Magnetic Field Induced Nonreciprocal Phonons in Noncentrosymmetric System

The thermal Hall effect has become an important probe of topological and chiral phonon transport. When time-reversal symmetry (TRS) is broken by magnetic fields, the acoustic phonon dynamics acquires a dissipationless Hall viscosity term of the Galilean-invariant form in centrosymmetric systems. Here, we explore a new regime in which both inversion and time-reversal symmetries are broken. Using a noncentrosymmetric honeycomb lattice as an example, we show that the phonon effective action gains an additional term with only first-order spatial derivatives, lower in order than the conventional Hall viscosity. This new contribution arises from the loss of Galilean invariance and opens a distinct channel for nonreciprocal phonon transport. This will also influence the phonon thermal transport, revealing a new pathway for controlling phonon flow in topological and magnetic crystals.