Electric field modulated topological magnetoelectric effect in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$

Topological insulators have been predicted to exhibit a variety of interesting phenomena including a quantized magnetoelectric response and novel spintronics effects due to spin textures on their surfaces. However, experimental observation of these phenomena has proved difficult due to the finite bulk carrier density which may overwhelm the intrinsic topological responses that are expressed at the surface. Here, we demonstrate an ionic gel gating technique to tune the chemical potential of ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ thin films while simultaneously performing THz spectroscopy. We can tune the carrier concentration by an order of magnitude and shift the Fermi energy $E_F$ to as low as $\simeq 10$ meV above the Dirac point. At high-bias voltages and magnetic fields, we observe a quantized Faraday angle consistent with the topological magnetoelectric effect that can be tuned by ionic gel gating through a number of plateau states.

Figure 1

(a) Schematic of the experimental setup to study the TME of the topological surface states tuned by electric field. $P_1$ (fixed), $P_2$ (rotating), and $P_3$ (fixed) are the wire grid polarizers for measuring the ${\theta }_F$ of the THz pulse. (b), (c) Real and imaginary parts of the conductance ($G=G_1+i{G}_2$) for 15-QL ${\mathrm{Bi}}_2{\mathrm{Se}}_3/{\mathrm{MoO}}_3$ film measured at different bias voltages.

Figure 2

Real and imaginary parts of the Faraday angle (${\theta }_F$) of an 8-QL ${\mathrm{Bi}}_2{\mathrm{Se}}_3/{\mathrm{MoO}}_3$ sample measured at different bias voltages ($V_{\text{bias}}$) and magnetic fields. The solid gray lines represent the real part of the ${\theta }_F$ expected from Eq. (3) assuming a certain number of filled Landau levels.

Figure 3

(a)–(d) Complex Faraday rotation and fits (as described in the SM) for an 8-QL ${\mathrm{Bi}}_2{\mathrm{Se}}_3/{\mathrm{MoO}}_3$ sample for different bias voltages. (e) Cyclotron frequency vs $B$ at different bias voltages $V_{\text{bias}}=(0,0.5,1.0,1.5,2.0,5.0)$ V. Fits are using Eq. (1) with the Fermi energy as a free parameter. (f) The Fermi energy as a function of applied voltage, calculated using both the fits from Eq. (1) for the cyclotron frequency as well as from the estimated spectral weight from fitting of complex ${\theta }_F$ data using both quadratic and linear parametrization to the dispersion.

Figure 4

(a) Real part of Faraday rotation (${\theta }_F$) at high magnetic field, $B\ge 5.5$ T. The gray lines are theoretically predicted values assuming particular filling factors of the surface states. (b) Average value of $\text{Re}\left[{\theta }_F\right]$ over a frequency range spanning from 0.2 to 0.8 THz at 6.5 T at different values of the bias voltage ($V_{\text{bias}}$).