arXiv subjects

G. E. Volovik

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

At least 91 records · Page 5Linked to original sources

arXiv2018

Half-quantum vortices and walls bounded by strings in the polar-distorted phases of topological superfluid $^3$He

Symmetries of the physical world have guided formulation of fundamental laws, including relativistic quantum field theory and understanding of possible states of matter. Topological defects (TDs) often control the universal behavior of macroscopic quantum systems, while topology and broken symmetries determine allowed TDs. Taking advantage of the symmetry-breaking patterns in the phase diagram of nanoconfined superfluid $^3$He, we show that half-quantum vortices (HQVs) -- linear topological defects carrying half quantum of circulation -- survive transitions from the polar phase to other superfluid phases with polar distortion. In the polar-distorted A phase, HQV cores in 2D systems should harbor non-Abelian Majorana modes. In the polar-distorted B phase, HQVs form composite defects -- walls bounded by strings hypothesized decades ago in cosmology. Our experiments establish the superfluid phases of $^3$He in nanostructured confinement as a promising topological media for further investigations ranging from topological quantum computing to cosmology and grand unification scenarios.

cond-mat.other↗

arXiv2018

Negative temperature for negative lapse function

Fermion dynamics distinguishes spacetimes having the same metric $g_{μν}$, but different tetrads $e_{μa}$, and in particular, it distinguishes a lapse with negative sign, $N<0$.[1] Here we show that the quasiequilibrium thermodynamic state may exist, in which the region with $N<0$ has negative local temperature $T({\bf r})<0$, while the global Tolman temperature $T_0$ remains positive. For bosons, only $N^2$ matters. However, if bosons are composite, they may inherit the negative $T({\bf r})$ from the fermions, and thus they may distinguish the spacetimes with positive and negative lapse functions via thermodynamics.

gr-qc↗

arXiv2018

Spin, orbital, Weyl and other glasses in topological superfluids

One of the most spectacular discoveries made in superfluid $^3$He confined in a nanostructured material like aerogel or nafen was the observation of the destruction of the long-range orientational order by a weak random anisotropy. The quenched random anisotropy provided by the confining material strands produces several different glass states resolved in NMR experiments in the chiral superfluid $^3$He-A and in the time-reversal-invariant polar phase. The smooth textures of spin and orbital order parameters in these glasses can be characterized in terms of the randomly distributed topological charges, which describe skyrmions, spin vortices and hopfions. In addition, in these skyrmion glasses the momentum-space topological invariants are randomly distributed in space. The Chern mosaic, Weyl glass, torsion glass and other exotic topological sates are examples of close connections between the real-space and momentum-space topologies in superfluid $^3$He phases in aerogel.

cond-mat.dis-nn↗

arXiv2018

Tetrads in solids: from elasticity theory to topological quantum Hall systems and Weyl fermions

Theory of elasticity in topological insulators has many common features with relativistic quantum fields interacting with gravitational field in the tetrad form. Here we discuss several issues in the effective topological (pseudo)electromagnetic response in three-dimensional weak crystalline topological insulators with no time-reversal symmetry that feature elasticity tetrads, including a mixed "axial-gravitational" anomaly. This response has some resemblance to "quasitopological" terms proposed for massless Weyl quasiparticles with separate, emergent fermion tetrads. As an example, we discuss the chiral/axial anomaly in superfluid 3He-A. We demonstrate the principal difference between the elasticity tetrads and the Weyl fermion tetrads in the construction of the topological terms in the action. In particular, the topological action expressed in terms of the elasticity tetrads, cannot be expressed in terms of the Weyl fermion tetrads since in this case the gauge invariance is lost.

cond-mat.str-el↗

arXiv2018

Observation of time quasicrystal and its transition to superfluid time crystal

We report experimental realization of a quantum time quasicrystal, and its transformation to a quantum time crystal. We study Bose-Einstein condensation of magnons, associated with coherent spin precession, created in a flexible trap in superfluid $^3$He-B. Under a periodic drive with an oscillating magnetic field, the coherent spin precession is stabilized at a frequency smaller than that of the drive, demonstrating spontaneous breaking of discrete time translation symmetry. The induced precession frequency is incommensurate with the drive, and hence the obtained state is a time quasicrystal. When the drive is turned off, the self-sustained coherent precession lives a macroscopically-long time, now representing a time crystal with broken symmetry with respect to continuous time translations. Additionally, the magnon condensate manifests spin superfluidity, justifying calling the obtained state a time supersolid or a time super-crystal.

