Accidental degeneracy in k-space, geometrical phase, and the perturbation of $$\pi$$ by spin-orbit interactions
Abstract
Since closed lines of accidental electronic degeneracies were demonstrated to be possible, even frequent, by Herring in 1937, no further developments arose for eight decades. The earliest report of such a nodal loop in a real material – aluminum – is recounted and elaborated on. Nodal loop semimetals have become a focus of recent activity, with emphasis on other issues. Band degeneracies are, after all, the origin of topological phases in crystalline materials. Spin-orbit interaction lifts accidental band degeneracies, with the resulting spectrum being provided here. The geometric phase γ(C) = ±π for circuits C surrounding a line of such degeneracy cannot survive completely unchanged. We report the change depends on how the spin is fixed during adiabatic evolution. For spin fixed along the internal spin-orbit field, γ(C) decreases to zero as the circuit collapses around the line of lifted degeneracy. For spin fixed along a perpendicular axis, the conical intersection persists and γ(C) = ±π is unchanged.
- Authors:
-
- Stony Brook University, NY (United States)
- University of California, Davis, CA (United States)
- Publication Date:
- Research Org.:
- Univ. of California, Davis, CA (United States); State Univ. of New York (SUNY), Albany, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC); National Science Foundation (NSF)
- OSTI Identifier:
- 1538716
- Alternate Identifier(s):
- OSTI ID: 1548657
- Grant/Contract Number:
- FG02-04ER46111; FG02-08ER46550; NIRT-0304122
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physica. C, Superconductivity
- Additional Journal Information:
- Journal Volume: 549; Journal Issue: C; Journal ID: ISSN 0921-4534
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Allen, Philip B., and Pickett, Warren E. Accidental degeneracy in k-space, geometrical phase, and the perturbation of $\pi$ by spin-orbit interactions. United States: N. p., 2018.
Web. doi:10.1016/j.physc.2018.02.024.
Allen, Philip B., & Pickett, Warren E. Accidental degeneracy in k-space, geometrical phase, and the perturbation of $\pi$ by spin-orbit interactions. United States. https://doi.org/10.1016/j.physc.2018.02.024
Allen, Philip B., and Pickett, Warren E. Thu .
"Accidental degeneracy in k-space, geometrical phase, and the perturbation of $\pi$ by spin-orbit interactions". United States. https://doi.org/10.1016/j.physc.2018.02.024. https://www.osti.gov/servlets/purl/1538716.
@article{osti_1538716,
title = {Accidental degeneracy in k-space, geometrical phase, and the perturbation of $\pi$ by spin-orbit interactions},
author = {Allen, Philip B. and Pickett, Warren E.},
abstractNote = {Since closed lines of accidental electronic degeneracies were demonstrated to be possible, even frequent, by Herring in 1937, no further developments arose for eight decades. The earliest report of such a nodal loop in a real material – aluminum – is recounted and elaborated on. Nodal loop semimetals have become a focus of recent activity, with emphasis on other issues. Band degeneracies are, after all, the origin of topological phases in crystalline materials. Spin-orbit interaction lifts accidental band degeneracies, with the resulting spectrum being provided here. The geometric phase γ(C) = ±π for circuits C surrounding a line of such degeneracy cannot survive completely unchanged. We report the change depends on how the spin is fixed during adiabatic evolution. For spin fixed along the internal spin-orbit field, γ(C) decreases to zero as the circuit collapses around the line of lifted degeneracy. For spin fixed along a perpendicular axis, the conical intersection persists and γ(C) = ±π is unchanged.},
doi = {10.1016/j.physc.2018.02.024},
journal = {Physica. C, Superconductivity},
number = C,
volume = 549,
place = {United States},
year = {Thu Mar 01 00:00:00 EST 2018},
month = {Thu Mar 01 00:00:00 EST 2018}
}
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