Conversion Rules for Weyl Points and Nodal Lines in Topological Media
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 twoband 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 nodalline and nodalchain semimetals that exhibit both Fermiarc 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 tightbinding models. Finally, the outlined homotopy description can be directly generalized to systems with multiple bands and other choices of symmetry.
 Authors:

^{[1]};
^{[1]};
^{[1]}
 Stanford Univ., CA (United States). Department of Physics, McCullough Building and Stanford Center for Topological Quantum Physics
 Publication Date:
 Grant/Contract Number:
 AC0276SF00515; GBMF4302
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review Letters
 Additional Journal Information:
 Journal Volume: 121; Journal Issue: 10; Journal ID: ISSN 00319007
 Publisher:
 American Physical Society (APS)
 Research Org:
 SLAC National Accelerator Lab., Menlo Park, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
 OSTI Identifier:
 1475416
Sun, XiaoQi, Zhang, ShouCheng, and Bzdušek, Tomáš. Conversion Rules for Weyl Points and Nodal Lines in Topological Media. United States: N. p.,
Web. doi:10.1103/physrevlett.121.106402.
Sun, XiaoQi, Zhang, ShouCheng, & Bzdušek, Tomáš. Conversion Rules for Weyl Points and Nodal Lines in Topological Media. United States. doi:10.1103/physrevlett.121.106402.
Sun, XiaoQi, Zhang, ShouCheng, and Bzdušek, Tomáš. 2018.
"Conversion Rules for Weyl Points and Nodal Lines in Topological Media". United States.
doi:10.1103/physrevlett.121.106402.
@article{osti_1475416,
title = {Conversion Rules for Weyl Points and Nodal Lines in Topological Media},
author = {Sun, XiaoQi and Zhang, ShouCheng 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 twoband 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 nodalline and nodalchain semimetals that exhibit both Fermiarc 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 tightbinding 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 = {2018},
month = {9}
}
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