Quantized Polarization Redefines Polar Interfaces

Abstract

In crystalline solids, the electronic polarization follows the \emph{generalized Neumann's principle}, under which all crystallographic point groups can, in principle, support ferroelectric polarization. However, in high-symmetry structures, polarization is constrained by symmetry operations and becomes quantized into discrete values. We demonstrate that this quantized polarization (QP) is not a mathematical artifact but a \emph{symmetry-protected invariant} that encodes intrinsic information about a material's symmetry and electronic structure. Because of its discrete and non-continuous nature, when two materials with different QPs form an interface, their bulk polarization states cannot be connected adiabatically, compelling the system to develop pronounced interfacial responses: such as metallic states, bound charges, or strong lattice distortions. This theoretical framework provides a unified reinterpretation of classical systems such as the LaAlO$_3$/SrTiO$_3$ interface, revealing it as a prototypical case of QP mismatch. By establishing QP as a fundamental bulk invariant, our work uncovers a universal mechanism governing interfacial electronic phenomena and opens new pathways for the design of functional quantum materials through engineered polarization mismatch.

Figures (4)

• Figure 1: QP mismatch drives emergent interfacial phenomena. Schematic showing that an interface between materials with distinct QPs cannot be connected adiabatically, leading to polarization discontinuity and emergent interfacial phenomena such as two-dimensional electron gas (2DEG) or large lattice distortion etc.
• Figure 2: Electronic structure and interfacial states of the (AgCl)$_{10}$/(NaCl)$_{10}$ superlattice. (a) Band structure of the superlattice, where red denotes states localized at the interfaces and blue corresponds to bulk-like states. (b) Layer-resolved PDOS for layers at different distances from IF$_1$ and IF$_2$, with metallic states emerging at IF$_1$. (c) Partial charge density of the metallic band near the Fermi level, showing strong electron localization at IF$_1$ corresponding to a 2DEG.
• Figure 3: Electronic structure and interfacial states of the (AgNbO$_3$)$_{10}$/(CaSnO$_3$)$_{10}$ superlattice. (a) Band structure of the superlattice, where red denotes states localized at the interfaces and blue corresponds to bulk-like states. (b) Layer-resolved PDOS for atomic layers at varying distances from IF$_1$ and IF$_2$, showing that metallic states emerge at IF$_1$.
• Figure 4: Electronic structure of the (SrTiO$_3$)$_{10}$/(CaSnO$_3$)$_{10}$ superlattice. (a) Band structure of the superlattice revealing a large band gap with no interface states appearing near the Fermi level. (b) Layer-resolved PDOS at varying distances from IF$_1$ and IF$_2$, indicating close similarity to the bulk electronic structure with large band gap.