Hopping Integrals Research Articles

Orbital order in La0.5Sr1.5MnO4: Beyond a common local Jahn-Teller picture

The standard way to find the orbital occupation of Jahn-Teller (JT) ions is to use structural data, with the assumption of a one-to-one correspondence between the orbital occupation and the associated JT distortion, e.g. in O6 octahedron. We show, however, that this approach in principle does not work for layered systems. Specifically, using the layered manganite La0.5Sr1.5MnO4 as an example, we found from our x-ray absorption measurements and theoretical calculations, that the type of orbital ordering strongly contradicts the standard local distortion approach for the Mn3+O6 octahedra, and that the generally ignored long-range crystal field effect and anisotropic hopping integrals are actually crucial to determine the orbital occupation. Our findings may open a pathway to control of the orbital state in multilayer systems and thus of their physical properties.

Aharonov-Bohm interference for a hole in a two-dimensional Ising antiferromagnet in a transverse magnetic field

We show that a proper consideration of the contribution of Trugman loops leads to a fairly low effective mass for a hole moving in a square lattice Ising antiferromagnet, if the bare hopping and the exchange energy scales are comparable. This contradicts the general view that because of the absence of spin fluctuations, this effective mass must be extremely large. Moreover, in the presence of a transverse magnetic field, we show that the effective hopping integrals acquire an unusual dependence on the magnetic field, through Aharonov-Bohm interference, in addition to significant retardation effects. The effects of the Aharonov-Bohm interference on the cyclotron frequency (for small magnetic fields) and the Hofstadter butterfly (for large magnetic fields) are analyzed.

Magneto-transport in series coupled Aharonov–Bohm rings: The proximity effect and related issues

We present an exact analysis of one electron transport across a coupled system of model mesoscopic rings threaded by a uniform magnetic flux. In particular, we examine the effect of the proximity of the rings on the transmission characteristics within a tight binding formulation where, the ‘proximity’ is controlled by varying the inter-ring hopping integral. We show that such a system exhibits very interesting transmission characteristics, including flux controlled switching mechanism, a feature that may be observed in recently proposed molecular bridge systems.

Strictly localised triplet dimers on one- and two-dimensional lattices

Electrons may form inter-site pairs (dimers) by a number of mechanisms. For example, long-range (Fröhlich) electron-phonon interactions and strong on-site Hubbard U allow formation of small light bipolarons in some lattices. We identify circumstances under which triplet dimers are strictly localised by interference in certain one- and two-dimensional lattices. We assume a U-V Hamiltonian with nearest- and next-nearest-neighbour hopping integrals t and t′, large positive U and attractive nearest- and next-nearest-neighbour interactions V and V′. In the square ladder and some two-dimensional bilayers, if the dimer Hilbert space is restricted to nearest- and next-nearest-neighbour dimers, triplet dimers become strictly localised for certain values of these parameters. For example, in a square ladder with t′ = t and V′ = V, all triplet bands become flat due to exact cancellation of hopping paths. We identify the localised eigenstates for all flat bands in each lattice. We show that many of the flat bands persist for arbitrary t/t′ so long as other restrictions still apply.

Polaronic signatures and spectral properties of graphene antidot lattices

We explore the consequences of electron-phonon (e-ph) coupling in graphene antidot lattices (graphene nanomeshes), i.e., triangular superlattices of circular holes (antidots) in a graphene sheet. They display a direct band gap whose magnitude can be controlled via the antidot size and density. The relevant coupling mechanism in these semiconducting counterparts of graphene is the modulation of the nearest-neighbor electronic hopping integrals due to lattice distortions (Peierls-type e-ph coupling). We compute the full momentum dependence of the e-ph vertex functions for a number of representative antidot lattices. Based on the latter, we discuss the origins of the previously found large conduction-band quasiparticle spectral weight due to e-ph coupling. In addition, we study the nonzero-momentum quasiparticle properties with the aid of the self-consistent Born approximation, yielding results that can be compared with future angle-resolved photoemission spectroscopy measurements. Our principal finding is a significant e-ph mass enhancement, an indication of polaronic behavior. This can be ascribed to the peculiar momentum dependence of the e-ph interaction in these narrow-band systems, which favors small phonon momentum scattering. We also discuss implications of our study for recently fabricated large-period graphene antidot lattices.

