Topology-Symmetry Analysis and Design of Nonlinear Optical Borate-Halide Polytypes

Abstract

Symmetry and topological features are crucial for understanding the nonlinear optical (NLO) effects of functional crystals. Here, we apply the topology-symmetry approach of Dornberger-Schiff's order-disorder (OD) theory, combined with topological analysis of underlying nets, to systematically investigate the only practically used deep-ultraviolet (DUV) NLO crystal KBe2BO3F2 (KBBF) and related compounds. The local symmetry of KBBF-type layers and interlayer spaces is characterized, and the maximum degree of order (MDO) polytypes for KBBF, as well as for KBBF-like family Pb2BO3X (X = Cl, Br, I), are described using symmetry groupoids. Topological analysis shows that KBBF and Pb2BO3X structures possess different topological types, despite identical local layer symmetries. Guided by these results, we designed two novel KBBF polytypes with the Pb2BO3X topology of underlying net, and confirmed their thermodynamic stability by first-principles calculations. The designed KBBF-P321 phase exhibits significantly enhanced second harmonic generation (d22 = 0.58 pm/V compared to 0.47 pm/V for KBBF-R32) due to optimal alignment of [BO3] anionic groups in adjacent layers. This work demonstrates that the integration of symmetry-based OD analysis, topological analysis, and first-principles calculations provides a powerful framework for the rational design of advanced nonlinear optical materials with tailored properties.