Fig. 1.

A previously unidentified route to strongly coupling NGBs and quasiparticles—electron–phonon interaction in a uniform magnetic field. A lattice distortion (phonon fluctuation) with $\overrightarrow{\nabla }\cdot \overrightarrow{u}\ne 0$ changes the local flux threading each unit cell (darker blue indicates a larger flux), inducing fluctuations of the phase of the hopping matrix $t_{ij}$. The phonon therefore couples like a gauge field to the fermions, without spatial derivatives.