We study hard-core bosons on the honeycomb lattice in the presence of anisotropic nearest-neighbor repulsive interactions. Using a quantum Monte Carlo (QMC) technique, we extract the phase diagram of the model in terms of the filling and the anisotropy. At half-filling we find a dimer insulator phase near maximum anisotropy that is characterized by a finite topological entanglement entropy $\ln(2)/2$, indicative of a fractional quantum Hall state for bosons. We identify the presence of edge states and derive a QMC-based method to extract and verify their chirality. Remarkably, this phase arises in the absence of magnetic flux and without explicit lattice frustration.
The topological properties of hardcore bosons on ribbons of honeycomb lattice are studied using quantum Monte Carlo simulations. We map out a rich phase diagram with the superfluid and insulator phases at various fillings. Particularly, it is revealed that the insulator state at half filling is a topological bosonic state, which is characterized by a nontrivial Berry phase and a pair of edge states. We provide intuitive picture to understand this topological bosonic insulator state by showing that it can be adiabatically mapped to a topological fermionic model. It is also shown that the topolo…
Linelike hardcore bosonic domain walls in a staggered potential on honeycomb lattice are studied using quantum Monte Carlo simulations. The phase diagrams of ribbons with zigzag and armchair domain walls are mapped, which contain superfluid and insulator phases at various fillings. In the $ρ=\frac{1}{2}$ insulator, the domain wall separates two charge-density-wave (CDW) regions with opposite Berry curvatures. Associated with the change of topological properties, superfluid transport occurs down the domain wall. The superfluid density associated with a zigzag domain wall is much larger than tha…
A semimetal-insulator transition in the Hubbard model on the honeycomb lattice is studied by using the dynamical mean field theory. Electrons in the honeycomb lattice resemble the Dirac electron liquid and for weak interactions the system is semimetal. With increasing the local interaction a semimetal-insulator transition occurs. We find a nonanalytical structure of the phase transition which consists of a first-order transition line ending in a second-order transition point and high-temperature crossover line. A phase separation of semimetal and insulator occurs at low temperatures. Maxwell c…
By quantum Monte Carlo simulations of bosons in gapped honeycomb lattices, we show the existence of bosonic edge states. For single layer honeycomb lattice, bosonic edge states can be controlled to appear, cross the gap and merge into bulk states by an on-site potential applied on the outmost sites of the boundary. On bilayer honeycomb lattice, bosonic edge state traversing the gap at half filling is demonstrated. The topological origin of the bosonic edge states is discussed with pseudo Berry curvature. The results will simulate experimental studies of these exotic bosonic edge states with ul…
We study the interplay of strong electron correlations and intra-triangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-$1$ Mott insulator, a metal, and a spin-$0$ Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intra-triangle multi-orbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenou…
The $t_{2g}$ orbitals of an edge-shared transition-metal oxide with a honeycomb lattice structure form dispersionless electronic bands when only hopping mediated by the edge-sharing oxygens is accessible. This is due to the formation of isolated quasimolecular orbitals (QMOs) in each hexagon, introduced recently by Mazin et al. [Phys. Rev. Lett. 109, 197201 (2012)], which stabilizes a band insulating phase for $t_{2g}^5$ systems. However, with help of the exact diagonalization method to treat the electron kinetics and correlations on an equal footing, we find that the QMOs are fragile against …
Phase transition in a honeycomb lattice is studied by the means of the two dimensional Hubbard model and the exact diagonalization dynamical mean field theory at zero temperature. At low energies, the dispersion relation is shown to be a linear function of the momentum. In the limit of weak interactions, the system is in the semi-metal phase. By increasing the on site interaction a semi-metal to insulator transition takes place in the paramagnetic phase. Calculation of double occupancy shows such a phase transition is of the second order. The respective phase transition point and critical on-s…
Realization and design of topological insulators emerging from electron correlations, called topological Mott insulators (TMIs), is pursued by using mean-field approximations as well as multi-variable variational Monte Carlo (MVMC) methods for Dirac electrons on honeycomb lattices. The topological insulator phases predicted in the previous studies by the mean-field approximation for an extended Hubbard model on the honeycomb lattice turn out to disappear, when we consider the possibility of a long-period charge-density-wave (CDW) order taking over the TMI phase. Nevertheless, we further show t…
