Topological materials, which hold promise for a wide range of technological applications due to their exotic electronic properties, have attracted a great deal of theoretical and experimental interest over the past decade, culminating in the 2016 Nobel Prize in physics. In this talk, I will explore the universal topological properties of p-orbitals placed in 2 dimensional D_6h symmetry which is realized in real materials made of 2D group V-elements (Sb, As). I will show that this system starts off as a symmetry-protected nodal line semimetal in the flat form (C₆), which upon slight buckling turns into Dirac semimetallic phase with multiple Dirac cones [1]. These cones, upon further buckling, are shown to annihilate in pairs at two critical angles. I will then proceed to show that the buckled lowest energy form at the end of this series of topological transitions is a weak topological crystalline insulator (TCI) in the obstructed atomic limit (OAL). I will walk through the relation of this system to the kagome, Kekule, and Su-Schrieffer-Heeger systems. We will see that this property of systems resulting in OAL (non-trivial vacuum) is universally true for all annihilating Dirac fermions [3]. Further using group-theoretical analysis, I will show that the final buckled system is the first example of (d-2) higher-order topological insulator for d=2 with protected corner states [2]. Using this property, I finally propose working principles of two devices 1. Topological quantum switch and 2. controllable quasi 1D wires [4].

[1] Radha, Santosh Kumar, and Walter RL Lambrecht. “Topological band structure transitions in honeycomb antimonene as a function of buckling.” arXiv:1912.03755 (2019).

[2] Radha, Santosh Kumar, and Walter RL Lambrecht. “Buckled honeycomb group-$ V $-$ S_6 $ symmetric $(d-2) $ higher order topological insulators.” arXiv:2003.12656 (2020).

[3] Radha, Santosh Kumar, and Walter RL Lambrecht. “Topological obstructed atomic limit by annihilating Dirac fermions.” arXiv:2011.04098 (2020).

[4] Radha, Santosh Kumar, and Walter RL Lambrecht. “Topological quantum switch and controllable quasi 1D wires in antimonene.” arXiv:2005.06096 (2020).