Hall viscosity for optical phonons

Abstract

We generalize the notion of dissipationless, topological Hall viscosity tensor to optical phonons in thin film Weyl semimetals. By using the strained Porphyrin thin film Weyl semimetal as a model example, we show how optical phonons can couple to Weyl electrons as chiral pseudo gauge fields. These chiral vector fields lead to a novel dissipationless two-rank viscosity tensor in the effective dynamics of optical phonons whose origin is the chiral anomaly. We also compute the contribution to this two rank Hall viscosity tensor due to the presence of an external magnetic field, whose origin is the conventional Hall response of Weyl electrons. Finally, the phonon dispersion relations of the system at the long-wavelength limit with and without an electromagnetic field are calculated showing a measurable shift in the Raman response of the system. Our results can be investigated by Raman scattering or infrared spectroscopy by attenuated total reflectance experiments.

Phonon helicity induced by electronic Berry curvature in Dirac materials

“…Therefore, a nonzero Σ AB mixes the longitudinal and transverse modes of the in-plane phonons to form elliptical vibrational modes. The longitudinal-transverse mixing has been discussed previously in the context of the phonon Hall viscosity [42][43][44] . However, there is an essential difference: our system does not break TR symmetry while the phonon Hall viscosity breaks TR.…”

Extrinsic phonon thermal Hall transport from Hall viscosity

“…There have been theoretical proposals for the origin of electronic chirality in the pseudogap [10][11][12][13][14][15][16], and de la Torre et al [17] have noted a connection to recent optical second harmonic generation experiment. Given chiral electrons, then the electron-phonon coupling is known to induce non-dissipative phonon Hall viscosity terms in the effective action for the phonons [9,[18][19][20][21][22][23]. For the square lattice case relevant to the cuprates, the phonon Hall viscosity induced by a model of chiral spinons [12] is described in a separate paper [24].…”

Lattice dynamics with molecular Berry curvature: chiral optical phonons

“…In a periodic lattice, the molecular Berry curvature associated with this phase can influence directly the lattice dynamics and therefore the property of phonons 6,7 . In the long-wavelength limit, this Berry curvature manifests as a Hall viscosity [8][9][10] that can modify the dispersion, polarization, and the transport properties of the longwavelength phonons 6,7 . By considering a finite overlap between electronic wavefunctions on neighboring sites, a recent work studied the molecular Berry curvature induced by a magnetic field B in a nonmagnetic insulator in the linear order of B 11 .…”