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3 He Universe 2020

G. E. Volovik1,2 Received: 18 August 2020 / Accepted: 19 October 2020 © The Author(s) 2020

Abstract The latest news from 3 He Universe are presented together with the extended map of the Universe. Keywords  Topological superfluids · Topological defects · Chiral anomaly · Effective gravity

1 Introduction The old information on the 3 He Universe can be found in Refs.  [1–3]. The more recent information is in Refs. [4–8]. Here are the latest news from 3 He Universe 2020 (Fig. 1).

2 Topology Superfluid phases of 3 He opened the new area of the application of topological methods to condensed matter systems, see recent reviews in Refs. [5, 7, 8]. 2.1 Topological Superfluids The phases of superfluid 3 He are the best representatives of different families of topological materials. In bulk liquid 3He, there are two topologically different superfluid phases [1]. One is the chiral superfluid 3He-A with topologically protected Weyl points in the quasiparticle spectrum. In the vicinity of the Weyl points, quasiparticles behave as Weyl fermions moving in the effective gauge and gravitational fields. Another phase is the fully gapped time-reversal invariant superfluid 3He-B. It * G. E. Volovik [email protected] 1

Department of Applied Physics, Aalto University, P.O. Box 15100, 00076 Aalto, Finland

2

Landau Institute for Theoretical Physics, acad. Semyonov av., 1a, Chernogolovka, Russia 142432



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Journal of Low Temperature Physics

Fig. 1  3 He Universe-2020. On the Far East is a connection with the neighboring Abrikosov Universe, which was also born in 1971 [9, 10]. The 3 He Universe-1997 is in Fig. 1 of Ref. [11], and the comparison demonstrates inflating expansion of the 3 He Universe (Color figure online)

has topologically protected gapless Majorana fermions living on the surface. In 3 He confined in the nematically ordered aerogel, the polar phase of 3 He has been stabilized [12–14]. It is the time-reversal invariant superfluid, which contains Dirac nodal ring in the fermionic spectrum and flat band on the surface. 2.1.1 Chiral 3He‑A, Weyl Fermions, Flat Band of Majorana Fermions on Vortices Chirality of 3He-A has been probed in the torsional oscillator measurements that distinguished between states of opposite chiralities [15, 16]. The topological manifestation of chirality is the separation of left-handed and right-handed Weyl points in momentum space. Due to bulk-vortex correspondence, the separation of the Weyl points leads to the flat band of Majorana fermions living in the vortex core [17–19]. In topological Weyl semimetals, the similar bulk-surface correspondence produces the so-called Fermi arc on the surface of the material [20]. 2.1.2 3He‑B, Higher‑Order Topology The topological superfluid 3He-B is the prototype of topological insulators and provides an example of the higher-order topology. The boundary of the B-phase contains 2D gapless Majorana fermions, which are supported by topology and symmetry

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Journal of Low Temperature Physics

of the B-