Note that at inversion symmetric momenta Γi, which are also time-invariant momenta, the Bloch Hamiltonian commutes with the inversion operator HP=0 and the states |un,Γi〉 have defined parity eigenvalues (35)Pun,Γi〉=ζnΓiun,Γi〉=±1|un,Γi〉 As stated in the previous section, ...
If T symmetry is present and V is broken, there may exist on some symmetry lines Weyl nodes pinned to T-invariant momenta, which in some cases are unavoidable. In the absence of other symmetries, their classification depends on n, m, and the type of T symmetry. With spinless T such T...
For instance, the electric polarization of an inversion-symmetric one-dimensional atomic chain is either integer or semi-integer, with a quantized value that does not depend upon microscopic details, but is rather encoded in a gauge-invariant topological index28. More recently, it has been shown ...
system is called time-reversal invariant if from any given solution x ( t ), p ( t ) of Hamilton's equations an independent solution x ′( t ′), p ′( t ′),is obtained with t ′ = t and some operation relating x ′ and p ′ to the original coordinates x and momenta p ....
system is called time-reversal invariant if from any given solution x ( t ), p ( t ) of Hamilton's equations an independent solution x ′( t ′), p ′( t ′), is obtained with t′ = t and some operation relating x ′ and p ′ to the original coordinates x and momenta p ....
However, it is a highly nontrivial issue in translationally invariant systems since the time-reversal symmetry T plays an essential role, where the two states at crystal momentaand are connected in the band structure. Therefore, it has been considered that the external magnetic field () or the...
The black and orange dashed lines label the momenta invariant under the mirror/glide symmetry and the combination of mirror/glide and TR symmetries, respectively. The figures are first grouped according to the PGs and then ordered based on the GC scenarios listed in Table , whose labels are ...