- Letter
- Open Access
Chirality flip of Weyl nodes and its manifestation in strained
Phys. Rev. Research 3, L042017 – Published 5 November, 2021
DOI: https://doi.org/10.1103/PhysRevResearch.3.L042017
Abstract
Due to their topological charge, or chirality, the Weyl cones present in topological semimetals are considered robust against arbitrary perturbations. One well-understood exception to this robustness is the pairwise creation or annihilation of Weyl cones, which involves the overlap in energy and momentum of two oppositely charged nodes. Here we show that the topological charge can in fact change sign, in a process that involves the merging of not two, but three Weyl nodes. This is facilitated by the presence of rotation and time-reversal symmetries, which constrain the relative positions of Weyl cones in momentum space. We analyze the chirality flip process, showing that transport properties distinguish it from the conventional, double Weyl merging. Moreover, we predict that the chirality flip occurs in , where experimentally accessible strain leads to the merging of three Weyl cones close to the Fermi level. Our work sets the stage to further investigate and observe such chirality flipping processes in different topological materials.
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References (62)
- H. B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice. (I). Proof by homotopy theory, Nucl. Phys. B 185, 20 (1981).
- S. Murakami, Phase transition between the quantum spin Hall and insulator phases in 3D: Emergence of a topological gapless phase, New J. Phys. 9, 356 (2007).
- X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83, 205101 (2011).
- A. A. Burkov and L. Balents, Weyl Semimetal in a Topological Insulator Multilayer, Phys. Rev. Lett. 107, 127205 (2011).
- A. A. Burkov, M. D. Hook, and L. Balents, Topological nodal semimetals, Phys. Rev. B 84, 235126 (2011).
- C. K. Chiu, J. C. Y. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88, 035005 (2016).
- B. Yan and C. Felser, Topological materials: Weyl semimetals, Annu. Rev. Condens. Matter Phys. 8, 337 (2017).
- N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90, 015001 (2018).
- B. A. Bernevig, H. Weng, Z. Fang, and X. Dai, Recent progress in the study of topological semimetals, J. Phys. Soc. Jpn. 87, 041001 (2018).
- H. Weyl, Elektron und gravitation. I, Z. Phys. 56, 330 (1929).
- A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, Type-II Weyl semimetals, Nature (London) 527, 495 (2015).
- S. M. Young, S. Zaheer, J. C. Y. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, Dirac Semimetal in Three Dimensions, Phys. Rev. Lett. 108, 140405 (2012).
- Z. Wang, Y. Sun, X. Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Dirac semimetal and topological phase transitions in (, K, Rb), Phys. Rev. B 85, 195320 (2012).
- B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals, Science 353, aaf5037 (2016).
- L. Lepori, I. C. Fulga, A. Trombettoni, and M. Burrello, PT-invariant Weyl semimetals in gauge-symmetric systems, Phys. Rev. B 94, 085107 (2016).
- L. Lepori, I. C. Fulga, A. Trombettoni, and M. Burrello, Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials, Phys. Rev. A 94, 053633 (2016).
- I. C. Fulga and A. Stern, Triple point fermions in a minimal symmorphic model, Phys. Rev. B 95, 241116(R) (2017).
- C. Fang, H. Weng, X. Dai, and Z. Fang, Topological nodal line semimetals, Chin. Phys. B 25, 117106 (2016).
- E. J. Sie, C. M. Nyby, C. D. Pemmaraju, S. J. Park, X. Shen, J. Yang, M. C. Hoffmann, B. K. Ofori-Okai, R. Li, A. H. Reid, S. Weathersby, E. Mannebach, N. Finney, D. Rhodes, D. Chenet, A. Antony, L. Balicas, J. Hone, T. P. Devereaux, T. F. Heinz et al., An ultrafast symmetry switch in a Weyl semimetal, Nature (London) 565, 61 (2019).
- J. Liu and D. Vanderbilt, Weyl semimetals from noncentrosymmetric topological insulators, Phys. Rev. B 90, 155316 (2014).
- R.-J. Slager, V. Juričić, V. Lahtinen, and J. Zaanen, Self-organized pseudo-graphene on grain boundaries in topological band insulators, Phys. Rev. B 93, 245406 (2016).
- J. I. Facio, D. Efremov, K. Koepernik, J.-S. You, I. Sodemann, and J. van den Brink, Strongly Enhanced Berry Dipole at Topological Phase Transitions in BiTeI, Phys. Rev. Lett. 121, 246403 (2018).
