arXiv subjects

G. E. Volovik

Publications and source records attributed to G. E. Volovik.

At least 145 records · Page 8Linked to original sources

arXiv2013

Topological Fermi arcs in superfluid $^3$He

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 fermionic spectrum contains Fermi arcs which 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 which relates bulk values of 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 exact spectrum beyond quasiclassical approximation.

cond-mat.supr-con↗

arXiv2013

Euler - Heisenberg effective action and magnetoelectric effect in multilayer graphene

The low energy effective field model for the multilayer graphene (at ABC stacking) is considered. We calculate the effective action in the presence of constant external magnetic field $B$ (normal to the graphene sheet). We also calculate the first two corrections to this effective action caused by the in-plane electric field $E$ at $E/B \ll 1$ and discuss the magnetoelectric effect. In addition, we calculate the imaginary part of the effective action in the presence of constant electric field $E$ and the lowest order correction to it due to the magnetic field ($B/E \ll 1$).

cond-mat.mes-hall↗

arXiv2012

Spin superfluidity and magnon BEC

The spin superfluidity -- superfluidity in the magnetic subsystem of a condensed matter - is manifested as the spontaneous phase-coherent precession of spins first discovered in 1984 in 3He-B. This superfluid current of spins - spin supercurrent - is one more representative of superfluid currents known or discussed in other systems, such as the superfluid current of mass and atoms in superfluid 4He; superfluid current of electric charge in superconductors; superfluid current of hypercharge in Standard Model of particle physics; superfluid baryonic current and current of chiral charge in quark matter; etc. Spin superfluidity can be described in terms of the Bose condensation of spin waves - magnons. We discuss different phases of magnon superfluidity, including those in magnetic trap; and signatures of magnons superfluidity: (i) spin supercurrent, which transports the magnetization on a macroscopic distance more than 1 cm long; (ii) spin current Josephson effect which shows interference between two condensates; (iii) spin current vortex - a topological defect which is an analog of a quantized vortex in superfluids, of an Abrikosov vortex in superconductors, and cosmic strings in relativistic theories; (iv) Goldstone modes related to the broken U(1) symmetry - phonons in the spin-superfluid magnon gas; etc. We also touch the topic of spin supercurrent in general including spin Hall and intrinsic quantum spin Hall effects.

cond-mat.other↗

arXiv2012

Topology of quantum vacuum

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. 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. 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, give rise to emergent symmetries, including the effective Lorentz invariance, and emergent gauge and gravitational fields. The topological invariants in extended momentum and coordinate space determine the bulk-surface and bulk-vortex correspondence, connecting the topology in bulk with the real space. 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 Horava-Lifshitz gravity.

hep-ph↗

arXiv2012

The cosmological constant: A lesson from the effective gravity of topological Weyl media

Topological matter with Weyl points, such as superfluid 3He-A, provide an explicit example where there is a direct connection between the properly determined vacuum energy and the cosmological constant of the effective gravity emerging in condensed matter. This is in contrast to the acoustic gravity emerging in Bose-Einstein condensates, where the "value of this constant cannot be easily predicted by just looking at the ground state energy of the microscopic system from which spacetime and its dynamics should emerge" (S. Finazzi, S. Liberati and L. Sindoni, The cosmological constant: a lesson from Bose-Einstein condensates, Phys. Rev. Lett. 108, 071101 (2012)). The advantage of topological matter is that the relativistic fermions and gauge bosons emerging near the Weyl point obey the same effective metric and thus the effective gravity is more closely related to real gravity. We study this connection in the bi-metric gravity emerging in 3He-A, and its relation to the graviton masses, by comparison with a fully relativistic bi-metric theory of gravity. This shows that the parameter λ, which in 3He-A is the bi-metric generalization of the cosmological constant, coincides with the difference in the proper energy of the vacuum in two states (the nonequilibrium state without gravity and the equilibrium state in which gravity emerges) and is on the order of the characteristic Planck energy scale of the system. Although the cosmological constant λ is huge, the cosmological term itself is naturally non-constant and vanishes in the equilibrium vacuum, as dictated by thermodynamics. This suggests that the equilibrium state of any system including the final state of the Universe is not gravitating.

