  Symmetry plays an important role in the topological states of quantum matter.
Cartan found three symmetry classes, Altland and Zirnbauer extended it to the
ten-fold symmetry class for mesoscopic systems. We observe emergence of a new
symmetry class for BdG Hamiltonians. This new symmetry class appears for the
BdG Hamiltonian in spinful background. We also observe the interesting feature
that there is no evidence of Kramers's degeneracy for this BdG model
Hamiltonian either in spinless or in spinful background. We call the extra
symmetry class X, i.e, expanding the ten-fold symmetry classes for topological
states of quantum matter. These BdG show many new, interesting and insightful
results.
