Anomalous Thermal Hall Effect in Chiral Phases of $$^3$$He-Aerogel

We report theoretical results for heat transport by quasiparticle excitations in superfluid $^3$He infused into silica aerogel engineered with uniaxial anisotropy. For this system two distinct equal spin pairing (ESP) phases have been reported based on NMR spectroscopy. Theoretical analysis predicts the first ESP state to be chiral A phase axis aligned along strain axis, and lower temperature a polar-distorted random transverse fluctuations orientation of axis. calculations high phase, including an anomalous (zero field) thermal Hall current originating from branch conversion scattering Bogoliubov quasiparticles order parameter induced potential aerogel. Observation would provide direct signature underlying chirality topology "stretched" aerogels.