Hopping Anisotropy Research Articles

Irreversible island growth in the presence of anisotropic surface diffusion with long jumps

Kinetic Monte Carlo (KMC) simulations are used to investigate the dynamics of island growth during submonolayer epitaxy in the presence of anisotropic surface diffusion, and the influence of a recently hypothesized crowdion diffusion mechanism. An existing rate equation mean-field analysis of island growth is extended to include anisotropic diffusion. The mean-field analysis is found to be at odds with results from KMC simulations indicating that the details of the surface diffusion mechanism influence the nucleation rate. It is found that anisotropy in adatom hopping reduces the density of stable islands. It is also found that although the shape of the island size distribution is sensitive to island relaxation processes, it is not discernibly affected by hopping anisotropy with ratios ${D}_{xx}∕{D}_{yy}$ up to 16.

Increasing superconductingTc’s by a factor of 1000 with large hopping anisotropies in two-dimensionalt−Jmodel systems

We have studied the enhancement of the superconducting transition temperature ${T}_{c}$ in a $t\ensuremath{-}J\ensuremath{-}U$ model of electrons moving on a square lattice in which anisotropic electronic hopping is introduced. For this model we have calculated ${T}_{c}$ for singlet pairing using the non-self-consistent Thouless criterion, and find a dramatic enhancement of ${T}_{c}$ induced by large hopping anisotropies. Further, the maximum increase in ${T}_{c}$ is obtained when the system is pushed towards the extreme anisotropy limit, that is, when the hopping of electrons is confined to occur in only one dimension, while superexchange couples the electrons both parallel and perpendicular to the direction in which hopping occurs. We demonstrate that in this limit the increase in ${T}_{c},$ with respect to the isotropic system, can be of the order of 1000. We have also determined that in the extreme anisotropy limit the superconducting gap is an equal mixture of s and d pairing symmetries (two choices of such a combination being $s+d$ and $s+id)$ owing to the reduced (square to rectangular) symmetry of the system in the presence of hopping anisotropies. Thus the presence of d-wave superconducting features in materials whose symmetry is very different from that of a two-dimensional square lattice is not unexpected.

Heavy quarks on anisotropic lattices with standard and RG improved actions

On quenched lattice simulations, we examine the relation between the hopping and fermionic anisotropy parameter on anisotropic lattices with the clover O(a) improved action. For the gauge sector we used configurations for the standard and the RG(Iwasaki) improved actions.

A model of pairing enhanced by stripelike correlations

In this work we describe a simple model of pairing in systems with stripelike hopping anisotropy that mimics one feature of stripe correlations found in numerous transition-metal oxides. Allowing the carriers to interact via Heisenberg superexchange (using a two-dimensional t–J model), we have investigated the effects of such stripelike hopping on the superconducting transition temperature, Tc. In general, and most dramatically for d-wave pairing, we find a strong enhancement of Tc the greater the degree of hopping anisotropy. Thus, this simple model provides a robust demonstration supporting the conjecture that stripes can indeed augment pairing correlations.

Enhanced bound-state formation in two dimensions via stripelike hopping anisotropies

We have investigated two-electron bound state formation in a square two-dimensional t-J-U model with hopping anisotropies for zero electron density; these anisotropies are introduced to mimic the hopping energies similar to those expected in stripe-like arrangements of holes and spins found in various transition metal oxides. In this report we provide analytical solutions to this problem, and thus demonstrate that bound-state formation occurs at a critical exchange coupling, J_c, that decreases to zero in the limit of extreme hopping anisotropy t_y/t_x -> 0. This result should be contrasted with J_c/t = 2 for either a one-dimensional chain, or a two-dimensional plane with isotropic hopping. Most importantly, this behaviour is found to be qualitatively similar to that of two electrons on the two-leg ladder problem in the limit of t_interchain/t_intrachain -> 0. Using the latter result as guidance, we have evaluated the pair correlation function, thus determining that the bound state corresponds to one electron moving along one chain, with the second electron moving along the opposite chain, similar to two electrons confined to move along parallel, neighbouring, metallic stripes. We emphasize that the above results are not restricted to the zero density limit - we have completed an exact diagonalization study of two holes in a 12 X 2 two-leg ladder described by the t-J model and have found that the above-mentioned lowering of the binding energy with hopping anisotropy persists near half filling.

Tight-Binding Model for DNA Double Chains: Metal–Insulator Transition Due to the Formation of a Double Strand of DNA

A tight-binding model is formulated for the calculation of the electronic structure of a double strand of deoxyribonucleic acid (DNA). The theory is applied to DNA with a particular structure such as the ladder and decorated ladder structures. It is found that there is a novel type of metal–insulator transitions due to the hopping anisotropy of the system. A metal-semimetal-semiconductor transition is found in the former and an effective semiconductor-metal transition at finite temperature in the latter, as the effect of base paring between two strands of DNA is increased. The latter mechanism may be responsible for explaining the Meade and Kayyem's recent observation.

TIGHT-BINDING MODEL FOR THE QUANTUM LADDER IN A MAGNETIC FIELD

A tight-binding model is formulated for the calculation of the electronic structure and the ground state energy of the quantum ladder under a magnetic field, where the magnetic flux at the nth plaquette is given by ϕn. First, the theory is applied to obtain the electronic spectra of the quantum ladder models with particular magnetic fluxes such as uniform magnetic fluxes, ϕn=0 and 1/2, and the staggered magnetic flux, ϕn= (−1)n+1ϕ0. From these, it is found that as the effect of electron hopping between two chains—the anisotropy parameter r=ty/tx—is increased, there are a metal-semimetal transition at r=0 and a semimetal–semiconductor transition at r=2 in the first case, and metal-semiconductor transitions at r=0 in the second and third cases. These transitions are thought of as a new category of metal-insulator transition due to the hopping anisotropy of the system. Second, using the spectrum, the ground state energy is calculated in terms of the parameter r. It is found that the ground state energy in the first case diverges as r becomes arbitrarily large, while that in the second and third cases can have the single or double well structure with respect to r, where the system is stable at some critical value of r=rc and the transition between the single and double well structures is associated with whether tx is less than a critical value of txc. The latter cases are very reminiscent of physics in polyacetylene studied by Su, Schrieffer and Heeger.