Quantized Polarization Redefines Polar Interfaces

TL;DR

This paper introduces the concept of quantized polarization as a symmetry-protected invariant in high-symmetry crystalline solids, explaining interfacial phenomena like metallic states and lattice distortions due to polarization mismatch.

Contribution

It redefines the understanding of polarization in crystalline materials by establishing quantized polarization as a fundamental bulk invariant that influences interfacial properties.

Findings

Quantized polarization is a symmetry-protected invariant.

Interfaces between materials with different QPs exhibit unique electronic responses.

Reinterpretation of LaAlO3/SrTiO3 interface as a QP mismatch case.

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.