Vortex-parity-controlled diode effect in Corbino topological Josephson junctions

Abstract

Nonreciprocal supercurrents in Josephson junctions have recently emerged as a sensitive tool for investigating broken symmetries in superconducting quantum materials. Here, we report an even-odd Josephson diode effect (JDE) in Corbino-geometry junctions fabricated on the pristine surface of a bulk-insulating three-dimensional topological insulator (3DTI). We find that the diode polarity, which indicates the preferred direction of supercurrent flow, robustly alternates its sign depending on the parity (even or odd) of the enclosed vortex number. This behavior is absent in two key control devices: a non-topological graphene Corbino Josephson junction and a 3DTI-based linear Josephson junction. These results indicate that the polarity-tunable JDE is intrinsically linked to the unique combination of the proximitized topological superconductivity in the 3DTI surface and the Corbino device's closed-loop geometry. Our theoretical modeling attributes the observed sign change in diode polarity to the alternating sign of periodic boundary conditions in topological superconductors, supporting the interpretation that the vortex-parity-controlled JDE is a direct manifestation of the underlying Andreev bound state topology associated with the presence of non-Abelian anyons in the vortices.

Figures (4)

• Figure 1: Josephson interferometry on circular and square Corbino junctions.a, False-colour scanning electron microscopy (SEM) image of a circular Corbino Josephson junction (scale bar: $300~\text{nm}$). Grey: Au-capped Nb Corbino contacts; light red: Au air bridge; light blue: 3DTI surface with Te capping layer. See Extended Data (ED) Fig. 1 for a large-scale view. The schematic illustrates the quasi-4-probe voltage measurement setup. Upper right: The outer SC contact quantizes magnetic flux $\Phi_{\rm{JJ}}$ into integer multiples of $\Phi_0$. Lower right: Nb directly contacts the 3DTI surface (dark blue) through the milled Te film, with surface states (red) acting as the weak link. b, False-colour SEM of a square Corbino junction. The 3DTI flake edges are visible on the Te-coated $\rm{SiO_2/Si}$ substrate (dark grey). Right: Schematic model of the square geometry where four linear junctions are separated by a phase bias $\Delta\varphi$ associated with the corner area, leading to an interference pattern analogous to 4-slit optical diffraction. c,d, $I_{\rm{DC}}$--$V_{\rm{DC}}$ characteristics of the circular junction at zero flux (c) and at different integer flux quanta (d). e,f, Same as c,d for the square junction. g, Differential resistance of the circular junction as a function of $B$ and normalized DC bias current $I_{\rm{DC}}/I_{\rm{c}}(B=0)$. Periodic resistance jumps are visible whenever a vortex enters the weak link region, allowing us to assign an integer $n_{\rm{v}}$ in the junction. A SC (zero-resistance) state is visible only at $n_{\rm{v}}=0$, consistent with a single-slit Fraunhofer diffraction model with discrete sampling at the nodes. h, Same as g for the square junction. In agreement with the 4-slit interference model, re-entrant SC features with finite critical currents appear at $n_{\rm v} = \pm 4$, $\pm 8$, $\pm 12$. The additional features at $n_{\rm v} = \pm 2$ arise from the second harmonic of the CPR. Associated with Cooper pair cotunnelling, its doubled phase-winding frequency enables constructive interference at these half-period points where the fundamental mode vanishes. All data are taken at $T=1.6~\text{K}$.
• Figure 2: Vortex-parity-controlled JDE in 3DTI CJJs.a,b, Differential resistance maps of the circular (a) and square (b) junctions as a function of applied magnetic field and bias current normalized by $I_{\rm{c}}(0)$, taken at $T=0.25~\text{K}$. Unlike the 1.6 K data, finite critical currents are resolved across all vortex states. c--e, JDE analysis for the circular junction as a function of $B$ at various temperatures: c, Average critical current $I_{\rm c}^{\rm avg}(B)=(I_{\rm c}^+(B)+|I_{\rm c}^-(B)|)/2$ normalized by $I_{\rm{c}}(0)$. d, Critical current difference $\Delta I_{\rm c}(B)=I_{\rm c}^+(B)-|I_{\rm c}^-(B)|$ normalized by $I_{\rm{c}}(0)$. e, Diode efficiency $\eta(B) = \Delta I_{\rm c}(B)/2I_{\rm c}^{\rm avg}(B)$. f--h, Same as c--e for the square junction. For both devices, the polarity of JDE alternates its sign depending on the parity of the vortex number $n_{\rm{v}}$.
• Figure 3: Tight-binding model of proximity-induced superconductivity in a 3DTI CJJ.a, Schematic of a 3DTI CJJ. The device is modelled as a proximitized 3DTI weak link (light blue) acting as an effective $p+ip'$ superconductor between Corbino SC contacts (grey). 1D Majorana modes at the edges are denoted in yellow-orange (inner) and green (outer). An even number of magnetic flux quanta threading the junction (black Josephson vortices) leads to anti-periodic boundary conditions for both edge states, restricting their angular momenta $k$ to half-integers. Right: Linear dispersion (colored lines matching the schematic) with allowed states indicated by circles. b, Schematic for an odd number of flux quanta. The inner edge state retains half-integer angular momenta, whereas the outer edge state is restricted to integer angular momenta, including a mode at $E,k = 0$. c, Calculated Josephson diode efficiency using the topological tight-binding model. The diode polarity (blue: positive, red: negative) alternates with the vortex number parity. Nonzero even vortex numbers correspond to the regime in a, while odd vortex numbers correspond to b. d, Calculated diode efficiency using a topologically trivial tight-binding model (schematics not shown). In contrast to the topological case, no clear vortex-parity dependence is observed.
• Figure 4: Absence of vortex-parity-controlled JDE in non-topological graphene Corbino and linear 3DTI JJs.a, Normalized critical current versus applied magnetic field for an electron-doped graphene CJJ, measured at three temperatures. Periodic jumps in $I_{\rm{c}}^{\pm}(B)$ correspond to integer vortex states. Inset: Optical microscopy (OM) image of the device (scale bar: $2~\upmu\text{m}$). b, Josephson diode efficiency derived from a. No clear vortex-parity dependence is observed. See ED Fig. 4 for $\eta(B)$ in the extended parameter space. c, Normalized critical current versus applied magnetic field for a linear 3DTI JJ, where $\Phi_{\rm{JJ}}$ is tuned continuously, measured at four temperatures. Inset: OM image of the device (scale bar: $2~\upmu\text{m}$). d, Josephson diode efficiency derived from c. Curves are offset by $0.4$ for clarity. The inset Fourier transform reveals no clear periodicity. Vertical dash-dotted and dashed lines indicate the major and doubled periodicity of the Fraunhofer pattern in c, respectively; neither matches the frequency components of $\eta(B)$. The central $B$ region (green area, $-0.5 \le \Phi_{\rm{JJ}}/\Phi_{0} < 0.5$) is excluded from the Fourier analysis because the zero-vortex state introduces an additional $\Phi_{0}$ interval between the positive and negative flux branches.