Continuous switching between admissible Mixed-IWSM boundary matchings

Determine whether a particular boundary Hamiltonian for a Mixed irreducible Weyl semimetal can provide a continuous switching path between distinct admissible labeled chiral-incidence matrices while preserving the bulk Weyl configuration and projected terminal charges.

Background

Mixed irreducible Weyl semimetals can possess multiple labeled boundary-incidence matrices with identical row and column sums, because the bulk Weyl charges constrain only the total chiral flow entering and leaving each projected terminal. For the inventories {3,1,-2,-2} and {3,3,-2,-2,-2}, the paper gives explicit examples of distinct admissible incidence matrices.

The unresolved issue is whether a concrete boundary Hamiltonian can continuously interpolate between such distinct matchings. The bulk classification alone does not decide this, so answering the question requires a surface-specific analysis involving boundary termination, surface potentials, adsorption, or other perturbations, while checking that the bulk nodes and projected charges remain unchanged.