Controllability of ferromagnetism in graphene

We systematically study magnetic correlations in graphene within Hubbard model on a honeycomb lattice by using quantum Monte Carlo simulations. In the filling region below the Van Hove singularity, the system shows a short-range ferromagnetic correlation, which is slightly strengthened by the on-site Coulomb interaction and markedly by the next-nearest-neighbor hopping integral. The ferromagnetic properties depend on the electron filling strongly, which may be manipulated by the electric gate. Due to its resultant controllability of ferromagnetism, graphene-based samples may facilitate the development of many applications.

Numerical study of geometrical frustration: From square to triangular lattices

In this work we study the effects of geometrical frustration in square lattice which can be measured by the diagonal hopping integral. In the framework of the Hubbard model, we use quantum Monte Carlo method to calculate spin susceptibility and focus on magnetic fluctuations in this system. We find that in two filling regions, the effects of geometrical frustration are quite different. As a measure of geometrical frustration between square and triangular lattices, the diagonal hopping suppresses the anti-ferromagnetic fluctuation at half filling and enhances ferromagnetic fluctuation at 1.5 filling.

Thermoelectric power of single-orbital and two-orbital Hubbard models on triangular lattices

The thermoelectric power of the single-orbital and two-orbital correlated electron systems on a two-dimensional triangular lattice is investigated by the dynamical mean field theory with the exact diagonalization solver at finite temperature. It reveals that for the hole doping case, the geometrical frustration together with the Coulomb interaction greatly enhances thermoelectric power, in comparison with the electron doping case. In an anisotropic triangular lattice, we find a large thermoelectric power in the direction with small hopping integral in the anisotropic systems. In the two-orbital systems, we show that though the orbital entropy contributes to thermoelectric power, Hund's rule coupling may suppress the large thermoelectric power.

Electron-phonon coupling in graphene antidot lattices: An indication of polaronic behavior

We study graphene antidot lattices---superlattices of perforations (antidots) in a graphene sheet---using a model that accounts for the phonon modulation of the $\ensuremath{\pi}$-electron hopping integrals. We calculate the phonon spectra of selected antidot lattices using two different semiempirical methods. Based on the adopted model, we quantify the nature of charge carriers in the system by computing the quasiparticle weight due to the electron-phonon interaction for an excess electron in the conduction band. We find a very strong phonon-induced renormalization, with the effective electron masses exhibiting nonmonotonic dependence on the superlattice period for a given antidot diameter. Our study provides an indication of polaronic behavior and points to the necessity of taking into account the inelastic degrees of freedom in future studies of transport in graphene antidot lattices.

Two-orbital systems with crystal field splitting and interorbital hopping

The nondegenerate two-orbital Hubbard model is studied within the dynamic mean-field theory to reveal the influence of two important factors, i.e. crystal field splitting and interorbital hopping, on orbital selective Mott transition (OSMT) and realistic compound Ca$_{2-x}$Sr$_{x}$RuO$_{4}$. A distinctive feature of the optical conductivity of the two nondegenerate bands is found in OSMT phase, where the metallic character of the wide band is indicated by a nonzero Drude peak, while the insulating narrow band has its Drude peak drop to zero in the mean time. We also find that the OSMT regime expands profoundly with the increase of interorbital hopping integrals. On the contrary, it is shown that large and negative level splitting of the two orbitals diminishes the OSMT regime completely. Applying the present findings to compound Ca$_{2-x}$Sr$_{x}$RuO$_{4}$, we demonstrate that in the doping region from $x=0.2$ to 2.0, the negative level splitting is unfavorable to the OSMT phase.

Anharmonic softening of Raman active phonons in iron-pnictides: Estimating the Fe isotope effect due to anharmonic expansion

We present Raman measurements on the iron-pnictide superconductors CeFeAsO1-xFx and NdFeAsO1-xFx. Modeling the Fe-As plane in terms of harmonic and a cubic anharmonic Fe-As interactions, we calculate the temperature dependence of the energy and lifetime of the Raman active Fe B-1g mode and fit to the observed energy shift. The shifts and lifetimes are in good agreement with those measured also in other Raman studies which demonstrate that the phonon spectrum, at least at small wave numbers, is well represented by phonon-phonon interactions without any significant electronic contribution. Even at zero temperature there is a non-negligent effect of interactions on the phonon energy, which for the Fe B-1g mode corresponds to 6 cm(-1) or 3% of the total energy of the mode. We also estimate the anharmonic expansion from Fe (56 -> 54) isotope substitution to Delta a approximate to 5.1 x 10(-4) angstrom and Delta d(Fe-As) approximate to 2.5 x 10(-4) angstrom and the shift of harmonic zero-point fluctuations of bond lengths less than or similar to 3 x 10(-5) angstrom(2), giving a total relative average decrease in electronic hopping integrals of vertical bar delta vertical bar/t less than or similar to 2.0 x 10(-4). For a nonphonon-mediated weak-coupling superconductor this gives an isotope exponent alpha similar to 10(-2). The results pose a serious challenge for any theory of superconductivity in the pnictides that does not include electron-phonon interactions to produce a sizable Fe isotope effect.