Inspired by recent discovery of correlated insulating states in twisted bilayer graphene (TBG), we study a two-orbital Hubbard model on the honeycomb lattice with two electrons per unit cell. Based on the real-space density matrix renormalization group (DMRG) simulation, we identify a metal-insulator transition around $U_c/t=2.5\sim3$. In the vicinity of $U_c$, we find strong spin/orbital density wave fluctuations at commensurate wavevectors, accompanied by weaker incommensurate charge density wave (CDW) fluctuations. The spin/orbital density wave fluctuations are enhanced with increasing syst…
We study the orbitally frustrated singlet-triplet models that emerge in the context of spin-orbit coupled Mott insulators with $t_{2g}^4$ electronic configuration. In these compounds, low-energy magnetic degrees of freedom can be cast in terms of three-flavor "triplon" operators describing the transitions between spin-orbit entangled $J=0$ ionic ground state and excited $J=1$ levels. In contrast to a conventional, flavor-isotropic O(3) singlet-triplet models, spin-orbit entangled triplon interactions are flavor-and-bond selective and thus highly frustrated. In a honeycomb lattice, we find clos…
Semimetals, in which conduction and valence bands touch but do not form Fermi surfaces, have attracted considerable interest for their anomalous properties starting with the discovery of Dirac matter in graphene and other two-dimensional honeycomb materials. Here we introduce a family of three-dimensional honeycomb systems whose electronic band structures exhibit a variety of topological semimetals with Dirac nodal lines. We show that these nodal lines appear in varying numbers and mutual geometries, depending on the underlying lattice structure. They are stabilized, in most cases, by a combin…
Describing correlated electron systems near phase transitions has been a major challenge in computational condensed-matter physics. In this paper, we apply highly accurate fixed node quantum Monte Carlo techniques, which directly work with many body wave functions and simulate electron correlations, to investigate the metal to insulator transition of a correlated hydrogen lattice. By calculating spin and charge properties, and analyzing the low energy Hilbert space, we identify the transition point and identify order parameters that can be used to detect the transition. Our results provide a b…
The Kitaev model, characterized by bond-dependent Ising spin interactions among spin-orbit entangled dipole moments in Mott insulators, offered a new approach to quantum spin liquids. Motivated by another type of bond-dependent interaction among quadrupole moments in $5d^2$ Mott insulators, we provide a microscopic route to uncover the Kitaev multipolar liquid, featuring fractionalized excitations out of non-Kramers doublets carrying multipole moments. The key ingredient is the magnetic field that allows for bond-anisotropic quadrupole-octupole interactions via mixing with the excited triplet …
It has been recently shown that in the Heisenberg (anti)ferromagnet on the honeycomb lattice, the magnons (spin wave quasipacticles) realize a massless two-dimensional (2D) Dirac-like Hamiltonian. It was shown that the Dirac magnon Hamiltonian preserves time-reversal symmetry defined with the sublattice pseudo spins and the Dirac points are robust against magnon-magnon interactions. The Dirac points also occur at nonzero energy. In this paper, we propose a simple realization of nontrivial topology (magnon edge states) in this system. We show that the Dirac points are gapped when the inversion …
Novel ground states might be realized in honeycomb lattices with strong spin-orbit coupling. Here we study the electronic structure of $α$-RuCl$_3$, in which the Ru ions are in a d5 configuration and form a honeycomb lattice, by angle-resolved photoemission, x-ray photoemission and electron energy loss spectroscopy supported by density functional theory and multiplet calculations. We find that $α$-RuCl$_3$ is a Mott insulator with significant spin-orbit coupling, whose low energy electronic structure is naturally mapped onto Jeff states. This makes $α$-RuCl$_3$ a promising candidate for the re…
We report structural studies of the spin-orbit Mott insulator family K$_x$Ir$_y$O$_2$, with triangular layers of edge-sharing IrO$_6$ octahedra bonded by potassium ions. The potassium content acts as a chemical tuning parameter to control the amount of charge in the Ir-O layers. Unlike the isostructural families with Ir replaced by Co or Rh ($y=1$), which are metallic over a range of potassium compositions $x$, we instead find insulating behaviour with charge neutrality achieved via iridium vacancies, which order in a honeycomb supercell above a critical composition $x_c$. By performing densit…