gr-qc↗

arXiv2012

Bose analogs of MIT bag model of hadrons in coherent precession

Recently it was demonstrated that magnon condensation in the trap exhibits the phenomenon of self-localization. When the number of magnons in the textural trap increases, they drastically modify the profile of the gap and highly increase its size. The trap gradually transforms from the initial harmonic one to the box with walls almost impenetrable for magnons. The resulting texture-free "cavity" filled by the magnon condensate wave function becomes the bosonic analog of the MIT bag, in which hadron is seen as a cavity surrounded by the QCD vacuum, in which the free quarks are confined in the ground or excited state. Here we consider the bosonic analog of the MIT bag with quarks on the ground and excited levels.

cond-mat.other↗

arXiv2012

The Superfluid Universe

We discuss phenomenology of quantum vacuum. Phenomenology of macroscopic systems has three sources: thermodynamics, topology and symmetry. Thermodynamics of the self-sustained vacuum allows us to treat the problems related to the vacuum energy: the cosmological constant problems. The natural value of the energy density of the equilibrium the self-sustained vacuum is zero. Cosmology is discussed as the process of relaxation of vacuum towards the equilibrium state. The present value of the cosmological constant is very small compared to the Planck scale, because the present Universe is very old and thus is close to equilibrium. Momentum space topology determines the universality classes of fermionic vacua. The Standard Model vacuum both in its massless and massive states is topological medium. The vacuum in its massless state shares the properties of superfluid 3He-A, which is topological superfluid. It belongs to the Fermi-point universality class, which has topologically protected fermionic quasiparticles. At low energy they behave as relativistic massless Weyl fermions. Gauge fields and gravity emerge together with Weyl fermions at low energy. This allows us to treat the hierarchy problem in Standard Model: the masses of elementary particles are very small compared to the Planck scale because the natural value of the quark and lepton masses is zero. The small nonzero masses appear in the infrared region, where the quantum vacuum acquires the properties of another topological superfluid, 3He-B, and 3+1 topological insulators. The other topological media in dimensions 2+1 and 3+1 are also discussed. In most cases, topology is supported by discrete symmetry of the underlying microscopic system, which indicates the important role of discrete symmetry in Standard Model.

cond-mat.other↗

arXiv2012

Quantum electrodynamics with anisotropic scaling: Heisenberg-Euler action and Schwinger pair production in the bilayer graphene

We discuss quantum electrodynamics emerging in the vacua with anisotropic scaling. Systems with anisotropic scaling were suggested by Horava in relation to the quantum theory of gravity. In such vacua the space and time are not equivalent, and moreover they obey different scaling laws, called the anisotropic scaling. Such anisotropic scaling takes place for fermions in bilayer graphene, where if one neglects the trigonal warping effects the massless Dirac fermions have quadratic dispersion. This results in the anisotropic quantum electrodynamics, in which electric and magnetic fields obey different scaling laws. Here we discuss the Heisenberg-Euler action and Schwinger pair production in such anisotropic QED

cond-mat.str-el↗

arXiv2012

Flat band in topological matter: possible route to room-temperature superconductivity

Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. In gapless topological media, the bulk-surface and bulk-vortex correspondence produce topologically protected gapless fermions without dispersion - the flat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines and in the vortex core in systems with topologically protected Fermi points (Weyl points). Flat band has an extremely singular density of states, and this property may give rise in particular to surface superconductivity which in principle could exist even at room temperature.

cond-mat.str-el↗

arXiv2012

Momentum space topological invariants for the 4D relativistic vacua with mass gap

Topological invariants for the 4D gapped system are discussed with application to the quantum vacua of relativistic quantum fields. Expression $\tilde{\cal N}_3$ for the 4D systems with mass gap defined in \cite{Volovik2010} is considered. It is demonstrated that $\tilde{\cal N}_3$ remains the topological invariant when the interacting theory in deep ultraviolet is effectively massless. We also consider the 5D systems and demonstrate how 4D invariants emerge as a result of the dimensional reduction. In particular, the new 4D invariant $\tilde{\cal N}_5$ is suggested. The index theorem is proved that defines the number of massless fermions $n_F$ in the intermediate vacuum, which exists at the transition line between the massive vacua with different values of $\tilde{\cal N}_5$. Namely, $ 2 n_F$ is equal to the jump $Δ\tilde{\cal N}_5$ across the transition. The jump $Δ\tilde{\cal N}_3$ at the transition determines the number of only those massless fermions, which live near the hypersurface $ω=0$. The considered invariants are calculated for the lattice model with Wilson fermions.

