### Browsing by Author "Volovik, G.E."

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Item Comment on "Scaling of the quasiparticle spectrum for d-wave superconductors"(1997) Volovik, G.E.; Kopnin, N.B.; Department of Neuroscience and Biomedical EngineeringA Comment on the Letter by Steven H. Simon and Patrick A. Lee, Phys. Rev. Lett. 78, 1548 (1997). The authors of the Letter offer a Reply. Received 11 March 1997Item Comment on "T dependence of the magnetic penetration depth in unconventional superconductors at low temperatures: Can it be linear?(1998) Volovik, G.E.A Comment on the Letter by N. Schopohl and O. V. Dolgov, Phys. Rev. Lett. 80, 4761 (1998). The authors of the Letter offer a Reply.Item Composite defect extends analogy between cosmology and 3He(2000) Eltsov, V.B.; Kibble, T.W.B.; Krusius, M.; Ruutu, V.M.H.; Volovik, G.E.Spin-mass vortices have been observed to form in rotating superfluid 3He−B, following the absorption of a thermal neutron and a rapid transition from the normal to the superfluid state. The spin-mass vortex is a composite defect which consists of a planar soliton (wall) which terminates on a linear core (string). This observation fits well within the framework of a cosmological scenario for defect formation, known as the Kibble-Zurek mechanism. It suggests that in the early Universe analogous cosmological defects might have formed.Item Defect formation in Quench-cooled superfluid phase transition(1998) Ruutu, V.M.; Eltsov, V.B.; Krusius, M.; Makhlin, Yu.G.; Plaçais, B.; Volovik, G.E.We use neutron absorption in rotating 3He−B to heat locally a ∼100−μm−size volume into normal phase. When the heated region cools back in microseconds, vortex lines are formed. We record with NMR the number of lines vs the applied superflow velocity and compare to the Kibble-Zurek theory of vortex-loop freeze-out from a random network of defects. The measurements confirm the calculated loop-size distribution and indicate that the superfluid state itself forms as a patchwork of competing A− and B−phase blobs. The consequences to the A→B transition in supercooled 3He−A are discussed.Item Emergent Weyl spinors in multi-fermion systems(2014) Volovik, G.E.; Zubkov, M.A.In Ref. [1] Hořava suggested, that the multi-fermion many-body system with topologically stable Fermi surfaces may effectively be described (in a vicinity of the Fermi surface) by the theory with coarse-grained fermions. The number of the components of these coarse-grained fermions is reduced compared to the original system. Here we consider the 3+13+1 D system and concentrate on the particular case when the Fermi surface has co-dimension p=3p=3, i.e. it represents the Fermi point in momentum space. First we demonstrate explicitly that in agreement with Hořava conjecture, in the vicinity of the Fermi point the original system is reduced to the model with two-component Weyl spinors. Next, we generalize the construction of Hořava to the situation, when the original 3+13+1 D theory contains multi-component Majorana spinors. In this case the system is also reduced to the model of the two-component Weyl fermions in the vicinity of the topologically stable Fermi point. Those fermions experience the emergent gauge field and the gravitational field given by the emergent vierbein. Both these fields (the emergent gauge field and the emergent gravitational field) originate from certain collective excitations of the original system. We speculate, that the given construction may be relevant for the high energy physics in the paradigm, in which the Lorentz symmetry as well as the gravitational and gauge fields are the emergent phenomena, i.e. they appear dynamically in the low energy approximation of the underlined high energy theory.Item Event horizons and ergoregions in 3He(1998) Jacobson, T.A.; Volovik, G.E.Event horizons for fermion quasiparticles naturally arise in moving textures in superconductors and Fermi superfluids. We discuss the example of a planar soliton moving in a superfluid 3He−A, which is closely analogous to a charged rotating black hole. The moving soliton will radiate quasiparticles via the Hawking effect at a temperature of about 5 μK, and via vacuum polarization induced by the effective “electromagnetic field” and “ergoregion.” The superfluid 3He−A thus appears to be a useful system for experimental and theoretical simulations of quantum effects related to event horizons and ergoregions.Item Flux flow in d-wave superconductors: Low temperature universality and scaling(1997) Kopnin, N.B.; Volovik, G.E.; Department of Neuroscience and Biomedical EngineeringWe demonstrate that superclean d-wave superconductors with Δ2∞τ/EF≫1 display a novel type of vortex dynamics: At low temperatures, both dissipative and transverse components of the flux-flow conductivity are found to approach universal values even in the limit of infinite relaxation time. A finite