Transport Signatures of Quasiparticle Poisoning in a Majorana Island

We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, “shadow” diamonds appear, shifted by $1e$ in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island ($\sim 1\mu \mathrm{s}$) and sets a bound for a weakly coupled island ($>10\mu \mathrm{s}$). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. When converted from gate voltage to energy units, fluctuations are consistent with previous measurements.

Figure 1

(a) Top: Electron micrograph (false color) of a similar Majorana island device. The applied bias voltage $V_{\mathrm{SD}}$, gate voltage $V_G$, and measured current $I$ are indicated. Bottom: Schematic top view (looking down onto the Si wafer) of the InAs nanowire (green) with two-facet epitaxial Al shell (light blue), showing the direction of applied magnetic fields $B_{\perp }$ and $B_{\mathrm{tr}}$. (b) Charge-state energies of the island as a function of gate induced charge $N_G$. Spacings between degeneracies indicated with $S_e$ and $S_o$. (c) Schematics of transport processes for degeneracies indicated with red circles and green squares in (b).

Figure 2

(a) Experimental differential conductance $g$ as a function of gate voltage, $V_G$, and source-drain voltage, $V_{\mathrm{SD}}$, at zero magnetic field, showing a series of $2e$-periodic Coulomb diamonds with a second set of weaker shadow diamonds offset from the main diamonds by $1e$. (b) Numerically calculated differential conductance as a function of gate-induced charge $N_G$ and source-drain voltage. See main text for model parameters.

Figure 3

(a) Measured zero-bias differential conductance $g$ as a function of perpendicular magnetic field, $B_{\perp }$, and gate voltage, $V_G$, showing a series of strong even-odd Coulomb peaks with weaker shadow peaks in the even valleys between main peaks. Both sets of peaks split with increasing field and merge at $B_{\perp }\sim 0.16\mathrm{T}$. (b) Simulated differential conductance as a function of Zeeman energy, $E_Z$, and dimensionless gate voltage (charge number), $N_G$. (c) Measured differential conductance vs $V_G$ at $B_{\perp }=50\mathrm{mT}$ [white line in (a)]. The average heights of the main and shadow peaks are indicated by $g_m$ and $g_s$, respectively. (d) Simulated differential conductance as a function of $N_G$ for poisoning times ${\tau }_p=0.2$, 1.2, and $6\mu \mathrm{s}$. Simulations show an increase in $g_s$ and decrease in $g_m$ for decreasing ${\tau }_p$.

Figure 4

Upper panels: Differential conductance $g$ as a function $V_G$ and magnetic fields perpendicular ($B_{\perp }$, left) and transversal ($B_{\mathrm{tr}}$, right) to the nanowire. White dashed lines indicate the fitted peak positions. Lower panels: Extracted average peak spacing for even and odd Coulomb valleys, $⟨S_{e,o}⟩$, as a function of magnetic field. The left axis has units of gate voltage, the right axis shows the associated energy scale $\eta S-E_C\propto E_0$.