We study the spinless and spinful extended Hubbard models with repulsive interactions on the kagome and the decorated honeycomb ("star") lattice. Using Hartree-Fock mean-field theory, we show that interaction-driven insulating phases with non-trivial topological invariants (Chern number or $Z_2$ invariant) exist for an experimentally reasonable range of parameters. These phases occur at filling fractions which involve either Dirac points or quadratic band crossing points in the non-interacting limit. We present comprehensive mean-field phase diagrams for these lattices and discuss the competit…
The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the $e_{g}$ Mott insulator Ba$_{3}$CuSb$_{2}$O$_{9}$ and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantu…
We examine the role of spin-orbit coupling in the electronic structure of $α$-RuCl3, in which Ru ions in 4d5 configuration form a honeycomb lattice. The measured optical spectra exhibit a clear optical gap and excitations within the t2g orbitals. The spectra can be described very well with first-principles electronic structure calculations obtained by taking into account both spin orbit coupling and electron correlations. Furthermore, our X-ray absorption spectroscopy measurements at the Ru L-edges exhibit distinct spectral features associated with the presence of substantial spin- orbit coupl…
Ferromagnetism in the two-dimensional CrI$_3$ has generated a lot of excitement, and it was recently proposed that the spin-orbit coupling (SOC) in Iodine may generate bond-dependent spin interactions leading to magnetic anisotropy. Here we derive a microscopic spin model of S=3/2 on transition metals surrounded by heavy ligands in honeycomb Mott insulators using a strong-coupling perturbation theory. For ideal octahedra we find Heisenberg and Kitaev interactions, which favor the magnetic moment along the cubic axis via quantum fluctuations. When a slight trigonal distortion of the octahedra i…
In this paper, the honeycomb Hubbard model in optical lattices is investigated using O(3) non-linear sigma model. A possible quantum non-magnetic insulator in a narrow parameter region is found near the metal-insulator transition. We study the corresponding dynamics of magnetic properties, and find that the narrow region could be widened by hole doping.
Quantum information storage using charge-neutral quasiparticles are expected to play a crucial role in the future of quantum computers. In this regard, magnons or collective spin-wave excitations in solid-state materials are promising candidates in the future of quantum computing. Here, we study the quantum squeezing of Dirac and topological magnons in a bosonic honeycomb optical lattice with spin-orbit interaction by utilizing the mapping to quantum spin-$1/2$ XYZ Heisenberg model on the honeycomb lattice with discrete Z$_2$ symmetry and a Dzyaloshinskii-Moriya interaction. We show that the s…
We show how to construct fully symmetric, gapped states without topological order on a honey- comb lattice for S = 1/2 spins using the language of projected entangled pair states(PEPS). An explicit example is given for the virtual bond dimension D = 4. Four distinct classes differing by lattice quantum numbers are found by applying the systematic classification scheme introduced by two of the authors [S. Jiang and Y. Ran, Phys. Rev. B 92, 104414 (2015)]. Lack of topological degeneracy or other conventional forms of symmetry breaking, and the existence of energy gap in the proposed wave functio…
We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the non-interacting theory at half-filling the Fermi energy lies within a flat band where strong correlations are enhanced. The lattice is highly frustrated. We find a correlation driven first-order metal-insulator transition to two different insulating ground states - a dimer valence bond solid Mott insulator when inter-triangle correlations dominate, and a broken $\mathcal{C}_3$-symmetry antiferromagnet that arises from frustration when intra-triangle correlations dominate. The metal-insulator transi…
We study the Kane-Mele-Hubbard model with an additional inversion-symmetry-breaking term. Using the topological Hamiltonian approach, we calculate the $\mathbb{Z}_2$ invariant of the system as function of spin-orbit coupling, Hubbard interaction $U$, and inversion-symmetry-breaking on-site potential. The phase diagram calculated in that way shows that, on the one hand, a large term of the latter kind destroys the topological non-trivial state. On the other hand, however, this inversion-symmetry-breaking field can enhance the topological state, since for moderate values the transition from the …
We investigate the competition between the spin-orbit interaction of itinerant electrons and their Kondo coupling with local moments densely distributed on the honeycomb lattice. We find that the model at half-filling displays a quantum phase transition between topological and Kondo insulators at a nonzero Kondo coupling. In the Kondo-screened case, tuning the electron concentration can lead to a new topological insulator phase. The results suggest that the heavy-fermion phase diagram contains a new regime with a competition among topological, Kondo-coherent and magnetic states, and that the r…
