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<p>Carbon nanotubes (CNTs) exhibit tunable electronic and structural properties based on their chiral indices, making them versatile for nanoscale applications. The electronic behavior at CNT junctions is particularly significant, prompting a theoretical exploration of their geometric foundations. The Contub algorithm, designed to connect CNTs with arbitrary chiral vectors, identifies the positioning of pentagon and heptagon defects. Despite its theoretical efficiency, the geometrical interpretation of how chiral vectors relate to defect positions remain unclear. In this study, we introduce a unified geometric framework based on carbon nanocones (CNCs). This approach maps all possible chiral indices onto a CNC, providing a direct visual guide to defect positions. We show that all junctions can be systematically classified into two fundamental types: Type I (cone-mediated) and Type II (mitered pipe), with the former recovering the known conical junctions and the latter addressing the limiting cases where cone-based constructions fail. A phase diagram based on the relative diameter difference (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\eta\)</EquationSource> </InlineEquation>) and the angle between chiral vectors (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\phi\)</EquationSource> </InlineEquation>) not only classifies all possible connections but, crucially, provides an analytical boundary that separates the regime of each junction type.</p>

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General construction strategy for carbon nanotube heterojunctions with two arbitrary chiral vectors that contain only a single pentagon-heptagon pair

  • 期刊论文

  • 发表日期：

    2026年1月10日

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  • Hou-Hsun Ho,
  • Chern Chuang,
  • Bih-Yaw Jin

摘要

Carbon nanotubes (CNTs) exhibit tunable electronic and structural properties based on their chiral indices, making them versatile for nanoscale applications. The electronic behavior at CNT junctions is particularly significant, prompting a theoretical exploration of their geometric foundations. The Contub algorithm, designed to connect CNTs with arbitrary chiral vectors, identifies the positioning of pentagon and heptagon defects. Despite its theoretical efficiency, the geometrical interpretation of how chiral vectors relate to defect positions remain unclear. In this study, we introduce a unified geometric framework based on carbon nanocones (CNCs). This approach maps all possible chiral indices onto a CNC, providing a direct visual guide to defect positions. We show that all junctions can be systematically classified into two fundamental types: Type I (cone-mediated) and Type II (mitered pipe), with the former recovering the known conical junctions and the latter addressing the limiting cases where cone-based constructions fail. A phase diagram based on the relative diameter difference ( \(\eta\) ) and the angle between chiral vectors ( \(\phi\) ) not only classifies all possible connections but, crucially, provides an analytical boundary that separates the regime of each junction type.