Single-particle Hopping Research Articles

Superconductivity and Magnetism in Quasi-One-Dimensional Two-Band Systems.

We study crossovers from one to quasi-one dimensions in doped two-leg ladder systems, using a renormalization group method. When quasi-one dimensionality is regarded as controlled by incomplete interference between the Cooper and Peierls channels, we obtain spin-density wave, d-wave superconductor, and metallic phases with decreasing dominance of the Peierls channel. When transverse single-particle hopping is treated perturbationally, we obtain a one-particle crossover from incoherent to coherent transverse motion for weak interaction and a two-particle crossover from short- to long-range ordering of a d-wave superconductor for strong interaction. We also study a magnetic property in a doped Heisenberg-Kondo chain, using the exact diagonalization method. A fully saturated ferromagnetism in the ferromagnetic Kondo chain is destroyed by rather weak antiferromagnetic Heisenberg coupling between localized S=1/2 spins.

Dimensional crossover and metal-insulator transition in quasi-two-dimensional disordered conductors

We study the metal-insulator transition in weakly coupled disordered planes on the basis of a nonlinear sigma model (NL\ensuremath{\sigma}M). Using two different methods, a renormalization-group approach and an auxiliary-field method, we calculate the crossover length between a two-dimensional (2D) regime at small length scales and a 3D regime at larger length scales. The 3D regime is described by an anisotropic 3D NL\ensuremath{\sigma}M with renormalized coupling constants. We obtain the critical value of the single-particle interplane hopping, which separates the metallic and insulating phases. We also show that a strong parallel magnetic field favors the localized phase and derive the phase diagram.

Spin-charge separation, anomalous scaling, and the coherence of hopping in exactly solved two-chain models

The coherence of transport between two one-dimensional interacting Fermi liquids, coupled by single-particle hopping and interchain interaction, is examined in the context of two exactly soluble models. It is found that the coherence of the interchain hopping depends on the interplay between interchain hopping and interchain interaction terms, and not simply on the ground state spectral properties of an isolated chain. Specifically, the splitting of levels associated with interchain hopping in a ${\mathrm{g}}_{4}$ soluble model is found to be enhanced by the introduction of interchain interaction. It is also shown that, for an exactly solvable model with both ${\mathrm{g}}_{2}$ and ${\mathrm{g}}_{4}$ interactions, coherent interchain hopping coexists with anomalous scaling and non-Fermi liquid behavior in the chain direction.

Collective modes in the electronic polarization of double-layer systems in the superconducting state.

Standard weak coupling methods are used to study collective modes in the superconducting state of a double-layer system with intralayer and interlayer interaction, as well as a Josephson-type coupling and single particle hopping between the layers by calculating the electronic polarization function perpendicular to the layers. New analytical results are derived for the mode frequencies corresponding to fluctuations of the relative phase and amplitude of the layer order parameters in the case of interlayer pairing and finite hopping $t$. A new effect is found for finite $k$-dependent hopping: then the amplitude and phase fluctuations are coupled. Therefore two collective modes may appear in the dynamical c-axis conductivity below the threshold energy for breaking Cooper pairs. With help of numerical calculations we investigate the temperature dependence of the collective modes and show how a plasmon corresponding to charge fluctuations between the layers evolves in the normal state.

Spin and charge excitations in a three-legs fermionic ladder: a renormalization-group study

We study the spin and charge phase diagram of a three-legs ladder (at zero temperature) as a function of fermion density and of transverse single-particle hopping by means of a renormalization-group analysis rigorously controlled in the weak-coupling limit. Periodic boundary conditions in the direction transverse to the ladder produce frustrated magnetic excitations yielding a spin-gapped phase in a large region about and at half filling. Spin correlations are instead enhanced when open transverse boundary conditions are considered, yielding an ungapped phase in a wide region about half filling (as observed in the Sr n−1 Cu n+1 O 2 n stripes compounds) and at half filling down to a critical value of the transverse hopping t t . At that critical value, the system undergoes a Mott transition at half filling by decreasing t t] .

Single particle hopping between luttinger liquids: A spectral function approach

We present a pedagogical account of our approach to the problem of Luttinger liquids coupled by interliquid single particle hopping. It is shown that the key issue is that of coherence/incoherence of interliquid hopping, and not of relevance/irrelevance in a renormalization group sense. A clear signal of coherence, present in the case of coupled Fermi liquids, is absent for Luttinger liquids, and we argue for the existence of an incoherent regime when the interliquid hopping rate is sufficiently small. The problem is relevant to any sufficiently anisotropic, strongly correlated metal, and in particular to understanding the anomalous c-axis conductivity in the cuprate superconductors, and the physics of the quasi-1D organic conductors.

