Modeling of Geometrical Currents at Magneto-dimensional Resonance

Student: Safianov Grigorii

Supervisor: Evgeny Vybornyi

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Mathematical Methods of Modelling and Computer Technologies (Master)

Year of Graduation: 2020

We consider a motion of a spinless charge in a thin layer with parabolic confinement located in a strong homogeneous magnetic field. In case of coincidence of cyclotron and transversal oscillations frequency Hamiltonian becomes 2-D oscillator with degenerate spectrum. We consider a small deformation of a layer shape. Such a deformation causes the appearance of geometric current and Landau levels splitting. We obtain spectrum decomposition and eigenfunctions of Hamiltonian up to second order of small parameter describing layer curvature. Finally, the classical equations for guiding center was constructed.

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