Abstract
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.
Highlights
The thermoelectric signal, an electric response of a material upon applying a temperature gradient, encodes how entropy is transferred into the electronic system
The detail theory based on Random Phase Approximation (RPA) applied to Bi was derived elsewhere [17]
One manifestation of the plasmonphonon resonance is a novel component of the phonon drag – plasmon mediated phonon drag
Summary
The thermoelectric signal, an electric response of a material upon applying a temperature gradient, encodes how entropy is transferred into the electronic system. The finite Fermi surface is due to a small (smaller than 3◦) lattice distortion which turns a cubic lattice into a rhombohedral lattice, space group A7 This implies that the small density of fermions available at lowest energies should be strongly coupled with the lattice distortions. When writing equation (1) we focus on a parabolic part of fermionic dispersion, excluding a non-parabolicity of the bands which enters into the problem for energies above 20 meV This simplification is justified as we work in the lowest temperatures, in a low magnetic field (in Bi magnetic field can in principle cause inter-band transitions) and in the long-wavelength limit where our interest is in a coupling with acoustic phonons (even high energy optical phonons in Bi have energies ≈12 meV). One must keep in mind that the excluded high energy fermions contribute indirectly, for instance through a short-wavelength screening or a finite lattice elasticity
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