Surface State Charge Dynamics of a High-Mobility Three-Dimensional Topological Insulator

We present a magneto-optical study of the three-dimensional topological insulator, strained HgTe, using a technique which capitalizes on advantages of time-domain spectroscopy to amplify the signal from the surface states. This measurement delivers valuable and precise information regarding the surface-state dispersion within $<1\mathrm{meV}$ of the Fermi level. The technique is highly suitable for the pursuit of the topological magnetoelectric effect and axion electrodynamics.

Figure 1

Time-domain measurement of the normal-incidence Kerr angle. (a) Illustration of the magneto-optical THz apparatus. ${\theta }_P$ was set to 51.2° throughout. (b) Subset of the angle-dependent measurements of the 1st and 2nd pulses. Vertical lines show the cuts used to separate the pulses into $E_1$ and $E_2$. (c) Measured $|E_2{|}^2$ (red dashes) and the fit from Eq. (1) (blue lines) used to determine the Faraday angle ${\theta }_{F,2}(\omega )$ for $+1.4T$ and $-1.4T$. (d) Pictorial rationale for the expression ${\theta }_{F,2}-{\theta }_{F,1}={\theta }_K$. (e) The measured ${\theta }_K$ for several magnetic field values.

Figure 2

Properties of the surface-state cyclotron resonance. Real (a) and imaginary (b) Kerr angle ${\theta }_K(\omega ,B)$ determined from terahertz ellipsometry. (c) The experimentally determined ${\omega }_c$ (red squares) and a linear fit (purple lines) showing the $B$-linear CR behavior. ${\omega }_c$ corresponds to the inflections in $\mathrm{Re}{\theta }_K(\omega )$, as demonstrated by the experimental frequency derivative $\mathrm{Re}d{\theta }_K/d\omega$, shown as a false color plot in the background. (d),(e) Fit parameters $\gamma$ and ${\omega }_f$. The error bars arise from scatter in the determined CR parameters.

Figure 3

Dispersion of the surface-state band. (a) Constraints on Fermi parameters $k_F$ and $v_F$ consistent with the magneto-optical data. Black line shows the constraint from the observed ${\omega }_c/B$, and purple dashes indicate the error bars on this quantity. Green (light gray) solid curve is a constraint from the observed ${\omega }_f$ assuming the CR is due solely to two identical surface states at the surface and interface, with solid orange (medium gray) curves indicating the error bars. Dashed orange (medium gray) and green (light gray) curves show the effect of breaking this assumption and allowing 25% of the Drude weight to be attributed to the confined conduction band states. (b) Possible realizations of a minimal surface-state model in 22 which are consistent with our observations for different choices of $A$ and $C_2$. The Fermi level ${\mu }_F$, shown in black, intersects the surface and confined bulk conduction subbands. (c) Dispersion of the surface-state quasiparticles determined in this work with a 75% surface-state signal, $A=25\mathrm{meV}\mathrm{nm}$, and $C_2=890\mathrm{meV}{\mathrm{nm}}^2$.