Motivated by the recent proposal of Bosonic Dirac materials (BDM), we revisited the Ising model on a honeycomb lattice in the presence of the longitudinal and transverse fields. We apply linear spin-wave theory to obtain the magnon dispersion and its degenerated points. These special degenerated points emerge on the excitation spectrum as a function of the external fields and can be identified as Bosonic Dirac Points (BDP). Since that, in the vicinity of these points the Magnons becomes massless with a linear energy spectrum as well as insensible in relation to weak impurity, exactly as it occ…
We examine the effects of quantum fluctuations on a classical spin liquid state in the fully-frustrated honeycomb lattice Bose Hubbard model using quantum Monte Carlo simulations. Frustration is induced explicitly in the model by modulating the sign of the interaction spatially around each lattice hexagon. A superfluid to Mott insulating quantum phase transition can be induced by varying the relative strength of the classical interaction and quantum hopping. In the cases where the interaction has a regular spatial modulation, hopping promotes a phase transition to a symmetry-broken valence-bon…
Using density functional theory calculations with a Hubbard $U$, we explore topologically nontrivial phases in $X_2$O$_3$ honeycomb layers with $X=$ $4d$ and $5d$ cation inserted in the band insulator $α$-Al$_2$O$_3$ along the [0001]-direction. Several promising candidates for quantum anomalous Hall insulators (QAHI) are identified. In particular, for $X$=Tc and Pt spin-orbit coupling (SOC) opens a gap of 54 and 59 meV, respectively, leading to Chern insulators (CI) with $C$=--2 and --1. The nature of different Chern numbers is related to the corresponding spin textures. The Chern insulating p…
The Hubbard model on the honeycomb lattice undergoes a quantum phase transition from a semimetallic to a Mott insulating phase and from a disordered to an anti-ferromagnetically phase. We show that these transitions occur simultaneously and we calculate the critical coupling $U_c=3.835(14)$ as well as the critical exponents $ν=1.181(43)$ and $β=0.898(37)$ which are expected to fall into the $SU(2)$ Gross-Neveu universality class. For this we employ Hybrid Monte Carlo simulations, extrapolate the single particle gap and the spin structure factors to the thermodynamic and continuous time limits,…
We investigate the quantum many-body instabilities of the extended Hubbard model for spinless fermions on the honeycomb lattice with repulsive nearest-neighbor and 2nd nearest-neighbor density-density interactions. Recent exact diagonalization and infinite density matrix renormalization group results suggest that a putative topological Mott insulator phase driven by the 2nd nearest-neighbor repulsion is suppressed, while other numerically exact approaches support the topological Mott insulator scenario. In the present work, we employ the functional renormalization group (fRG) for correlated fe…
The Kitaev spin liquid, a ground state of the bond-dependent Kitaev model in a honeycomb lattice has been a centre of attraction, since a microscopic theory to realize such an interaction in solid-state materials was discovered. A challenge in real materials though is the presence of the Heisenberg and another bond-dependent Gamma interactions detrimental to the Kitaev spin liquid, and there have been many debates on their relative strengths. Here we offer a strategy to extract the Kitaev interaction out of a full microscopic model by utilizing the symmetries of the Hamiltonian. Two tilted mag…
The emergence of the Haldane Chern insulator state due to strong short range repulsive interactions in the half-filled fermionic spinless honeycomb lattice model has been proposed and challenged with different methods and yet it still remains controversial. In this work we revisit the problem using the infinite density matrix renormalization group method and report numerical evidence supporting i) the absence of the Chern insulator state, ii) two previously unnoticed charge ordered phases and iii) the existence and stability of all the non-topological competing orders that were found previousl…
We study the combined effects of lattice deformation, e-e interaction and spin-orbit coupling in a two-dimensional (2D) honeycomb lattice. We adopt different kinds of hopping modulation--generalized dimerization and a Kekule distortion--and calculate topological invariants for the non-interacting system and for the interacting system. We identify the parameter range (Hubbard U, hopping modulation, spin-orbit coupling) where the 2D system behaves as a trivial insulator or Quantum Spin Hall Insulator.