Multilayer Scaling and Universal Behavior of Molecular Beam Epitaxy Grown Surfaces

Extensive kinetic Monte Carlo simulations have been used to model the growth of epitaxial films by molecular beam epitaxy (MBE). We allow both deposition and diffusion (single particle hopping events) to occur simultaneously and have investigated several different rules for hopping. Simple solid-on-solid models have been used with L x L substrate sizes and with nearest neighbor interactions only. Interfacial width and reflection high energy electron diffraction (RHEED) intensity have been determined as measures of the roughness of the surface. We find that in the long time limit the interfacial width has a logarithmic dependence on time and substrate size, although there is a pronounced crossover region for moderate times which depends on both temperature and flux. These results suggest that these models fall in the universality class of the Edwards-Wilkinson model. Comparison with experimental results shows similar behavior up to intermediate times and suggests that experimental data are needed over longer time scales.

LDA energy bands, low-energy hamiltonians, t′, t″, t⊥ ( k), andJ⊥

We describe the LDA band structre of YBa 2Cu 3O 7 in the ϵ F ± 2 eV range using orbital projections and compare with YBa 2Cu 4O 8. Then, the high-energy and chain-related degrees of freedom are integrated out and we arrive at two, nearest-neighbor, orthogonal, two-center, 8-band Hamiltonians, H 8 + and H 8 −, for respectively the even and odd bands of the bi-layer. Of the 8 orbitals, Cu x 2 − y 2 , O2 x , O3 y , and Cu s have σ character and Cu xz , Cu yz , O2 z , and O3 z have π character. The roles of the Cu s orbital, which has some Cu 3 z 2 − 1 character, and the four π orbitals are as follows: Cu s provides 2nd- and 3rd-nearest-neighbor ( t′ and t″) intra-plane hopping, as well as hopping between planes ( t ⊥). The π-orbitals are responsible for bifurcation of the saddle-points for dimpled planes. The 4-σ-band Hamiltonian is generic for flat CuO 2 planes and we use it for analytical studies. The k ∥-dependence is expressed as one on u ≡ (cos bk y + cos ak x) 2 and one on v ≡ (cos bk y − cos ak x) 2 . The latter arises solely through the influence of Cu s . The reduction of the σ-Hamiltonian to 3- and 1-band Hamiltonians is explicitly discussed and we point out that, in addition to the hoppings commonly included in many-body calculations, the 3-band Hamiltonian should include hopping between all 2nd-nearest-neighbor oxygens and that the 1-band Hamiltonian should include 3rd-nearest-neighbor hoppings. We calculate the single-particle hopping between the planes of a bi-layer and show that it is generically: t⊥ (k ∥) ≈ 0.25 eV · v 2 (1 − 2ut′ t ) −2 . The hopping through insulating spacers such as (BaO)Hg(BaO) is an order of magnitude smaller, but seems to have the same k∥-dependence. We show that the inclusion of t′ is crucial for understanding ARPES for the anti-ferromagnetic insulator Sr 2CuO 2Cl 2. Finally, we estimate the value of the inter-plane exchange constant J ⊥ for an un-doped bi-layer in meanfield theory using different single-particle Hamiltonians, the LDA for YBa 2Cu 3O 6, the eight- and four-band Hamiltonians, as well as an analytical calculation for the latter. We conclude that J⊥ ~ − 20 meV.

The ground state of the Penson-Kolb-Hubbard model

The ground state of the one-dimensional half-filled Penson-Kolb-Hubbard model (with competing single-particle and pair hoppings in the presence of on-site Coulomb repulsion) has been investigated by a real space renormalization group method. The ground state energy, energy gap, local moment and several correlation functions are studied to obtain the phase diagram. The phase diagram consists of a spin density wave (SDW) state, a superconducting (SC) phase and a quasi-metallic phase dominated by short range SC correlations for positive values of the pair hopping amplitude; when this amplitude is negative, the phase diagram contains a near-metallic commensurate charge density wave and an SC phase of pairs with centre-of-mass momentum q= pi apart from an SDW phase.

