Formal polarization as a Quantized Bulk Invariant: Implications for Interface Phenomena

In crystalline solids, symmetry can constrain formal polarization to discrete values. We show that this quantized formal polarization (QFP) should be understood as a symmetry-protected bulk invariant that encodes intrinsic information about a material’s symmetry and electronic structure. From this viewpoint, mismatch between the QFPs of different materials or phases represents a bulk incompatibility with potentially broad physical consequences. In particular, when such materials form an interface, the QFP mismatch imposes a nontrivial compensation requirement, which may be realized through metallic states, bound charges, structural reconstructions, or other mechanisms. Through the examples of the ZnS/MgS heterostructure, the HfZnN₂ domain wall, and the GaAs domain wall, we demonstrate that bulk QFP provides a predictive criterion for determining whether nontrivial interfacial compensation is required, without explicitly constructing the interface or domain wall. The specific realization of this compensation, however, must be determined from explicit calculations for each material system. Our work thus elevates formal polarization from a quantity used mainly in interface electrostatics to a more general bulk principle relevant to phase compatibility and related phenomena, and suggests a route toward designing functional quantum materials through controlled quantized polarization mismatch.