Motivated by superconductivity (SC) in layered nitrides, we study an ionic-Hubbard model on a honeycomb lattice, which consists of two sublattices with an energy-level offset, by using an optimization variational Monte Carlo method. Parameter values for the Coulomb interaction and the energy-level offset, to realize a band insulator in non-doped state, are evaluated, and the SC state is investigated in a carrier-doped band insulator. It is found that, in a weakly doped band insulator, spin fluctuation remains and the spin-singlet d-wave SC state is realized. Present results support an unconven…
Magnetic exchange couplings can be tuned by coupling to periodic light, where the frequency and amplitude are typically varied: a process known as Floquet engineering. The polarization of the light is also important, and in this paper, we show how different polarizations, including several types of unpolarized light, can tune the exchange couplings in distinct ways. Using unpolarized light, for example, it is possible to tune the material without breaking either time-reversal or any lattice symmetries. To illustrate these effects generically, we consider single-band Hubbard models at half-fill…
The Haldane model of the Chern insulator is considered on the Lieb and honeycomb lattices. We provide a detailed analysis of the model's ground-state phase diagram and demonstrate a scenario of the topological phase transitions in the system with a single-particle spectrum that includes flat and dispersion bands, that is realized on the Lieb lattice. We find that the Chern number of the flat band is non-zero, depending on the parameters of the model. We define the topological metal state as an intermediate state between topological insulator and trivial metal. The phase transition between topo…
We study the effect of disorder on the semimetal -- Mott insulator transition in the half-filled repulsive Hubbard model on a honeycomb lattice, a system that features vanishing density of states at the Fermi level. Using the determinant quantum Monte Carlo method, we characterize various phases in terms of the bulk-limit antiferromagnetic (AF) order parameter, compressibility, and temperature-dependent DC conductivity. In the clean limit, our data are consistent with previous results showing a single quantum critical point separating the semi-metallic and AF Mott insulating phases. With the p…
A low-temperature intervening metallic regime arising in the two-dimensional superconductor-insulator transition challenges our understanding of electronic fluids. Here we develop a gauge theory revealing that this emergent anomalous metal is a bosonic topological insulator where bulk transport is suppressed by mutual statistics interactions between out-of-condensate Cooper pairs and vortices and the longitudinal conductivity is mediated by symmetry-protected gapless edge modes. We explore the magnetic-field-driven superconductor-insulator transition in a niobium titanium nitride device and fi…
The Mott transition in honeycomb compounds with significant spin-orbit coupling is explored. At finite temperatures we identify a novel semimetallic phase located between a topological insulator and a topological Mott insulator. This semimetal is characterized by having no charge gap, no quasiparticles and gapped spin excitations with non-trivial topological properties. While charge conduction is incoherent involving mean-free paths violating the Mott-Ioffe-Regel limit, spin excitations can be transported ballistically along the edges giving rise to a quantized spin conductance. Such bad topol…
We study the phases of hard-core-bosons on a two-dimensional periodic honeycomb lattice in the presence of an on-site potential with alternating sign along the different y-layers of the lattice. Using quantum Monte Carlo simulations supported by analytical calculations, we identify a weak topological insulator, characterized by a zero Chern number but non-zero Berry phase, which is manifested at either density 1/4 or 3/4, as determined by the potential pattern. Additionally, a charge-density-wave insulator is observed at 1/2-filling, whereas the phase diagram at intermediate densities is occup…
The possible emergence of a spin liquid phase in the half-filled Hubbard model on the honeycomb lattice; a simple model of graphene, is studied using the variational cluster approximation. We found that the critical interaction strength of a magnetic transition is slightly lower than that of the non-magnetic metal-to-insulator transition. Thus a semi-metallic state becomes a magnetic insulator as the interaction strength increases and a non-magnetic insulating state does not occur. Therefore a spin liquid state characterized by an insulating state without long range order, is not realized in t…
