Topological quantization by controlled paths: application to Cooper pairs pumps

Raphaël Leone (1) , Laurent Lévy (1)

1 NEEL - QuantECA - Circuits électroniques quantiques Alpes

When physical systems are tunable by three classical parameters, level degeneracies may occur at isolated points in parameter space. A topological singularity in the phase of the degenerate eigenvectors exists at these points. When a path encloses such point, the accumulated geometrical phase is sensitive to its presence. Furthermore, surfaces in parameter space enclosing such point can be used to characterize the eigenvector singularities through their Chern indices, which are integers. They can be used to quantize a physical quantity of interest. This quantity changes continuously during an adiabatic evolution along a path in parameter space. Quantization requires to turn this path into a surface with a well defined Chern index. We analyze the conditions necessary to a {\em Topological Quantization by Controlled Paths}. It is applied to Cooper pair pumps. For more general problems, a set of four criteria are proposed to check if topological quantization is possible.

Mots clés: Cooper Pair Pump; Chern indices; Quantization

Domaines: Systèmes mésoscopiques et effet Hall quantique [cond-mat.mes-hall]; Supraconductivité [cond-mat.supr-con]; Physique Quantique [quant-ph]

Raphaël Leone, Laurent Lévy. Topological quantization by controlled paths: application to Cooper pairs pumps. Physical Review B: Condensed Matter and Materials Physics (1998-2015), 2008, 77, pp.064524. ⟨10.1103/PhysRevB.77.064524⟩. ⟨hal-00184767⟩