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  • 1. Jain, Sandeep K.
    et al.
    Juricic, Vladimir
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Barkema, Gerard T.
    Probing the shape of a graphene nanobubble2017In: Physical Chemistry, Chemical Physics - PCCP, ISSN 1463-9076, E-ISSN 1463-9084, Vol. 19, no 11, p. 7465-7470Article in journal (Refereed)
    Abstract [en]

    Gas molecules trapped between graphene and various substrates in the form of bubbles are observed experimentally. The study of these bubbles is useful in determining the elastic and mechanical properties of graphene and adhesion energy between graphene and the substrate, and manipulating the electronic properties via strain engineering. In our numerical simulations, we use a simple description of the elastic potential and adhesion energy to show that for small gas bubbles (similar to 10 nm) the van derWaals pressure is in the order of 1 GPa. These bubbles show universal shape behavior irrespective of their size, as observed in recent experiments. With our results, the shape and volume of the trapped gas can be determined via the vibrational density of states (VDOS) using experimental techniques such as inelastic electron tunneling and inelastic neutron scattering. The elastic energy distribution in the graphene layer which traps the nanobubble is homogeneous apart from its edge, but the strain depends on the bubble size; thus variation in bubble size allows control of the electronic and optical properties.

  • 2. Jain, Sandeep K.
    et al.
    Juričić, Vladimir
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Universiteit Utrecht, The Netherlands.
    Barkema, Gerard T.
    Boundaries determine the formation energies of lattice defects in two-dimensional buckled materials2016In: Physical Review B, ISSN 2469-9950, Vol. 94, no 2, article id 020102Article in journal (Refereed)
    Abstract [en]

    Lattice defects are inevitably present in two-dimensional materials, with direct implications on their physical and chemical properties. We show that the formation energy of a lattice defect in buckled two-dimensional crystals is not uniquely defined as it takes different values for different boundary conditions even in the thermodynamic limit, as opposed to their perfectly planar counterparts. Also, the approach to the thermodynamic limit follows a different scaling: inversely proportional to the logarithm of the system size for buckled materials, rather than the usual power-law approach. In graphene samples of similar to 1000 atoms, different boundary conditions can cause differences exceeding 10 eV. Besides presenting numerical evidence in simulations, we show that the universal features in this behavior can be understood with simple bead-spring models. Fundamentally, our findings imply that it is necessary to specify the boundary conditions for the energy of the lattice defects in the buckled two-dimensional crystals to be uniquely defined, and this may explain the lack of agreement in the reported values of formation energies in graphene. We argue that boundary conditions may also have an impact on other physical observables such as the melting temperature.

  • 3. Jain, Sandeep K.
    et al.
    Juričić, Vladimir
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Barkema, Gerard T.
    Structure of twisted and buckled bilayer graphene2017In: 2d materials, ISSN 2053-1583, Vol. 4, no 1, article id 015018Article in journal (Refereed)
    Abstract [en]

    We study the atomic structure of twisted bilayer graphene, with very small mismatch angles (theta similar to 0.28(0)), a topic of intense recent interest. We use simulations, in which we combine a recently presented semi-empirical potential for single-layer graphene, with a new term for out-of-plane deformations, (Jain et al. 2015 J. Phys. Chem. C119 9646) and an often-used interlayer potential (Kolmogorov et al 2005 Phys. Rev. B 71 235415). This combination of potentials is computationally cheap but accurate and precise at the same time, allowing us to study very large samples, which is necessary to reach very small mismatch angles in periodic samples. By performing large scale atomistic simulations, we show that the vortices appearing in the Moire pattern in the twisted bilayer graphene samples converge to a constant size in the thermodynamic limit. Furthermore, the well known sinusoidal behavior of energy no longer persists once the misorientation angle becomes very small (theta < 1(0)). We also show that there is a significant buckling after the relaxation in the samples, with the buckling height proportional to the system size. These structural properties have direct consequences on the electronic and optical properties of bilayer graphene.