A one-dimensional integrable model of fermions with multi-particle hopping

A model with both single-particle and multi-particle hopping of electrons on a one-dimensional 'triangular' lattice is formulated and solved exactly by Bethe ansatz. On the basis of the exact calculation of the asymptotic behaviour of correlation functions we find a transition between the normal state and a state with a tendency to 'superconductivity'. The latter state is confined to small densities of electrons up to a critical density rho c.

Incoherence of single particle hopping between Luttinger liquids.

We demonstrate that for general spin-charge separated Luttinger liquids there exists a critical value of the inter-Luttinger-liquid single particle hopping, ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}^{\mathit{c}}$, below which there is no coherent single particle hopping between the liquids. In the absence of coherent single particle hopping, two Luttinger liquids coupled by ${\mathit{t}}_{\mathrm{\ensuremath{\perp}}}$ will not exhibit split Fermi surfaces. For many Luttinger liquids, no band dipsersing between the liquids will form, and thus the system will retain a one-dimensional Fermi surface. This will have dramatic implications for the physical properties of such a system.

Penson-Kolb-Hubbard model: A study of the competition between single-particle and pair hopping in one dimension.

In this paper, we present a study of the ground-state phase diagram of a one-dimensional quantum chain, the Penson-Kolb-Hubbard model, H=-${\mathcal{J}}_{\mathrm{i},\mathrm{\ensuremath{\eta}}=\ifmmode\pm\else\textpm\fi{}1,\mathrm{\ensuremath{\sigma}}}$ (${\mathit{tc}}_{\mathit{i}+\mathrm{\ensuremath{\eta}}\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${\mathit{c}}_{\mathit{i}\mathrm{\ensuremath{\sigma}}}$+${\mathit{Vc}}_{\mathit{i}+\mathrm{\ensuremath{\eta}}\mathrm{\ensuremath{\uparrow}}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${\mathit{c}}_{\mathit{i}+}$ $_{\mathrm{\ensuremath{\eta}}\mathrm{\ensuremath{\downarrow}}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${\mathit{c}}_{\mathit{i}\mathrm{\ensuremath{\downarrow}}}$${\mathit{c}}_{\mathit{i}\mathrm{\ensuremath{\uparrow}}}$)+ ${\mathcal{J}}_{\mathit{i}}$ U${\mathit{n}}_{\mathit{i}\mathrm{\ensuremath{\uparrow}}}$${\mathit{n}}_{\mathit{i}\mathrm{\ensuremath{\downarrow}}}$ at half filling. We have examined the system using exact diagonalization for samples of up to 12 sites and employed two techniques, eigenprojection decomposition and twisted-boundary conditions, in analyzing the data. These techniques allow us to characterize the ground state in a manner insensitive to changes in sample size and provide us with a clean way to visualize the physics. When used with the ``correct'' order parameter, qualitative features emerge even for sample sizes as small as six sites. We find that the second-order charge-density-wave--spin-density-wave transition in the weak-coupling limit (t\ensuremath{\gg}U\ensuremath{\sim}2V) turns into a first-order superconducting--antiferromagnetic transition in the strong-coupling regime [t\ensuremath{\ll}U\ensuremath{\sim}(4/\ensuremath{\pi})V]. We also observe evidence of a charge-density-wave--superconducting transition in the parameter range (t\ensuremath{\sim}V\ensuremath{\gg}U). These three transition lines meet together at a tricritical point at (t:U:V)\ensuremath{\sim}(0.04:0.54:0.42). A naive renormalization-group analysis in the intermediate-coupling regime produces results consistent with this conclusion.

Microscopic description of superconductor-normal-metal superlattices

We study a model for superconductor-normal-metal superlattices in which adjacent layers are coupled via single-particle hopping. Examples include the high-T c superconductor Bi2Sr2CaCu2O8+δ, where the BiO sheets seem to have normal metallic character. Using a BCS treatment, we investigate the influence of the interlayer hopping between the superconducting and the normal-metal slabs on the superconducting density of states, the tunneling characteristics for tunneling into both superconducting and normal-metal slabs as well as the temperature dependence of the London penetration depth.

"Confinement" in the one-dimensional Hubbard model: Irrelevance of single-particle hopping.

We demonstrate, by direct use of the asymptotic Green's functions of Korepin and Ren, that the one-dimensional repulsive U Hubbard model has the property of ``confinement,'' in that weak interchain coupling does not cause coherent particle motion in the transverse direction at absolute zero. Implications for real one-dimensional systems and for the two-dimensional Hubbard model are discussed.