cond-mat.other↗

arXiv2018

Graphite, graphene and the flat band superconductivity

Superconductivity with transition temperature $T_c=1.7$ K has been reported in bilayer graphene [1,2]. The main factors, which may shed light on the mechanism of the formation of this superconductivity, are the following. Superconductivity is observed in bilayer graphene, when the two layers are twisted, and the maximum of $T_c$ takes place at the "magic angle" of twist, at which the electronic band structure becomes nearly flat. The same factors have been suggested [3] to explain the experiments in graphite [4-8], which reported high-T superconductivity in highly oriented pyrolytic graphite (HOPG). The hints of room-T superconductivity are present, only when the sample contains quasi two-dimensional interfaces between the domains of HOPG. These domains should be twisted with respect to each other in order to form the flat band in electronic spectrum. This dispersionless energy spectrum has a singular density of states, which provides the transition temperature being proportional to the coupling constant instead of the exponential suppression. The graphite and its superconductivity is now becoming the mainstream. One may say that we are coming to graphite era of superconductivity. It is time to combine the theoretical and experimental efforts to reach the bulk room-T superconductivity in graphite and in similar real or artificial materials.

cond-mat.supr-con↗

arXiv2018

Polar phase of superfluid $^3$He: Dirac lines in the parameter and momentum spaces

The time reversal symmetric polar phase of the spin-triplet superfluid $^3$He has two types of Dirac nodal lines. In addition to the Dirac loop in the spectrum of the fermionic Bogoliubov quasiparticles in the momentum space $(p_x,p_y,p_z)$, the spectrum of bosons (magnons) has Dirac loop in the 3D space of parameters -- the components of magnetic field $(H_x,H_y,H_z)$. The bosonic Dirac system lives on the border between the type-I and type-II.

cond-mat.other↗

arXiv2017

Topology of the $^3$He-A film on corrugated graphene substrate

Thin film of superfluid $^3$He on a corrugated graphene substrate represents topological matter with a smooth disorder. It is possible that the atomically smooth disorder produced by the corrugated graphene does not destroy the superfluidity even in a very thin film, where the system can be considered as quasi two-dimensional topological material. This will allow us to study the effect of disorder on different classes of the $2+1$ topological materials: the chiral $^3$He-A with intrinsic quantum Hall effect and the time reversal invariant planar phase with intrinsic spin quantum Hall effect. In the limit of smooth disorder, the system can be considered as a Chern mosaic -- a collection of domains with different values of Chern numbers. In this limit, the quantization of the Hall conductance is determined by the percolated domain, while the density of the fermionic states is determined by the edge modes on the boundaries of the finite domains. This system can be useful for the general consideration of disorder in the topological matter.

cond-mat.str-el↗

arXiv2017

Dimensional crossover of effective orbital dynamics in polar distorted 3He-A: Transitions to anti-spacetime

Topologically protected superfluid phases of $^3$He allow one to simulate many important aspects of relativistic quantum field theories and quantum gravity in condensed matter. Here we discuss a topological Lifshitz transition of the effective quantum vacuum in which the determinant of the tetrad field changes sign through a crossing to a vacuum state with a degenerate fermionic metric. Such a transition is realized in polar distorted superfluid $^3$He-A in terms of the effective tetrad fields emerging in the vicinity of the superfluid gap nodes: the tetrads of the Weyl points in the chiral A-phase of $^3$He and the degenerate tetrad in the vicinity of a Dirac nodal line in the polar phase of $^3$He. The continuous phase transition from the $A$-phase to the polar phase, i.e. in the transition from the Weyl nodes to the Dirac nodal line and back, allows one to follow the behavior of the fermionic and bosonic effective actions when the sign of the tetrad determinant changes, and the effective chiral space-time transforms to anti-chiral "anti-spacetime". This condensed matter realization demonstrates that while the original fermionic action is analytic across the transition, the effective action for the orbital degrees of freedom (pseudo-EM) fields and gravity have non-analytic behavior. In particular, the action for the pseudo-EM field in the vacuum with Weyl fermions (A-phase) contains the modulus of the tetrad determinant. In the vacuum with the degenerate metric (polar phase) the nodal line is effectively a family of $2+1$d Dirac fermion patches, which leads to a non-analytic $(B^2-E^2)^{3/4}$ QED action in the vicinity of the Dirac line.

