Fermionic Hopf solitons and Berry's phase in topological surface superconductors

Abstract

A central theme in many body physics is emergence - new properties arise when several particles are brought together. Particularly fascinating is the idea that the quantum statistics may be an emergent property. This was first noted in the Skyrme model of nuclear matter, where a theory formulated entirely in terms of a bosonic order parameter field contains fermionic excitations. These excitations are smooth field textures, and believed to describe neutrons and protons. We argue that a similar phenomenon occurs in topological insulators when superconductivity gaps out their surface states. Here, a smooth texture is naturally described by a three component real vector. Two components describe superconductivity, while the third captures the band topology. Such a vector field can assume a 'knotted' configuration in three dimensional space - the Hopf texture - that cannot smoothly be unwound. Here we show that the Hopf texture is a fermion. To describe the resulting state, the regular Landau-Ginzburg theory of superconductivity must be augmented by a topological Berry phase term. When the Hopf texture is the cheapest fermionic excitation, striking consequences for tunneling experiments are predicted.

References in corpus (9)

• Topological Insulators
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• The quantum spin Hall effect and topological insulators
• Superconductivity in CuxBi2Se3 and its implications for pairing in the undoped topological insulator
• Helical Metal Inside a Topological Band Insulator
• Majorana Fermions and Non-Abelian Statistics in Three Dimensions
• Chiral Topological Insulators, Superconductors and other competing orders in three dimensions
• Low-Energy Limit of Yang-Mills with Massless Adjoint Quarks: Chiral Lagrangian and Skyrmions

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• Josephson current between topological and conventional superconductors
• Constructing a class of topological solitons in magnetohydrodynamics
• Decorated defect condensate, a window to unconventional quantum phase transitions in Weyl semimetals
• Topological Orders with Global Gauge Anomalies
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• Probing topological properties of 3D lattice dimer model with neural networks
• Superconductor Vortex Spectrum Including Fermi Arc States in Time-Reversal Symmetric Weyl Semimetals
• Persistent current in 2D topological superconductors
• Hopf symmetry protected topological phases in the vicinity of spin orders
• Vortex-state-mediated Josephson effect