dissipation in the superclean limit is explained in terms of the Landau damping on zero-frequency vortex modes which appear due to minigap nodes in the bound-state spectrum in the vortex core. In the moderately clean regime the scaling law at low T and low field is obtained.Item High-temperature surface superconductivity in topological flat-band systems(2011) Kopnin, N.B.; Heikkilä, T.T.; Volovik, G.E.; O.V.Lounasmaa-laboratorioWe show that the topologically protected flat band emerging on a surface of a nodal fermionic system promotes the surface superconductivity due to an infinitely large density of states associated with the flat band. The critical temperature depends linearly on the pairing interaction and can be thus considerably higher than the exponentially small bulk critical temperature. We discuss an example of surface superconductivity in multilayered graphene with rhombohedral stacking.Item Hopf term for a two-dimensional electron gas(1997) Volovik, G.E.; Yakovenko, V.M.; Department of Neuroscience and Biomedical EngineeringItem Kopnin and Volovik Reply to comment "invalidity of classes of approximate Hall effect calculations(1998) Kopnin, N.B.; Volovik, G.E.A Reply to the Comment by P. Ao. Received 26 January 1998Item Macroscopic parity violating effects and 3He-A(2000) Volovik, G.E.; Vilenkin, A.We discuss parity violating effects in relativistic quantum theory and their analogues in the effective field theory of superfluid 3He−A. A mixed axial-gravitational Chern-Simons term in the relativistic effective action and its condensed matter analogue are responsible for the chiral fermion flux along the rotation axis of the heat bath in a relativistic system and for the unusual Ω-odd dependence of the zero-temperature density of the normal component on the rotation velocity in 3He−A.Item Magnon Condensation into a Q Ball in 3He−B(2007) Bunkov, Yu.M.; Volovik, G.E.; KylmälaboratorioThe theoretical prediction of Q balls in relativistic quantum fields is realized here experimentally in superfluid 3He−B. The condensed-matter analogs of relativistic Q balls are responsible for an extremely long-lived signal of magnetic induction observed in NMR at the lowest temperatures. This Q ball is another representative of a state with phase coherent precession of nuclear spins in 3He−B, similar to the well-known homogeneously precessing domain, which we interpret as Bose-Einstein condensation of spin waves—magnons. At large charge Q, the effect of self-localization is observed. In the language of relativistic quantum fields it is caused by interaction between the charged and neutral fields, where the neutral field provides the potential for the charged one. In the process of self-localization the charged field modifies locally the neutral field so that the potential well is formed in which the charge Q is condensed.Item Mirror as polaron with internal degrees of freedom(2014) Volovik, G.E.; Zubkov, M.A.; O.V.Lounasmaa-laboratorio; University of Western OntarioWe consider the model suggested by Wang and Unruh [Phys. Rev. D 89, 085009 (2014)] for the 1+1-dimensional mirror moving in the quantum vacuum. We consider the relation of this model to the problem of the polaron—the electron moving in the vacuum of the quantum field of phonons. We introduce the field-theoretical model of such a mirror. It contains the multicomponent spinor field interacting with the scalar field. We discuss the source of the logarithmic divergence in the mirror mass and its relation to the problem of the divergencies in vacuum energy.Item Nambu sum rule and the relation between the masses of composite Higgs bosons(2013) Volovik, G.E.; Zubkov, M.A.We review the known results on the bosonic spectrum in various Nambu-Jona-Lasinio models both in condensed matter physics and in relativistic quantum field theory including 3He−B, 3He−A, the thin films of superfluid 3He, and QCD (Hadronic phase and the color-flavor locking phase). Next, we calculate the bosonic spectrum in the relativistic model of top quark condensation suggested in [Phys. Lett. B 221, 177 (1989)]. In all considered cases, the sum rule appears, which relates the masses (energy gaps) Mboson of the bosonic excitations in each channel with the mass (energy gap) of the condensed fermion Mf as ∑M2boson=4M2f. Previously, this relation was established by Nambu for 3He−B and for the s-wave superconductor. We generalize this relation to the wider class of models and call it the Nambu sum rule. We discuss the possibility to apply this sum rule to various models of top quark condensation. In some cases, this rule allows us to calculate the masses of extra Higgs bosons that are the Nambu partners of the125 GeV Higgs.Item Rotating vortex core: An instrument for detecting core excitations(1998) Kopnin, N.B.; Volovik, G.E.Effects of fermion zero modes (bound states in a vortex core) on the rotational dynamics of vortices with