arXiv subjects

Igor F. Herbut

Publications and source records attributed to Igor F. Herbut.

At least 73 records · Page 4Linked to original sources

arXiv2014

Interaction-induced anomalous quantum Hall state on the honeycomb lattice

We examine the existence of the interaction-generated quantum anomalous Hall phase on the honeycomb lattice. For the spinless model at half filling, the existence of a quantum anomalous Hall phase (Chern insulator phase) has been predicted using mean-field methods. However, recent exact diagonalization studies for small clusters with periodic boundary condition have not found a clear sign of an interaction-driven Chern insulator phase. We use exact diagonalization method to study properties of small clusters with open boundary condition and, contrary to previous studies, we find clear signatures of the topological phase transition for finite size clusters. We also examine applicability of the entangled-plaquette state (correlator-product state) ansatz to describe the ground states of the system. Within this approach the lattice is covered with plaquettes and the ground state wave-function is written in terms of the plaquette coefficients. Configurational weights can then be optimized using a variational Monte Carlo algorithm. Using the entangled-plaquette state ansatz we study the ground state properties of the system for larger system sizes and show that the results agree with the exact diagonalization results for small clusters. This confirms validity of the entangled-plaquette state ansatz to describe the ground states of the system and provides further confirmation of the existence of the quantum anomalous Hall phase in the thermodynamic limit, as predicted by the mean-field theory calculations.

cond-mat.str-el↗

arXiv2014

Nematic, topological and Berry phases when a flat and a parabolic band touch

A (single flavor) quadratic band crossing in two dimensions is known to have a generic instability towards a quantum anomalous Hall (QAH) ground state for infinitesimal repulsive interactions. Here we introduce a generalization of a quadratic band crossing which is protected only by rotational symmetry. By focusing on the representative case of a parabolic and flat band touching, which also allows for a straightforward lattice realization, the interaction induced nematic phase is found generally to compete successfully with the QAH insulator, and to become the dominant instability in certain parts of the phase diagram already at weak coupling. The full phase diagram of the model, together with its topological properties, is mapped out using a perturbative renormalization group, strong coupling analysis, the mean-field theory. Interestingly, the Berry flux varies continuously in the single flavour limit with various control parameters.

cond-mat.str-el↗

arXiv2013

Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators

The quantum phase transition between the three dimensional Dirac semimetal and the diffusive metal can be induced by increasing disorder. Taking the system of disordered $\mathbb{Z}_2$ topological insulator as an important example, we compute the single particle density of states by the kernel polynomial method. We focus on three regions: the Dirac semimetal at the phase boundary between two topologically distinct phases, the tricritical point of the two topological insulator phases and the diffusive metal, and the diffusive metal lying at strong disorder. The density of states obeys a novel single parameter scaling, collapsing onto two branches of a universal scaling function, which correspond to the Dirac semimetal and the diffusive metal. The diverging length scale critical exponent $ν$ and the dynamical critical exponent $z$ are estimated, and found to differ significantly from those for the conventional Anderson transition. Critical behavior of experimentally observable quantities near and at the tricritical point is also discussed.

cond-mat.mes-hall↗

arXiv2013

Pinning the order: the nature of quantum criticality in the Hubbard model on honeycomb lattice

In numerical simulations, spontaneously broken symmetry is often detected by computing two-point correlation functions of the appropriate local order parameter. This approach, however, computes the square of the local order parameter, and so when it is {\it small}, very large system sizes at high precisions are required to obtain reliable results. Alternatively, one can pin the order by introducing a local symmetry breaking field, and then measure the induced local order parameter infinitely far from the pinning center. The method is tested here at length for the Hubbard model on honeycomb lattice, within the realm of the projective auxiliary field quantum Monte Carlo algorithm. With our enhanced resolution we find a direct and continuous quantum phase transition between the semi-metallic and the insulating antiferromagnetic states with increase of the interaction. The single particle gap in units of the Hubbard $U$ tracks the staggered magnetization. An excellent data collapse is obtained by finite size scaling, with the values of the critical exponents in accord with the Gross-Neveu universality class of the transition.

cond-mat.str-el↗

arXiv2013

Coupling, merging, and splitting Dirac points by electron-electron interaction

The manipulation and movement of Dirac points in the Brillouin zone by the electron-electron interaction is considered within leading order perturbation theory. At the merging point, an infinitesimal interaction is shown to cause opening of the gap or splitting of the Dirac points, depending on the inter- or intrasublattice nature of the merging and the sign of the interaction. The topology of the spectrum can therefore be efficiently changed by simply tuning the interaction between particles, as opposed to the usual careful band structure engineering. This is illustrated around the merging transition of one, two, and three dimensional Dirac-Weyl fermions. A simple Weyl-like Hamiltonian that describes the quadratic band-crossing in three dimensions is also proposed, and its stability under interactions is addressed.

