Conversion Rules for Weyl Points and Nodal Lines in Topological Media
Abstract
According to a widely held paradigm, a pair of Weyl points with opposite chirality mutually annihilate when brought together. In contrast, we show that such a process is strictly forbidden for Weyl points related by a mirror symmetry, provided that an effective two-band description exists in terms of orbitals with opposite mirror eigenvalue. Instead, such a pair of Weyl points convert into a nodal loop inside a symmetric plane upon the collision. Similar constraints are identified for systems with multiple mirrors, facilitating previously unreported nodal-line and nodal-chain semimetals that exhibit both Fermi-arc and drumhead surface states. Additionally, we further find that Weyl points in systems symmetric under a π rotation composed with time reversal are characterized by an additional integer charge that we call helicity. A pair of Weyl points with opposite chirality can annihilate only if their helicities also cancel out. We base our predictions on topological crystalline invariants derived from relative homotopy theory, and we test our predictions on simple tight-binding models. Finally, the outlined homotopy description can be directly generalized to systems with multiple bands and other choices of symmetry.
- Authors:
-
- Stanford Univ., CA (United States). Department of Physics, McCullough Building and Stanford Center for Topological Quantum Physics
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1475416
- Alternate Identifier(s):
- OSTI ID: 1468838
- Grant/Contract Number:
- AC02-76SF00515; GBMF4302
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 121; Journal Issue: 10; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Sun, Xiao-Qi, Zhang, Shou-Cheng, and Bzdušek, Tomáš. Conversion Rules for Weyl Points and Nodal Lines in Topological Media. United States: N. p., 2018.
Web. doi:10.1103/physrevlett.121.106402.
Sun, Xiao-Qi, Zhang, Shou-Cheng, & Bzdušek, Tomáš. Conversion Rules for Weyl Points and Nodal Lines in Topological Media. United States. https://doi.org/10.1103/physrevlett.121.106402
Sun, Xiao-Qi, Zhang, Shou-Cheng, and Bzdušek, Tomáš. Wed .
"Conversion Rules for Weyl Points and Nodal Lines in Topological Media". United States. https://doi.org/10.1103/physrevlett.121.106402. https://www.osti.gov/servlets/purl/1475416.
@article{osti_1475416,
title = {Conversion Rules for Weyl Points and Nodal Lines in Topological Media},
author = {Sun, Xiao-Qi and Zhang, Shou-Cheng and Bzdušek, Tomáš},
abstractNote = {According to a widely held paradigm, a pair of Weyl points with opposite chirality mutually annihilate when brought together. In contrast, we show that such a process is strictly forbidden for Weyl points related by a mirror symmetry, provided that an effective two-band description exists in terms of orbitals with opposite mirror eigenvalue. Instead, such a pair of Weyl points convert into a nodal loop inside a symmetric plane upon the collision. Similar constraints are identified for systems with multiple mirrors, facilitating previously unreported nodal-line and nodal-chain semimetals that exhibit both Fermi-arc and drumhead surface states. Additionally, we further find that Weyl points in systems symmetric under a π rotation composed with time reversal are characterized by an additional integer charge that we call helicity. A pair of Weyl points with opposite chirality can annihilate only if their helicities also cancel out. We base our predictions on topological crystalline invariants derived from relative homotopy theory, and we test our predictions on simple tight-binding models. Finally, the outlined homotopy description can be directly generalized to systems with multiple bands and other choices of symmetry.},
doi = {10.1103/physrevlett.121.106402},
journal = {Physical Review Letters},
number = 10,
volume = 121,
place = {United States},
year = {Wed Sep 05 00:00:00 EDT 2018},
month = {Wed Sep 05 00:00:00 EDT 2018}
}
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