Calculations of electric capacitance in carbon and BN nanotubes, and zigzag nanographite (BN, BCN) ribbons

Electronic states in nanographite ribbons with zigzag edges are studied using the extended Hubbard model with nearest neighbor Coulomb interactions. The electronic states with the opposite electric charges separated along both edges are analogous as nanocondensers. Therefore, electric capacitance, defined using a relation of polarizability, is calculated to examine nano-functionalities. We find that the behavior of the capacitance is widely different depending on whether the system is in the magnetic or charge polarized phases. In the magnetic phase, the capacitance is dominated by the presence of the edge states while the ribbon width is small. As the ribbon becomes wider, the capacitance remains with large magnitudes as the system develops into metallic zigzag nanotubes. It is proportional to the inverse of the width, when the system corresponds to the semiconducting nanotubes and the system is in the charge polarized phase also. The latter behavior could be understood by the presence of an energy gap for charge excitations. In the BN (BCN) nanotubes and ribbons, the electronic structure is always like that of semiconductors. The calculated capacitance is inversely proportional to the distance between the positive and negative electrodes.     

Correlation effects in quantum spin-Hall insulators: a quantum Monte Carlo study

We consider the Kane-Mele model supplemented by a Hubbard U term. The phase diagram is mapped out using projective auxiliary field quantum Monte Carlo simulations. The quantum spin liquid of the Hubbard model is robust against weak spin-orbit interaction, and is not adiabatically connected to the spin-Hall insulating state. Beyond a critical value of U>U(c) both states are unstable toward magnetic ordering. In the quantum spin-Hall state we study the spin, charge, and single-particle dynamics of the helical Luttinger liquid by retaining the Hubbard interaction only on a ribbon edge. The Hubbard interaction greatly suppresses charge currents along the edge and promotes edge magnetism but leaves the single-particle signatures of the helical liquid intact.     

Spectral functions in the two-dimensional Hubbard model within a spin-charge rotating frame approach

We have performed electronic spectral function calculations for the Hubbard model on the square lattice using recently developed quantum SU(2) × U(1) rotor approach that enables a self-consistent treatment of the antiferromagnetic state. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green’s function in the space-time domain as a product of the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. Consequently, the calculation of the spectral line shapes now reduces to performing the convolution of spin, charge and pseudo-fermion Green’s functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.     

Structural stability and electronic properties of Ni-doped armchair graphene nanoribbons

The size dependent electronic properties of armchair graphene nanoribbons (AGNR) with Ni doped atoms have been investigated using spin-unrestricted density functional theory. We predict antiferromagnetic (AFM) ground states for Ni-termination and one edge Ni-doping. The computed formation energy reveals that one edge Ni-terminated AGNR are energetically more favourable as compared to pristine ribbons. One edge substitutional doping is energetically more favourable as compared to centre doping by ∼1 eV whereas both edge doping is unfavourable. The bond length of substitutional Ni atoms is shorter than that of Ni adsorption in GNR, implying a stronger binding for substitutional Ni atoms. It is evident that binding energy is also affected by the coordination number of the foreign atom. The results show that Ni-interaction perturbs the electronic structure of the ribbons significantly, causing enhanced metallicity for all configurations irrespective of doping site. The band structures reveal the separation of spin up and down electronic states indicating towards the existence of spin polarized current in Ni-terminated and one edge doped ribbons. Our calculation predicts that AGNR containing Ni impurities can play an important role for the fabrication of spin filters and spintronic devices.     

Edge magnetization in Bernal-stacked trilayer zigzag graphene nanoribbons

We have used a tight-binding Hamiltonian of an ABA-stacked trilayer zigzag graphene nanoribbon with β-alignment edges to study the edge magnetizations. Our model includes the effect of the intralayer next-nearest-neighbor hopping, the interlayer hopping responsible for the trigonal warping and the interaction between electrons, which is considered by a single band Hubbard model in the mean field approximation. Firstly, in the neutral system we analyzed the two magnetic states in which both edge magnetizations reach their maximum value; the first one is characterized by an intralayer ferromagnetic coupling between the magnetizations at opposite edges, whereas in the second state that coupling is antiferromagnetic. The band structure, the location of the edge-state bands and the local density of states resolved in spin are calculated in order to understand the origins of the edge magnetizations. We have also introduced an electron doping so that the number of electrons in the ribbon unit cell is higher than in neutral case. As a consequence, we have obtained magnetization steps and charge accumulation at the edges of the sample, which are caused by the edge-state flat bands.     

