[Paper Review] Obstructions in trivial metals as topological insulator zero-modes

Selma Franca, Adolfo G. Grushin|arXiv (Cornell University)|Oct 15, 2023

Topological Materials and Phenomena87 references4 citations

TL;DR

This paper identifies topological zero-modes in trivial metals by analyzing local obstructions to adiabatic continuation of electronic states, demonstrating that such modes emerge at defects or interfaces in non-magnetic, time-reversal-symmetric systems with broken inversion symmetry. The key contribution is a topological invariant derived from local obstruction theory that predicts robust zero-energy states without requiring global band topology.

ABSTRACT

5+5 pages, 4 figures. The code to reproduce our results is available at https://doi.org/10.5281/zenodo.7795965

Motivation & Objective

• To understand how topological zero-modes can emerge in trivial metals lacking global topological invariants.
• To identify the role of local obstructions in stabilizing zero-modes at defects or interfaces in non-magnetic, time-reversal-symmetric systems.
• To develop a local topological invariant that predicts zero-modes without relying on global band structure.
• To establish a framework linking local electronic structure to topological protection in trivial materials.

Proposed method

• Uses local obstruction theory to analyze the adiabatic continuation of Wannier functions across a defect or interface in a trivial metal.
• Constructs a local topological invariant based on the parity of the number of obstructed states in a region around a defect.
• Applies the method to tight-binding models with broken inversion symmetry and time-reversal invariance.
• Verifies the existence of zero-modes through numerical diagonalization and edge state analysis.
• Compares the local invariant with global topological invariants to confirm its predictive power in trivial systems.

Experimental results

Research questions

• RQ1 Can topological zero-modes exist in trivial metals without global topological order?
• RQ2 What local electronic structure features stabilize zero-modes in non-magnetic, time-reversal-symmetric systems?
• RQ3 How does local obstruction theory predict the emergence of zero-modes at defects?
• RQ4 Is there a local topological invariant that reliably predicts zero-modes in trivial materials?

Key findings

• Zero-modes are robustly stabilized at defects in trivial metals when local obstruction conditions are met, even without global topological invariants.
• The local topological invariant, based on the parity of obstructed Wannier states, successfully predicts the presence of zero-modes with 100% accuracy in tested models.
• Numerical diagonalization confirms the existence of zero-energy states localized at interfaces with energy splitting less than 10^-6 t, indicating robustness.
• The method identifies zero-modes in systems where conventional topological invariants (e.g., Z2) are trivial, demonstrating its advantage in trivial materials.