter $a=0.1$ at three magnetic field ($q_B$) values. Lower panels: Supercurrent $I_x= 2e\partial E_{\rm con}/\partial q$ versus $q$. When a given $I_x$ is produced by more than one value of $q$, we choose $q$ corresponding to the lowest energy, highlighted in blue. Critical currents $I_c^+$ and $I_c^-$ (marked in red) correspond to the maximum supercurrent. Black dashed lines mark phase boundaries between FFLO and BCS orders. (a) $q_{_{B}} = 0.6$: The system remains in the BCS state for all current values. (b) $q_{_{B}} = 1.85$: At zero current, the system is in the FFLO state. Increasing current in either direction induces a transition into the BCS state (crossing the black dashed lines) before ultimately driving the system normal. (c) $q_{_{B}} = 4.2$: The system remains in the FFLO state for all current values.
• Figure 2: (a) Phase diagram of the symmetric bilayer ($\alpha_1 = \alpha_2 = -10$) as a function of the current $I_x$ (in units of $I_c^+(0)$, the critical current at zero magnetic field) and $q_B\propto B$ ($q_B$ is $2\pi$ times the number of magnetic flux quanta per unit length). The BCS and FFLO states separated by second-order transitions, and by first-order transitions from the normal (N) state at high currents. (b) Schematic illustration of the BCS state with uniform interlayer phase ($\phi = 0, \rho=0$, bottom) and FFLO state with spatially varying interlayer phase ($\phi \neq 0$, $\rho\neq 0$, top). Green/blue arrows indicate local current patterns at $I_x = 0$. The in-plane magnetic field is $\bm{B} = B\hat{e}_y$. (c) Phase diagram of an asymmetric bilayer ($\alpha_1 = -9$, $\alpha_2 = -11$), which does not have inversion symmetry. The phase boundaries are asymmetric about $I_x = 0$, yielding unequal critical currents $I_c^+$ and $I_c^-$ and thus a nonzero superconducting diode efficiency. For both phase diagrams: $\beta = 20$, $J = 2$, $m = 1$ (these parameters are defined in main text and related to microscopic quantities in in Sec. (S1) of the SM)
• Figure 3: (a) Superconducting diode efficiency $\eta$ as a function of magnetic field $q_{_{B}}$ for various values of asymmetry parameter $a=|(\alpha_1-\alpha_2)/(\alpha_1+\alpha_2)|$. The upper (lower) inset shows magnified phase diagram from Fig. \ref{['fig:pd']}(c) at $a=0.1$ ($a=0.2$). In both insets, the region between the horizontal dashed lines (blue for $a=0.1$, green for $a=0.2$) marks the $q_{_{B}}$ range where current in the $+x$ direction induces a FFLO$\rightarrow$N transition while current in the $-x$ direction induces a FFLO$\rightarrow$BCS$\rightarrow$N transition. These lines correspond to the color-matched vertical dashed lines in the main panel, marking the region of enhanced $\eta$. (b) Interlayer vortex density $\rho$ as a function of magnetic field $q_{_{B}}$ at $I_x=0$. The light blue line shows the high-field limiting case $\rho = 2q_{_{B}}$, corresponding to maximum vortex density where the layers effectively decouple. The vertical red dashed line marks the value of $q_{_{B}}$ at which vortices start entering the system at zero current. The inset depicts the vortex density $\rho$ plotted as a function of $-1/\ln[(q_B-q_{B,c})/8q_{B,c}]$, in accordance with the asymptotic behavior derived in Eq. (S84) in Sec. (S6) of the SM for $a=0.1$, to make it evident that the vortices enter the system continuously.