Topological insulator single-electron transistors for charge sensing applications

Abstract

We present topological insulator (TI)-based single-electron transistors (SETs) as magnetic-field-compatible charge sensing devices that are easily integrable with TI-superconductor hybrid platforms. We observe well-resolved Coulomb diamonds in the charge-stability diagrams of our devices confirming the charge quantization and single-electron transport. In some devices, the Coulomb resonances show persistent shifts corresponding up to $\sim$ e/2 charge. An axial magnetic field further displaces these shifts to higher or lower gate voltages. We find that the axial magnetic-field dependence of the shifts is consistent with the Zeeman shift of a trap state coupled to the SET, and we reproduce the observations using numerical simulations. The resonance shifts are therefore identified as a consequence of the sensitivity of our TI-SET devices to charges in proximity. Establishing this charge sensing capability is a first step toward integrating TI-SETs as charge sensors in more complex TI-based hybrid devices, with the overarching goal of detecting and braiding Majorana zero modes.

Figures (4)

• Figure 1: Topological insulator SET and its charge-stability diagram. a False-colour scanning electron microscope (SEM) image of the SET device made of BSTS2 nanowire (sky blue) contacted by Pt/Au electrodes (yellow) at two ends. b Typical charge-stability diagram of the TI-SET showing differential conductance $G$ as a function of $V_{\mathrm{bias}}$ and $V_{\mathrm{bg}}$. It exhibits similar sized Coulomb diamonds across several charge degeneracy points tuned by the back-gate voltage. The bottom panel shows a zero-bias gate trace of the conductance taken from the upper panel. c Color plot of zero-bias conductance as a function of $V_{\mathrm{bg}}$ and $B_{||}$ showing the evolution of Coulomb resonances with axial magnetic field $B_{||}$. At around 1 T, the resonances shift to lower $V_{\mathrm{bg}}$ values while preserving the peak-to-peak spacing. d Charge-stability diagrams of of the SET at various $B_{||}$ values close to 1 T. The diamonds are distorted at the $V_{\mathrm{bg}}$ values where the zero-bias resonances show shifts in panel c.
• Figure 2: Magnetic-field dependence of the Coulomb resonances in a large $V_{\mathrm{bg}}$ range. The energy of the trap state shifts linearly with in-plane magnetic field. In the first region, denoted by '1', the slope of the linear line is negative revealing a spin orientation in the opposite direction of the $B_{||}$. In the second region, denoted by '2', the two parallel lines with positive slope correspond to the same trap state which has a spin polarization in the direction of $B_{||}$. The trajectory followed by the trap signature is shown with a dashed line. The inset shows the fine shifts of the resonances in region '1' that correspond to $\sim$$e/5$ charge at low $B_{||}$ field.
• Figure 3: a Equivalent circuit diagram of the main SET island tunnel-coupled to a charge trap that mimics a small quantum dot. b Total electrostatic energy of the system follows one of the two sets of charge parabolas depending on whether the relevant trap state is empty (gray line) or occupied (orange line). The ground state switches from empty to occupied configuration near the trap state degeneracy. c The mean occupation probability of the trap state as a function of $V_{\mathrm{bias}}$ and $V_{\mathrm{bg}}$. The probability fluctuates near the trap state degeneracy corresponding to the switching of the ground state of the total system.
• Figure 4: Comparison between the measured and simulated conductance data. a Zero-bias Coulomb resonances as a function of $B_{||}$ in the region '2' shown in Fig. \ref{['fig:Fig2']}. The resonances shift to higher $V_{\mathrm{bg}}$ values as the $B_{||}$ is increased. b Charge-stability diagram of the TI-SET at $B_{||}=5.0$ T (lower panel) and at $B_{||}=5.4$ T (upper panel). The diamond distortions are again visible in the vicinity of the resonance shifts observed in a. c Linecuts of the two panels in b taken at zero-bias voltage. In each of the two panels the suppression of the conductance peaks occurs at the $V_{\mathrm{bg}}$ values where the distorted diamonds are observed in their corresponding panels in b. d Simulated conductance plot of a SET-trap system that includes the Zeeman shift of the trap energy. e Numerical simulation of the stability diagram of the SET-trap model at two different magnetic fields; $5.0$ T in the lower panel and $5.4$ T in the upper panel. The trap degeneracy is shifted by the magnetic field due to Zeeman effect. f Linecuts taken from the two panels in e at zero-bias voltage indicated by thick orange and blue ticks. See Supplementary Information for the list of parameter values used in the simulation.