Ambipolar magneto-optical response of ultralow carrier density topological insulators

We have investigated the THz range magneto-optical response of ultralow carrier density films of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ using time-domain THz polarimetry. Undoped ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ has a chemical potential that lies inside the bulk valence band. Thus, its topological response is masked by bulk carriers. However, with appropriate buffer-layer engineering and chemical doping, ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ thin films can be grown with extremely low electron or hole densities. The ultralow carrier density samples show unusual optical properties and quantized response in the presence of magnetic fields. Consistent with the expectations for Dirac fermions, a quantized Hall response is seen even in samples where the zero field conductivity falls below detectable levels. The discontinuity in the Faraday angle with small changes in the filling fraction across zero is a manifestation of the parity anomaly in 2D Dirac systems with broken time reversal symmetry (TRS).

Figure 1

(a) Schematic diagram of the band structure of ${\mathrm{Sb}}_2{\mathrm{Te}}_3$ showing the Fermi level of the samples (not to scale). (b) The real part of the optical conductivity of the undoped and Ti-doped samples.

Figure 2

Real and imaginary parts of optical conductance of the undoped sample at 5 K in the left (a), (b) and right (c), (d) circular basis, respectively. (e)–(f) Real and imaginary parts of Faraday rotation.

Figure 3

Real [imaginary] parts of the Faraday rotation for different magnetic fields for four different samples with hole (a), (b) [(e), (f)] and electronic (c), (d) [(g), (h)] charge carriers. Grey solid lines represent the expected quantized Faraday angle for filling factors $n=0,1$ for both hole and electronic carriers.

Figure 4

(a) Real part of the average Faraday rotation as a function of magnetic field for the Ti-doped samples. (b) Average Faraday angle as a function of inverse magnetic field. Black dashed line is a guide to eye for the expected evolution. Black solid line marks the discontinuous jump unique to Dirac electrons.