cond-mat.str-el↗

arXiv2013

Topological insulators in strained graphene at weak interaction

The nature of the electronic ground states in strained undoped graphene at weak interaction between electrons is discussed. After providing a lattice realization of the strain-induced axial magnetic field we numerically find the self-consistent solution for the time reversal symmetry breaking quantum anomalous Hall order-parameter, at weak second-nearest-neighbor repulsion between spinless fermions. The anomalous Hall state is obtained in both uniform and nonuniform axial magnetic fields, with the spatial profile of the order-parameter resembling that of the axial field itself. When the electron spin is included, the time reversal symmetric anomalous spin Hall state becomes slightly preferred energetically at half filling, but the additional anomalous Hall component should develop at a finite doping.

cond-mat.mes-hall↗

arXiv2013

Universal conductivity of graphene in the ultra-relativistic regime

We calculate the optical (cutoff >> frequency >> temperature) conductivity in clean graphene in the ultimate low-energy regime, when retardation effects of the electromagnetic interaction become important and when the full Lorentz symmetry emerges. In contrast to what happens with the short range or with the Coulomb long-range instantaneous interactions, the optical conductivity is now no longer equal to its non interacting value, but acquires universal corrections in powers of the fine structure constant. The coefficient of the first order correction is computed, and found to be of order one. We also present the result for the conductivity in the large-N limit, with $N$ as the number of Dirac fermions species, to the order $1/N^2$.

cond-mat.str-el↗

arXiv2013

Majorana mass, time reversal symmetry, and the dimension of space

The Weyl fermions with a well defined chirality are known to demand that the dimension of space which they inhabit must be odd. It is shown here, however, that not all odd dimensional spaces are equally good hosts: in particular, an arbitrary number of chiral Weyl fermions can acquire a Majorana mass only in three (modulo eight) dimensions. The argument utilizes a) the precise analogy that exists between the Majorana mass term and the Cooper pairing of time-reversed Weyl fermions, and b) the conditions on the requisite time-reversal operator, which are implied by the Clifford algebra. The theorem connects the observed odd number of neutrino flavors, the time reversal symmetry, and the dimension of our space, and strengthens the argument for the possible violation of the lepton number conservation law.

hep-th↗

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

Conserved charges of order-parameter textures in Dirac systems

A simple expression for the induced fermion current in the presence of a texture in mass-order-parameters in two-dimensional condensed-matter Dirac systems is derived using the representation theory of Clifford algebras. In particular, it is shown that every texture in three mutually anticommuting order parameters, in graphene for example, implies an induced density of a properly defined conserved charge. The sufficient condition for the general charge to be the familiar electrical charge is that the remaining two anticommuting order parameters allowed by the particle-hole symmetry are the two phase components of some superconducting order. This allows eight different types of electrically charged textures in graphene or in the $π$-flux Hamiltonian on the square lattice. Generalized charge of mass-textures on the surfaces of thin films of topological insulators, or in spinless Dirac fermions hopping on the honeycomb lattice is also discussed.

cond-mat.str-el↗

arXiv2012

Zero modes and charged Skyrmions in graphene bilayer

We show that the electric charge of the Skyrmion in the vector order parameters that characterize the quantum anomalous spin Hall state and the layer-antiferromagnet in a graphene bilayer is four and zero, respectively. The result is based on the demonstration that a vortex configuration in two broken symmetry states in bilayer graphene with the quadratic band crossing has the number of zero modes doubled relative to the single layer. The doubling can be understood as a result of Kramers' theorem implied by the "pseudo time reversal" symmetry of the vortex Hamiltonian. Disordering the quantum anomalous spin Hall state by Skyrmion condensation should produce a superconductor of an elementary charge 4e.

cond-mat.str-el↗

arXiv2012

Isospin of topological defects in Dirac systems

We study the Dirac quasiparticles in $d$-dimensional lattice systems of electrons in the presence of domain walls ($d=1$), vortices ($d=2$), or hedgehogs ($d=3$) of superconducting and/or insulating, order parameters, which appear as mass terms in the Dirac equation. Such topological defects have been known to carry non-trivial quantum numbers such as charge and spin. Here we discuss their additional internal degree of freedom: irrespectively of the dimensionality of space and the nature of orders that support the defect, an extra mass-order-parameter is found to emerge in their core. Six linearly independent local orders, which close two mutually commuting three-dimensional Clifford algebras are proven to be in general possible. We show how the particle-hole symmetry restricts the defects to always carry the quantum numbers of a single effective isospin-1/2, quite independently of the values of their electric charge or true spin. Examples of this new degree of freedom in graphene and on surfaces of topological insulators are discussed.

