We review the recent,mainly theoretical,progress in the study of topological nodal line semimetals in three dimensions.In these semimetals,the conduction and the valence bands cross each other along a one-dimensional ...We review the recent,mainly theoretical,progress in the study of topological nodal line semimetals in three dimensions.In these semimetals,the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone,and any perturbation that preserves a certain symmetry group（generated by either spatial symmetries or time-reversal symmetry） cannot remove this crossing line and open a full direct gap between the two bands.The nodal line（s） is hence topologically protected by the symmetry group,and can be associated with a topological invariant.In this review,（ⅰ） we enumerate the symmetry groups that may protect a topological nodal line;（ⅱ） we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface,establishing a topological classification;（ⅲ） for certain classes,we review the proposals for the realization of these semimetals in real materials;（ⅳ） we discuss different scenarios that when the protecting symmetry is broken,how a topological nodal line semimetal becomes Weyl semimetals,Dirac semimetals,and other topological phases;and（ⅴ） we discuss the possible physical effects accessible to experimental probes in these materials.展开更多
基金Project partially supported by the National Key Research and Development Program of China(Grant Nos.2016YFA0302400 and 2016YFA0300604)the National Natural Science Foundation of China(Grant Nos.11274359 and 11422428)+1 种基金the National Basic Research Program of China(Grant No.2013CB921700)the "Strategic Priority Research Program(B)" of the Chinese Academy of Sciences(Grant No.XDB07020100)
文摘We review the recent,mainly theoretical,progress in the study of topological nodal line semimetals in three dimensions.In these semimetals,the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone,and any perturbation that preserves a certain symmetry group（generated by either spatial symmetries or time-reversal symmetry） cannot remove this crossing line and open a full direct gap between the two bands.The nodal line（s） is hence topologically protected by the symmetry group,and can be associated with a topological invariant.In this review,（ⅰ） we enumerate the symmetry groups that may protect a topological nodal line;（ⅱ） we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface,establishing a topological classification;（ⅲ） for certain classes,we review the proposals for the realization of these semimetals in real materials;（ⅳ） we discuss different scenarios that when the protecting symmetry is broken,how a topological nodal line semimetal becomes Weyl semimetals,Dirac semimetals,and other topological phases;and（ⅴ） we discuss the possible physical effects accessible to experimental probes in these materials.
