Topological frequency conversion in Weyl semimetals

Abstract

FIG. 2. (a): Energy bands of the linearized Hamiltonian in Eq. (1) in the plane ky = 0, with ε0 = 0, Rij = δij3.87 • 10 5 m/s, and v = (0, 0, 3.1 • 10 5 m/s). The red line shows an example of the Fermi surface (with Fermi energy −115 meV) when projected into the same plane. (b): Trajectory of eA(t)/ resulting from two modes with circular polarization in the xz and yz planes with amplitudes E1 = 0.74 MV/m, E2 = 1 MV/m and frequencies, f2 = 1, THz, f1 = √ 5−1 2 f2 (blue). Also shown is the surface B0 (gray). See main text for further details. (c): Cross-section of B0 for the same parameters as in (b). Within the red and blue sub-surfaces W (k) takes value 1 and −1, respectively, while W (k) = 0 outside the surface. (d): Trajectory of eA(t)/ for the same values of E2 and f2 as in (b), and with E1 = 0.72 MV/m, f1 = 2 3 f2 (resulting in a commenusrate frequency ratio). The different value of E1 is chosen to ensure that the vector potential of mode 1 has the same amplitude in panels (b) and (d), such that the topological phase boundary B0 is the same for panels (b-d).