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Browsing by Subject "torsion"

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  • Laurila, Sara (2023)
    Certain topological phases of matter exhibit low-energy quasiparticles that closely resemble relativistic Weyl fermions due to their linear dispersion. This notion leads to a quasirelativistic description for these non-relativistic condensed matter quasiparticles. In relativistic quantum field theory, Weyl fermions are subject to chiral anomalies when coupled to gauge fields or non-trivial background geometries. Condensed matter Weyl quasiparticles similarly experience anomalies from their background fields, leading to anomalous transport phenomena. We review the field theory of relativistic fermions in curved spacetimes with torsion, and the macroscopic BCS theory of superconductors and superfluids. Using the example of p+ip-paired superfluids and superconductors, we show how their gapless excitations are quasirelativistic Weyl fermions in an emergent spacetime determined by their background fields. With a simple Landau level argument, we then argue that the presence of torsion in this emergent spacetime leads to a chiral anomaly for the Weyl quasiparticles. In the context of relativistic theory, the torsional contribution to the chiral anomaly is controversial, not least because it depends on a non-universal UV cut-off. The Landau level calculation presented here is also ambiguous for relativistic Weyl fermions. However, as we will show, the quasirelativistic approximation we use and the properties of the underlying superfluid or superconductor lead to a natural cut-off for the quasiparticle anomaly. We match this emergent torsional anomaly to the hydrodynamic anomaly in the p+ip-superfluid 3He-A.