Evidence for three-dimensional Dirac conical bands in TlBiSSe by optical and magneto-optical spectroscopy

TlBiSSe is a rare realization of a three-dimensional semimetal with a conically dispersing band that has an optical response which is well isolated from other contributions in a broad range of photon energies. We report optical and magneto-optical spectroscopy on this material. When the compound is chemically tuned into a state of the lowest carrier concentration, we find a nearly linear frequency dependence of the optical conductivity below 0.5 eV. Landau level spectroscopy allows us to describe the system with a massive Dirac model, giving a gap $2\mathrm{\Delta }=32$ meV and an in-plane velocity parameter $v_{xy}=4.0\times {10}^5$ m/s.

Figure 1

(a) Hexagonal crystal structure of TlBiSSe. (b)–(d) Reflectance for the samples $S_1, S_2$, and $S_3$ up to 0.8 eV for various temperatures. Insets show the reflectance at 300 K in the full energy range up to 6.5 eV.

Figure 2

Energy dependence of the real part of the optical conductivity ${\sigma }_1\left(\omega \right)$ for samples (a) $S_1$, (b) $S_2$, and (c) $S_3$. The main panels show the low-energy range, while the insets show the full energy range of ${\sigma }_1\left(\omega \right)$ at 300 K on a logarithmic scale. The optical conductivity is obtained from Kramers-Kronig transformation on the reflectance data shown in Fig. 1. (d) Band-structure calculations in a trigonal primitive cell after unfolding the $2\times 2\times 2$ trigonal supercell band structure. The blue color scale represents the amplitude of the supercell eigenstates projection into the primitive cell eigenstates [17]. Dashed lines indicate the approximate positions of the Fermi level for the three samples. (e) Low-energy optical conductivity including a fit of the phonon modes [28].

Figure 3

Color plot of (a) the relative magnetotransmission measured at 4.2 K, $T_B/T_0$, and (b) its derivative $d/dB$ ($T_B/T_0$). (c), (d) Magnetic field dependence of the energy positions and FWHM of the LLs fitted using Gaussian distributions.