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There is variation in the electrical conductivity of materials - metals, semiconductors, and insulators that are showcased with the help of the energy band diagrams.
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Topological materials with extensive flat-band surface states.

Protyush Nandi1, Subinay Dasgupta2

  • 1Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|December 4, 2025
PubMed
Summary

Materials with zero-energy flat band states may exhibit surface superconductivity. This study theoretically identifies conditions for topological nodal line semimetals to host such surface states, enabling new superconducting phenomena.

Keywords:
flat-band surface statetopological insulatortopological nodal line semimetaltopological phase transition

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Theoretical Physics

Background:

  • Zero-energy flat band states on material surfaces are linked to potential surface superconductivity.
  • Topological nodal line semimetals are a class of materials with unique electronic band structures.

Purpose of the Study:

  • To theoretically investigate the conditions under which a topological nodal line semimetal exhibits zero-energy flat band surface states.
  • To explore the potential for realizing surface superconductivity in these materials.

Main Methods:

  • Analytical calculations to derive the conditions for zero-energy surface states.
  • Numerical simulations to confirm the theoretical predictions.
  • Phase diagram analysis to identify new transitions.

Main Results:

  • Identified specific conditions (anisotropic hopping and onsite energy limits) for zero-energy surface eigenstates in a topological nodal line semimetal slab.
  • Confirmed the existence of these surface states through analytical and numerical methods.
  • Discovered new phase transitions within the material's parameter space.

Conclusions:

  • The theoretical framework predicts the emergence of zero-energy flat band surface states in topological nodal line semimetals under specific conditions.
  • These findings suggest a pathway for designing materials with potential surface superconductivity.
  • The proposed Hamiltonian can be realized in stacked layered systems, broadening experimental possibilities.