spontaneously broken axisymmetry are considered. The results are compared with the Helsinki NMR experiments where the vortex cores were driven to a fast rotation and torsional oscillations by an NMR rf field. We predict a resonance NMR absorption on localized states at the external frequency comparable with the interlevel distance which is similar to the cyclotron Landau damping. The resonances can resolve the localized levels in vortex cores. For a pure rotation of the core, the effect depends on the relative signs of the vortex winding and of the core rotation; thus it is sensitive to the direction of rotation of the container. The similarity with fermion zero modes on fundamental strings, which simulate the thermodynamics of black holes, is discussed.Item Self-trapping of magnon Bose-Einstein Condensates in the ground state and on excited levels: from harmonic to box confinement(2012) Autti, S.; Bunkov, Yu.M.; Eltsov, V.B.; Heikkinen, P.J.; Hosio, J.J.; Hunger, P.; Krusius, M.; Volovik, G.E.; O.V.Lounasmaa-laboratorioLong-lived coherent spin precession of 3He−B at low temperatures around 0.2Tc is a manifestation of Bose-Einstein condensation of spin-wave excitations or magnons in a magnetic trap which is formed by the order-parameter texture and can be manipulated experimentally. When the number of magnons increases, the orbital texture reorients under the influence of the spin-orbit interaction and the profile of the trap gradually changes from harmonic to a square well, with walls almost impenetrable to magnons. This is the first experimental example of Bose condensation in a box. By selective rf pumping the trap can be populated with a ground-state condensate or one at any of the excited energy levels. In the latter case the ground state is simultaneously populated by relaxation from the exited level, forming a system of two coexisting condensates.Item Stable spin precession at one half of equilibrium magnetization in superfluid 3He-B(1997) Dmitriev, V.V.; Kosarev, I.V.; Krusius, M.; Ponarin, D.V.; Ruutu, V.M.H.; Volovik, G.E.; Department of Neuroscience and Biomedical EngineeringNew modes of spin precession have been observed in superfluid 3He−B with a precessing magnetization M=pMeq, where p=1, 12, and ≈0. These dynamic order parameter states are the first examples of stable precession with a magnetization different from the equilibrium value Meq. The p=12 mode is the second example of a phase-coherent state of a spin superfluid. The new states can be excited close to Tc in the range 1−T/Tc≲0.02 where dissipation is low and the energy barriers between the different local minima of the spin-orbit energy are small.Item Superflow-stabilized nonlinear NMR in rotating 3He-B(1999) Dmitriev, V.V.; Eltsov, V.B.; Krusius, M.; Ruohio, J.J.; Volovik, G.E.; KylmälaboratorioNonlinear spin precession has been observed in 3He−B in large counterflow of the normal and superfluid fractions. The new precessing state is stabilized at a high rf excitation level and displays frequency-locked precession over a large range of frequency shifts, with the magnitude of magnetization at its equilibrium value. Comparison to analytical and numerical calculation indicates that in this state the orbital angular momentum L of the Cooper pairs is oriented transverse to the external magnetic field in a “non-Leggett” configuration with broken spin-orbit coupling. The resonance shift depends on the tipping angle θ of the magnetization as ω−ωL=(Ω2B/2ωL)(cosθ−1/5). The phase diagram of the precessing modes with arbitrary orientation of L is constructed.Item Superfluid vortex front at T -> 0: decoupling from the reference frame(2011) Hosio, J.J.; Eltsov, V.B.; de Graaf, R.; Heikkinen, P.J.; Hänninen, R.; Krusius, M.; "L'vov", V.S.; Volovik, G.E.; O.V.Lounasmaa-laboratorioSteady-state turbulent motion is created in superfluid 3He−B at low temperatures in the form of a turbulent vortex front, which moves axially along a rotating cylindrical container of 3He−B and replaces vortex-free flow with vortex lines at constant density. We present the first measurements on the thermal signal from dissipation as a function of time, recorded at 0.2Tc during the front motion, which is monitored using NMR techniques. Both the measurements and the numerical calculations of the vortex dynamics show that at low temperatures the density of the propagating vortices falls well below the equilibrium value, i.e., the superfluid rotates at a smaller angular velocity than the container. This is the first evidence for the decoupling of the superfluid from the container reference frame in the zero-temperature limit.Item Topological Fermi arcs in superfluid 3He(2012) Silaev, M.A.; Volovik, G.E.We consider fermionic states bound on domain walls in a Weyl superfluid 3He-A and on interfaces between 3He-A and a fully gapped topological superfluid 3He-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.