Conductance quantization in PbTe nanowires

PbTe nanowires coupled to a superconductor have recently been proposed as a potential Majorana platform. The hallmark of the one-dimensional nature of ballistic nanowires is their quantized conductance. Here, we report the observation of conductance plateaus at multiples of the quantized value $2e^2/h$ in PbTe nanowires at finite magnetic fields. The quantized plateaus, as a function of source-drain bias and magnetic field, allow for the extraction of the Landé $g$ factor, sub-band spacing, and effective mass. The coefficient of 2 in the plateau conductance indicates the presence of valley degeneracy arising from the crystal orientation of the nanowires, which are grown on a (001) substrate. Occasionally, this degeneracy can be lifted by a gate voltage that breaks the mirror symmetry. Our results demonstrate the one dimensionality of PbTe nanowires and fulfill one of the necessary conditions for the realization of Majorana zero modes.

Figure 1

(a) SEM of device A. Scale bar, 1 $\mu \mathrm{m}$. (b) Schematic (simplified) of device A and the measurement circuit. (c) $G$ vs $V_{\text{G}}$ for the five devices. $V$ = 0. $B$ = 6 T. $V_{\text{G}}$ sweeps from negative to positive (see the arrow). (d) Opposite sweeping direction of $V_{\text{G}}$. For clarity, $V_{\text{G}}$ of device D (E) was horizontally shifted by 0.5 (1.5) V in (c) and 2 (0.7) V in (d). (e) Schematic of the device cross section. (f) 3D illustration of the four valleys. The directions of the [$1\overline{1}1$] valley (red) and the [$\overline{1}11$] valley (orange) are also sketched in (e).

Figure 2

(a) $G$ vs $V$ and $V_{\text{G}}$ at $B$ = 6 T for device A. (b) Zero-bias line cut. (c) Transconductance ($dG/d{V}_{\text{G}}$) of (a). A minor smoothing (low-pass, averaging window of 2) along $V_{\text{G}}$ was performed for clarity. (d) Waterfall plot of (a). Each curve corresponds to a fixed $V_{\text{G}}$.

Figure 3

(a) Zero-bias $G$ vs $B$ and $V_{\text{G}}$ for device A. (b) Several line cuts of (a). The curves are offset horizontally (by 0.5 V between each curve) for clarity. (c) Transconductance of (a). (d) Sketch of the lowest four spin-resolved sub-bands.

Figure 4

(a) $G$ vs $V$ and $V_{\text{G}}$ for device B at $B$ = 6 T. (b) Zero-bias line cut. A charge jump is visible between the second and the third plateau due to the device instability. (c) Zero-bias $G$ vs $B$ and $V_{\text{G}}$ for device B. (d) Line cuts from (c) with horizontal offsets (by 0.6 V between each curve) for clarity. (e) $G$ vs $V$ and $V_{\text{G}}$ for device C at $B$ = 6 T. (f) Zero-bias line cut. (g) Zero-bias $G$ vs $B$ and $V_{\text{G}}$ for device C. (h) Line cuts from (g) with horizontal offsets (0.5 V for each curve) for clarity.