cond-mat.supr-con↗

arXiv2017

Bose-Einstein condensation of magnons and spin superfluidity in the polar phase of $^3$He

The polar phase of $^3$He, which is topological spin-triplet superfluid with the Dirac nodal line in the spectrum of Bogolubov quasiparticles, has been recently stabilized in a nanoconfined geometry. We pump magnetic excitations (magnons) into the sample of polar phase and observe how they form a Bose-Einstein condensate, revealed by coherent precession of the magnetization of the sample. Spin superfluidity, which supports this coherence, is associated with the spontaneous breaking of U(1) symmetry by the phase of precession. We observe the corresponding Nambu-Goldstone boson and measure its mass emerging when applied rf field violates the U(1) symmetry explicitly. We suggest that the magnon BEC in the polar phase is a powerful probe for topological objects such as vortices and solitons and topological nodes in the fermionic spectrum.

cond-mat.other↗

arXiv2017

Effective Minkowski to Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar 3He

We discuss the effective metric experienced by the Nambu-Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose-Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid 3He, experimentally observed in uniaxial aerogel 3He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar "ghost" condensate.

cond-mat.other↗

arXiv2017

Relaxation of vacuum energy in q-theory

The $q$-theory formalism aims to describe the thermodynamics and dynamics of the deep quantum vacuum. The thermodynamics leads to an exact cancellation of the quantum-field zero-point-energies in equilibrium, which partly solves the main cosmological constant problem. But, with reversible dynamics, the spatially-flat Friedmann-Robertson-Walker universe asymptotically approaches the Minkowski vacuum only if the Big Bang already started out in an initial equilibrium state. Here, we extend $q$-theory by introducing dissipation from irreversible processes. Neglecting the possible instability of a de-Sitter vacuum, we obtain different scenarios with either a de-Sitter asymptote or collapse to a final singularity. The Minkowski asymptote still requires fine-tuning of the initial conditions. This suggests that, within the $q$-theory approach, the decay of the de-Sitter vacuum is a necessary condition for the dynamical solution of the cosmological constant problem.

hep-th↗

arXiv2017

Exotic Lifshitz transitions in topological materials

Topological Lifshitz transitions involve many types of topological structures in momentum and frequency-momentum spaces: Fermi surfaces, Dirac lines, Dirac and Weyl points, etc. Each of these structures has their own topological invariant ($N_1$, $N_2$, $N_3$, $\tilde N_3$, etc.), which supports the stability of a given topological structure. The topology of the shape of Fermi surfaces and Dirac lines, as well as the interconnection of the objects of different dimensions, lead to numerous classes of Lifshitz transitions. The consequences of Lifshitz transitions are important in different areas of physics. The singularities emerging at the transition may enhance the transition temperature to superconductivity; the Lifshitz transition can be in the origin of the small masses of elementary particles in our Universe; the black hole horizon serves as the surface of Lifshitz transition between the vacua with type-I and type-II Weyl points; etc.

cond-mat.other↗

arXiv2017

Propagation of self-localised Q-ball solitons in the $^3$He universe

In relativistic quantum field theories, compact objects of interacting bosons can become stable owing to conservation of an additive quantum number $Q$. Discovering such $Q$-balls propagating in the Universe would confirm supersymmetric extensions of the standard model and may shed light on the mysteries of dark matter, but no unambiguous experimental evidence exists. We report observation of a propagating long-lived $Q$-ball in superfluid $^3$He, where the role of $Q$-ball is played by a Bose-Einstein condensate of magnon quasiparticles. We achieve accurate representation of the $Q$-ball Hamiltonian using the influence of the number of magnons, corresponding to the charge $Q$, on the orbital structure of the superfluid $^3$He order parameter. This realisation supports multiple coexisting $Q$-balls which in future allows studies of $Q$-ball dynamics, interactions, and collisions.

