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Majorana edge states in interacting one-dimensional systems.

Suhas Gangadharaiah1, Bernd Braunecker, Pascal Simon

  • 1Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland.

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|August 16, 2011
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Electron-electron interactions threaten Majorana edge states in superconductors. Weak interactions, however, allow these exotic states to persist, and we propose strategies to access this stable regime.

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Area of Science:

  • Condensed matter physics
  • Quantum materials

Background:

  • One-dimensional electron systems near superconductors can host Majorana edge states.
  • These exotic states are crucial for topological quantum computing.
  • Electron-electron interactions are a known factor influencing quantum phenomena.

Purpose of the Study:

  • To investigate the impact of electron-electron interactions on Majorana edge states.
  • To identify conditions under which Majorana edge states remain stable.
  • To propose methods for accessing a stable regime for Majorana edge states.

Main Methods:

  • Theoretical analysis of one-dimensional electron systems coupled to a superconductor.
  • Renormalization group techniques to study interaction effects.
  • Analysis of the superconducting gap stability under varying interaction strengths.

Main Results:

  • Strong electron-electron interactions generically destroy the superconducting gap, destabilizing Majorana edge states.
  • Weak interactions lead to nonuniversal gap renormalization.
  • A regime where Majorana edge states persist under weak interactions has been identified.

Conclusions:

  • Electron-electron interactions pose a significant challenge to the stability of Majorana edge states.
  • Weak interactions offer a pathway to preserve Majorana edge states.
  • Strategies for reaching and utilizing this interaction regime are presented.