Scaling of Majorana Zero-Bias Conductance Peaks

We report an experimental study of the scaling of zero-bias conductance peaks compatible with Majorana zero modes as a function of magnetic field, tunnel coupling, and temperature in one-dimensional structures fabricated from an epitaxial semiconductor-superconductor heterostructure. Results are consistent with theory, including a peak conductance that is proportional to tunnel coupling, saturates at $2e^2/h$, decreases as expected with field-dependent gap, and collapses onto a simple scaling function in the dimensionless ratio of temperature and tunnel coupling.

Figure 1

(a) Device schematic close to the tunneling junction, as in the dashed box in (b). The end of the Al wire and the top Al plane (blue) are separated by a narrow InAs junction (red). Two gates (yellow) allow independent tuning of the chemical potential in the wire (gate voltage $V_W$) and of the junction transmission (gate voltage $V_t$). (b) False color scanning electron micrograph of a typical device. The Al pattern is visible through the top gate. The epitaxial Al below the gates is colored gray, the semiconductor below the gates is colored red. (c) Tunneling conductance as a function of in-plane magnetic field $B_{\parallel }$ for normal state transmission $G_N=0.019\times 2e^2/h$. The colored line indicates the position where the linecuts of (e) and (f) were taken. Color extrema have been saturated. (d) As in (c) for $G_N=0.67\times 2e^2/h$. (e) ZBP conductance at $B_{\parallel }=2.3\mathrm{T}$ for several values of $G_N$, indicated in the figure in units of $2e^2/h$. (f) Selection of curves from (e), plotted on a linear scale.

Figure 2

(a) Conductance of a ZBP at $B_{\parallel }=2.3\mathrm{T}$ and $G_N=0.19\times 2e^2/h$ for various temperatures. Temperatures are 40 (black), 60, 80, 100, 150, 200, 300, and 600 mK (pink). (b) As in (a), but for $G_N=0.67\times 2e^2/h$. (c) Temperature dependence ZBP conductance, $G_P$, at $B_{\parallel }=2.3\mathrm{T}$, measured for different values of $G_N$ (colored dots) together with fits to Eq. (1) (gray curves). For the experimental data, the same colors as in Fig. 1 are used.

Figure 3

(a) Extracted relation between the tunnel broadening, $\mathrm{\Gamma }$, obtained from the fits in Fig. 2, and the normal-state conductance, $G_N$ (dots), along with a linear fit (gray line). (b) Magnetic field dependence of the ZBP conductance, $G_P$, together with theoretical predictions based on Eq. (1), with $\mathrm{\Gamma }\propto {\mathrm{\Delta }}^{*}(B_{\parallel })$.

Figure 4

Zero bias conductance of the entire data set (for $T\le 150\mathrm{mK}$) plotted as a function of temperature scaled by the extracted values of $\mathrm{\Gamma }$ (colored dots) and compared to the theoretical expectation of Eq. (1) (gray curve).