Expansion of orbitals and electron-electron interaction in crystals

The effect of the expansion of orbitals caused by the intra-atomic Coulomb repulsion is considered. The investigation is based on a model of a one-dimensional crystal with a delta-like pseudopotential. Due to this effect a term Va + i,σ a i+1,σ ( n̂ i,-σ + n̂ i+1,-σ ) appears in the Hamiltonian. V depends exponentially upon the on-site repulsion and has the same sign as the single particle hopping amplitude. Such an interaction is attractive for electrons in bonding states and so can lead to superconductivity in the case of a sufficiently low electron density.

Electron correlation effects in chemisorption theory at finite submonolayer coverages

Within the generalized Anderson-Newns Hamiltonian the coverage dependence of the chemisorption characteristics such as the adatom charge and adatom local density of states has been calculated. The electron correlation effects on the adatom were included up to second order in V (the single particle hopping strength between the adatom and the substrate) and the Bragg-Williams approximation for the ionic adsorbate component was used. For a model system of the hydrogen chemisorption on the transition metal surfaces a progressive neutralization of the adatoms with increasing coverage was obtained and all values of the adatom charge are much smaller than the corresponding ones calculated within the Hartree-Fock (HF) approach for general coverages or beyond HF for zero coverages.

Hole superconductivity: The strong coupling limit

A Hamiltonian describing hole superconductivity is studied in the limit where the single particle hopping amplitude t goes to zero. It is shown that superconductivity can occur in this regime with purely repulsive Coulomb interactions, similarly to what occurs in the weak coupling case. The critical temperature remains finite as t→0. No bound pairs exist above T c except for extremely low density of holes, and above T c holes are localized.

Hopping conduction in a two-dimensional impurity band.

The temperature dependence (380 mKT80 K) and electric field dependence (50 mV/cmF150 V/cm) of hopping conduction have been measured as a function of the impurity concentration, surface electric field, and carrier density in a quasi-two-dimensional impurity band formed in the inversion layer of a sodium-doped silicon metal-oxide--semiconductor field-effect transistor. The conductivity is found to be an exponential function of the temperature and applied electric field. Our observations can be accommodated by noninteracting, single-particle hopping models based on percolation theory in which the Coulomb repulsion between electrons on different sites is ignored. For impurity concentrations in the range 2\ifmmode\times\else\texttimes\fi{}${10}^{11}$ to 1.14\ifmmode\times\else\texttimes\fi{}${10}^{12}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ and localization lengths from 3.4 to 7.5 nm, the noninteracting theories accurately describe eight-orders-of-magnitude change in the conductivity of a half-filled impurity band observed for a factor-of-80 change in temperature, and three-orders-of-magnitude change in the non-Ohmic current observed for a factor-of-15 change in electric field. The observed temperature dependence of the conductivity is not consistent with the temperature dependence predicted by Efros and Shklovskii for a Coulomb gap in the single-particle excitation spectrum, although their theory was expected to predict the conductivity under the conditions examined in this experiment.

Importance of one-dimensional correlations in the phase diagram of the (TMTTF) 2-(TMTSF) 2-X salts

In this work, we explain the ingredients of a model for a semi-quantitative analysis of the large variety of phase transitions observed in the two similar families of organic compounds (TMTTF) 2X and (TMTSF) 2X (X=PF 6, AsF 6, Br, TaF 6 …). We find that the sequence of magnetic transitions in the (TMTTF) 2X family up to moderate pressure are dominated by significant changes in the one-dimensional (1D) or intrachain correlations of the 1D electron and electron-phonon systems. These 1D effects are stabilized by the interchain pair tunneling processes generated by the single-particle hopping. In the (TMTSF) 2X family, however, these interchain interactions significantly decrease the range in temperature (T<T X 1) in which there is 3D nesting while contributing to the superconductivity pairing interaction below the crossover temperature (T X 1).

Absence of a Coulomb gap in a two-dimensional impurity band.

The temperature dependence (30K&gt;T&gt;400 mK) and magnetic field dependence (H&lt;50 kG) of hopping conduction have been measured as a function of impurity concentration and surface electric field in a quasi-two-dimensional impurity band formed in the inversion layer of a sodium-doped Si metal-oxide-semiconductor field-effect transistor. We find that our observations can be accommodated by noninteracting, single-particle hopping models based on percolation theory in which the effect of Coulomb interactions between electrons on different sites is ignored. Our observations are not consistent with the existence of a Coulomb gap in the single-particle excitation spectrum, although the gap was expected to determine the conductivity under the conditions examined in these experiments.