In-plane magnetic field driven conductance modulations in topological insulator kinks

We present low-temperature magnetoconductance measurements on ${\mathrm{Bi}}_{1.5}{\mathrm{Sb}}_{0.5}{\mathrm{Te}}_{1.8}{\mathrm{Se}}_{1.2}$ kinks with ribbon-shaped legs. The conductance displays a clear dependence on the in-plane magnetic field orientation. The conductance modulation is consistent with orbital effect-driven trapping of the topological surface states on different side facets of the legs of the kink, which affects their transmission across the kink. This magnetic field driven trapping and conductance pattern can be explained with a semiclassical picture and is supported by quantum transport simulations. The interpretation is corroborated by varying the angle of the kink and analyzing the temperature dependence of the observed magnetoconductance pattern, indicating the importance of phase coherence along the cross-section perimeter of the kink legs.

Figure 1

(a) Schematic of the ${90}^{\circ }$ kink. The red arrow indicates the orientation of the magnetic field with respect to the kink structure. The magnetic field angle ${\theta }_B$ is set to ${\theta }_B=3\pi /4$, which is the position for minimum transmission in the kink structure. The green surfaces on the legs of the kink indicate the trapping on opposite sides (reducing the transmission) of the surface-state channels due to the orbital effect of the external magnetic field. (b) Scanning electron micrograph of the ${90}^{\circ }$ kink devices. Note that the spare electrodes (in gray) were kept as open contacts in order to avoid any interference. The red annotations indicate the measurement setup. (c) Corresponding schematic of the ${120}^{\circ }$ kink, with the red arrow indicating the magnetic field angle of ${\theta }_B=5\pi /6$. (d) Scanning electron micrograph of the ${120}^{\circ }$ kink devices.

Figure 2

Conductance of the $90{}^{\circ }$ and $120{}^{\circ }$ kink structures at $1.5\mathrm{K}$. (a) Conductance of the $90{}^{\circ }$ kink in units of $G_0=2e^2/h$ as a function of the in-plane magnetic field. The single lines are color coded, where the color represents the angle under which the magnetic field is applied with respect to the device. (b) Color map of the effective conductance $\mathrm{\Delta }G/G_0$ [see Eq. (1)] of the $90{}^{\circ }$ kink as a function of magnetic field angle ${\theta }_B$ and absolute magnetic field $\left|B\right|$. (c) Calculated normalized transmission $T/T_{\max }$ as a function of absolute magnetic field $\left|B\right|$ and magnetic field angle ${\theta }_B$. (d)–(f) Corresponding plots for the $120{}^{\circ }$ kink.

Figure 3

Linecuts of the effective conductance change $\mathrm{\Delta }G/G_0$ (dotted lines) and of the normalized transmission $T-{\left|T\right|}_{B=\mathrm{const}}$ (dashed lines) as a function of ${\theta }_B$ at magnetic fields ranging from 2 to $10\mathrm{T}$ in steps of $2\mathrm{T}$ for the (a) $90{}^{\circ }$ and (b) $120{}^{\circ }$ kink (taken from Fig. 2). Note that the individual curves are offset for better clarity.

Figure 4

(a)–(d) Effective normalized conductance $\mathrm{\Delta }G/G_0$ of the $90{}^{\circ }$ kink as a function of ${\theta }_B$ and $B$ at (a) 1, (b) 5, (c) 10, and (d) 20 K. The periodic pattern as a function of in-plane magnetic field angle is clearly vanishing with increasing temperature. (e) The peak-to-valley difference $\mathrm{\Delta }{G}_{{\theta }_B}$ averaged over all magnetic fields in comparison to the average conductance $G_{\mathrm{av}}$ of the sample averaged over all angles and magnetic fields. These values are displayed as a function of temperature. It is clearly visible that the average conductance of the sample is rather constant with increasing temperature, whereas the peak-to-valley difference exponentially drops to zero.