We show that the decorated honeycomb lattice supports a number of topological insulating phases with a non-trivial Z_2 invariant and time-reversal symmetry protected gapless edge modes. We investigate the stability of these phases with respect to various symmetry breaking perturbations and demonstrate the connection to the recently discovered exactly solvable S=1/2 chiral spin liquid model [Phys. Rev. Lett. 99, 247203 (2007)] with non-Abelian and Abelian excitations on the same lattice. Our work highlights the relationship between topological band insulators and topologically ordered spin syst…
Effects of electron many-body interactions amplify in an electronic system with a narrow bandwidth opening a way to exotic physics. A narrow band in a two-dimensional (2D) honeycomb lattice is particularly intriguing as combined with Dirac bands and topological properties but the material realization of a strongly interacting honeycomb lattice described by the Kane-Mele-Hubbard model has not been identified. Here we report a novel approach to realize a 2D honeycomb-lattice narrow-band system with strongly interacting 5$d$ electrons. We engineer a well-known triangular lattice 2D Mott insulator…
We examine the low energy effective theory of phase oscillations in a two-dimensional granular superconducting sheet where the grains are arranged in honeycomb lattice structure. Using the example of graphene we present the evidence for the engineered Dirac nodes in the bosonic excitations: the spectra of the collective bosonic modes cross at the K and K points in the Brillouin zone and form Dirac nodes. We show how two different types of collective phase oscillations are obtained and that they are analogous to the Leggett and the Bogoliubov-Anderson-Gorkov modes in a two-band superconductor. …
The topological Haldane model (THM) on a honeycomb lattice is a prototype of systems hosting topological phases of matter without external fields. It is the simplest model exhibiting the quantum Hall effect without Landau levels, which motivated theoretical and experimental explorations of topological insulators and superconductors. Despite its simplicity, its realization in condensed matter systems has been elusive due to a seemingly difficult condition of spinless fermions with sublattice-dependent magnetic flux terms. While there have been theoretical proposals including elaborate atomic-sc…
The search for robust examples of the magnetic version of topological insulators, referred to as quantum anomalous Hall insulators or simply Chern insulators, so far lacks success. Our groups have explored two distinct possibilities based on multiorbital 3d oxide honeycomb lattices. Each has a Chern insulating phase near the ground state, but materials parameters were not appropriate to produce a viable Chern insulator. Further exploration of one of these classes, by substituting open shell 3d with 4d and 5d counterparts, has led to realistic prediction of Chern insulating ground states. Here …
We study the many-body instabilities of correlated electrons on the half-filled honeycomb lattice with enhanced exchange coupling. The system is described by an extended Hubbard model including the next-nearest-neighbor Coulomb repulsion ($V_2$) and the nearest-neighbor exchange interaction ($J$). We use the truncated unity functional renormalization group approach to determine a schematic ground-state phase diagram with higher resolution in the parameter space of $V_2$ and $J$. In the absence of the on-site repulsion and presence of sizable next-nearest-neighbor repulsion and enhanced nearest…
Light enables ultrafast, direct and nonthermal control of the exchange and Dzyaloshinskii-Moriya interactions. We consider two-dimensional honeycomb lattices described by the Kane-Mele-Hubbard model at half filling and in the strongly correlated limit, i.e., the Mott insulator phase of a canted antiferromagnet. Based on Floquet theory, we demonstrate that by changing the amplitude and frequency of polarized laser pulses, one can tune the amplitudes and signs of and even the ratio between the exchange and Dzyaloshinskii-Moriya spin interactions. Furthermore, the renormalizations of the spin int…
We study the effects of longitudinal magnetic field and temperature on the thermodynamic properties of two dimensional Heisenberg antiferromagnet on the honeycomb lattice in the presence of anisotropic Dzyaloshinskii-Moriya interaction and next nearest neighbor coupling exchange constant. In particular, the temperature dependence of specific heat have been investigated for various physical parameters in the model Hamiltonian. Using a hard core bosonic representation, the behavior of thermodynamic properties has been studied by means of excitation spectrum of mapped bosonic gas. The effect of D…
In this paper we study the quantum properties of the lattice vacancy in topological band insulators (TBIs) and topological superconductors (TSCs) on honeycomb lattice with particle-hole symmetry. Each vacancy has one zero mode for the Haldane model and two zero modes for the Kane-Mele model. In addition, in TSCs on honeycomb lattice with particle-hole symmetry, we found the existence of the Majorana zero modes around the vacancies. These zero energy modes are protected by particle-hole symmetry of these topological sates.
