Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Rearrangement of Energy Levels Between Energy Super-Bands Characterized by Second Chern Class

Version 1 : Received: 6 November 2021 / Approved: 9 November 2021 / Online: 9 November 2021 (13:36:52 CET)

How to cite: Sadovskii, D.; Zhilinskii, B. Rearrangement of Energy Levels Between Energy Super-Bands Characterized by Second Chern Class. Preprints 2021, 2021110172 (doi: 10.20944/preprints202111.0172.v1). Sadovskii, D.; Zhilinskii, B. Rearrangement of Energy Levels Between Energy Super-Bands Characterized by Second Chern Class. Preprints 2021, 2021110172 (doi: 10.20944/preprints202111.0172.v1).

Abstract

We generalize the dynamical analog of the Berry geometric phase setup to the quaternionic model of Avron et al. In our dynamical quaternionic system, the fast half-integer spin subsystem interacts with a slow two-degrees-of-freedom subsystem. The model is invariant under the 1:1:2 weighted SO(2) symmetry and spin inversion. There is one formal control parameter in addition to four dynamical variables of the slow subsystem. We demonstrate that the most elementary qualitative phenomenon associated with the rearrangement of the energy super-bands of our model consists of the rearrangement of one energy level between two energy superbands which takes place when the formal control parameter takes the special isolated value associated with the conical degeneracy of the semi-quantum eigenvalues. This qualitative phenomenon is of the topological origin, and is characterized by the second Chern class of the associated semi-quantum system. The correspondence between the number of redistributed energy levels and the second Chern number is confirmed through a series of examples.

Keywords

energy bands; Chern number; Kramers degeneracy; semi-quantum approach

Subject

PHYSICAL SCIENCES, Mathematical Physics

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