TY - JOUR

T1 - Polarization transport of transverse acoustic waves

T2 - Berry phase and spin Hall effect of phonons

AU - Bliokh, K. Yu

AU - Freilikher, V. D.

PY - 2006

Y1 - 2006

N2 - We carry out a detailed analysis of the short-wave (semiclassical) approximation for the linear equations of the elasticity in a smoothly inhomogeneous isotropic medium. It is shown that the polarization properties of the transverse waves are completely analogous to those of electromagnetic waves and can be considered as spin properties of optical phonons. In particular, the Hamiltonian of the transverse waves contains an additional term of the phonon spin-orbit interaction arising from the Berry gauge potential in the momentum space. This potential is diagonal in the basis of the circularly polarized waves and corresponds to the field of two "magnetic monopoles" of opposite signs for phonons of opposite helicities. This leads to the appearance of the Berry phase in the equation for the polarization evolution and an additional "anomalous velocity" term in the ray equations. The anomalous velocity has the form of the "Lorentz force" caused by the Berry gauge field in momentum space and gives rise to the transverse transport of waves of opposite helicities in opposite directions. This is a manifestation of the spin Hall effect of optical phonons. The effect directly relates to the conservation of total angular momentum of phonons and also influences reflection from a sharp boundary (acoustic analog of the transverse Ferdorov-Imbert shift).

AB - We carry out a detailed analysis of the short-wave (semiclassical) approximation for the linear equations of the elasticity in a smoothly inhomogeneous isotropic medium. It is shown that the polarization properties of the transverse waves are completely analogous to those of electromagnetic waves and can be considered as spin properties of optical phonons. In particular, the Hamiltonian of the transverse waves contains an additional term of the phonon spin-orbit interaction arising from the Berry gauge potential in the momentum space. This potential is diagonal in the basis of the circularly polarized waves and corresponds to the field of two "magnetic monopoles" of opposite signs for phonons of opposite helicities. This leads to the appearance of the Berry phase in the equation for the polarization evolution and an additional "anomalous velocity" term in the ray equations. The anomalous velocity has the form of the "Lorentz force" caused by the Berry gauge field in momentum space and gives rise to the transverse transport of waves of opposite helicities in opposite directions. This is a manifestation of the spin Hall effect of optical phonons. The effect directly relates to the conservation of total angular momentum of phonons and also influences reflection from a sharp boundary (acoustic analog of the transverse Ferdorov-Imbert shift).

UR - http://www.scopus.com/inward/record.url?scp=33751244247&partnerID=8YFLogxK

U2 - 10.1103/physrevb.74.174302

DO - 10.1103/physrevb.74.174302

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AN - SCOPUS:33751244247

SN - 1098-0121

VL - 74

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 17

M1 - 174302

ER -