Cosmiclike domain walls in superfluid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="italic">B</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>: Instantons and diabolical points in (<i>k</i>,<i>r</i>) space

Salomaa, M.M.; Volovik, G. E.

doi:10.1103/physrevb.37.9298

Cited by 114 publications

(158 citation statements)

References 20 publications

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“…1(a). This solution shows a well defined domain wall, and is similar as found earlier 8 . It is characterized by a sign change in the component A yy .…”

Section: B-b-10supporting

confidence: 76%

“…5(b) and also found in Ref. 8. We find that this structure deforms further with a very small activation energy.…”

Section: B-b-12supporting

confidence: 65%

“…These include the interfaces 2 and 3 of Ref. 8. The interface free energy σ is 0.90 f B c ξ GL in the weak coupling but decreases to 0.83 f B c ξ GL at the pressure of 28 bar.…”

Section: B-b-10mentioning

confidence: 99%

“…These defects are non-topological and thus disappear by a sufficiently large perturbation. Using numerical solution of the Ginzburg-Landau equations we study the decay modes of the five structures suggested by Salomaa and Volovik 8 . We find that only one of them is stable against small perturbations (Sec.…”

Section: Introductionmentioning

confidence: 99%

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Hard domain walls in superfluidHe3−B

2014

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We study theoretically planar interfaces between two domains of superfluid 3 He-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 ξGL. We study the stability and decay schemes of five inequivalent structures of such domain walls using onedimensional 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→B transition and study textures at B-B interfaces. The B-B interface has a strong orienting effect on the spin-orbit rotation axisn 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. The energies of bound quasiparticle excitations are studied in a simple model.

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“…1(a). This solution shows a well defined domain wall, and is similar as found earlier 8 . It is characterized by a sign change in the component A yy .…”

Section: B-b-10supporting

confidence: 76%

“…5(b) and also found in Ref. 8. We find that this structure deforms further with a very small activation energy.…”

Section: B-b-12supporting

confidence: 65%

“…These include the interfaces 2 and 3 of Ref. 8. The interface free energy σ is 0.90 f B c ξ GL in the weak coupling but decreases to 0.83 f B c ξ GL at the pressure of 28 bar.…”

Section: B-b-10mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hard domain walls in superfluidHe3−B

2014

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“…2(b). We also consider Fermi arcs emerging at the interface between two topologically different quantum vacua: the 3 He-A with Weyl points and the fully gapped 3 He-B, which also has nontrivial topology in momentum space 12,[21][22][23] (AB interface). The Fermi arcs in superfluid 3 He solitons studied in the present paper differ qualitatively from that existing in other systems such as the surface of 3 He-A and Weyl semimetals.…”

Section: Introductionmentioning

confidence: 99%

Topological Fermi arcs in superfluid3He

Силаев

Volovik

2012

Phys. Rev. B

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We consider fermionic states bound on domain walls in a Weyl superfluid 3 He-A and on interfaces between 3 He-A and a fully gapped topological superfluid 3 He-B. We demonstrate that in both cases the fermionic spectrum contains Fermi arcs that are continuous nodal lines of energy spectrum terminating at the projections of two Weyl points to the plane of surface states in momentum space. The number of Fermi arcs is determined by the index theorem that relates bulk values of the topological invariant to the number of zero-energy surface states. The index theorem is consistent with an exact spectrum of Bogolubov-de Gennes equation obtained numerically, meanwhile, the quasiclassical approximation fails to reproduce the correct number of zero modes. Thus we demonstrate that topology describes the properties of the exact spectrum beyond the quasiclassical approximation.

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The Topology of the Quantum Vacuum

Volovik

2013

Lecture Notes in Physics

111

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Topology in momentum space is the main characteristics of the ground states of a system at zero temperature, the quantum vacua. The gaplessness of fermions in bulk, on the surface or inside the vortex core is protected by topology, and is not sensitive to details of the microscopic physics (atomic or trans-Planckian). Irrespective of the deformation of the parameters of the microscopic theory, the energy spectrum of these fermions remains strictly gapless. This solves the main hierarchy problem in particle physics: for fermionic vacua with Fermi points the masses of elementary particles are naturally small. The quantum vacuum of Standard Model is one of the representatives of topological matter alongside with topological superfluids and superconductors, topological insulators and semi-metals, etc. There is a number of of topological invariants in momentum space of different dimensions. They determine universality classes of the topological matter and the type of the effective theory which emerges at low energy. In many cases they also give rise to emergent symmetries, including the effective Lorentz invariance, and emergent phenomena such as effective gauge and gravitational fields. The topological invariants in extended momentum and coordinate space determine the bulk-surface and bulkvortex correspondence. They connect the momentum space topology in bulk with the real space. These invariants determine the gapless fermions living on the surface of a system or in the core of topological defects (vortices, strings, domain walls, solitons, monopoles, etc.). The momentum space topology gives some lessons for quantum gravity. In effective gravity emerging at low energy, the collective variables are the tetrad field and spin connections, while the metric is the composite object of tetrad field. This suggests that the Einstein-Cartan-Sciama-Kibble theory with torsion field is more relevant. There are also several scenarios of Lorentz invariance violation governed by topology, including splitting of Fermi point and development of the Dirac points with quadratic and cubic spectrum. The latter leads to the natural emergence of the Hořava-Lifshitz gravity.

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Cosmiclike domain walls in superfluidB3: Instantons and diabolical points in (k,r) space

Cited by 114 publications

References 20 publications

Hard domain walls in superfluidHe3−B

Hard domain walls in superfluidHe3−B

Topological Fermi arcs in superfluid3He

The Topology of the Quantum Vacuum

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