Structure-imposed electronic topology in cove-edged graphene nanoribbons

Abstract

In cove-edged zigzag graphene nanoribbons (ZGNR-C), one terminal group per length unit is removed on each zigzag edge, forming a regular pattern of coves which controls their electronic structure. Based on three structural parameters that unambiguously characterize the atomistic structure of ZGNR-C, we present a scheme that classifies their electronic state, i.e., if they are metallic, topological insulators or trivial semiconductors, for all possible widths N, unit lengths a and cove position offsets at both edges b, thus showing the direct structure-electronic structure relation. We further present an empirical formula to estimate the band gap of the semiconducting ribbons from N,a, and b. Finally, we identify all geometrically possible ribbon terminations and provide rules to construct ZGNR-C with well-defined electronic structure.

DOI: 10.1103/PhysRevLett.129.216401

Content of repository

The repository contains the inputs and outputs of tight-binding (TB) calculations of ZGNR-C based on PythTB. For each analysed structure one subdirectory is created, labelled as "N-ZGNR-C_a_b_inv_cell\(\alpha\)_termination". This corresponds to a N-ZGNR-C(a,b) with inversion center at the unit cell boundary S or L ("inv"), unit cell angle \(\alpha\) ("cell\(\alpha\)": 60°, 90°, or 120°) and a given unit cell termination (armchair, zigzag or bearded). Each directory contains the atomic structure in xsf and cif format, the PythTB input file, the output as a json file, and the calculated band structure as image file. The json file contains the band structure information (path and eigenvalues), the raw Zak phase in units of \(\pi\) without modulo 2, and the final \(\mathbb{Z}_2\) invariant.