arXiv subjects

G. E. Volovik

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

At least 127 records · Page 7Linked to original sources

arXiv2015

Emergent geometry experienced by fermions in graphene in the presence of dislocations

In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov - Bohm effect while the torsion singularity results in Stodolsky effect.

cond-mat.mes-hall↗

arXiv2014

Orbital momentum of chiral superfluids and spectral asymmetry of edge states

This is comment to preprint arXiv:1409.7459 by Y. Tada, Wenxing Nie and M. Oshikawa "Orbital angular momentum and spectral flow in two dimensional chiral superfluids", where the effect of spectral flow along the edge states on the magnitude of the orbital angular momentum is discussed. The general conclusion of the preprint on the essential reduction of the angular momentum for the higher values of chirality, $|ν|>1$, is confirmed. However, we show that if parity is violated, the reduction of the angular momentum takes place also for the $p$-wave superfluids with $|ν|=1$.

cond-mat.str-el↗

arXiv2014

Mirror as polaron with internal degrees of freedom

We consider the model suggested by Wang and Unruh \cite{WangUnruh2013} for the $1+1$ D mirror moving in the quantum vacuum. We consider the relation of this model to the problem of 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 multi - component 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.

gr-qc↗

arXiv2014

Andreev-Majorana bound states in superfluids

We consider Andreev-Majorana (AM) bound states with zero energy on surfaces, interfaces and vortices in different phases of the $p$-wave superfluids. We discuss the chiral superfluid $^3$He-A, and time reversal invariant phases: superfluid $^3$He-B, planar and polar phases. The AM zero modes are determined by topology in bulk, and they disappear at the quantum phase transition from the topological to non-topological state of the superfluid. The topology demonstrates the interplay of dimensions. In particular, the zero-dimensional Weyl points in chiral superfluids (the Berry phase monopoles in momentum space) give rise to the one-dimensional Fermi arc of AM bound states on the surface and to the one-dimensional flat band of AM modes in the vortex core. The one-dimensional nodal line in the polar phase produces the two-dimensional flat band of AM modes on the surface. The interplay of dimensions also connects the AM states in superfluids with different dimensions. For example, the topological properties of the spectrum of bound states in the three-dimensional $^3$He-B is connected to the properties of the spectrum in the two-dimensional planar phase (thin film).

cond-mat.other↗

arXiv2014

Topology of the planar phase of superfluid $^3$He and bulk-boundary correspondence for three dimensional topological superconductors

We provide topological classification of possible phases with the symmetry of the planar phase of superfluid $^3$He. Compared to the B-phase (class DIII in classification of Altland and Zirnbauer), it has an additional symmetry, which modifies the topology. We analyze the topology in terms of explicit mappings from the momentum space and also discuss explicitly topological invariants for the B-phase. We further show, how the bulk-boundary correspondence for the 3D B-phase can be inferred from that for the 2D planar phase. A general condition is derived for the existence of topologically stable zero modes at the surfaces of 3D superconductors with class DIII symmetries.

cond-mat.other↗

arXiv2014

Emergent Weyl fermions and the origin of $i=\sqrt{-1}$ in quantum mechanics

Conventional quantum mechanics is described in terms of complex numbers. However, all physical quantities are real. This indicates, that the appearance of complex numbers in quantum mechanics may be the emergent phenomenon, i.e. complex numbers appear in the low energy description of the underlined high energy theory. We suggest a possible explanation of how this may occur. Namely, we consider the system of multi - component Majorana fermions. There is a natural description of this system in terms of real numbers only. In the vicinity of the topologically protected Fermi point this system is described by the effective low energy theory with Weyl fermions. These Weyl fermions interact with the emergent gauge field and the emergent gravitational field.

hep-ph↗

arXiv2014

Emergent Weyl spinors in multi-fermion systems

In Ref. \cite{Horava2005} 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 $3+1$ D system and concentrate on the particular case when the Fermi surface has co-dimension $p=3$, 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 $3+1$ 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 veirbein. 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.

cond-mat.mes-hall↗

arXiv2014

Topological matter: graphene and superfluid 3He

Physics of graphene and physics of superfluid phases of 3He have many common features. Both systems are topological materials where quasiparticles behave as relativistic massless (Weyl, Majorana or Dirac) fermions. We formulate the points where these features are overlapping. This will allow us to use graphene for study the properties of superfluid 3He, to use superfluid 3He for study the properties of graphene, and to use the combination to study the physics of topological quantum vacuum. We suggest also some particular experiments with superfluid 3He using graphene as an atomically thin membrane impenetrable for He atoms but allowing for spin, momentum and energy transfer.

