Berry curvature dipole induced chiral terahertz gain and lasing threshold in bulk tellurium

We investigate the use of Berry curvature dipole in $n$-doped Tellurium as a mechanism for achieving terahertz amplification and lasing by applying a DC electric field. When the electrical bias and wave vector are aligned along the trigonal $c$-axis, the right-handed circularly polarized mode experiences amplification at relatively low bias, while the left-handed mode is attenuated. Furthermore, when the electrical bias and wave vector are orthogonal to the $c$-axis, the structure supports elliptically polarized eigenmodes that also exhibit gain under suitable bias conditions, where the degree of ellipticity is tunable by the applied bias. We also investigate lasing conditions for a Fabry-Perot cavity incorporating biased Te as an active medium. Due to the resonance in the dielectric permittivity of Tellurium, there are discrete lasing intervals. Our results show that bulk chiral Tellurium could be used as an electrically tunable, polarization-selective gain medium for micrometer-scale terahertz lasers, with lasing achievable at bias fields below the material's breakdown threshold, paving the way towards new terahertz devices.