  • 4.
    Juricic, Vladimir
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Abergel, David S. L.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Balatsky, Alexander V.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Los Alamos National Laboratory, USA; ETH Institute for Theoretical Studies, Switzerland.
    First-order quantum phase transition in three-dimensional topological band insulators2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 16, article id 161403Article in journal (Refereed)
    Abstract [en]

    Topological states of matter are characterized by global topological invariants which change their value across a topological quantum phase transition. It is commonly assumed that the transition between topologically distinct noninteracting gapped phases of fermions is necessarily accompanied by the closing of the band gap as long as the symmetries of the system are maintained. We show that such a quantum phase transition is possible without closing the gap in the case of a three-dimensional topological band insulator. We demonstrate this by calculating the free energy of the minimal model for a topological insulator, the Bernevig-Hughes-Zhang model, and show that as the band curvature continuously varies, a jump between the band-gap minima corresponding to the topologically trivial and nontrivial insulators occurs. Therefore, this first-order phase transition is a generic feature of three-dimensional topological band insulators. For a certain parameter range we predict a reentrant topological phase transition. We discuss our findings in connection with the recent experimental observation of a discontinuous topological phase transition in a family of topological crystalline insulators.

  • 5. Milovanovic, M. V.
    et al.
    Ciric, M. Dimitrijevic
    Juricic, Vladimir
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Pairing instabilities of Dirac composite fermions2016In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 94, no 11, article id 115304Article in journal (Refereed)
    Abstract [en]

    Recently, a Dirac (particle-hole symmetric) description of composite fermions in the half-filled Landau level (LL) was proposed [D. T. Son, Phys. Rev. X 5, 031027 (2015)], and we study its possible consequences on BCS (Cooper) pairing of composite fermions (CFs). One of the main consequences is the existence of anisotropic states in single-layer and bilayer systems, which was previously suggested in Jeong and Park [J. S. Jeong and K. Park, Phys. Rev. B 91, 195119 (2015)]. We argue that in the half-filled LL in the single-layer case the gapped states may sustain anisotropy, because isotropic pairings may coexist with anisotropic ones. Furthermore, anisotropic pairings with the addition of a particle-hole symmetry-breaking mass term may evolve into rotationally symmetric states, i.e., Pfaffian states of Halperin-Lee-Read (HLR) ordinary CFs. On the basis of the Dirac formalism, we argue that in the quantum Hall bilayer at total filling factor 1, with decreasing distance between the layers, weak pairing of p-wave paired CFs is gradually transformed from Dirac to ordinary, HLR-like, with a concomitant decrease in the CF number. Global characterization of low-energy spectra based on the Dirac CFs agrees well with previous calculations performed by exact diagonalization on a torus. Finally, we discuss features of the Dirac formalism when applied in this context.

  • 6. Roy, Bitan
    et al.
    Goswami, Pallab
    Juricic, Vladimir
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Interacting Weyl fermions: Phases, phase transitions, and global phase diagram2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 20, article id 201102Article in journal (Refereed)
    Abstract [en]

    We study the effects of short-range interactions on a generalized three-dimensional Weyl semimetal, where the band touching points act as the (anti) monopoles of Abelian Berry curvature of strength n. We show that any local interaction has a negative scaling dimension -2/n. Consequently, all Weyl semimetals are stable against weak short-range interactions. For sufficiently strong interactions, we demonstrate that the Weyl semimetal either undergoes a first-order transition into a band insulator or a continuous transition into a symmetry breaking phase. A translational symmetry breaking axion insulator and a rotational symmetry breaking semimetal are two prominent candidates for the broken symmetry phase. At the one-loop order, the correlation length exponent for continuous transitions is upsilon = n/2, indicating their non-Gaussian nature for any n > 1. We also discuss the scaling of the thermodynamic and transport quantities in general Weyl semimetals as well as inside broken symmetry phases.

  • 7. Roy, Bitan
    et al.
    Juricic, Vladimir
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Optical conductivity of an interacting Weyl liquid in the collisionless regime2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 96, no 15, article id 155117Article in journal (Refereed)
    Abstract [en]

    Optical conductivity (OC) can serve as a measure of correlation effects in a wide range of condensed-matter systems. We show that the long-range tail of the Coulomb interaction yields a universal correction to the OC in a three-dimensional Weyl semimetal sigma(Omega) = sigma(0)(Omega)[1 + 1/N+1], where sigma(0)(Omega) = Ne-0(2)Omega/(12hv) is the OC in the noninteracting system, with v as the actual (renormalized) Fermi velocity of Weyl quasiparticles at frequency Omega, and e(0) is the electron charge in vacuum. Such universal enhancement of OC, which depends only on the number of Weyl nodes near the Fermi level (N), is a remarkable consequence of an intriguing conspiracy among the quantum-critical nature of an interacting Weyl liquid, marginal irrelevance of the long-range Coulomb interaction, and violation of hyperscaling in three dimensions, and can directly be measured in recently discovered Weyl as well as Dirac materials. By contrast, a local density-density interaction produces a nonuniversal correction to the OC, stemming from the nonrenormalizable nature of the corresponding interacting field theory.

