Magnetoterahertz Response and Faraday Rotation from Massive Dirac Fermions in the Topological Crystalline Insulator ${\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}\mathrm{Te}$

${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Te}$ has been shown to be an interesting tunable topological crystalline insulator system. We present a magnetoterahertz spectroscopic study of thin films of ${\mathrm{Pb}}_{0.5}{\mathrm{Sn}}_{0.5}\mathrm{Te}$. The complex Faraday rotation angle and optical conductivity in the circular basis are extracted without any additional assumptions. Our quantitative measures of the THz response allow us to show that the sample studied contains two types of bulk carriers. One is $p$ type and originates in 3D Dirac bands. The other is $n$ type and appears to be from more conventional 3D bands. These two types of carriers display different cyclotron resonance dispersions. Through simulating the cyclotron resonance of hole carriers, we can determine the Fermi energy and Fermi velocity. Furthermore, the scattering rates of $p$-type and $n$-type carriers were found to show opposite field dependences, which can be attributed to their different Landau level broadening behaviors under magnetic field. Our work provides a new way to isolate real topological signatures of bulk states in Dirac and Weyl semimetals.

Figure 1

(a) Schematic of experimental setups used to collect data in Faraday geometry. (b) Schematic of 3D massive Dirac bands. (c) Real part of optical conductances of thin films with three different thicknesses at 6 K. (d) The temperature-dependent real part of optical conductivity of a thin film with thickness of 325 nm. (e) Drude model fit of complex optical conductivity at 6 K.

Figure 2

(a) Real part of the magneto-optical conductivity under circular basis at 6 K. Right-hand and left-hand optical conductivity are displayed as positive and negative frequencies, respectively. (b) and (c) Drude fits of real and imaginary parts of optical conductivity under circular basis at 7 T.

Figure 3

(a) and (c) Real and imaginary parts of Faraday rotation angle at 6 K. (b) and (d) Two Drude fits of real and imaginary parts of Faraday rotation angles at 7 T.

Figure 4

(a) Cyclotron resonances of holes and electrons as functions of field. The gray (red) curves show the simulations of the cyclotron resonances between different LLs of holes (electrons). (b) Field dependence of scattering rates of free carriers in the Faraday geometry. The red curve is a $a+b{B}^{2/3}$ model of the field-dependent scattering rates of electrons. Here $a$ and $b$ are positive coefficients. $a$ represents the zero-field impurity scattering strength that is found to be $\sim 1\mathrm{THz}$. The gray curve is added to guide the eye.