Effect of Coulomb repulsion on spin and orbital magnetism of cobalt–benzene complex: A relativistic density functional study

We have demonstrated electronic configurations and magnetic properties of single Co adatom on benzene (Bz) molecule in the framework of relativistic density functional theory. A sequence of fixed spin moment (FSM) calculations were carried out with and without Coulomb repulsion (U). We have investigated that varying the strength of Coulomb repulsion results to different equilibrium positions for the Co adatom on benzene molecule. It was shown that inclusion of the on-site Coulomb repulsion in the Co 3d orbitals affects significantly the geometry of Co–Bz complex. We also found two stable low-spin and high-spin multiplicities for the complex. The nature of the high-spin configuration was explained according to the Hubbard electron–electron correlation in 3d shell of the Co adatom. Our FSM results indicate that the high-spin state is a global minimum in the presence of Hubbard parameter U. The relativistic spin–orbit coupling and using orbital polarization correction induce considerable orbital magnetism in both low and high spin states of the Co–Bz complex. We have also calculated magnetic anisotropy energies for two spin states and we found out that an out-of-plane magnetic orientation of Co adatom is more favorable in the low spin state whereas the Coulomb repulsion (U = 2 eV and U = 4 eV) predicts an in-plane magnetic orientation for Co adatom. Our findings can be implicitly taken into account for the extended system of added single Co atom on graphene.     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

The Hubbard model extended by nearest‐neighbor Coulomb and exchange interaction on a cubic cluster – rigorous and exact results

The Hubbard model on a cube was revisited and extended by both nearest‐neighbor Coulomb correlation W and nearest‐neighbor Heisenberg exchange J. The complete eigensystem was computed exactly for all electron occupancies and all model parameters ranging from minus infinity to plus infinity. For two electrons on the cluster the eigensystem is given in analytical form. For six electrons and infinite on‐site correlation U we determinded the groundstate and the groundstate energy of the pure Hubbard model analytically. For fixed electron numbers we found a multitude of ground state level crossings depending on the various model parameters. Furthermore the groundstates of the pure Hubbard model in dependence on a magnetic field h coupled to the spins are shown for the complete U‐h plane. The critical magnetic field, where the zero spin groundstate breaks down is given for four and six electrons. Suprisingly we found parameter regions, where the ground state spin does not depend monotonously on J in the extended model. For the cubic cluster gas, i.e. an ensemble of clusters coupled to an electron bath, we calculated the density n (μ, T, h) and the thermodynamical density of states from the grand potential. The ground states and the various spin‐spin correlation functions are studied for both attractive and repulsive values of the three interaction constants. We determined the various anomalous degeneration lines, where n (μ, T = 0, h = 0) shows steps higher than one, since in this parameter regions exotic phenomena as phase separation are to expect in extended models. For the cases where these lines end in triple points, i.e. groundstates of three different occupation numbers are degenerated, we give the related parameter values. Regarding the influence of the nn‐exchange and the nn‐Coulomb correlation onto the anomalous degeneration we find both lifting and inducing of degeneracies depending on the parameter values.     

Dynamical spin and charge response functions in the doped two-dimensional Hubbard model

Dynamical properties of the spin and charge response functions in the doped two-dimensional Hubbard model are calculated by taking into account the drastic separation of the single-particle spectral function into the low-energy coherent and high-energy incoherent parts due to the strong Coulomb interaction. We show that this evolution of the electronic states is the origin of the broad and structureless feature in the charge response function. In the weak coupling regime the low-energy enhancement of the spin excitation is produced which can be explained within the random phase approximation. However, for the larger interaction close to the antiferromagnetic Stoner condition, the low-energy intensity of the spin excitation is suppressed. Received: 25 September 1997 / Revised: 19 December 1997 / Accepted: 9 January 1998     

Diagnostics of many-particle electronic states: Non-stationary currents and residual charge dynamics

We propose the method for identifying many particle electronic states in the system of coupled quantum dots (impurities) with Coulomb correlations. We demonstrate that different electronic states can be distinguished by the complex analysis of localized charge dynamics and non-stationary characteristics. We show that localized charge time evolution strongly depends on the properties of initial state and analyze different time scales in charge kinetics for initially prepared singlet and triplet states. We reveal the conditions for existence of charge trapping effects governed by the selection rules for electron transitions between the states with different occupation numbers.     

Quasi‐particle peak due to magnetic order in strongly correlated electron systems

We study the electron spectral function of the antiferromagnetically ordered phase of the three dimensional Hubbard model, using recently formulated low‐energy theory based on the 2D half‐filled Hubbard model which describes both collective spin and charge fluctuations for arbitrary value of the Coulomb repulsion U. The model then is solved by a saddle‐point approximation within the CP¹ representation for the Neel field. The single‐particle properties are obtained by writing the fermion field in terms of a U(1) phase, Schwinger boson SU(2) fields and a pseudofermion variables. We demonstrate that the appearance of a sharp peak in the electron spectral function in the antiferromagnetic state points to the emergence of the bosonic mode, which is associated with spin ordering.     

Charge fractionalization in biased bilayer graphene

Fractional charge may arise when fermionic zero modes exist in a topological background field. In biased bilayer graphene (BBLG), the bias plays the role of the nontrivial background field. When semi-infinite BBLG with a zigzag edge is used, the dynamics induces an odd number of zero-energy modes, which, together with the conjugation symmetry between positive-?and negative-energy states, are the requisite conditions for fractionalization. Exploiting the trigonal interaction to isolate a given zero-energy mode on the zigzag edge, we consider extended and localized modes (the latter being obtained from a localized wavepacket generated by prior irradiation of the sample with an electromagnetic vortex). The valley degeneracy is lifted by a layer asymmetry, while an edge-induced spin polarization breaks the spin degeneracy. We describe scenarios for the detection of charge-[Formula: see text] edge states.     

