Torsional chiral magnetic effect due to skyrmion textures in a Weyl superfluid ${}^3$He-A

Abstract

We investigate torsional chiral magnetic effect (TCME) induced by skyrmion-vortex textures in the A phase of the superfluid ${}^3$He. In ${}^3$He-A, Bogoliubov quasiparticles around point nodes behave as Weyl fermions, and the nodal direction represented by the $\ell$-vector may form a spatially modulated texture. $\ell$-textures generate a chiral gauge field and a torsion field directly acting on the chirality of Weyl-Bogoliubov quasiparticles. It has been clarified by G. E. Volovik [Pi'sma Zh. Eksp. Teor. Fiz. {\bf 43}, 428 (1986)] that, if the $\ell$-vector is twisted, the chiral gauge field is responsible for the chiral anomaly, leading to an anomalous current along $\ell$. Here we show that, even for non-twisted $\ell$-vector fields, a torsion arising from $\ell$-textures brings about contributions to the equilibrium currents of Weyl-Bogoliubov quasiparticles along $\mathrm{curl}\ell$. This implies that while the anomalous current appears only for the twisted (Bloch-type) skyrmion of the $\ell$-vector, the extra mass current due to TCME always exists regardless of the skyrmion type. Solving the Bogoliubov-de Gennes equation, we demonstrate that both Bloch-type and Néel-type skyrmions induce chiral fermion states with spectral asymmetry, and possess spatially inhomogeneous structures of Weyl bands in the real coordinate space. Furthermore, we discuss the contributions of Weyl-Bogoliubov quasiparticles and continuum states to the mass current density in the vicinity of the topological phase transition. In the weak coupling limit, continuum states give rise to backflow to the mass current generated by Weyl-Bogoliubov quasiparticles, which makes a non-negligible contribution to the orbital angular momentum. As the topological transition is approached, the mass current density is governed by the contribution of continuum states.

12 pages, 7 figures

References in corpus (12)

• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological response in Weyl semimetals and the chiral anomaly
• Weyl Semimetals, Fermi Arcs and Chiral Anomalies (A Short Review)
• Surface States, Edge Currents and the Angular Momentum of Chiral p-wave Superfluids
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Edge Current due to Majorana Fermions in Superfluid ${}^3$He A- and B-Phases
• Quasiparticle Excitations and Evidence for Superconducting Double Transitions in Monocrystalline U0.97Th0.03Be13
• Topology and symmetry of surface Majorana arcs in cyclic superconductors
• Negative thermal magnetoresistivity as a signature of chiral anomaly in Weyl superconductors
• Spin triplet nematic pairing symmetry and superconducting double transition in U${}_{1-x}$Th${}_x$Be${}_{13}$
• Spontaneous helical order of a chiral p-wave superfluid confined in nano-scale channels
• Supercurrent-induced Skyrmion dynamics and Tunable Weyl points in Chiral Magnet with Superconductivity

Cited by in corpus (14)

• Emergent spacetime and gravitational Nieh-Yan anomaly in chiral $p+ip$ Weyl superfluids and superconductors
• Mixed axial-torsional anomaly in Weyl semimetals
• Torsional Landau levels and geometric anomalies in condensed matter Weyl systems
• Topological magnetotorsional effect in Weyl semimetals
• On chiral responses to geometric torsion
• Topological piezoelectric effect and parity anomaly in nodal line semimetals
• Torsion-induced chiral magnetic current in equilibrium
• Topological Anomalous Skin Effect in Weyl Superconductors
• Pseudo-gauge Fields in Dirac and Weyl Materials
• Transitions in vortex skyrmion structures in superfluid ${}^3$He-A driven by an analogue of the zero-charge effect
• Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators
• Holographic quantum singularity
• Impurity bands, line-nodes, and anomalous thermal Hall effect in Weyl superconductors
• Thermal response of the Nieh-Yan term