Probing the quantum metric of 3D topological insulators

Abstract

The surface states of 3D topological insulators possess geometric structures that imprint distinctive signatures on electronic transport. A prime example is the Berry curvature, which controls, for instance, electric frequency doubling via its higher order moments. In addition to the Berry curvature, topological surface states are expected to exhibit a nontrivial quantum metric, which plays a key role in governing nonlinear magnetotransport. However, its manifestation has yet to be experimentally observed and controlled in 3D topological insulators. Here, we provide evidence for a nonlinear response activated by the quantum metric of the topological surface states of Sb$_2$Te$_3$. We measure a time-reversal odd, nonlinear magnetoresistance that is independent from the temperature and the scattering time below 30 K, and is thus of intrinsic geometrical origin. This quantum metric magnetoresistance can be controlled by tuning the contributions of the top and bottom topological surface states by voltage gating. Our measurements thus demonstrate the existence and tunability of quantum geometry-induced transport in topological phases of matter and provide strategies for designing novel functionalities in topological devices.

Figures (11)

• Figure 1: Quantum geometry of a 3D topological insulator.a, Left: Surface Dirac cone and quantum metric (diagonal component $g_{xx}$) of a 3D topological insulator with trigonal warping $\lambda = 0$. Right: spin-momentum locking of the Dirac states in the case $\lambda = 0$ and $\lambda \neq 0$. b, Fermi line with $\lambda = 0$, with and without a magnetic field $\mathbf{B} \parallel \hat{y}$. The color codes for the band-energy normalized quantum metric $G^{xx}$ multiplied by the band velocity $v_x = \frac{\partial\epsilon}{\partial k_x}$, scaled to the maximum value. c, Calculated dependence of the quantum metric-driven nonlinear conductivity on the surface carrier density at three effective magnetic fields $g_{\textrm{L}}B_y$, with $g_{\textrm{L}}$ the Landé factor. The warping parameter is $\lambda = 340$ eVÅ$^3$. The two sketches show the position of the Dirac cone (in violet) and bulk states (in green) relative to the the Fermi level $E_{\textrm{F}}$ in the low-doping (left) and high-doping (right) regimes.
• Figure 1: Linear transport.a, Temperature dependence of the resistivity of Sb$_2$Te$_3$(30 nm) showing a metallic behavior. b, Temperature dependence of the total (hole) carrier density $p$ and hole mobility $\mu$ estimated from measurements of the ordinary Hall effect.
• Figure 2: Sb$_2$Te$_3$ topological insulator.a, Schematic atomic structure of Sb$_2$Te$_3$ quintuple layers (QL) separated by van der Waals (vdW) gaps. b, X-ray diffraction (XRD) of Sb$_2$Te$_3$(30 nm) grown on Si(111). c, Sketch of the device geometry and nonlinear transport measurement configuration before the fabrication of the top electrode (Methods). The yellow shade represents the top electrode. The scale bar corresponds to 20 µ m. d, Magnetoconductance of Sb$_2$Te$_3$(30 nm) normalized to the quantum of conductance $\sigma_0 = e^2/\pi h$ at increasing temperature. The solid lines are fits of Eq. \ref{['eq:WAL']} to the data (Methods). e, Weak antilocalization prefactor $\alpha$ and coherence length $l_{\phi}$ extracted from d. The solid line is a fit of Eq. \ref{['eq:phaseCoherence']} to the data (Methods).
• Figure 2: Current dependence of the linear and nonlinear magnetoresistance.a, Linear magnetoresistance measured at 10 K at increasing current with the field applied in the sample plane and perpendicular to the current direction. b, Nonlinear magnetoresistance measured simultaneously to the linear magnetoresistance in a. c Two-probe linear I-V curve demonstrating ohmic contacts.
• Figure 3: Nonlinear magnetotransport.a,b, Nonlinear magnetoresistance as a function of temperature at a current of 500 µ A. The orientation of the in-plane magnetic field relative to the current is shown in the sketch of the device. c, Angular dependence of the nonlinear magnetoresistance as a function of temperature at a current of 300 µ A and magnetic field of 9 T. The lines are sinusoidal fits to the data. The azimuthal angle is measured from the direction of the electric current, as shown in the sketch. d, Current dependence of the nonlinear magnetoresistance at 10 K and selected magnetic fields. The lines are linear fits with zero intercept.