Magnetoconductance evolution across the topological-trivial phase transition in ${In_{x}}({Bi_{0.3}}{Sb_{0.7}})_{2-x}{Te_3}$ thin films

TL;DR

This work addresses how topology, spin–orbit coupling, and disorder co-determine magnetotransport across a tunable topological phase transition in TI thin films. By systematically varying $x$ in In$_x$(Bi$_{0.3}$Sb$_{0.7}$)$_{2-x}$Te$_3$ and measuring resistivity and magnetoconductance over temperature and magnetic field, the authors map diffusive weak antilocalization (WAL) behavior to a high-disorder, variable-range hopping (VRH)–dominated localization regime. They identify a band-inversion–driven transition near $x \\approx 7\%$ evidenced by the nonmonotonic evolution of the HLN prefactor $\alpha$ and activation energy, and a diffusive-to-VRH crossover near $x \\approx 15\%$ accompanied by a sign change in low-field MC. A coherent physical picture emerges by combining Nguyen’s hopping interference in the VRH regime with Raikh’s incoherent hopping mechanism and wavefunction shrinkage, linking topology, spin–orbit coupling, and disorder to the full field–temperature magnetotransport landscape in this material class.

Abstract

We investigate the evolution of electronic transport across the topological-trivial phase transition in ${\rm In}_{x}({\rm Bi}_{0.3}{\rm Sb}_{0.7})_{2-x}{\rm Te}_3$ thin films by systematically tuning the indium concentration $x$. Increasing $x$ reduces the effective spin-orbit coupling, driving a topological quantum phase transition near $x \approx 7\%$, and at higher disorder a crossover from diffusive to strongly localized transport around $x \approx 15\%$. In the diffusive regime, the magnetoconductance is well described by the Hikami-Larkin-Nagaoka formalism, with the evolution of the WAL prefactor $α$ correlating with the band-inversion transition. Beyond the diffusive limit, transport crosses into variable-range hopping, accompanied by a striking reversal of magnetoconductance from negative to positive. The observed positive low-field magnetoconductance, its pronounced anisotropy, and its temperature evolution point to an orbital origin of the response. These features are naturally captured by incorporating the incoherent hopping mechanism of Raikh \textit{et al.} together with wavefunction shrinkage, rather than by conventional quantum-correction frameworks. Our results provide a unified picture of how topology, spin-orbit coupling, and disorder collectively determine the full field-temperature magnetotransport landscape in this material class, establishing a clear experimental link between the topological phase transition and the onset of incoherent hopping-dominated conduction.

Figures (6)

• Figure 1: (a) Temperature dependence of the resistance for ${\rm In}_{x}({\rm Bi}_{0.3}{\rm Sb}_{0.7})_{2-x}{\rm Te}_3$ thin films with varying In concentration $x$. The inset shows $R(T)/R(290\,{\rm K})$ for $x=0\%$ and $7\%$, both exhibiting metallic behavior at low temperatures. (b) X-ray diffraction patterns for $x = 0\%, 7\%, 10\%, 15\%, 25\%$, where the dominant $(003n)$ reflections confirm highly oriented $c$-axis growth. (c) Scaling of resistance with temperature, where the linear behavior indicates a 3D Mott VRH dependence for films with $x \ge 15\%$. (d) Dimensionless Drude conductivity illustrating the crossover from diffusive to localized transport. The threshold conductivity $g = 1/\pi$ marks the transition from negative to positive magnetoconductance as $x$ increases.
• Figure 2: The temperature dependence of $\rho_{xx}$ (in logarithmic scale) and $\sigma_{xx}$ (in linear scale) are plotted as function of $T^{-1/4}$ and T (in logarithmic scale) respectively. The difference in the x scale of the two sets of figures exhibits their respective temperature dependence. As disorder (doping concentration $x$) in the electronic system increases, the transport mechanism evolves from weak antilocalization to Mott variable-range hopping. Black solid lines are the liner fitting.
• Figure 3: Magnetoconductivity curves as a function of temperature for different doping percentages $x$. In Fig. (a–e), the solid black lines are fits using Eq. (3), combining the HLN and quadratic terms. In Fig. (f–i), the solid black lines are guides to the eye.
• Figure 4: (a) Hikami–Larkin–Nagaoka (HLN) fitting parameter $\alpha$ extracted at $T=2$ K as a function of doping concentration $x$, together with the activation energy obtained from Arrhenius fits to the temperature-dependent resistance in the diffusive transport regime. (b) Temperature dependence of the phase-coherence length $L_{\phi}$ for different doping concentrations $x$, determined from HLN analysis of the weak antilocalization magnetoconductance. (c) Magnetoconductance (MC) measured under in-plane and out-of-plane magnetic field configurations for $x = 18\%$, highlighting the pronounced anisotropic response.
• Figure 5: Representative low field magnetoconductivity curves for different temperature and doping percentage $x$. Solid black line are the linear fit in the low field regime.