  • 8. Roy, Bitan
    et al.
    Juricic, Vladimir
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Utrecht University, The Netherlands.
    Herbut, Igor F.
    Emergent Lorentz symmetry near fermionic quantum critical points in two and three dimensions2016In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 4, article id 018Article in journal (Refereed)
    Abstract [en]

    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 6-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.

  • 9. Roy, Bitan
    et al.
    Juricic, Vladimir
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Sarma, Sankar Das
    Universal optical conductivity of a disordered Weyl semimetal2016In: Scientific Reports, ISSN 2045-2322, E-ISSN 2045-2322, Vol. 6, article id 32446Article in journal (Refereed)
    Abstract [en]

    Topological Weyl semimetals, besides manifesting chiral anomaly, can also accommodate a disorder-driven unconventional quantum phase transition into a metallic phase. A fundamentally and practically important question in this regard concerns an experimentally measurable quantity that can clearly distinguish these two phases. We show that the optical conductivity while serving this purpose can also play the role of a bonafide order parameter across such disorder-driven semimetal-metal quantum phase transition by virtue of displaying distinct scaling behavior in the semimetallic and metallic phases, as well as inside the quantum critical fan supporting a non-Fermi liquid. We demonstrate that the correction to the dielectric constant and optical conductivity in a dirty Weyl semimetal due to weak disorder is independent of the actual nature of point-like impurity scatterers. Therefore, optical conductivity can be used as an experimentally measurable quantity to study the critical properties and to pin the universality class of the disorder-driven quantum phase transition in Weyl semimetals.

  • 10. Slager, Robert-Jan
    et al.
    Juricic, Vladimir
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Lahtinen, Ville
    Zaanen, Jan
    Self-organized pseudo-graphene on grain boundaries in topological band insulators2016In: Physical Review B, ISSN 2469-9950, Vol. 93, no 24, article id 245406Article in journal (Refereed)
    Abstract [en]

    Semimetals are characterized by nodal band structures that give rise to exotic electronic properties. The stability of Dirac semimetals, such as graphene in two spatial dimensions, requires the presence of lattice symmetries, while akin to the surface states of topological band insulators, Weyl semimetals in three spatial dimensions are protected by band topology. Here we show that in the bulk of topological band insulators, self-organized topologically protected semimetals 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 a valley anomaly in two dimensions influencing edge spin transport, whereas in three dimensions they appear as graphenelike states that may exhibit an odd-integer quantum Hall effect. The general mechanism underlying these semimetals-the hybridization of spinon modes bound to the grain boundary-suggests that topological semimetals can emerge in any topological material where lattice dislocations bind localized topological modes.

  • 11. Slager, Robert-Jan
    et al.
    Juričić, Vladimir
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Roy, Bitan
    Dissolution of topological Fermi arcs in a dirty Weyl semimetal2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 96, no 20, article id 201401Article in journal (Refereed)
    Abstract [en]

    Weyl semimetals (WSMs) have recently attracted a great deal of attention as they provide a condensed matter realization of chiral anomaly, feature topologically protected Fermi arc surface states, and sustain sharp chiral Weyl quasiparticles up to a critical disorder at which a continuous quantum phase transition (QPT) drives the system into a metallic phase. We here numerically demonstrate that with increasing strength of disorder, the Fermi arc gradually loses its sharpness, and close to the WSM-metal QPT it completely dissolves into the metallic bath of the bulk. The predicted topological nature of the WSM-metal QPT and the resulting bulk-boundary correspondence across this transition can be directly observed in angle-resolved photoemission spectroscopy (ARPES) and Fourier transformed scanning tunneling microscopy (STM) measurements by following the continuous deformation of the Fermi arcs with increasing disorder in recently discovered Weyl materials.

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