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A substance that reaches superconductivity, a state in which magnetic fields cannot penetrate, and there is no electrical resistance, is referred to as a superconductor. In 1911, Heike Kamerlingh Onnes of Leiden University, a Dutch physicist, observed a relation between the temperature and the resistance of the element mercury. The mercury sample was then cooled in liquid helium to study the linear dependence of resistance on temperature. It was observed that, as the temperature decreased, the...
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Symmetry protected topological superfluid (3)He-B.

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Superfluid Helium-3 (3He) exhibits topological properties, featuring symmetry-protected Majorana fermions and odd-frequency pairing. These phenomena influence surface states and quantum criticality, offering insights into topological phase transitions.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Materials
  • Topological Phases

Background:

  • Superfluid Helium-3 (3He) is a rich system for studying topology and symmetry.
  • Bulk superfluidity in 3He is well-understood, providing a foundation for exploring topological aspects.

Purpose of the Study:

  • To review recent advancements in understanding topological superfluidity in 3He.
  • To focus on symmetry-protected topological superfluidity of 3He-B in a slab geometry.
  • To investigate topological phase transitions and emergent phenomena.

Main Methods:

  • Symmetry analysis
  • Jackiw-Rebbi's index theorem
  • Quasiclassical theory
  • Microscopic calculations including magnetic dipole interactions

Main Results:

  • 3He-B in a magnetic field exhibits distinct topological and non-topological phases.
  • Symmetry-protected Majorana fermions characterize the topological phase.
  • Topological phase transitions are triggered by hidden discrete symmetry breaking.
  • Odd-frequency Cooper pair amplitudes emerge in low-lying quasiparticles.
  • Surface state coupling is prohibited by symmetry, while transitions show anomalous quantum criticality.

Conclusions:

  • Symmetry-protected topological superfluidity in 3He-B is characterized by Majorana fermions and odd-frequency pairing.
  • These features lead to unique behaviors in surface states and quantum criticality.
  • Common topological features exist between topological crystalline superconductors and symmetry-protected topological superfluids.