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Vladimir Juricic

Publications and source records attributed to Vladimir Juricic.

At least 55 records · Page 3Linked to original sources
arXiv2016

Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions

We study the renormalization group flow of the velocities in the field theory describing the coupling of the massless quasi-relativistic fermions to the bosons through the Yukawa coupling, as well as with both bosons and fermions coupled to a fluctuating $U(1)$ gauge field in two and three spatial dimensions. Different versions of this theory describe quantum critical behavior of interacting Dirac fermions in various condensed-matter systems. We perform an analysis using one-loop $ε-$expansion about three spatial dimensions, which is the upper critical dimension in the problem. In two dimensions, we find that velocities of both charged fermions and bosons ultimately flow to the velocity of light, independently of the initial conditions, the number of fermionic and bosonic flavors, and the value of the couplings at the critical point. In three dimensions, due to the analyticity of the gauge field propagator, both the $U(1)$ charge and the velocity of light flow, which leads to a richer behavior than in two dimensions. We show that all three velocities ultimately flow to a common terminal velocity, which is non-universal and different from the original velocity of light. Therefore, emergence of the Lorentz symmetry in the ultimate infrared regime seems to be a rather universal feature of this class of theories in both two and three dimensions.

hep-th↗
arXiv2016

Self-organized pseudo-graphene on grain boundaries in topological band insulators

Semi-metals are characterized by nodal band structures that give rise to exotic electronic properties. The stability of Dirac semi-metals, such as graphene in two spatial dimensions (2D), requires the presence of lattice symmetries, while akin to the surface states of topological band insulators, Weyl semi-metals in three spatial dimensions (3D) are protected by band topology. Here we show that in the bulk of topological band insulators, self-organized topologically protected semi-metals can emerge along a grain boundary, a ubiquitous extended lattice defect in any crystalline material. In addition to experimentally accessible electronic transport measurements, these states exhibit valley anomaly in 2D influencing edge spin transport, whereas in 3D they appear as graphene-like states that may exhibit an odd-integer quantum Hall effect. The general mechanism underlying these novel semi-metals -- the hybridization of spinon modes bound to the grain boundary -- suggests that topological semi-metals can emerge in any topological material where lattice dislocations bind localized topological modes.

cond-mat.mes-hall↗
arXiv2015

Probing crystallinity of graphene samples via the vibrational density of states

The purity of graphene samples is of crucial importance for their experimental and practical use. In this regard, the detection of the defects is of direct relevance. Here, we show that structural defects in graphene samples give rise to clear signals in the vibrational density of states (VDOS) at the specific peaks at high and low frequencies.These can be used as an independent probe of the defect density. In particular, we consider grain boundaries made of pentagon-heptagon pairs, and show that they lead to a shift of the characteristic vibrational D mode towards higher frequency; this distinguishes these line defects from the Stone-Wales point defects, which do not lead to such a shift. Our findings may be instrumental for the detection of structural lattice defects using experimental techniques that can directly measure VDOS, such as inelastic electron tunneling and inelastic neutron spectroscopy.

cond-mat.mtrl-sci↗
arXiv2015

Kekule versus hidden superconducting order in graphene-like systems: Competition and coexistence

We theoretically study the competition between two possible exotic superconducting orders that may occur in graphene-like systems, assuming dominant nearest-neighbor attraction: the gapless hidden superconducting order, which renormalizes the Fermi velocity, and the Kekule order, which opens a superconducting gap. We perform an analysis within the mean-field theory for Dirac electrons, at finite-temperature and finite chemical potential, as well as at half filling and zero-temperature, first excluding the possibility of the coexistence of the two orders. In that case, we find the dependence of the critical (more precisely, crossover) temperature and the critical interaction on the chemical potential. As a result of this analysis, we find that the Kekule order is preferred over the hidden order at both finite temperature and finite chemical potential. However, when the coexistence of the two superconducting orders is allowed, using the coupled mean-field gap equations, we find that above a critical value of the attractive interaction a mixed phase sets in, in which these orders coexist. We show that the critical value of the interaction for this transition is greater than the critical coupling for the hidden superconducting state in the absence of the Kekule order, implying that there is a region in the phase diagram where the Kekule order is favored as a result of the competition with the hidden superconducting order. The latter, however, eventually sets in and coexists with the Kekule state. According to our mean-field calculations, the transition from the Kekule to the mixed phase is of the second order, but it may become first order when fluctuations are considered. Finally, we investigate whether these phases could be possible in honeycomb superlattices of self-assembled semiconducting nanocrystals, which have been recently experimentally realized with CdSe and PbSe.

