pseudospin

Pseudospin is an abstract two-state degree of freedom used to describe systems with a two-component wavefunction. It behaves like spin-1/2 under certain symmetries but is not real angular momentum. It labels internal states arising from lattice, band, or mode structure.

In condensed matter, graphene provides the archetypal example. The lattice is bipartite with two sublattices, A and B. Near the Dirac points, electronic states are a two-component spinor with components on A and B. Pauli matrices act on this pseudospin space, yielding an effective Dirac-type Hamiltonian. Pseudospin explains features such as suppression of backscattering and phenomena like Klein tunneling. In bilayer graphene or other layered systems, pseudospin can label layer or orbital degrees of freedom and governs interlayer coupling.

Valley pseudospin is another common usage, treating the inequivalent momentum valleys K and K' as a two-state system. This concept underpins valleytronics and can be engineered in photonic, phononic, and cold-atom platforms as synthetic pseudospin.

In nuclear physics, a related idea is pseudospin symmetry, an approximate SU(2) symmetry of the Dirac Hamiltonian that accounts for near-degenerate shell-model levels.

Pseudospin thus provides a convenient description of two-state systems and their dynamics, linking lattice symmetry, topology, and quantum transport.