Doubling theorem and boundary states of five-dimensional Weyl semimetal
Abstract
We study the generic band structures of the five-dimensional (5D) Weyl semimetal, in which the band degeneracies are 2D Weyl surfaces in the momentum space, and may have nontrivial linkings with each other if they carry nonzero second Chern numbers. We prove a number of theorems constraining the topological linking configurations of the Weyl surfaces, which can be viewed as a 5D generalization of the celebrated doubling theorem for 3D Weyl semimetal. As a direct physical consequence of these constraints, the 5D Weyl semimetal hosts a rich structure of topological boundary states. We show that on the 4D boundary of the 5D Weyl semimetal, there are 3D chiral Fermi hypersurfaces protected by bulk Weyl surfaces. On top of that, for bulk Weyl surfaces that are linked and carry nonzero second Chern numbers, the associated boundary 3D Fermi hypersurfaces will shrink to singularities at certain energies, which trace out a protected 1D Weyl nodal arc, in analogy to the Fermi arc on the 3D Weyl semimetal surface.
- Authors:
-
[1];
- Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics
- Princeton Univ., NJ (United States). Princeton Center for Theoretical Science
- Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics, and Stanford Center for Topological Quantum Physics
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1560630
- Alternate Identifier(s):
- OSTI ID: 1557345
- Grant/Contract Number:
- GBMF4302; AC02-76SF00515
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 7; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Chen, Jing-Yuan, Lian, Biao, and Zhang, Shou-Cheng. Doubling theorem and boundary states of five-dimensional Weyl semimetal. United States: N. p., 2019.
Web. doi:10.1103/physrevb.100.075112.
Chen, Jing-Yuan, Lian, Biao, & Zhang, Shou-Cheng. Doubling theorem and boundary states of five-dimensional Weyl semimetal. United States. https://doi.org/10.1103/physrevb.100.075112
Chen, Jing-Yuan, Lian, Biao, and Zhang, Shou-Cheng. Tue .
"Doubling theorem and boundary states of five-dimensional Weyl semimetal". United States. https://doi.org/10.1103/physrevb.100.075112. https://www.osti.gov/servlets/purl/1560630.
@article{osti_1560630,
title = {Doubling theorem and boundary states of five-dimensional Weyl semimetal},
author = {Chen, Jing-Yuan and Lian, Biao and Zhang, Shou-Cheng},
abstractNote = {We study the generic band structures of the five-dimensional (5D) Weyl semimetal, in which the band degeneracies are 2D Weyl surfaces in the momentum space, and may have nontrivial linkings with each other if they carry nonzero second Chern numbers. We prove a number of theorems constraining the topological linking configurations of the Weyl surfaces, which can be viewed as a 5D generalization of the celebrated doubling theorem for 3D Weyl semimetal. As a direct physical consequence of these constraints, the 5D Weyl semimetal hosts a rich structure of topological boundary states. We show that on the 4D boundary of the 5D Weyl semimetal, there are 3D chiral Fermi hypersurfaces protected by bulk Weyl surfaces. On top of that, for bulk Weyl surfaces that are linked and carry nonzero second Chern numbers, the associated boundary 3D Fermi hypersurfaces will shrink to singularities at certain energies, which trace out a protected 1D Weyl nodal arc, in analogy to the Fermi arc on the 3D Weyl semimetal surface.},
doi = {10.1103/physrevb.100.075112},
journal = {Physical Review B},
number = 7,
volume = 100,
place = {United States},
year = {Tue Aug 06 00:00:00 EDT 2019},
month = {Tue Aug 06 00:00:00 EDT 2019}
}
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Figures / Tables:
FIG. 1: Illustration of the computation relating the second Chern number to the linking number. The green loop represents the 2D WS component $W^{i}_{n+1/2}$, bounding the yellow region which represents the 3D $Σ^{i}_{n+1/2}$. The blue loop represents the 2D WS component $W^{j}_{n+1/2}$. The grey torus represents the 4D “narrow tube”more » , whose “inside” V contains the green loop. The linking number is witnessed by the black dot, the intersection point of $Σ^{i}_{n+1/2}$ and $W^{j}_{n+1/2}$.
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