cond-mat.mes-hall↗
arXiv2015

Stability of the X-Y-phase of the two-dimensional C4 point group insulator

Noninteracting insulating electronic states of matter can be classified according to their symmetries in terms of topological invariants which can be related to effective surface theories. These effective surface theories are in turn topologically protected against the effects of disorder. Topological crystalline insulators are, on the other hand, trivial in the sense of the above classification but still possess surface modes. In this work we consider an extension of the Bernevig-Hughes-Zhang model that describes a topological crystalline insulator. We explicitly show that the surface properties of this state can be as robust as in topologically nontrivial insulators, but only if the $S_z$-component of the spin is conserved. However, in the presence of Rashba spin-orbit coupling this protection vanishes and the surface states localize, even if the crystalline symmetries are intact on average.

cond-mat.mes-hall↗
arXiv2014

Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band-insulators

We elucidate the general rule governing the response of dislocation lines in three-dimensional topological band insulators. According to this ${\bf K}\text{-}{\bf b}\text{-}{\bf t}$ rule, the lattice topology, represented by dislocation lines oriented in direction ${\bf t}$ with Burgers vector ${\bf b}$, combines with the electronic-band topology, characterized by the band-inversion momentum ${\bf K}_{\rm inv}$, to produce gapless propagating modes when the plane orthogonal to the dislocation line features a band inversion with a nontrivial ensuing flux $Φ={\bf K}_{\rm inv}\cdot {\bf b}\,\, ({\rm mod\,\,2π})$. Although it has already been discovered by Y. Ran {\it et al.}, Nature Phys. {\bf 5}, 298 (2009), that dislocation lines host propagating modes, the exact mechanism of their appearance in conjunction with the crystal symmetries of a topological state is provided by the ${\bf K}\text{-}{\bf b}\text{-}{\bf t}$ rule . Finally, we discuss possible experimentally consequential examples in which the modes are oblivious for the direction of propagation, such as the recently proposed topologically-insulating state in electron-doped BaBiO$_3$.

cond-mat.mes-hall↗
arXiv2014

Tight-binding theory of spin-orbit coupling in graphynes

We investigate the effects of Rashba and intrinsic spin-orbit couplings in graphynes. First, we develop a general method to address spin-orbit couplings within the tight-binding theory. Then, we apply this method to $α$, $β$, and $γ$-graphyne, and determine the SOC parameters in terms of the microscopic hopping and on-site energies. We find that for $α$-graphyne, as in graphene, the intrinsic SOC opens a non-trivial gap, whereas the Rashba SOC splits each Dirac cone into four. In $β$ and $γ$ graphyne, the Rashba SOC can lead to a Lifshitz phase transition, thus transforming the zero-gap semiconductor into a gapped system or vice versa, when pairs of Dirac cones annihilate or emerge. The existence of internal (within the benzene ring) and external SOC in these compounds allow us to explore a myriad of phases not available in graphene.

cond-mat.mes-hall↗
arXiv2014

High-Chern-number bands and tunable Dirac cones in $β$-graphyne

Graphynes represent an emerging family of carbon allotropes that recently attracted much interest due to the tunability of the Dirac cones in the band structure. Here, we show that the spin-orbit couplings in $β$-graphyne could produce various effects related to the topological properties of its electronic bands. Intrinsic spin-orbit coupling yields high- and tunable Chern-number bands, which may host both topological and Chern insulators, in the presence and absence of time-reversal symmetry, respectively. Furthermore, Rashba spin-orbit coupling can be used to control the position and the number of Dirac cones in the Brillouin zone. These findings suggest that spin-orbit-related physics in $β$-graphyne is very rich, and, in particular, that this system could provide a platform for the realization of a two-dimensional material with tunable topological properties.

