Weak-link Josephson Junctions Made from Topological Crystalline Insulators

We report on the fabrication of Josephson junctions using the topological crystalline insulator ${\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}\mathrm{Te}$ as the weak link. The properties of these junctions are characterized and compared to those fabricated with weak links of PbTe, a similar material yet topologically trivial. Most striking is the difference in the ac Josephson effect: junctions made with ${\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}\mathrm{Te}$ exhibit a rich subharmonic structure consistent with a skewed current-phase relation. This structure is absent in junctions fabricated from PbTe. A discussion is given on the origin of this effect as an indication of novel behavior arising from the topologically nontrivial surface state.

Figure 1

Temperature dependence of the differential resistance $R$, where superconducting features appear below $T=500\mathrm{mK}$. The peaks in $R$ occur at values $I_{\mathrm{dc}}=I_C$. (Inset, upper left) Scanning electron micrograph of a device similar to the ones studied in this Letter showing two superconducting (SC) aluminum leads (dark grey) and the TCI material ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$ (green). Scale bar shown in white is $1\mu \mathrm{m}$. The spacing between the two SC leads is 100 nm. (Inset, upper right) Schematic of the band structure of ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$ where 4 Dirac cones appear across the $\overline{X}$ point in k-space [10].

Figure 2

(a) Plot of $R(B,I_{\mathrm{dc}})$ revealing a Fraunhofer-like pattern consistent with a (nearly) uniform supercurrent across the width of the device. (b) One-dimensional cuts in the data from (a) at $B=0$, 5.00 mT (black) and 2.75, 7.25 mT (green), where the latter two show the variation in $R$ between at the first and second minimum in $I_C$.

Figure 3

A comparison of ${\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}\mathrm{Te}$ and PbTe at $f=3\mathrm{GHz}$ and applied rf power of $-6.75\mathrm{dBm}$. (a) Plot of $R$ showing minima at both expected values for Shapiro steps and at half integer values. Numerical integrated $I-V$ data (red) shows Shapiro steps at $nhf/2e=n*6.2\mu \mathrm{V}$ and additional features at fractional values of $1/2$ and $3/2$. (b) By comparison, a PnTe device showing only integer values of the Shapiro steps, both in $R$ (black) and $I-V$ (red).

Figure 4

(a) Power dependence of the ac Josephson effect taken at $f=2.2\mathrm{GHz}$ and applied power range $-27.25$ to $-9\mathrm{dBm}$. In addition to the main Shapiro steps observed (black regions indicated by white numbers), the structure in between the primary steps is measured (along the vertical indicated by white arrows). (b) A cut of $R$ taken along the grey line in Fig. 4. (c) Simulation of the RSJ model using a CPR for KO-2 theory for a ballistic Josephson junction, simulated over a similar range of parameters as the experimental data [Fig. 4]. The saw-tooth behavior of the CPR is necessary to contain the higher harmonics in the CPS needed to mimic the experimental data. (Inset) A plot of the CPR for the KO-2 theory (solid line) is compared to a pure sine wave (dashed line). (d) A cut of the simulated differential resistance $\delta R$ qualitatively reproduces that observed in the experiment.