Observation of the surface hybridization gap in the electrical transport properties of the ultrathin topological insulator (Bi$_{1-x}$Sb$_{x}$)$_2$Te$_3$

TL;DR

This work investigates whether ultrathin BST topological insulators can exhibit a surface-state hybridization gap at the Dirac point, potentially yielding an insulating or QSH phase depending on thickness. Using MBE-grown BST films of $d \approx 6$ and $9$ nm, patterned Hall bars, and gate-tunable transport measurements, the authors observe a robust insulating region near the Dirac point in the 6 nm sample, consistent with a hybridization gap $E_G$, while the 9 nm sample shows little to no gap. Magnetic-field measurements reveal device-dependent gap behavior with no unambiguous Zeeman-driven transition to a QSH state, suggesting that disorder and multi-band effects significantly influence transport in these ultrathin films. The results confirm surface-state hybridization as a transport mechanism in ultrathin BST but indicate a need for revised theory to account for disorder and thickness-dependent, nontrivial gap evolution, paving the way for thickness-tuned QSH exploration in MBE-grown BST.

Abstract

We study the three-dimensional topological insulator (Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_{3}$ in its ultrathin limit i.e. when the thickness is of the same order as the surface state penetration depth. It is expected that in this limit a hybridization gap opens at the Dirac point, which gives rise to a quantum spin Hall (QSH) or insulating phase, depending on the material thickness. We fabricate (Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_{3}$ Hall bars with a thicknesses of 6 and 9 nm and measure an insulating phase around the Dirac point for low bias and at sub-Kelvin temperatures only in samples fabricated from the 6 nm films, which indicates the presence of a hybridization gap. The effect of a perpendicular magnetic field on the hybridization gap is studied but remains partially unresolved. The results form an important step towards experimentally realizing the quantum spin Hall state via hybridization in ultrathin films of (Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_{3}$, yet, they also expose a knowledge gap regarding transport measurements in these systems.

Figures (8)

• Figure 1: Magnitude of the hybridization gap, $E_\textup{G}$, as function of film thickness $d$ for varying ratios $x$ in (Bi1-$x$Sb$x$)2Te3. Limiting cases $x = 0$$(1)$ are plotted for the pure compounds Bi2Te3 (Sb2Te3) alongside the ratio $x=0.72$ (in white) used in the films studied in this work.
• Figure 2: (a) Atomic force microscopy image of ultrathin BST (nominal thickness 6 nm) deposited on Al2O3. Holes in the film reach the substrate surface. The graph inset shows the height profile and the scale bar corresponds to 1 $\mu$m. This film is used to fabricate the device measured in Fig. \ref{['fig:gateIV_Au']}(a). (b) and (c) Optical microscopy picture of a generation 1 (Ti/Pd contacts) and generation 2 (Au contacts) BST Hall bar, respectively. The scale bars correspond to 100 $\mu$m. The top gated area, covering both device and Ohmic contacts in generation 1 and only the region between voltage probes in generation 2 is shaded in blue. (b) was taken prior to depositing the Ti/Pd gate contact, so the gate metal itself is not shown.
• Figure 3: Longitudinal resistance R$_{xx}$ as function of top gate voltage at $B = 0\;$T. Inset: Anti-symmetrized Hall resistance versus out-of-plane magnetic field for varying top gate voltages, as indicated next to the graphs. The data was obtained on a $L \cross W = 14.8\; \mu \mathrm{m} \cross 3.2 \;\mu \mathrm{m}$ Hall bar with Ti/Pd contacts in a 4 terminal configuration at $T = 4.5$ K. This data was obtained using standard lock-in techniques.
• Figure 4: Differential conductance ($\dd I / \dd V$) as function of $V_\mathrm{TG}$ and (a) $V_\mathrm{bias}$ or (b) $V_{xx}$ at $T = 100$ mK. Blue dots on the inset Hall bars denote the current path and red dots denote the voltage probes. (a) 2-terminal data obtained on a $L \times W = 148$$\mu$m$\times 25.6$$\mu$m Hall bar with Ti/Pd contacts. (b) 4-terminal data obtained on a $L \times W = 80$$\mu$m$\times 5$$\mathrm{\mu}$m Hall bar with Au contacts. The insets in the bottom right of (a) and (b) show linecuts of the two figures respectively. The position of each of the linecuts is indicated by a white dotted line.
• Figure 5: Comparison between 2-terminal ($V_\mathrm{bias}$) and 4-terminal ($V_{xx}$) voltage as a function of source voltage bias. The 2-terminal voltage ($V_\mathrm{bias}$) follows the source voltage (we use a current measurement to convert these traces to $\dd I/\dd V$). The 4-terminal voltage shows a slope change when the gapped region ($I = 0$) is entered. Here, $V_\mathrm{bias}=V_{xx}$ (see inset): the entire bias voltage drops over the region between the voltage probes.