cond-mat.mes-hall↗
arXiv2014

Strain-induced time-reversal odd superconductivity in graphene

Time-reversal symmetry breaking superconductors are exotic phases of matter with fascinating properties, which are, however, encountered rather sparsely. Here we identify the possibility of realizing such a superconducting ground state that exhibits an $f+is$ pairing symmetry in strained graphene. Although the underlying attractive interactions need to be sufficiently strong and comparable in pristine graphene to support such pairing state, we argue that strain can be conducive for its formation even for weak interactions. We show that quantum-critical behavior near the transition is controlled by a multicritical point, characterized by various critical exponents computed here in the framework of an $ε$-expansion near four spacetime dimensions. Furthermore, a vortex in this mixed superconducting state hosts a pair of Majorana fermions supporting a quartet of insulating and superconducting orders, among which topologically nontrivial quantum spin Hall insulator. These findings suggest that strained graphene could provide a platform for the realization of exotic superconducting states of Dirac fermions.

cond-mat.mes-hall↗
arXiv2013

Quantum superconducting criticality in graphene and topological insulators

The field theory of the semimetal-superconductor quantum phase transition for graphene and surface states of topological insulators is presented. The Lagrangian possesses the global U(1) symmetry, with the self-interacting complex bosonic order-parameter and the massless Dirac fermions coupled through a Yukawa term. The same theory also governs the quantum critical behavior of graphene near the transition towards the bond-density-wave (Kekule) insulator. The local U(1) gauged version of the theory which describes the quantum semimetal-superconductor transition in the ultimate critical regime is also considered. Due to the Yukawa coupling the transitions are found to be always continuous, both with and without the fluctuating gauge field. The critical behavior is addressed within the dimensional regularization near four space-time dimensions, and the calculation of various universal quantities, including critical exponents and the universal mass-ratio, is reported.

cond-mat.str-el↗
arXiv2012

The space group classification of topological band insulators

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice symmetries in the physics of these topological states remained elusive. Here we provide the classification of TBIs protected not only by time-reversal, but also by crystalline symmetries. We find three broad classes of topological states: (a) Gamma-states robust against general time-reversal invariant perturbations; (b) Translationally-active states protected from elastic scattering, but susceptible to topological crystalline disorder; (c) Valley topological insulators sensitive to the effects of non-topological and crystalline disorder. These three classes give rise to 18 different two-dimensional, and, at least 70 three-dimensional TBIs, opening up a route for the systematic search for new types of TBIs.

cond-mat.mes-hall↗
arXiv2012

Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator

We show that the existence of a pair of zero-energy modes bound to a vortex carrying a pi-flux is a generic feature of the topologically non-trivial phase of the M-B model, which was introduced to describe the topological band insulator in HgTe quantum wells. We explicitly find the form of the zero-energy states of the corresponding Dirac equation, which contains a novel momentum-dependent mass term and describes a generic topological transition in a band insulator. The obtained modes are exponentially localized in the vortex-core, with the dependence of characteristic length on the parameters of the model matching the dependence extracted from a lattice version of the model. We consider in full generality the short-distance regularization of the vector potential of the vortex, and show that a particular choice yields the modes localized and simultaneously regular at the origin. Finally, we also discuss a realization of two-dimensional spin-charge separation through the vortex zero-modes.

cond-mat.mes-hall↗
arXiv2012

Universal probes of two-dimensional topological insulators: Dislocation and pi-flux