hep-ph↗

arXiv2011

Superluminal neutrino and spontaneous breaking of Lorentz invariance

Generally speaking, the existence of a superluminal neutrino can be attributed either to re-entrant Lorentz violation at ultralow energy from intrinsic Lorentz violation at ultrahigh energy or to spontaneous breaking of fundamental Lorentz invariance (possibly by the formation of a fermionic condensate). Re-entrant Lorentz violation in the neutrino sector has been discussed elsewhere. Here, the focus is on mechanisms of spontaneous symmetry breaking.

hep-ph↗

arXiv2011

Self-localization of magnon Bose-Einstein condensates in the ground state and on excited levels: from harmonic to box-like trapping potential

Long-lived coherent spin precession of 3He-B at low temperatures around 0.2 Tc 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.

cond-mat.quant-gas↗

arXiv2011

Evolution of edge states in topological superfluids during the quantum phase transition

The quantum phase transition between topological and non-topological insulators or between fully gapped superfluids/superconductors can occur without closing the gap. We consider the evolution of the Majorana edge states on the surface of topological superconductor during transition to the topologically trivial superconductor on example of non-interacting Hamiltonian describing the spin-triplet superfluid 3He-B. In conventional situation when the gap is nullified at the transition, the spectrum of Majorana fermions shrinks and vanishes after the transition to the trivial state. If the topological transition occurs without the gap closing, the Majorana fermion spectrum disappears by escaping to ultraviolet, where Green's function approaches zero. This demonstrates the close connection between the topological transition without closing the gap and zeroes in the Green's function. Similar connection takes place in interacting systems where zeroes may occur due to interaction.

cond-mat.str-el↗

arXiv2011

From Analogue Models to Gravitating Vacuum

We discuss phenomenology of quantum vacuum. Phenomenology of macroscopic systems has three sources: thermodynamics, topology and symmetry. Momentum space topology determines the universality classes of fermionic vacua. The vacuum in its massless state belongs to the Fermi-point universality class, which has topologically protected fermionic quasiparticles. At low energy they behave as relativistic massless Weyl fermions. Gauge fields and gravity emerge together with Weyl fermions at low energy. Thermodynamics of the self-sustained vacuum allows us to treat the problems related to the vacuum energy: the cosmological constant problems. The natural value of the energy density of the equilibrium the self-sustained vacuum is zero. Cosmology is the process of relaxation of vacuum towards the equilibrium state. The present value of the cosmological constant is very small compared to the Planck scale, because the present Universe is very old and thus is close to equilibrium.

gr-qc↗

arXiv2011

Dynamics of the quantum vacuum: Cosmology as relaxation to the equilibrium state

The behavior of the gravitating vacuum energy density in an expanding universe is discussed. A scenario is presented with a step-wise relaxation of the vacuum energy density. The vacuum energy density moves from plateau to plateau and follows, on average, the steadily decreasing matter energy density. The current plateau with a small positive value of the vacuum energy density (effective cosmological constant) may result from a still not equilibrated contribution of the light massive neutrinos to the quantum vacuum.

gr-qc↗

arXiv2011

Flat bands in topological media

Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. Here we show that in gapless topological media, the bulk-surface and bulk-vortex correspondence is more effective: it produces topologically protected gapless fermions without dispersion -- the flat band. Fermion zero modes forming the flat band are localized on the surface of topological media with protected nodal lines and in the vortex core in systems with topologically protected Fermi points (Weyl points). Flat band has an extremely singular density of states, and we show that this property may give rise in particular to surface superconductivity which could exist even at room temperature.

cond-mat.str-el↗

arXiv2011

Superfluid vortex front at T -> 0: Decoupling from the reference frame

Steady-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 0.2 Tc 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.

cond-mat.other↗

arXiv2011

High-temperature surface superconductivity in topological flat-band systems

We 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.

cond-mat.supr-con↗