Even if Weyl semimetals are characterized by quasiparticles with well-defined chirality, exploiting this experimentally is severely hampered by Weyl lattice-fermions coming in pairs with opposite chirality, typically causing the net chirality picked
up by experimental probes to vanish. Here we show this issue can be circumvented in a controlled manner when both time-reversal- and inversion- symmetry are broken. To this end, we investigate chirality-disbalance in the carbide family RMC$_2$ (R a rare-earth and M a transition metal), showing several members to be Weyl semimetals. Using the noncentrosymmetric ferromagnet NdRhC$_2$ as an illustrating example, we show that an odd number of Weyl nodes can be stabilized at its Fermi surface by properly tilting its magnetization. The tilt direction determines the sign of the resulting net chirality, opening up a simple route to control it.
The bulk photovoltaic effect generates intrinsic photocurrents in materials without inversion symmetry. Shift current is one of the bulk photovoltaic phenomena related to the Berry phase of the constituting electronic bands: photo-excited carriers co
herently shift in real space due to the difference in the Berry connection between the valence and conduction bands. Ferroelectric semiconductors and Weyl semimetals are known to exhibit such nonlinear optical phenomena. Here we consider chalcopyrite semiconductor ZnSnP$_2$ which lacks inversion symmetry and calculate the shift current conductivity. We find that the magnitude of the shift current is comparable to the recently measured values on other ferroelectric semiconductors and an order of magnitude larger than bismuth ferrite. The peak response for both optical and shift current conductivity, which mainly comes from P-3$p$ and Sn-5$p$ orbitals, is several eV above the bandgap.