We show that the pi-flux and the dislocation represent topological observables that probe two-dimensional topological order through binding of the zero-energy modes. We analytically demonstrate that pi-flux hosts a Kramers pair of zero modes in the topological Gamma (Berry phase skyrmion at the zero momentum) and M (Berry phase skyrmion at a finite momentum) phases of the M-B model introduced for the HgTe quantum spin Hall insulator. Furthermore, we analytically show that the dislocation acts as a pi-flux, but only so in the M phase. Our numerical analysis confirms this through a Kramers pair of zero modes bound to a dislocation appearing in the M phase only, and further demonstrates the robustness of the modes to disorder and the Rashba coupling. Finally, we conjecture that by studying the zero modes bound to dislocations all translationally distinguishable two-dimensional topological band insulators can be classified.

cond-mat.mes-hall↗
arXiv2010

Conductivity of interacting massless Dirac particles in graphene: Collisionless regime

We provide detailed calculation of the a.c. conductivity in the case of 1/r-Coulomb interacting massless Dirac particles in graphene in the collisionless limit when ω>> T. The analysis of the electron self-energy, current vertex function and polarization function, which enter into the calculation of physical quantities including the a.c. conductivity, is carried out by checking the Ward-Takahashi identities associated with the electrical charge conservation and making sure that they are satisfied at each step. We adopt a variant of the dimensional regularization of Veltman and t'Hooft by taking the spatial dimension D=2-ε, for ε> 0. The procedure adopted here yields a result for the conductivity correction which, while explicitly preserving charge conservation laws, is nevertheless different from the results reported previously in literature.

cond-mat.mes-hall↗
arXiv2009

Relativistic Mott criticality in graphene

We formulate the effective Gross-Neveu-Yukawa theory of the semimetal-insulator transitions on the honeycomb lattice and compute its quantum critical behavior near three (spatial) dimensions. We find that at the critical point Dirac fermions do not survive as coherent excitations and that the $\sim 1/r$ tail of the weak Coulomb interaction is an irrelevant coupling. The emergent Lorentz invariance near criticality implies a universal ratio of the low-temperature specific heats of the metallic and the rotational-symmetry-broken insulating phase.

cond-mat.str-el↗
arXiv2009

Coulomb interaction at the metal-insulator critical point in graphene

We compute the renormalization group flow of the long-ranged electron-electron interaction at the Gross-Neveu quantum critical point between the semimetal and the excitonic insulator in graphene, perturbatively in the small parameter $ε=d-1$, with $d$ as the spatial dimension. The $O(ε)$ correction to the usual beta-function makes the long-range interaction only more irrelevant at the critical than at the Gaussian fixed point. A weak long-range tail of the Coulomb interaction is found to be marginally irrelevant also in arbitrary dimension when the number of Dirac fermions is large. Its ultimate irrelevancy notwithstanding, it is shown that the metal-insulator transition may still be induced by increasing only the long-range tail of the Coulomb interaction.

cond-mat.str-el↗
arXiv2009

Theory of interacting electrons on the honeycomb lattice

The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated by the lattice is D_2 x U_c(1) x (time reversal), where D_2 is the dihedral group, and U_c(1) is a subgroup of the SU_c(2) "chiral" group of the non-interacting Lagrangian, that represents translations in Dirac language. The Lagrangian describing spinless particles respecting this symmetry is parameterized by six independent coupling constants. We show how first imposing the rotational, then Lorentz, and finally chiral symmetry to the quartic terms, in conjunction with the Fierz transformations, eventually reduces the set of couplings to just two, in the "maximally symmetric" local interacting theory. We identify the two critical points in such a Lorentz and chirally symmetric theory as describing metal-insulator transitions into the states with either time-reversal or chiral symmetry being broken. In the site-localized limit of the interacting Hamiltonian the low-energy theory describes the continuous transitions into the insulator with either a finite Haldane's (circulating currents) or Semenoff's (staggered density) masses, both in the universality class of the Gross-Neveu model. The picture of the metal-insulator transition on a honeycomb lattice emerges at which the residue of the quasiparticle pole at the metallic and the mass-gap in the insulating phase both vanish continuously as the critical point is approached. We argue that the Fermi velocity is non-critical as a consequence of the dynamical exponent being fixed to unity by the emergent Lorentz invariance. Effects of long-range interaction and the critical behavior of specific heat and conductivity are discussed.

cond-mat.str-el↗