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Register a new userHard domain walls in superfluid 3He-B
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We study theoretically planar interfaces between two domains of superfluid 3He-B. The structure of the B-B walls is determined on the scale of the superfluid condensation energy, and thus the domain walls have thickness on the order of the Ginzburg-Landau coherence length. We study the stability and decay schemes of five inequivalent structures of such domain walls using one-dimensional Ginzburg-Landau simulation. We find that only one of the structures is stable against small perturbations. We also argue that B-B interfaces could result from adiabatic A to B transition and study textures at B-B interfaces. The B-B interface has a strong orienting effect on spin-orbit rotation producing textures similar as caused by external walls. We study the B-B interface in a parallel-plate geometry and find that the conservation of spin current sets an essential condition on the structure. The stable B-B interface gives rise to half-quantum circulation.
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In recent work it was shown that new anisotropic p-wave states of superfluid 3He can be stabilized within high porosity silica aerogel under uniform positive strain [1]. In contrast, the equilibrium phase in an unstrained aerogel, is the isotropic superfluid B-phase [2]. Here we report that this phase stability depends on the sign of the strain. For negative strain of ~20% achieved by compression, the B-phase can be made more stable than the anisotropic A-phase resulting in a tricritical point for A, B, and normal phases with a critical field of ~100 mT. From pulsed NMR measurements we identify these phases and the orientation of the angular momentum.
Superfluid 3He is an unconventional neutral superfluid in a p-wave state with three different superfluid phases each identified by a unique set of characteristic broken symmetries and non- trivial topology. Despite natural immunity of 3He from defects and impurity of any kind, it has been found that they can be artificially introduced with high porosity silica aerogel. Furthermore, it has been shown that this modified quantum liquid becomes a superfluid with remarkably sharp thermodynamic transitions from the normal state and between its various phases. They include new superfluid phases that are stabilized by anisotropy from uniform strain imposed on the silica aerogel framework and they include new phenomena in a new class of anisotropic aerogels consisting of nematically ordered alumina strands. The study of superfluid 3He in the presence of correlated, quenched disorder from aerogel, serves as a model for understanding the effect of impurities on the symmetry and topology of unconventional superconductors.
The theoretical study of topological superfluids and superconductors has so far been carried out largely as a translation of the theory of noninteracting topological insulators into the superfluid language, whereby one replaces electrons by Bogoliubov quasiparticles and single-particle band Hamiltonians by Bogoliubov-de Gennes Hamiltonians. Band insulators and superfluids are, however, fundamentally different: while the former exist in the absence of inter-particle interactions, the latter are broken symmetry states that owe their very existence to such interactions. In particular, unlike the static energy gap of a band insulator, the gap in a superfluid is due to a dynamical order parameter that is subject to both thermal and quantum fluctuations. In this work, we explore the consequences of bulk quantum fluctuations of the order parameter in the $B$ phase of superfluid $^3$He on the topologically protected Majorana surface states. Neglecting the high-energy amplitude modes, we find that one of the three spin-orbit Goldstone modes in $^3$He-$B$ couples to the surface Majorana fermions. This coupling in turn induces an effective short-range two-body interaction between the Majorana fermions, with coupling constant inversely proportional to the strength of the nuclear dipole-dipole interaction in bulk $^3$He. A mean-field theory estimate of the value of this coupling suggests that the surface Majorana fermions in $^3$He-$B$ are in the vicinity of a quantum phase transition to a gapped time-reversal symmetry breaking phase.
Motivated by experiments on the superfluid 3He confined in a thin slab, we design a concrete experimental setup for observing the Majorana surface states. We solve the quasi-classical Eilenberger equation, which is quantitatively reliable, to evaluate several quantities, such as local density of states (LDOS), mass current for the A-phase, and spin current for the B-phase. In connection with realistic slab samples, we consider the upper and lower surfaces and the side edges including the corners with several thicknesses. Consequently the influence on the Majorana zero modes from the spatial variation of l-vector for the A-phase in thick slabs and the energy splitting of the zero-energy quasi-particles for the B-phase confined in thin slabs are demonstrated. The corner of slabs in the B-phase is accompanied by the unique zero-energy LDOS of corner modes. On the basis of the quantitative calculation, we propose several feasible and verifiable experiments to check the existence of the Majorana surface states, such as the measurement of specific heat, edge current, and anisotropic spin susceptibility.
The discovery of superfluidity in 3He in 1971, published in 1972, [1, 2] has influenced a wide range of investigations that extend well beyond fermionic superfluids, including electronic quantum ma- terials, ultra-cold gases and degenerate neutron matter. Observation of thermodynamic transitions from the 3He Fermi liquid to two other liquid phases, A and B-phases, along the melting curve of liquid and solid 3He, discovered by Osheroff, Richardson, and Lee, were the very first indications of 3He superfluidity leading to their Nobel prize in 1996. This is a brief retrospective specifically focused on the AB transition.
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