Higher Order Topological Insulators (HOTI) are $d$-spatial dimensional systems featuring topologically protected gap-less states at their $(d-n)$-dimensional boundaries. With the help of \textit{ab-initio} calculations and tight binding models along with symmetry considerations we show that monolayer buckled honeycomb structures of group-V elements (Sb,As), which have already been synthesized, belong in this category and have a charge fractionalization of $\frac{e}{2}$ at the corner states as well as weak topological edge states, all protected by their properties under the inversion operation …
Fermions hopping on a hexagonal lattice represent one of the most active research field in condensed matter since the discovery of graphene in 2004 and its numerous applications. Another exciting aspect of the interplay between geometry and quantum mechanical effects is given by the Haldane model (F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988)) where spinless fermions experiencing a certain flux pattern on the honeycomb lattice leads to the stabilization of a topological phase of matter, distinct from a Mott insulator and dubbed Chern insulator nowadays. In this context, it is crucial to u…
We investigate the Hubbard model on the honeycomb lattice with intrinsic spin orbit interactions as a paradigm for two-dimensional topological band insulators in the presence of interactions. Applying a combination of Hartree-Fock theory, slave-rotor techniques, and topological arguments, we show that the topological band insulating phase persists up to quite strong interactions. Then we apply the slave-rotor mean-field theory and find a Mott transition at which the charge degrees of freedom become localized on the lattice sites. The spin degrees of freedom, however, are still described by the…
We study the interplay between spin-orbit coupling (SOC) and Coulomb repulsion in a Hubbard model on a decorated honeycomb lattice which leads to a plethora of phases. While a quantum spin hall insulator is stable at weak Coulomb repulsion and moderate SOC, a semimetallic phase emerges at large SOC in a broad range of Coulomb repulsion. This semimetallic phase has topological properties not observed in conventional metals such as a finite, non-quantized spin Hall conductivity. At large Coulomb repulsion and negligible spin-orbit coupling, electronic correlations stabilize a resonance valence b…
It is well known that a Bosonic Mott insulator can be realized by condensing vortices of a bo- son condensate. Usually, a vortex becomes an anti-vortex (and vice-versa) under time reversal symmetry, and the condensation of vortices results in a trivial Mott insulator. However, if each vortex or anti-vortex interacts with a spin trapped at its core, the time reversal transformation of the composite vortex operator will contain an extra minus sign. It turns out that such a composite vortex condensed state is a bosonic topological insulator (BTI) with gapless boundary excitations protected by $U(…
e provide a detailed analysis of a topological structure of a fermion spectrum in the Hofstadter model with different hopping integrals along the $x,y,z$-links ($t_x=t, t_y=t_z=1$), defined on a honeycomb lattice. We have shown that the chiral gapless edge modes are described in the framework of the generalized Kitaev chain formalism, which makes it possible to calculate the Hall conductance of subbands for different filling and an arbitrary magnetic flux $ϕ$. At half-filling the gap in the center of the fermion spectrum opens for $t>t_c=2^ϕ$, a quantum phase transition in the 2D-topological i…
In this paper we study transport properties of electrons on the two-dimensional honeycomb lattice. We consider a half-filled system in the vicinity of a symmetry-breaking transition from a semimetallic phase towards an insulating phase with either charge density or spin density wave order. The effect of either order is to break the sublattice inversion symmetry which induces a finite gap for the electronic single-particle excitations. Phenomenologically, such a scenario is described in the framework of a Gross-Neveu theory. We analyze two related formulations of the model by means of (i) a con…
Within the Landau paradigm, phases of matter are distinguished by spontaneous symmetry breaking. Implicit here is the assumption that a completely symmetric state exists: a paramagnet. At zero temperature such quantum featureless insulators may be forbidden, triggering either conventional order or topological order with fractionalized excitations. Such is the case for interacting particles when the particle number per unit cell, f, is not an integer. But, can lattice symmetries forbid featureless insulators even at integer f? An especially relevant case is the honeycomb (graphene) lattice --- …
