Structure-imposed electronic topology in cove-edged graphene nanoribbons

<p><strong>Abstract</strong></p> <p>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 <em>N</em>, unit lengths <em>a</em> and cove position offsets at both edges <em>b</em>, thus showing the direct structure-electronic structure relation. We further present an empirical formula to estimate the band gap of the semiconducting ribbons from <em>N</em>,<em>a</em>, and <em>b</em>. Finally, we identify all geometrically possible ribbon terminations and provide rules to construct ZGNR-C with well-defined electronic structure.</p> <p>DOI: 10.1103/PhysRevLett.129.216401</p> <p><strong>Content of repository</strong></p> <p>The repository contains the inputs and outputs of tight-binding (TB) calculations of ZGNR-C based on <a href="http://www.physics.rutgers.edu/pythtb/">PythTB</a>. For each analysed structure one subdirectory is created, labelled as &quot;N-ZGNR-C_a_b_inv_cell<span class="math-tex">\(\alpha\)</span>_termination&quot;. This corresponds to a <em>N</em>-ZGNR-C(<em>a</em>,<em>b</em>) with inversion center at the unit cell boundary <em><strong>S</strong></em> or <em><strong>L</strong></em> (&quot;inv&quot;), unit cell angle <span class="math-tex">\(\alpha\)</span> (&quot;cell<span class="math-tex">\(\alpha\)</span>&quot;: 60&deg;, 90&deg;, or 120&deg;) 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&nbsp;<span class="math-tex">\(\pi\)</span> without modulo 2, and the final <span class="math-tex">\(\mathbb{Z}_2\)</span> invariant.</p> <p>&nbsp;</p>