- C. L. Zhang, S. Y. Xu, C. M. Wang, Z. Lin, Z. Z. Du, C. Guo, C. C. Lee, H. Lu, Y. Feng, S. M. Huang, G. Chang, C. H. Hsu, H. Liu, H. Lin, L. Li, C. Zhang, J. Zhang, X. C. Xie, T. Neupert, M. Z. Hasan et al., Magnetic-tunnelling-induced Weyl node annihilation in TaP, Nat. Phys. 13, 979 (2017).
- J. Cano, B. Bradlyn, Z. Wang, M. Hirschberger, N. P. Ong, and B. A. Bernevig, Chiral anomaly factory: Creating Weyl fermions with a magnetic field, Phys. Rev. B 95, 161306(R) (2017).
- M. P. Ghimire, J. I. Facio, J.-S. You, L. Ye, J. G. Checkelsky, S. Fang, E. Kaxiras, M. Richter, and J. van den Brink, Creating Weyl nodes and controlling their energy by magnetization rotation, Phys. Rev. Research 1, 032044(R) (2019).
- R. Ray, B. Sadhukhan, M. Richter, J. I. Facio, and J. van den Brink, Tunable chirality of noncentrosymmetric magnetic Weyl semimetals, arXiv:2006.10602.
- R.-J. Slager, V. Juričić, and B. Roy, Dissolution of topological Fermi arcs in a dirty Weyl semimetal, Phys. Rev. B 96, 201401(R) (2017).
- B. Roy, R.-J. Slager, and V. Juričić, Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality, Phys. Rev. X 8, 031076 (2018).
- J. H. Pixley, D. A. Huse, and S. Das Sarma, Rare-Region-Induced Avoided Quantum Criticality in Disordered Three-Dimensional Dirac and Weyl Semimetals, Phys. Rev. X 6, 021042 (2016).
- J. H. Pixley and J. H. Wilson, Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors, Ann. Phys. (NY) 168455 (2021), doi: 10.1016/j.aop.2021.168455.
- S. Singh, J. Kim, K. M. Rabe, and D. Vanderbilt, Engineering Weyl Phases and Nonlinear Hall Effects in , Phys. Rev. Lett. 125, 046402 (2020).
- P. H. Fu, H. J. Duan, R. Q. Wang, and H. Chen, Phase transitions in three-dimensional Dirac semimetal induced by off-resonant circularly polarized light, Phys. Lett. A 381, 3499 (2017).
- P. H. Fu, J. Wang, J. F. Liu, and R. Q. Wang, Josephson signatures of Weyl node creation and annihilation in irradiated Dirac semimetals, Phys. Rev. B 100, 115414 (2019).
- C. Fang, M. J. Gilbert, X. Dai, and B. A. Bernevig, Multi-Weyl Topological Semimetals Stabilized by Point Group Symmetry, Phys. Rev. Lett. 108, 266802 (2012).
- I. C. Fulga, L. Fallani, and M. Burrello, Geometrically protected triple-point crossings in an optical lattice, Phys. Rev. B 97, 121402(R) (2018).
- S. Thirupathaiah, Y. S. Kushnirenk, K. Koepernik, B. R. Piening, B. Buechner, S. Aswartham, J. van den Brink, S. Borisenko, and I. C. Fulga, Sixfold fermion near the Fermi level in cubic PtBi2, SciPost Phys. 10, 004 (2021).
- Q. Xu, Y. Zhang, K. Koepernik, W. Shi, J. van den Brink, C. Felser, and Y. Sun, Comprehensive scan for nonmagnetic Weyl semimetals with nonlinear optical response, Npj Comput. Mater. 6, 1 (2020).
- A. Tamai, Q. S. Wu, I. Cucchi, F. Y. Bruno, S. Riccò, T. K. Kim, M. Hoesch, C. Barreteau, E. Giannini, C. Besnard, A. A. Soluyanov, and F. Baumberger, Fermi Arcs and Their Topological Character in the Candidate Type-II Weyl Semimetal , Phys. Rev. X 6, 031021 (2016).
- We calculate the Chern number using the occupied bands with the Berry curvature defined as , where . This definition is chosen to be consistent with the FPLO code.
- A. Bouhon, A. M. Black-Schaffer, and R.-J. Slager, Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry, Phys. Rev. B 100, 195135 (2019).
- A. Bouhon, G. F. Lange, and R.-J. Slager, Topological correspondence between magnetic space group representations and subdimensions, Phys. Rev. B 103, 245127 (2021).
- F. N. Ünal, A. Bouhon, and R.-J. Slager, Topological Euler Class as a Dynamical Observable in Optical Lattices, Phys. Rev. Lett. 125, 053601 (2020).
- J. Ahn, S. Park, and B.-J. Yang, Failure of Nielsen-Ninomiya Theorem and Fragile Topology in Two-Dimensional Systems with Space-Time Inversion Symmetry: Application to Twisted Bilayer Graphene at Magic Angle, Phys. Rev. X 9, 021013 (2019).