cond-mat.mes-hall↗

arXiv2011

Time reversal, fermion doubling, and the masses of lattice Dirac fermions in three dimensions

Motivated by recent examples of three-dimensional lattice Hamiltonians with massless Dirac fermions in their (bulk) spectrum, I revisit the problem of fermion doubling on bipartite lattices. The number of components of the Dirac fermion in a time-reversal and parity invariant d-dimensional lattice system is determined by the minimal representation of the Clifford algebra of $d+1$ Hermitian Dirac matrices that allows a construction of the time-reversal operator with the square of unity, and it equals $2^d$ for $d=2,3$. Possible mass-terms for (spinless) Dirac fermions are listed and discussed. In three dimensions there are altogether eight independent masses, out of which four are even, and four are odd under time reversal. A specific violation of time-reversal symmetry that leads to (minimal) four-component massless Dirac fermion in three dimensions at low energies is constructed.

cond-mat.mes-hall↗

arXiv2011

Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene

The Dirac mass-vortex at the surface of a topological insulator or in graphene is considered. Within the linear approximation for the vortex amplitude's radial dependence, the spectrum is a series of degenerate bound states, which can be classified by a set of accidental SU(2) and supersymmetry generators (I. F. Herbut and C.-K. Lu, Phys. Rev. B 83 125412 (2011)). Here we discuss further the properties and manifestations of the supersymmetry of the vortex Hamiltonian, and point out some interesting analogies to the Runge-Lenz-Pauli vector in the non-relativistic hydrogen atom. Symmetry breaking effects due to a finite chemical potential, and the Zeeman field are also analyzed. We find that a residual accidental degeneracy remains only in the special case of equal magnitudes of both terms, whereas otherwise it becomes removed entirely.

cond-mat.mes-hall↗

arXiv2011

Inhomogeneous magnetic catalysis on graphene's honeycomb lattice

We investigate the ordering instability of interacting (and for simplicity, spinless) fermions on graphene's honeycomb lattice by numerically computing the Hartree self-consistent solution for the charge-density-wave order parameter in presence of both uniform and non-uniform magnetic fields. For a uniform field the overall behavior of the order parameter is found to be in accord with the continuum theory. In the inhomogeneous case, the spatial profile of the order parameter resembles qualitatively the form of the magnetic field itself, at least when the interaction is not overly strong. We find that right at the zero-field critical point of the infinite system the local order parameter scales as the square-root of the local strength of the magnetic field, apparently independently of the assumed field's profile. The finite size effects on various parameters of interest, such as the critical interaction and the universal amplitude ratio of the interaction-induced gap to the Landau level energy at criticality are also addressed.

cond-mat.mes-hall↗

arXiv2011

Spectrum of the Dirac Hamiltonian with the mass-hedgehog in arbitrary dimension

It is shown that the square of the Dirac Hamiltonian with the isotropic mass-hedgehog potential in d dimensions is the number operator of fictitious bosons and fermions over d quantum states. This result allows one to obtain the complete spectrum and degeneracies of the Dirac Hamiltonian with the hedgehog mass configuration in any dimension. The result pertains to low-energy states in the core of a general superconducting or insulating vortex in graphene in two dimensions, and in the superconducting vortex at the topological - trivial insulator interface in three dimensions, for example. The spectrum in d=2 is also understood in terms of the underlying accidental SU(2) symmetry and the supersymmetry of the Hamiltonian.

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↗

arXiv2010

Pairing symmetry and vortex zero-mode for superconducting Dirac fermions

We study the vortex zero-energy bound states in presence of pairing among the low-energy Dirac fermions on the surface of a topological insulator. The pairing symmetries considered include the $s$-wave, $p$-wave, and, in particular, the mixed-parity symmetry, which arises in absence of the inversion symmetry on the surface. The zero-mode is analyzed within the generalized Jackiw-Rossi-Dirac Hamiltonian that contains a momentum-dependent mass-term, and includes the effects of the electromagnetic gauge field and the Zeeman coupling as well. At a finite chemical potential, as long as the spectrum without the vortex is fully gapped, the presence of a single Fermi surface with a definite helicity always leads to one Majorana zero-mode, in which both electron's spin projections participate. In particular, the critical effects of the Zeeman coupling on the zero-mode are discussed.

cond-mat.supr-con↗