Hamiltonian Decomposition for Bulk and Surface States

We demonstrate that a tight-binding Hamiltonian with nearest- and next-nearest-neighbor hopping integrals can be decomposed into bulk and boundary parts for honeycomb lattice systems. The Hamiltonian decomposition reveals that next-nearest-neighbor hopping causes sizable changes in the energy spectrum of surface states even if the correction to the energy spectrum of bulk states is negligible. By applying the Hamiltonian decomposition to edge states in graphene systems, we show that the next-nearest-neighbor hopping stabilizes the edge states. The application of Hamiltonian decomposition to a general lattice system is discussed.

Effect of the intermolecular thermal motions on the tail of the electronic density of states in polyacene crystals

The thermal fluctuation of the intermolecular hopping integral in the series of polyacene crystals (naphthalene, anthracene, tetracene, pentacene) was evaluated computationally using a combined molecular dynamics and quantum chemistry approach. It was shown that these large fluctuations can manifest themselves in a temperature-dependent relatively broad tail of the density of states extending from the valence band into the gap. It was also shown that this tail accounts for a large fraction of all states in the valence band and therefore it may be essential for accurately describing the charge transport and optical properties.

Zero-temperature phase diagram of two dimensional Hubbard model

We investigate the two-dimensional Hubbard model on the triangular lattice with anisotropic hopping integrals at half filling. By means of a self-energy functional approach, we discuss how stable the non-magnetic state is against magnetically ordered states in the system. We present the zero-temperature phase diagram, where the normal metallic state competes with magnetically ordered states with (π, π) and (2π /3, 2π /3) structures. It is shown that a nonmagnetic Mott insulating state is not realized as the ground state, in the present framework, but as a meta-stable state near the magnetically ordered phase with (2π /3, 2π/3) structure.

Intrinsic electron and hole bands in electron-doped cuprate superconductors

Based on the analysis of the measurement data of angle-resolved photoemission spectroscopy (ARPES) and optics, we show that the charge transfer gap is significantly smaller than the optical one and is reduced by doping in electron doped cuprate superconductors. This leads to a strong charge fluctuation between the Zhang-Rice singlet and the upper Hubbard bands. The basic model for describing this system is a hybridized two-band $t$-$J$ model. In the symmetric limit where the corresponding intra- and inter-band hopping integrals are equal to each other, this two-band model is equivalent to the Hubbard model with an antiferromagnetic exchange interaction (i.e. the $t$-$U$-$J$ model). The mean-field result of the $t$-$U$-$J$ model gives a good account for the doping evolution of the Fermi surface and the staggered magnetization.

Monotonicd-wave superconducting gap of the optimally dopedBi2Sr1.6La0.4CuO6superconductor by laser-based angle-resolved photoemission spectroscopy

We propose that the upper Hubbard band (electronlike) and the Zhang-Rice singlet band (holelike) are two essential components in describing low-energy excitations of electron-doped cuprate superconductors. We find that the gap between these two bands is significantly smaller than the charge-transfer gap measured by optics and is further reduced upon doping. This indicates that the charge fluctuation is strong and the system is in the intermediate correlation regime. A two-band model is derived. In the limit that the intraband and interband hopping integrals are equal to each other, this model is equivalent to the unconstrained t-J model with on-site Coulomb repulsions.

Effective Hamiltonian of a three-orbital Hubbard model on the pyrochlore lattice: Application toLiV2O4

