Fractional Fermion Number and Hall Conductivity of Domain Walls

Abstract

In this letter the fractional fermion number of thick domain walls is computed. The analysis is achieved by developing the heat kernel expansion of the spectral eta functon of the Dirac Hamiltonian governing the fermionic fluctuations around the domain wall. A formula is derived showing that a non null fermion number is always accompanied by a Hall conductivity induced on the wall. In the limit of thin and impenetrable walls the chiral bag boundary conditions arise, and the Hall conductivity is computed for this case as well.

9 pages

References in corpus (2)

• Electron fractionalization for two-dimensional Dirac fermions
• Quantum Dirac fermions in half space and their interaction with electromagnetic field

Cited by in corpus (9)

• Fermions in the presence of topological structures under geometric constrictions
• How many surface modes does one see on the boundary of a Dirac material?
• Fractionalized Quasiparticles in Dense Baryonic Matter
• Non-topological fractional fermion number in the Jackiw-Rossi model
• On the (im)possibility of Casimir repulsion between Chern-Simons surfaces
• Anomaly inflow for local boundary conditions
• Mapping topology to nuclear dilaton-HLS effective field theory for dense baryonic matter
• Mapping topology of skyrmions and fractional quantum Hall droplets to nuclear EFT for ultra-dense baryonic matter
• Remark on the synergy between the heat kernel techniques and the parity anomaly