Rotation and electric-field responses and absolute enantioselection in chiral crystals

Abstract

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.

On the definition of chirality and enantioselective fields

“…The typical example of the elemental Tellurium is found in ref. [16]. It is notable that 𝐺𝐺 0 term in chiral Tellurium is quite large with respect to other terms in the Hamiltonian.…”

“…In general, 𝐺𝐺 0 can be decomposed into 𝑸𝑸 𝑎𝑎 • (𝑸𝑸 𝑏𝑏 × 𝑸𝑸 𝑐𝑐 ), 𝑸𝑸 • (𝑴𝑴 𝑎𝑎 × 𝑴𝑴 𝑏𝑏 ), and so on where 𝑸𝑸 𝑎𝑎,𝑏𝑏,𝑐𝑐 and 𝑴𝑴 𝑎𝑎,𝑏𝑏 are the electric and magnetic dipoles, respectively. It is interesting to see, in a physical point of view, that such a structure indeed appears both in the Hamiltonian of Tellurium as a latticespin coupling, 𝑹𝑹 • (𝒍𝒍 × 𝝈𝝈) [16], and in the parity-violation term due to weak interaction of elementary particles (see next section), which is a source of chiral response.…”

On the definition of chirality and enantioselective fields

“…A typical example of the elemental Tellurium is found in ref. [16]. It is notable that 𝐺𝐺 0 term in chiral Tellurium is quite large with respect to other terms in the Hamiltonian.…”

“…In general, 𝐺𝐺 0 can be decomposed into 𝑸𝑸 𝑎𝑎 • (𝑸𝑸 𝑏𝑏 × 𝑸𝑸 𝑐𝑐 ), 𝑸𝑸 • (𝑴𝑴 𝑎𝑎 × 𝑴𝑴 𝑏𝑏 ), and so on where 𝑸𝑸 𝑎𝑎,𝑏𝑏,𝑐𝑐 and 𝑴𝑴 𝑎𝑎,𝑏𝑏 are the electric and magnetic dipoles, respectively. It is interesting to see, in a physical point of view, that such a structure indeed appears both in the Hamiltonian of Tellurium as a latticespin coupling, 𝑹𝑹 • (𝒍𝒍 × 𝝈𝝈) [16], and in the parity-violation term due to weak interaction of elementary particles (see next section), which is a source of chiral response.…”