Phonon and Electron Statistics in Metals

L. F. Novikov

Pinaki Sengupta, Anders W. Sandvik, David K Campbell

Giovanni Gallavotti, J. Ginibre, G. Velo

Hiroshi Ichimura

The problem of the interaction between conduction electrons and the thermal vibration of the lattice ions in the metal is treated by a statistical mechanical method. We adopt the free electron and the phonon models as usual, using the Bloch-Bethe type interaction Hamiltonian. By the method of expanding the grand partition function in powers of the interaction parameter, we get a formula for the free energy of the system of conduction electrons in the presence of the interaction. A technique analogous to the renormalization method in the quantum mechanics is utilized in the calculation.

Mattia Moroder, Matteo Mitrano, Ulrich Schollwöck +2 more

We introduce phonon state tomography (PST) as a diagnostic probe of electron dynamics in solids whose phonons are optically excited by a laser pulse at initial time. Using a projected-purified matrix-product states algorithm, PST decomposes the exact correlated electron-phonon wavefunction into contributions from purely electronic states corresponding to statistically typical configurations of the optically accessible phononic response, enabling a "tomographic" reconstruction of the electronic dynamics generated by the phonons. Thus, PST may be used to diagnose electronic behavior in experiments that access only the phonon response, such as thermal diffuse X-ray and electron scattering. We study the dynamics of a metal whose infrared phonons are excited by an optical pulse at initial time and use it to simulate the sample-averaged momentum-resolved phonon occupancy and accurately reconstruct the electronic correlations. We also use PST to analyze the influence of different pulse shapes on the light-induced enhancement and suppression of electronic correlations.

Michele Fabrizio, Claudio Castellani, C. Di Castro

We consider a one-dimensional system of electrons interacting via a short-range repulsion and coupled to phonons close to the metal-insulator transition at half-filling. We argue that the metal-insulator transition can be described as a standard one-dimensional incommensurate to commensurate transition, even if the electronic system is coupled to the lattice distortion. By making use of known results for this transition, we prove that low-momentum phonons, with the inclusion of the 4kF (≃2π near half-filling) scattering, do not play any relevant role close to the metal-insulator transition, unless their coupling to the electrons is large in comparison with the other energy scales present in the problem. In other words the effective strength of the low-momentum transferred electron-phonon coupling does not increase close to the metal-insulator transition, even though the effective velocity of the mobile carriers is strongly diminished.