Three-dimensional topological crystalline insulator without spin-orbit coupling in nonsymmorphic photonic metacrystal

By including certain point group symmetry in the classification of band topology,Fu proposed a class of threedimensionaltopological crystalline insulators(TCIs)without spin-orbit coupling in 2011.In Fu’s model,surface states(ifpresent)doubly degenerate atГandM when time-reversal and C4 symmetries are preserved.The analogs of Fu’s modelwith surface states quadratically degenerate atM are widely studied,while surface states with quadratic degeneracy atГare rarely reported.In this study,we propose a three-dimensional TCI without spin-orbit coupling in a judiciously designednonsymmorphic photonic metacrystal.The surface states of photonic TCIs exhibit quadratic band degeneracy in the(001)surface Brillouin zone(BZ)center(Гpoint).The gapless surface states and their quadratic dispersion are protected by C4and time-reversal symmetries,which correspond to the nontrivial band topology characterized by Z_(2)topological invariant.Moreover,the surface states along lines fromГto the(001)surface BZ boundary exhibit zigzag feature,which is interpretedfrom symmetry perspective by building composite operators constructed by the product of glide symmetries with timereversalsymmetry.The metacrystal array surrounded with air possesses high order hinge states with electric fields highlylocalized at the hinge that may apply to optical sensors.The gapless surface states and hinge states reside in a cleanfrequency bandgap.The topological surface states emerge at the boundary of the metacrystal and perfect electric conductor(PEC),which provide a pathway for topologically manipulating light propagation in photonic devices.

Symmetry-enforced two-dimensional Dirac node-line semimetals

Based on symmetry analysis and lattice model calculations,we demonstrate that Dirac nodal line(DNL)can stably exist in two-dimensional(2D)nonmagnetic as well as antiferromagnetic systems.We focus on the situations where the DNLs are enforced by certain symmetries and the degeneracies on the DNLs are inevitable even if spin–orbit coupling is strong.After thorough analysis,we find that five space groups,namely 51,54,55,57 and 127,can enforce the DNLs in 2D nonmagnetic semimetals,and four type-III magnetic space groups(51.293,54.341,55.355,57.380)plus eight type-IV magnetic space groups(51.299,51.300,51.302,54.348,55.360,55.361,57.387 and 127.396)can enforce the DNLs in 2D antiferromagnetic semimetals.By breaking these symmetries,the different 2D topological phases can be obtained.Furthermore,by the first-principles electronic structure calculations,we predict that monolayer YB4C4 is a good material platform for studying the exotic properties of 2D symmetry-enforced Dirac node-line semimetals.

Node line semimetal states in tungsten-based materials

Node line semimetals(NLSMs) were characterized by one-dimensional band crossings in their bulk electronic structures.The nontrivial band topology of NLSM gives rise to "drumhead" surface electronic excitations that exhibits exotic physical properties.The symmetries of crystalline provide the needed protection of node line from being gapped out by the perturbations that preserve the symmetry.The progress of NLSM in tungsten-based materials is reviewed with an emphasis on their symmetry-based protection,characteristic electronic band structures and their response to the spin-orbit coupling(SOC)and breaking of time-reversal symmetry.The potential exploration directions of tungsten-based NLSM in the future are also discussed.

Weyl points and Dirac lines protected by multiple screw rotations

In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron＇s energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 （P212121 ） and No. 198 （P213）, which have three orthogonal screw rotation axes. In the case of space groups No. 61 （Pbca） and No. 205 （Pa-3） that have extra inversion symmetry, Weyl points are promoted to four-fold degenerate line nodes in glide-invariant planes. The three-fold rotation symmetry present in the space groups No. 198 and No. 205 allows Weyl and Dirac points, respectively, to appear along its rotation axes in the Brillouin zone and generates four-fold and six-fold degeneracy at the F point and R point, respectively.