Symmetry constraints on boundary transport versus bulk transport

Transport measurements in crystalline materials are governed by symmetry constraints arising from Neumann's principle. For example, in an inversion-symmetric system, all even-order voltage responses vanish under bulk transport. However, it remains unclear whether these symmetry constraints remain valid when transport is dominated by boundary modes. In this talk, we introduce a symmetry framework that extends Neumann's principle to systems with boundary transport, explicitly incorporating the geometry of contacts and sample boundaries. This framework reveals new symmetry-allowed boundary responses that have no bulk counterpart. As a case study, we apply it to magnetic topological insulators, where the predicted boundary transport signatures are confirmed by both experiment and numerical simulation. Our results bridge symmetry-based transport theory with experimentally accessible boundary phenomena.