Keynote Talk

Authors: J. A. Sauls
Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208
August 18, 2017

Abstract: The quantum liquid phases of Helium are paradigms for spontaneous symmetry breaking in condensed matter physics. I start with a tutorial on the broken symmetries exhibited by the bulk A- and B-phases of ³He, and the resulting spectrum of Nambu-Goldstone and Higgs modes of these two possible ground states of ³He. I also highlight key experiments that have detected these Bosonic excitations. The superfluid phases ³He are also examples of topological quantum matter. I continue with a short tutorial on the topology of the A- and B-phase ground states, and the implications of non-trivial topology on the Fermionic excitation spectra - Majorana and Weyl Fermions - confined on boundaries, edges and topological defects - vortices and domain walls. An experimental frontier is the detection, characterization and control of Majorana and Weyl fermions that are signatures of the topology of the vacuum states. I highlight experimental signatures of (i) helical Majorana Fermions confined on the surface of ³He-B, and (ii) chiral Weyl Fermions on edge boundaries of ³He-A. For the latter I connect the spectrum of chiral Weyl Fermions with the experimental observation of an anomalous Hall effect for electron transport in ³He-A.

This research was supported by NSF Grant: DMR-1508730

1. J. A. Sauls,  T. Mizushima, On Nambu's Boson-Fermion Mass Relations and Superfluid ³He-B, Phys. Rev. B  95,  094515 ( 2017).
2. O. Shevtsov and  J. A. Sauls,  Electron Bubbles and Weyl Fermions in Chiral Superfluid ³He-A Phys. Rev. B  94,  064511 ( 2016).

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