Resonant plasmon-phonon coupling and its role in magneto-thermoelectricity in bismuth

Using diagrammatic methods we derive an effective interaction between a low energy collective movement of fermionic liquid (acoustic plasmon) and acoustic phonon. We show that the coupling between the plasmon and the lattice has a very non-trivial, resonant structure. When real and imaginary parts of the acoustic plasmon's velocity are of the same order as the phonon's velocity, the resonance qualitatively changes the nature of phonon-drag. In the following we study how magneto-thermoelectric properties are affected. Our result suggests that the novel mechanism of energy transfer between electron liquid and crystal lattice can be behind the huge Nernst effect in bismuth.