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Effective electron coupling to phonon mechanical angular momentum in helical systems

Akihito Kato, Nobuhiko Yokoshi, Jun-ichiro Kishine

Abstract

In chiral crystals, two types of phonon angular momenta have been introduced. One is crystal angular momentum (CAM) arising from the rotational or screw-rotational symmetry and the other is mechanical angular momentum (MAM) associated with the circular motion of atomic displacements about equilibrium positions. Recently, the electron--phonon coupling that respects the screw-rotational symmetry is derived, whereby the CAM between electrons and phonons is interconverted. Here, we show that, in addition to CAM, MAM can also be converted to the electronic degrees of freedom by deriving a second-order perturbative Hamiltonian proportional to phonon MAM. This finding highlights that the electronic motion is directly affected by phonon MAM, and consequently, that phonon degrees of freedom can play a crucial role in phenomena related to electronic orbital and spin polarizations.

Effective electron coupling to phonon mechanical angular momentum in helical systems

Abstract

In chiral crystals, two types of phonon angular momenta have been introduced. One is crystal angular momentum (CAM) arising from the rotational or screw-rotational symmetry and the other is mechanical angular momentum (MAM) associated with the circular motion of atomic displacements about equilibrium positions. Recently, the electron--phonon coupling that respects the screw-rotational symmetry is derived, whereby the CAM between electrons and phonons is interconverted. Here, we show that, in addition to CAM, MAM can also be converted to the electronic degrees of freedom by deriving a second-order perturbative Hamiltonian proportional to phonon MAM. This finding highlights that the electronic motion is directly affected by phonon MAM, and consequently, that phonon degrees of freedom can play a crucial role in phenomena related to electronic orbital and spin polarizations.

Paper Structure

This paper contains 13 sections, 43 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Model
  3. Schrieffer--Wolff Transformation
  4. Emergence of phonon MAM in electron--phonon coupling
  5. Resonant cases
  6. Effect on electronic orbital angular momentum
  7. Concluding Remarks
  8. Microscopic Description of the Model
  9. Electronic Hamiltonian
  10. Electron--Phonon coupling Hamiltonian
  11. Mechanical Angular Momentum of Phonons
  12. Orbital Angular Momentum of Bloch Electrons
  13. Electronic Band Dispersions

Figures (1)

  • Figure 1: Electronic energy bands (a) without and (b) with the electron--phonon interaction, respectively. Other parameters are set to $\hbar^2\zeta^2/M = \qty{3.0d-6}{\eV}$ and $T = \qty{0}{\kelvin}$.