cond-mat.mes-hall↗

arXiv2013

On symmetry and topological origin of Weyl particles

We suggest that the Weil spinors originate from the multi - component fermion fields. Those fields belong to the unusual theory that, presumably, exists at extremely high energies. In this theory there is no Lorentz symmetry. Moreover, complex numbers are not used in the description of its dynamics. Namely, the one - particle wave functions are real - valued, the functional integral that describes the second - quantised theory does not contain the imaginary unit as well. In the low energy effective theory the two - component Weil spinors appear. Their appearance is related to the Atiyah-Bott-Shapiro construction and to the expansion of the real matrix near the topologically protected nodes in three dimensional momentum space. The complex numbers entering ordinary quantum mechanics emerge together with the Weil fermions. In this pattern gauge fields and gravitational fields appear as certain collective excitations (of the original theory) experienced by the low - energy Weil fermions.

physics.gen-ph↗

arXiv2013

Kopnin force and chiral anomaly

Kopnin spectral flow force acting on quantized vortices in superfluid and superconductors is discussed. Kopnin force represents the first realization of the chiral anomaly in condensed matter.

cond-mat.mes-hall↗

arXiv2013

On the broken time translation symmetry in macroscopic systems: precessing states and off-diagonal long-range order

The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the breaking of the time reversal symmetry is observable only if the charge Q is not strictly conserved and may decay. This dihotomy is resolved in systems with quasi-ODLRO. These systems have two well separated relaxation times: the relaxation time τ_Q of the charge Q and the energy relaxation time τ_E. If τ_Q >> τ_E, the perturbed system relaxes first to the state with the ODLRO, which persists for a long time τ_Q and finally relaxes to the full equilibrium static state. In the limit τ_Q -> \infty, but not in the strict limit case when the charge Q is conserved, the intermediate ODLRO state can be considered as the ground state of the system at fixed Q with the observable spontaneously broken time reversal symmetry. Examples of systems with quasi-ODLRO are provided by superfluid phase of liquid 4He, Bose-Einstein condensation of magnons (phase coherent spin precession) and precessing vortices.

cond-mat.other↗

arXiv2013

Spin-motive force and orbital-motive force: from magnon BEC to chiral Weyl superfluids

Spin-motive geometric force acting on electrons in metallic ferromagnets is extended to spin-motive force in magnon BEC, which is represented by phase-coherent precession of magnetization, and to the orbital-motive force in superfluid 3He-A. In 3He-A there are two contributions to the orbital-motive force. One of them comes from the chiral nature of this liquid. Another one originates from chiral Weyl fermions living in the vicinity of the topologically protected Weyl points, and is related to the phenomenon of chiral anomaly.

cond-mat.mes-hall↗

arXiv2013

Emergent gravity in graphene

We reconsider monolayer graphene in the presence of elastic deformations. It is described by the tight - binding model with varying hopping parameters. We demonstrate, that the fermionic quasiparticles propagate in the emergent 2D Weitzenbock geometry and in the presence of the emergent U(1) gauge field. Both emergent geometry and the gauge field are defined by the elastic deformation of graphene.

cond-mat.str-el↗

arXiv2013

Higgs bosons in particle physics and in condensed matter

Higgs bosons - the amplitude modes - have been experimentally investigated in condensed matter for many years. An example is superfluid $^3$He-B, where the broken symmetry leads to 4 Goldstone modes and at least 14 Higgs modes, which are characterized by angular momentum quantum number $J$ and parity. Based on the relation $E_{J+}^2+E_{J-}^2=4Δ^2$ for the energy spectrum of these modes, Yoichiro Nambu proposed the general sum rule, which relates masses of Higgs bosons and masses of fermions. If this rule is applicable to Standard Model, one may expect that the observed Higgs boson with mass $M_{{\rm H}1}=125$ GeV has a Nambu partner -- the second Higgs boson with mass $M_{{\rm H}2}=325$ GeV. Together they satisfy the Nambu relation $M_{{\rm H}1}^2 + M_{{\rm H}2}^2 = 4 M_{\rm top}^2$, where $M_{\rm top}$ is the top quark mass. Also the properties of the Higgs modes in superfluid $^3$He-A, where the symmetry breaking is similar to that of the Standard Model, suggest the possible existence of two electrically charged Higgs particles with masses $M_{{\rm H}+}=M_{{\rm H}-}\sim 245$ GeV, which together obey the Nambu rule $M_{{\rm H}+}^2 + M_{{\rm H}-}^2 = 4 M_{\rm top}^2$. A certain excess of events at 325 GeV and at 245 GeV has been reported in 2011, though not confirmed in 2012 experiments. Besides, we consider the particular relativistic model of top - quark condensation that suggests the possibility that two twice degenerated Higgs bosons contribute to the Nambu sum rule. This gives the mass around 210 GeV for the Nambu partner of the 125 GeV Higgs boson. We also discuss the other possible lessons from the condensed matter to Standard Model, such as hidden symmetry, where light Higgs emerges as quasi Nambu-Goldstone mode, and the role of broken time reversal symmetry.

