Александр Абанов — Квантовый эффект Холла и адиабатический транспорт скачать в хорошем качестве

Александр Абанов — Квантовый эффект Холла и адиабатический транспорт

Quantum Hall Effect is now a part of a vast field of research known as "topological phases of matter." I will start with an elementary introduction to the effect. We will consider the Quantum Hall effect from the point of view of adiabatic transport. First, we will review how the quantization of Hall conductivity can be understood as a consequence of the quantum adiabatic theorem. Then, following the seminal work of TKNN, we will connect the Hall conductance of periodic two-dimensional electronic systems to the first Chern class of the U(1) bundle over the Brillouin zone. We will also consider some generalizations of this construction and examples of other physical systems where the construction leads to non-trivial results. TKNN: D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982) "Quantized Hall Conductance in a Two-Dimensional Periodic Potential"