The exact factorization part II: Molecular Berry phases and the ab-initio description of phonon-mediated superconductivity
Eberhard K.U. Gross, Fritz Haber Center Institute of Chemistry, Israel
Thursday, October 28, 2021, 11 AM, Los Angeles Seminar Room
Geometric phases are ubiquitous in chemistry and physics. They can arise when the Hamiltonian of a system depends on a set of parameters. A prototypical example is the electronic Hamiltonian of a molecule in Born-Oppenheimer (BO) approximation, which depends parametrically on the nuclear coordinates. In this case, the geometric phase is obtained as the loop integral over a vector potential, the so-called Berry connection, with the loop enclosing a conical intersection of BO surfaces. The equations of motion of the exact factorization also contain a Berry-connection-like vector potential which gives rise to another geometric phase. How does this exact geometric phase relate to the BO one? We shall discuss a case where the exact Berry phase vanishes although there is a non-trivial Berry phase for the same system in BO approximation , while in another example the values of the two phases are similar . In all cases, the BO phase is a topological phase (i.e. it is quantized, with values either 0 or π), while the exact phase is geometric (i.e. non-quantized, with values in the interval [0, π]). As a second topic, the ab-initio description of phonon-mediated superconductivity will be discussed. Highly accurate results for the critical temperature will be presented  and the relation of the superconducting order parameter in real space to chemical bonding will be highlighted . First steps towards a realistic description of the laser-driven real-time dynamics of superconductors will be discussed.
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