To investigate heavy fermion behavior in the vanadium spinel ${\text{LiV}}_{2}{\text{O}}_{4}$, we start from a three-orbital Hubbard model on the pyrochlore lattice and derive its low-energy effective Hamiltonian by an approach of real-space renormalization-group type. We first derive the effective Hamiltonian numerically and then succeed in representing the results into an analytic form with physical operators for low-energy degrees of freedom in tetrahedron unit. The effective Hamiltonian is defined on the coarse-grained lattice, i.e., face-centered-cubic (fcc) lattice, and it operates in a restricted Hilbert space defined in terms of a specific molecular orbital ${T}_{2}$ in the unit. One important tetrahedron configuration has a threefold orbital degeneracy and spin $S=1$, and correspondingly, the effective Hamiltonian has spin and orbital exchange interactions of Kugel-Khomskii type as well as correlated electron hoppings. The coupling constants in the effective Hamiltonian are determined from the numerically obtained renormalized Hamiltonian and also by means of perturbation. We calculate and analyze low-energy states of the effective Hamiltonian for the unit of four coupled tetrahedra both analytically and numerically. Effective hopping elements in the effective Hamiltonian are renormalized to about 1/10 of the original hopping integral. It is important that different virtual processes make opposite contributions to the exchange term, and consequently the coupling constant is given by a remaining small value. This is particularly prominent in the spin-spin channel, where ferromagnetic double-exchange processes compete with antiferromagnetic superexchange processes. Another important point is that various spin and orbital exchange processes are competing to each other. Together with geometrical frustration of the effective fcc lattice, these two features result in nearly degenerate three lowest-energy states of different types in the four coupled tetrahedra, and each of the three has a finite degeneracy in spin and/or orbital. We also calculate spatial correlations of spin and orbital and found that short-range spin-spin correlations are strongly entangled with orbital configurations. This indicates that large remaining entropy at low temperature is related to slow coupled fluctuations of spin and orbital. These results suggest the absence of phase transition in spin and orbital spaces down to very low temperatures and their large fluctuations in the low-energy sector, which are key issues for understanding the heavy fermion behavior in ${\text{LiV}}_{2}{\text{O}}_{4}$.

Coexistence of Ferromagnetism with Spin Triplet Superconductivity

The experimental results for ZrZn2, URhGe, and in some pressure ranges also for UGe2, showed that the ferromagnetic superconductors are weak itinerant ferromagnets. Guided by these results we describe the phenomenon of coexistence between equal spin triplet pairing superconductivity and ferromagnetism using the extended Stoner model, which includes in Hamiltonian the on-site Coulomb interaction, U , and occupation dependent hopping integral. We use the Hartree–Fock approximation and the Green functions technique. In the Hartree–Fock approximation the on-site Coulomb interaction plays the role of the on-site exchange (Hund’s) field. All inter-site

Hall conductance, topological quantum phase transition, and the Diophantine equation on the honeycomb lattice

We consider a tight-binding model with the nearest-neighbor hopping integrals on the honeycomb lattice in a magnetic field. Assuming one of the three hopping integrals, which we denote by ${t}_{a}$, can take a different value from the two others, we study quantum phase structures controlled by the anisotropy of the honeycomb lattice. For weak and strong ${t}_{a}$ regions, the Hall conductances are calculated algebraically by using the Diophantine equation. Except for a few specific gaps, we completely determine the Hall conductances in these two regions including those for subband gaps. In a weak magnetic field, it is found that the weak ${t}_{a}$ region shows the unconventional quantization of the Hall conductance, ${\ensuremath{\sigma}}_{xy}=\ensuremath{-}({e}^{2}/h)(2n+1)$ $(n=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2,\dots{})$, near the half filling, while the strong ${t}_{a}$ region shows only the conventional one, ${\ensuremath{\sigma}}_{xy}=\ensuremath{-}({e}^{2}/h)n$ $(n=0,\ifmmode\pm\else\textpm\fi{}1,\ifmmode\pm\else\textpm\fi{}2,\dots{})$. From the topological nature of the Hall conductance, the existence of gap closing points and quantum phase transitions in the intermediate ${t}_{a}$ region is concluded. We also study numerically the quantum phase structure in detail and find that even when ${t}_{a}=1$, namely, in graphene case, the system is in the weak ${t}_{a}$ phase except when the Fermi energy is located near the Van Hove singularity or the lower and upper edges of the spectrum.

High pressure Raman study of La1-xCaxMnO3-δ manganites

We report a high-pressure Raman study on two members of the La1-xCaxMnO3-δ manganite family (x = 0.20, δ = 0 and δ = 0.08). The results obtained for the δ = 0 sample show a different behavior in the low and high pressure regime which is ascribed to the onset of a new pressure-activated interaction previously invoked in other manganite compounds. The comparison of our results with literature data gives further support to the identification of the Jahn-Teller sensitive stretching mode and shows that pressure-induced octahedral symmetrization is more effective in systems exhibiting a lower metallic character. On the contrary the new interaction sets in at a pressure which decreases on increasing the metallic character of the system indicating an important role of the Mn–Mn hopping integral in its activation.