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Current Operator and Particle Pumping

  • János K. Asbóth
  • László Oroszlány
  • András Pályi
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 919)

Abstract

In the previous chapter, we described quantized adiabatic pumping of particles in a one-dimensional lattice in an intuitive and visual fashion, using the concepts of the control-freak pumping cycle and the time evolution of the Wannier centers. Here, we provide a more formal description of the same effect. Based on Ehrenfest’s theorem, we identify the current operator describing the flow of probability density through a cross section of the one-dimensional lattice, and find that the momentum- and time-resolved current in a given filled band of the lattice is proportional to the Berry curvature associated to that band. Naturally, this leads to the same conclusion as we have seen before: that the number of particles adiabatically pumped through a cross section of the crystal is given by the Chern number of the corresponding filled band, and therefore it is an integer.

Keywords

Current Operator Berry Phase Adiabatic Limit Chern Number Arbitrary Cross Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • János K. Asbóth
    • 1
  • László Oroszlány
    • 2
  • András Pályi
    • 3
    • 4
  1. 1.Wigner Research Centre for PhysicsHungarian Academy of SciencesBudapestHungary
  2. 2.Department of Physics of Complex SystemsEötvös Loránd UniversityBudapestHungary
  3. 3.Department of Materials PhysicsEötvös Loránd UniversityBudapestHungary
  4. 4.Department of PhysicsBudapest University of Technology and EconomicsBudapestHungary

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