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Geometry significantly impacts Majorana zero modes in core-shell nanowires. A hexagonal core with a triangular shell enhances energy separation for localized states, crucial for topological quantum computing advancements.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Computing

Background:

  • Majorana zero modes are exotic quasiparticles with potential applications in topological quantum computing.
  • The geometry of core-shell nanowires is a critical factor influencing the hosting and manipulation of these modes.
  • Understanding geometric effects is essential for designing robust topological qubits.

Purpose of the Study:

  • To investigate how different core-shell geometries (hexagonal core/triangular shell and vice versa) affect Majorana zero modes.
  • To compare the energy separation of localized electronic states in various nanowire configurations.
  • To construct and analyze topological phase diagrams for these geometries.

Main Methods:

  • Theoretical modeling of core-shell nanowires with specified hexagonal and triangular geometries.
  • Calculation of energy spectra to determine the localization of electronic states.
  • Construction and comparison of topological phase diagrams for different geometric configurations.

Main Results:

  • A larger energy interval between corner and side localized states was observed in a triangular nanowire with a hexagonal core compared to a triangular core.
  • Topological phase diagrams were generated for both hexagonal-core/triangular-shell and triangular-core/hexagonal-shell nanowires.
  • Comparison with prismatic nanowires revealed distinct phase behaviors based on core-shell geometry matching.

Conclusions:

  • Nanowire geometry, specifically the combination of hexagonal and triangular shells, plays a crucial role in the properties of Majorana zero modes.
  • The observed energy separation differences suggest potential for improved control over Majorana modes.
  • A dual-core nanowire architecture is proposed as a necessary step for enabling braiding operations of Majorana zero modes.