- B. Jiang, A. Bouhon, Z.-K. Lin, X. Zhou, B. Hou, F. Li, R.-J. Slager, and J.-H. Jiang, Experimental observation of non-Abelian topological acoustic semimetals and their phase transitions, Nat. Phys. (2021), doi: 10.1038/s41567-021-01340-x.
- A. Bouhon, T. Bzdušek, and R.-J. Slager, Geometric approach to fragile topology beyond symmetry indicators, Phys. Rev. B 102, 115135 (2020).
- Q. Wu, A. A. Soluyanov, and T. Bzdušek, Non-Abelian band topology in noninteracting metals, Science 365, 1273 (2019).
- B. Peng, A. Bouhon, B. Monserrat, and R.-J. Slager, Non-Abelian braiding of phonons in layered silicates, arXiv:2105.08733.
- A. Bouhon, Q. Wu, R.-J. Slager, H. Weng, O. V. Yazyev, and T. Bzdušek, Non-Abelian reciprocal braiding of Weyl points and its manifestation in ZrTe, Nat. Phys. 16, 1137 (2020).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L042017 for (i) details of the conductivity calculation, (ii) details of the ab initio results, and (iii) animations of the Weyl-node dynamics as obtained from the model Hamiltonians and from the ab initio calculations. Input files used in this study as well as relevant data are available in the repository at [62].
- C. J. Tabert, J. P. Carbotte, and E. J. Nicol, Optical and transport properties in three-dimensional Dirac and Weyl semimetals, Phys. Rev. B 93, 085426 (2016).
- N. Xu, Z. W. Wang, A. Magrez, P. Bugnon, H. Berger, C. E. Matt, V. N. Strocov, N. C. Plumb, M. Radovic, E. Pomjakushina, K. Conder, J. H. Dil, J. Mesot, R. Yu, H. Ding, and M. Shi, Evidence of a Coulomb-Interaction-Induced Lifshitz Transition and Robust Hybrid Weyl Semimetal in , Phys. Rev. Lett. 121, 136401 (2018).
- K. Koepernik, D. Kasinathan, D. V. Efremov, S. Khim, S. Borisenko, B. Büchner, and J. van den Brink, : A ternary type-II Weyl semimetal, Phys. Rev. B 93, 201101(R) (2016).
- H. Weng, C. Fang, Z. Fang, and X. Dai, Coexistence of Weyl fermion and massless triply degenerate nodal points, Phys. Rev. B 94, 165201 (2016).
- K. Koepernik and H. Eschrig, Full-potential nonorthogonal local-orbital minimum-basis band-structure scheme, Phys. Rev. B 59, 1743 (1999).
- J. Yang, J. Colen, J. Liu, M. C. Nguyen, G.-w. Chern, and D. Louca, Elastic and electronic tuning of magnetoresistance in , Sci. Adv. 3, eaao4949 (2017).
- F.-T. Huang, S. J. Lim, S. Singh, J. Kim, L. Zhang, J.-W. Kim, M.-W. Chu, K. M. Rabe, D. Vanderbilt, and S.-W. Cheong, Polar and phase domain walls with conducting interfacial states in a Weyl semimetal , Nat. Commun. 10, 1 (2019).
- N. Aryal and E. Manousakis, Importance of electron correlations in understanding photoelectron spectroscopy and Weyl character of MoTe2, Phys. Rev. B 99, 035123 (2019).
- Z. Scherübl, A. Pályi, G. Frank, I. E. Lukács, G. Fülöp, B. Fülöp, J. Nygård, K. Watanabe, T. Taniguchi, G. Zaránd, and S. Csonka, Observation of spinorbit coupling induced Weyl points in a two-electron double quantum dot, Commun. Phys. 2, 108 (2019).
- G. Frank, Z. Scherübl, S. Csonka, G. Zaránd, and A. Pályi, Magnetic degeneracy points in interacting two-spin systems: Geometrical patterns, topological charge distributions, and their stability, Phys. Rev. B 101, 245409 (2020).
- B. van Heck, S. Mi, and A. R. Akhmerov, Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions, Phys. Rev. B 90, 155450 (2014).
- R. P. Riwar, M. Houzet, J. S. Meyer, and Y. V. Nazarov, Multi-terminal Josephson junctions as topological matter, Nat. Commun. 7, 11167 (2016).
- V. Könye, A. Bouhon, I. C. Fulga, R.-J. Slager, J. van den Brink, and J. I. Facio, Chirality flip of Weyl nodes and its manifestation in strained , Zenodo (2021).