Quantum spin Hall effect in graphene

We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are nonchiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.     

Magnetic and electric phase transitions in the Hubbard model

Within the Hubbard model, two boson Green’s functions that describe the propagation of collective excitations of the electronic system—magnons (states with a single electron spin flip) and doublons (states with two electrons at one site of the crystal lattice)—are calculated for a Coulomb interaction of arbitrary strength and for an arbitrary electron concentration by applying a decoupling procedure to the double-time X-operator Green’s functions. It is found that the magnon and doublon Green’s functions are similar in structure and there is a close analogy between them. Instability of the paramagnetic phase with respect to spin ordering is investigated using the magnon Green’s function, and instability of the metallic phase to charge ordering is analyzed with the help of the doublon Green’s function. Criteria for the paramagnet-ferromagnet and metal-insulator phase transitions are found.     

Spin polarization of two-dimensional electron system in different Laughlin states and around filling factor

The spin configuration of the ground state of a two-dimensional electron system is investigated for different FQHE states from an analysis of circular polarization of time-resolved luminescence. The method clearly distinguishes between fully spin polarized, partially spin polarized and spin unpolarized FQHE ground states. We demonstrate that FQHE states which are spin unpolarized or partially polarized at low magnetic fields become fully spin polarized at high fields. Temperature dependence of the spin polarization reveals a nonmonotonic behavior at . At and the electron system is found to be fully spin polarized. This result does not indicate the existence of any skyrmionic excitations in high magnetic field limit. However, at the observed spin depolarization of electron system at and becomes broader for lower magnetic fields, so that full spin polarization remains only in a small vicinity of . Such a behavior could be considered as a precursor of skirmionic depolarization, which would dominate for smaller ratios between Zeeman and Coulomb energies.We demonstrate that the spin polarization of 2D-electron system at and can be strongly affected by hyperfine interaction between electrons and optically spin-oriented nuclears. This result is due to the fact that hyperfine interaction can both enhance and suppress effective Zeeman splitting in fixed external magnetic field.     

Bound excitons in Sr2CuO3

We investigated temperature dependent optical spectra of the one-dimensional chain compound Sr2CuO3. The charge transfer transition polarized along the chain direction shows a strongly asymmetric line shape as expected in one-dimensional extended Hubbard model. At low temperature, the charge transfer peak shows a large blueshift and reveals additional sharp peaks at the gap. Even though many spectroscopic studies suggest that this material cannot have a bound exciton based on the one-dimensional extended Hubbard model, we attribute the additional sharp peaks to excitons, which come to exist due to the long-range Coulomb interaction.     

Spin structures and the nature of the pseudogap in cuprates

The spin and charge structures formed in a Hubbard model for a finite two-dimensional cluster have been studied in the mean field approximation. The self-consistent iterative procedure reduces an uncorrelated initial spin distribution into stable structures with characteristic spectral properties. It has been shown that the density of states of the system for any doping has a sharp minimum at the Fermi level, the pseudogap. This means that the pinning of the gap at the Fermi level is not an exclusive property of a superconducting state, but is also typical of a normal state of spin glasses.     

Charge and spin order on the triangular lattice: NaxCoO2 at x=0.5

The nature of electronic states due to strong correlation and geometric frustration on the triangular lattice is investigated in connection to the unconventional insulating state of NaxCoO2 at x=0.5. We study an extended Hubbard model using a spatially unrestricted Gutzwiller approximation. We find a new class of charge and spin ordered states at x=1/3 and x=0.5 where antiferromagnetic (AFM) frustration is alleviated via weak charge inhomogeneity. At x=0.5, we show that the square root of 3a x 2a off-plane Na dopant order induces weak square root of 3a x 1a charge order in the Co layer. The symmetry breaking enables successive square root of 3a x 1a AFM and 2a x 2a charge- or spin-ordering transitions at low temperatures. The Fermi surface is truncated by the 2a x 2a hexagonal zone boundary into small electron and hole pockets. We study the phase structure and compare to recent experiments.     

Exact transformation for spin-charge separation of spin-1/2 fermions without constraints

We demonstrate an exact local transformation which maps a purely Fermionic many-body system to a system of spinful bosons and spinless fermions, demonstrating a possible path to a non-Fermi-liquid state. We apply this to the half-filled Hubbard model and show how the transformation maps the ordinary spin half Fermionic degrees of freedom exactly and without introducing Hilbert space constraints to a chargelike quasicharge fermion and a spinlike quasispin Boson while preserving all the symmetries of the model. We present approximate solutions with localized charge which emerge naturally from the Hubbard model in this form. Our results strongly suggest that charge tends to remain localized for large values of the Hubbard U.