Table 1 Definition of new variables—Chern sector and pseudospin, from the valley and sublattice degrees of freedom.

Actions of symmetries on the internal indices are shown on the right, in both set of variables. In addition, the independent pseudospin rotations in the Chern sectors are generated by the ηP± where the projectors P±=12(1±γz) single out a specific Chern sector.

From valley/sublattice to Chern/pseudospin
(τ, σ) → (γ, η)
γ = (γx, γy, γz) = (σx, σyτz, σzτz)
η = (ηx, ηy, ηz) = (σxτx, σxτy, τz)
Basis
Valleyτz = K/K
Sublatticeσz = A/B
Chern sectorγz = σzτz = + /−
Pseudospinηz = τz = ↑ps/↓ps
Symmetries
Symm(τ, σ) basis(γ, η) basis
TτxKγxηxK
C2σxτxηx
UV(1)eiϕτzeiϕηz