Revealing Topological Superconductivity in Extended Quantum Spin Hall Josephson Junctions

Quantum spin Hall–superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting “fractional Josephson currents.” Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity—even when noise spoils parity conservation.

Figure 1

Extended QSH Josephson junctions that host 1D topological superconductivity. Topological superconductors reside either (a) at the outer boundary or (b) across the barrier depending on whether the superconductors dope the contacted QSH regions.

Figure 2

Interference patterns in (a),(b) the parity-conserving limit and (c),(d) with parity switching at low ($T_b=0.02\mathrm{\Delta }$) and high ($T_b=100\mathrm{\Delta }$) bath temperature. The color scale indicates voltage in units of $2eR\mathrm{\Delta }/\hslash$ while current is normalized by $e\mathrm{\Delta }/\hslash$. Data correspond to (a),(b) $T=0.05\mathrm{\Delta }$, (c) $T=0.02\mathrm{\Delta }$, $\tau =50{\tau }_R$, and (d) $T=0.02\mathrm{\Delta }$, $\tau =5{\tau }_R$.

Figure 3

Washboard potentials for select parity sectors in the three high-bath-temperature current regimes. For low currents $I<I_{c1}$ consecutive parity flips can mediate $\pm 2\pi$ phase slips as in (a) and (b). In (c) and (d) a steady phase drift always occurs.

Figure 4

(a) Color plot of $d^{2}V/d{I}^2$ and (b) voltage-current line cuts corresponding to the high-bath-temperature data in Fig. 2. The two critical currents $I_{c1}$ and $I_{c2}$ are clearly visible in both plots. Voltage and current are respectively expressed in units of $2eR\mathrm{\Delta }/\hslash$ and $e\mathrm{\Delta }/\hslash$.