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Fermi surface topology and topological numbers in conductivity of normal metals

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Topological Dynamics in the Physical and Biological Sciences

We consider the geometry of the quasiclassical electron trajectories on complicated Fermi surfaces in the presence of a strong magnetic field. Using rigorous topological theorems we present the classification of different topological types of open electron trajectories on the Fermi surfaces and consider the corresponding conductivity regimes in the limit $B ightarrow infty$. It is shown that the presence of the regular non-closed electron trajectories always leads to the presence of ‘topological numbers’ observable in the conductivity behaviour. On the other hand, the appearance of unstable non-closed electron trajectories may lead to rather interesting behaviour of conductivity, in particular, to the freezing of the longitudinal conductivity in the limit $B ightarrow infty$. The full picture of different regimes of magneto-conductivity behaviour can be considered as an important characteristic of the dispersion relation in metals.

(Joint work with S.P. Novikov).

This talk is part of the Isaac Newton Institute Seminar Series series.

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