cond-mat.other↗

arXiv2017

Type-III and IV interacting Weyl points

3+1-dimensional Weyl fermions in interacting systems are described by effective quasi-relativistic Green's functions parametrized by a 16 element matrix $e^μ_α$ in an expansion around the Weyl point. The matrix $e^μ_α$ can be naturally identified as an effective tetrad field for the fermions. The correspondence between the tetrad field and an effective quasi-relativistic metric $g_{μν}$ governing the Weyl fermions allows for the possibility to simulate different classes of metric fields emerging in general relativity in interacting Weyl semimetals. According to this correspondence, there can be four types of Weyl fermions, depending on the signs of the components $g^{00}$ and $g_{00}$ of the effective metric. In addition to the conventional type-I fermions with a tilted Weyl cone and type-II fermions with an overtilted Weyl cone for $g^{00}>0$ and respectively $g_{00}>0$ or $g_{00}<0$, we find additional "type-III" and "type-IV" Weyl fermions with instabilities (complex frequencies) for $g^{00}<0$ and $g_{00}>0$ or $g_{00}<0$, respectively. While the type-I and type-II Weyl points allow us to simulate the black hole event horizon at an interface where $g^{00}$ changes sign, the type-III Weyl point leads to effective spacetimes with closed timelike curves.

cond-mat.str-el↗

arXiv2017

Propagating q-field and q-ball solution

One possible solution of the cosmological constant problem involves a so-called $q$-field, which self-adjusts so as to give a vanishing gravitating vacuum energy density (cosmological constant) in equilibrium. We show that this $q$-field can manifest itself in other ways. Specifically, we establish a propagating mode ($q$-wave) in the nontrivial vacuum and find a particular soliton-type solution in flat spacetime, which we call a $q$-ball by analogy with the well-known $Q$-ball solution. Both $q$-waves and $q$-balls are expected to play a role for the equilibration of the $q$-field in the very early universe.

hep-th↗

arXiv2017

Lifshitz transitions, type-II Dirac and Weyl fermions, event horizon and all that

The type-II Weyl and type-II Dirac points emerge in semimetals and also in relativistic systems. In particular, the type-II Weyl fermions may emerge behind the event horizon of black holes. In this case the horizon with Painleve-Gullstrand metric serves as the surface of the Lifshitz transition. This relativistic analogy allows us to simulate the black hole horizon and Hawking radiation using the fermionic superfluid with supercritical velocity, and the Dirac and Weyl semimetals with the interface separating the type-I and type-II states. The difference between such type of the artificial event horizon and that which arises in acoustic metric is discussed. At the Lifshitz transition between type-I and type-II fermions the Dirac lines may also emerge, which are supported by the combined action of topology and symmetry. The type-II Weyl and Dirac points also emerge as the intermediate states of the topological Lifshitz transitions. Different configurations of the Fermi surfaces, involved in such Lifshitz transition, are discussed. In one case the type-II Weyl point connects the Fermi pockets, and the Lifshitz transition corresponds to the transfer of the Berry flux between the Fermi pockets. In the other case the type-II Weyl point connects the outer and inner Fermi surfaces. At the Lifshitz transition the Weyl point is released from both Fermi surfaces. These examples reveal the complexity and universality of topological Lifshitz transitions, which originate from the ubiquitous interplay of a variety of topological characters of the momentum-space manifolds. For the interacting electrons, the Lifshitz transitions may lead to the formation of the dispersionless (flat) band with zero energy and singular density of states, which opens the route to room-temperature superconductivity.

cond-mat.other↗

arXiv2017

Dark matter from dark energy in q-theory

A constant (spacetime-independent) $q$-field may play a crucial role for the cancellation of Planck-scale contributions to the gravitating vacuum energy density. We now show that a small spacetime-dependent perturbation of the equilibrium $q$-field behaves gravitationally as a pressureless perfect fluid. This makes the fluctuating part of the $q$-field a candidate for the inferred dark-matter component of the present universe. For a Planck-scale oscillation frequency of the $q$-field perturbation, the implication would be that direct searches for dark-matter particles would remain unsuccessful in the foreseeable future.

physics.gen-ph↗