Classification of emergent Weyl spinors in multi-fermion systems

Abstract

In the fermionic systems with topologically stable Fermi points the emergent two - component Weyl fermions appear. We propose the topological classification of these fermions based on the two invariants composed of the two - component Green function. We define these invariants using Wigner - Weyl formalism also in case of essentially non - homogeneous systems. In the case when values of these invariants are minimal ($\pm 1$) we deal with emergent relativistic symmetry. The emergent gravity appears, and our classification of Weyl fermions gives rise to the classification of vierbein. Transformations between emergent relativistic Weyl fermions of different types correspond to parity conjugation, time reversal, and charge conjugation.

Latex, 9 pages, published version

References in corpus (7)

• The electronic properties of graphene
• Classification of topological insulators and superconductors in three spatial dimensions
• Quantum Gravity at a Lifshitz Point
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Membranes at Quantum Criticality
• Emergent Weyl spinors in multi-fermion systems
• Euler - Heisenberg effective action and magnetoelectric effect in multilayer graphene

Cited by in corpus (2)

• Gravity from symmetry breaking phase transition
• Negative temperature: further extensions