Disorder-induced decoupled surface transport channels in thin films of doped topological insulators

Nonideal topological insulator (TI) films in which the bulk states are not insulating due to unintentional doping exhibit strong surface–bulk coupling. Such surface–bulk coupling can further induce intersurface coupling that affects the electrical conductivity of the TI films through a quantum interference effect known as weak antilocalization. Increased understanding and control of intersurface coupling is therefore crucial for the use of TI-based quantum devices. In this report on the transport properties of doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ films under perpendicular and parallel magnetic fields, we observe a crossover between coupled and decoupled surface channels that is mediated by intentional disorder controlled by a post-annealing process. The intentional disorder causes the surface state carriers to rapidly lose their quantum phase and coherence, and as a result, more disordered ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ films exhibit a shorter penetration depth of the surface state into the bulk states and weaker intersurface coupling, even though stronger surface–bulk coupling is expected. In previous studies, the role of disorder has generally been considered by determining its effect on surface–bulk scattering, but our results indicate that the role of disorder must be considered as a source of decoherence.

Figure 1

Structural analyses of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films for different annealing temperatures. Cross-sectional STEM images of the films annealed at (a) 175 °C and (b) 275 °C, respectively. The layered structure of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ films are clearly evident and the film thickness is 14 QL. (c) HR-XRD patterns $(\theta –2\theta$ scans) of the films. Only the (003) peak families corresponding to the single phase ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ are shown. The inset shows the rocking curve scan $(\omega$ scan) of the (003) peak. (d) Raman spectra of the films. After post-annealing, only the vibrational modes of the single phase ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ are evident. The results of these structural analyses indicate that the extent of disorder decreases as the annealing temperature increases.

Figure 2

Transport properties of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films for different annealing temperatures. (a) Temperature dependence of the sheet resistance in the 2–300 K range. The crystalline films exhibit the typical metallic behavior of doped TI films, while the amorphous film annealed at 150 °C exhibits insulating behavior. (b) Hall measurements at 2 K and (c) fitted results for the sheet carrier densities and mobilities. On account of the almost linear behavior of the Hall resistance with respect to the magnetic field, the results are fitted with a single carrier model of the low field data. (d) Ioffe–Regel criterions for different annealing temperatures. These results indicate that the extent of disorder decreases as the annealing temperature is increased.

Figure 3

WAL effect on the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films under a magnetic field. (a) Magnetoresistance measurements under a perpendicular magnetic field for different annealing temperatures. The inset shows the WL effect for a film annealed at 150 °C. (b) The corresponding MC for different annealing temperatures. (c) Fitted results obtained with the HLN equation. The number of coherent channels is reduced as the annealing temperature is increased. Schematics outlining how TSS penetration and possible closed carrier trajectories can induce a WAL effect for (d) insulating and (e) doped TI films. Perpendicular and parallel magnetic fields pierce the regions penetrated by the TSSs and break the coherence.

Figure 4

(a) Magnified MC image showing the effects of WAL on ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films under a parallel magnetic field. (b) Fitted results obtained using Eq. (2). The WAL effect under a parallel field arises from the penetration of TSSs into the bulk states. The prefactor $\alpha$ is plotted as a function of the penetration depth, $\lambda$. (c) MC of the 14-QL-thick film annealed at 175 °C and 28-QL-thick film annealed at 275 °C which are slightly thinner and thicker than $2\lambda$, respectively. (d) Estimation of the surface–bulk scattering time. Inter-surface coupling can occur when $\left({\tau }_{\varphi }-{\tau }_d\right)>2{\tau }_{\mathrm{SB}}$. Since the Fermi levels of our films are far from the conduction band edge, the difference in the surface–bulk scattering time does not depend significantly on the disorder.