527 citations · 6.4k across the 130 of their papers we have counts for
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Dirac Hamiltonians for bosonic spectra
P. Sathish Kumar, Igor F. Herbut, R. Ganesh
Dirac materials are of great interest as condensed matter realizations of the Dirac and Weyl equations. In particular, they serve as a starting point for the study of topological p…
Note on "Quantum superconducting criticality in graphene and topological insulators"
Bitan Roy, Vladimir Juricic, Igor F. Herbut
We correct our previous conclusion regarding the fate of a charged quantum critical point across the superconducting transition for two dimensional massless Dirac fermion. Within t…
Half vortex and fractional electrical charge in two dimensions
Bitan Roy, Igor F. Herbut
Despite fermion doubling, a two-dimensional quasi-relativistic spin-1/2 system can still lead to true fractionalization of electrical charge, when a massive ordered phase supports…
Zero-modes and global antiferromagnetism in strained graphene
Bitan Roy, Fakher F. Assaad, Igor F. Herbut
A novel magnetic ground state is reported for the Hubbard Hamiltonian in strained graphene. When the chemical potential lies close to the Dirac point, the ground state exhibits loc…
Density of States Scaling at the Semimetal to Metal Transition in Three Dimensional Topological Insulators
Koji Kobayashi, Tomi Ohtsuki, Ken-Ichiro Imura +1
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…
Topological insulators in strained graphene at weak interaction
Bitan Roy, Igor F. Herbut
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-indu…
Isospin of topological defects in Dirac systems
Igor F. Herbut
We study the Dirac quasiparticles in -dimensional lattice systems of electrons in the presence of domain walls (), vortices (), or hedgehogs () of superconducting…
Time reversal, fermion doubling, and the masses of lattice Dirac fermions in three dimensions
Igor F. Herbut
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…
Supersymmetric Runge-Lenz-Pauli vector for Dirac vortex in topological insulators and graphene
Chi-Ken Lu, Igor F. Herbut
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 spec…
Inhomogeneous magnetic catalysis on graphene's honeycomb lattice
Bitan Roy, Igor F. Herbut
We investigate the ordering instability of interacting (and for simplicity, spinless) fermions on graphene's honeycomb lattice by numerically computing the Hartree self-consistent…
Spectrum of the Dirac Hamiltonian with the mass-hedgehog in arbitrary dimension
Igor F. Herbut, Chi-Ken Lu
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 quan…
Conductivity of interacting massless Dirac particles in graphene: Collisionless regime
Vladimir Juricic, Oskar Vafek, Igor F. Herbut
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 anal…
Antilinear spectral symmetry and the vortex zero-modes in topological insulators and graphene
Igor F. Herbut, Chi-Ken Lu
We construct the general extension of the four-dimensional Jackiw-Rossi-Dirac Hamiltonian that preserves the antilinear reflection symmetry between the positive and negative energy…
Unconventional superconductivity on honeycomb lattice: the theory of Kekule order parameter
Bitan Roy, Igor F. Herbut
A spatially non-uniform superconducting phase is proposed as the electronic variational ground state for the attractive interactions between nearest neighbors on graphene's honeyco…
Zero-energy states of massive Dirac equation in magnetic fields
Igor F. Herbut
The Dirac equation with a U(1) vortex in the mass-term is solved in the presence of magnetic-like fields at zero energy. By drawing an analogy to classical mechanics, it is shown t…
Topological insulator in the core of the superconducting vortex in graphene
Igor F. Herbut
The core of the vortex in a general superconducting order parameter in graphene is argued to be ordered, with the possible order parameters forming the algebra U(1) X Cl(3), where…
Explanation for the isotropy of the Dirac cone in graphene
Igor F. Herbut
It is shown that in the absence of spontaneous symmetry breaking the Dirac cones in the system of interacting electrons on honeycomb lattice are isotropic at low energies. The effe…
Comment on "Minimal conductivity in graphene: Interaction corrections and ultraviolet anomaly" by Mishchenko E. G
Igor F. Herbut, Vladimir Juricic, Oskar Vafek +1
In this comment we wish to clarify and correct some of the statements made in a recent paper by E. G. Mishchenko (Europhys. Lett. 83 (2008) 17005).
Pseudo-magnetic catalysis of the time-reversal symmetry breaking in graphene
Igor F. Herbut
Finite flux of the (time-reversal-symmetric) pseudo-magnetic field, which represents the effect of wrinkling of the graphene sheet for example, is shown to be a catalyst for sponta…
Quantum critical scaling in magnetic field near the Dirac point in graphene
Igor F. Herbut, Bitan Roy
Motivated by the recent measurement of the activation energy at the quantum Hall state at the filling factor f=1 in graphene we discuss the scaling of the interaction-induced gaps…
Coulomb interaction, ripples, and the minimal conductivity of graphene
Igor F. Herbut, Vladimir Juricic, Oskar Vafek
We argue that the unscreened Coulomb interaction in graphene provides a positive, universal, and logarithmic correction to scaling of zero-temperature conductivity with frequency.…
SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
Igor F. Herbut
I consider the Hubbard model of graphene in an external magnetic field and in the Hartree-Fock approximation. In the continuum limit, the ground state energy at half filling become…
Theory of integer quantum Hall effect in graphene
Igor F. Herbut
The observed quantization of the Hall conductivity in graphene at high magnetic fields is explained as being due to the dynamically generated spatial modulation of either the elect…
Interactions and phase transitions on graphene's honeycomb lattice
Igor F. Herbut
The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is sh…