Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling
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| Format: | Preprint |
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2021
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| _version_ | 1866909404394160128 |
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| author | Yang, Jian Liu, Zheng-Xin Fang, Chen |
| author_facet | Yang, Jian Liu, Zheng-Xin Fang, Chen |
| contents | Symmetry invariants of a group specify the classes of quasiparticles, namely the classes of projective irreducible co-representations in systems having that symmetry. More symmetry invariants exist in discrete point groups than the full rotation group $\mathrm{O(3)}$, leading to new quasiparticles restricted to lattices that do not have any counterpart in a vacuum. We focus on the fermionic quasiparticle excitations under ``spin-space group'' symmetries, applicable to materials where long-range magnetic order and itinerant electrons coexist. We provide a list of 218 classes of new quasiparticles that can only be realized in the spin-space groups. These quasiparticles have at least one of the following properties that are qualitatively distinct from those discovered in magnetic space group(MSG)s, and distinct from each other:(i) degree of degeneracy,(ii) dispersion as function of momentum, and(iii) rules of coupling to external probe fields. We rigorously prove this result as a theorem that directly relates these properties to the symmetry invariants, and then illustrate this theorem with a concrete example, by comparing three 12-fold fermions having different sets of symmetry invariants including one discovered in MSG. Our approach can be generalized to realize more quasiparticles whose little co-groups are beyond those considered in our work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2105_12738 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling Yang, Jian Liu, Zheng-Xin Fang, Chen Mesoscale and Nanoscale Physics Strongly Correlated Electrons Symmetry invariants of a group specify the classes of quasiparticles, namely the classes of projective irreducible co-representations in systems having that symmetry. More symmetry invariants exist in discrete point groups than the full rotation group $\mathrm{O(3)}$, leading to new quasiparticles restricted to lattices that do not have any counterpart in a vacuum. We focus on the fermionic quasiparticle excitations under ``spin-space group'' symmetries, applicable to materials where long-range magnetic order and itinerant electrons coexist. We provide a list of 218 classes of new quasiparticles that can only be realized in the spin-space groups. These quasiparticles have at least one of the following properties that are qualitatively distinct from those discovered in magnetic space group(MSG)s, and distinct from each other:(i) degree of degeneracy,(ii) dispersion as function of momentum, and(iii) rules of coupling to external probe fields. We rigorously prove this result as a theorem that directly relates these properties to the symmetry invariants, and then illustrate this theorem with a concrete example, by comparing three 12-fold fermions having different sets of symmetry invariants including one discovered in MSG. Our approach can be generalized to realize more quasiparticles whose little co-groups are beyond those considered in our work. |
| title | Symmetry invariants and classes of quasiparticles in magnetically ordered systems having weak spin-orbit coupling |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2105.12738 |