  Microscopic origin of chirality and possible electric-field induced rotation
and rotation-field induced electric polarization are investigated. By building
up a realistic tight-binding model for elemental Te crystal in terms of
symmetry-adopted basis, we identify the microscopic origin of the chirality and
essential couplings among polar and axial vectors with the same time-reversal
properties. Based on this microscopic model, we elucidate quantitatively that
the inter-band process, driven by the nearest-neighbor spin-dependent imaginary
hopping, is the key factor in the electric-field induced rotation and its
inverse response. From the symmetry point of view, these couplings are
characteristic common to any chiral material, leading to a possible
experimental approach to achieve absolute enantioselection by simultaneously
applied electric and rotation fields, or magnetic field and electric current,
and so on, as a conjugate field of the chirality.
