Superconductor-nanowire devices from tunneling to the multichannel regime: Zero-bias oscillations and magnetoconductance crossover

We present transport measurements in superconductor-nanowire devices with a gated constriction forming a quantum point contact. Zero-bias features in tunneling spectroscopy appear at finite magnetic fields and oscillate in amplitude and split away from zero bias as a function of magnetic field and gate voltage. A crossover in magnetoconductance is observed: Magnetic fields above $\sim$0.5 T enhance conductance in the low-conductance (tunneling) regime but suppress conductance in the high-conductance (multichannel) regime. We consider these results in the context of Majorana zero modes as well as alternatives, including the Kondo effect and analogs of 0.7 structure in a disordered nanowire.

Figure 1

(a) Scanning electron micrograph of one of the devices measured (device 2). An InSb nanowire was deposited over HfO${}_2$-insulated bottom gates and contacted by Ti/Au leads (N) on the ends and a Ti/NbTiN lead (S) in the middle. (b) Zero-bias differential conductance $g$ at $B=0$ (blue curve) and $B_y=0.5$ T (red curve) as a function of the voltage $V_g$ on the gate labeled in (a). (c) $g$ as a function of $B_y$ and $V_{\mathrm{sd}}$ applied to the normal lead for $V_g=1.6$ V [left dashed line in (b)]. (d) Cuts from (c) for $B_y$ between 0 and 1 T, offset for clarity except for the $B=0$ trace. (e) $g$ as a function of $B_y$ and $V_{\mathrm{sd}}$ for $V_g=3$ V [right dashed line in (b)]. (f) Cuts from (e) for $B_y$ between 0 and 1 T, offset for clarity except for the $B=0$ trace. All data are from device 1.

Figure 2

(a) Differential conductance $g$ as a function of source-drain voltage $V_{\mathrm{sd}}$ and axial magnetic field $B_y$(device 1, temperature 0.1 K, $V_g=2.5$ V). (b) Differential conductance with average over $V_{\mathrm{sd}}$ subtracted at each field, $\tilde{g}\left(B\right)$. (c) Cuts of the data in (b) at $V_{\mathrm{sd}}=0$ (black) and $0.07$ mV (red). (d) Conductance concavity $d^{2}g/d{V}_{\mathrm{sd}}^2$ at $V_{\mathrm{sd}}=0$. Vertical lines are placed at integer multiples of the position of the first large dip in $d^{2}g/d{V}_{\mathrm{sd}}^2$ at $B_y=0.45$ T. (e) Peak positions obtained from the local minima in (d) vs peak index. The red (blue) dashed line has a slope of 1 (2) in the log-log plot. (f) Squared Fourier amplitudes of $d^{2}g/d{V}_{\mathrm{sd}}^2$ as a function of $B_y$, calculated row by row at each value of $V_{\mathrm{sd}}$.

Figure 3

Zero-bias conductance $g$ as a function of $V_g$ and $B_y$ shown (a) in color scale and (b) as offset line traces for $V_g$ from $-0.2$ to $-1.0$ V. Data are from device 2, with a temperature of 0.5 K.

Figure 4

(a) Zero-bias conductance $g$ as a function of $V_g$ and $B_y$ (device 2, temperature 0.5 K). The inset shows cuts along $B_y$ at $V_g=-0.75$ V (orange) and $V_g=0.49$ V (purple). (b) $g$ as a function of $V_g$ from (a) averaged over the ranges of $B_y$ indicated by colored bars along the top axis of (a): $B_y=-0.2$ to 0.2 T (blue curve), $B_y=0.5$ to 2 T (red curve), and $B_y=2.5$ to 5 T (black curve).

Figure 5

Zero-bias conductance $g$ of device 2 as a function of $V_g$ and $B_y$ at 4 K. The inset shows cuts along $B_y$ at $V_g=-0.75$ V (orange) and $V_g=1.49$ V (purple). (b) $g$ as a function of $V_{\mathrm{sd}}$ for device 1 at various temperatures between 0.04 and 4 K at $B_y=0.5$ T. Curves are offset vertically for clarity.