hep-ph↗

arXiv2013

Emergent Horava gravity in graphene

First of all, we reconsider the tight - binding model of monolayer graphene, in which the variations of the hopping parameters are allowed. We demonstrate that the emergent 2D Weitzenbock geometry as well as the emergent U(1) gauge field appear. The emergent gauge field is equal to the linear combination of the components of the zweibein. Therefore, we actually deal with the gauge fixed version of the emergent 2+1 D teleparallel gravity. In particular, we work out the case, when the variations of the hopping parameters are due to the elastic deformations, and relate the elastic deformations with the emergent zweibein. Next, we investigate the tight - binding model with the varying intralayer hopping parameters for the multilayer graphene with the ABC stacking. In this case the emergent 2D Weitzenbock geometry and the emergent U(1) gauge field appear as well, the emergent low energy effective field theory has the anisotropic scaling.

cond-mat.mes-hall↗

arXiv2013

Unruh effect in vacua with anisotropic scaling: Applications to multilayer graphene

We extend the calculation of the Unruh effect to the universality classes of quantum vacua obeying topologically protected invariance under anisotropic scaling ${\bf r} \rightarrow b {\bf r}$, $t \rightarrow b^z t$. Two situations are considered. The first one is related to the accelerated detector which detects the electron - hole pairs. The second one is related to the system in external electric field, when the electron - hole pairs are created due to the Schwinger process. As distinct from the Unruh effect in relativistic systems (where $z=1$) the calculated radiation is not thermal, but has properties of systems in the vicinity of quantum criticality. The vacuum obeying anisotropic scaling can be realized, in particular, in multilayer graphene with the rhombohedral stacking. Opportunities of the experimental realization of Unruh effect in this situation are discussed.

cond-mat.mes-hall↗

arXiv2013

The Nambu sum rule and the relation between the masses of composite Higgs bosons

We review the known results on the bosonic spectrum in various NJL models both in the condensed matter physics and in relativistic quantum field theory including $^3$He-B, $^3$He-A, the thin films of superfluid He-3, and QCD (Hadronic phase and the Color Flavor Locking phase). Next, we calculate bosonic spectrum in the relativistic model of top quark condensation suggested in \cite{Miransky}. In all considered cases the sum rule appears that relates the masses (energy gaps) $M_{boson}$ of the bosonic excitations in each channel with the mass (energy gap) of the condensed fermion $M_f$ as $\sum M_{boson}^2 = 4 M_f^2$. Previously this relation was established by Nambu in \cite{Nambu} for $^3$He-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 to calculate the masses of extra Higgs bosons that are the Nambu partners of the 125 GeV Higgs.

hep-ph↗

arXiv2013

Nambu sum rule in the NJL models: from superfluidity to top quark condensation

It may appear that the recently found resonance at 125 GeV is not the only Higgs boson. We point out the possibility that the Higgs bosons appear in models of top-quark condensation, where the masses of the bosonic excitations are related to the top quark mass by the sum rule similar to the Nambu sum rule of the NJL models \cite{Nambu}. This rule was originally considered by Nambu for superfluid $^3$He-B and for the BCS model of superconductivity. It relates the two masses of bosonic excitations existing in each channel of Cooper pairing to the fermion mass. An example of the Nambu partners is provided by the amplitude and the phase modes in the BCS model describing Cooper pairing in the s-wave channel. This sum rule suggests the existence of the Nambu partners for the 125 GeV Higgs boson. Their masses can be predicted by the Nambu sum rule under certain circumstances. For example, if there are only two states in the given channel, the mass of the Nambu partner is $\sim$ 325 GeV. They together satisfy the Nambu sum rule $M_1^2 + M_2^2 = 4 M_t^2$, where $M_t \sim $174 GeV is the mass of the top quark. If there are two doubly degenerated states, then the second mass is $\sim$ 210 GeV. In this case the Nambu sum rule is $2 M_1^2 + 2 M_2^2 = 4 M_t^2$. In addition, the properties of the Higgs modes in superfluid $^3$He-A, where the symmetry breaking is similar to that of the Standard Model of particle physics, suggest the existence of two electrically charged Higgs particles with masses around 245 GeV, which together also obey the Nambu sum rule $M_+^2 + M_-^2 = 4 M_t^2$.

hep-ph↗