A unified treatment of the cohesive and conducting properties of metallic nanostructures in terms of the electronic scattering matrix is developed. A simple picture of metallic nanocohesion in which conductance channels act as delocalized chemical bonds is derived in the jellium approximation. Universal force oscillations of order´F͞l F are predicted when a metallic quantum wire is stretched to the breaking point, which are synchronized with quantized jumps in the conductance.[S0031-9007(97)04243-9] PACS numbers: 73.20.Dx, 03.40.Dz, 62.20.Fe, 73.40.Jn Cohesion in metals is due to the formation of bands, which arise from the overlap of atomic orbitals. In a metallic constriction with nanoscopic cross section, the transverse motion is quantized, leading to a finite number of subbands below the Fermi energy´F. A striking consequence of these discrete subbands is the phenomenon of conductance quantization [1]. The cohesion in a metallic nanoconstriction must also be provided by these discrete subbands, which may be thought of as chemical bonds which are delocalized over the cross section. In this Letter, we confirm this intuitive picture of metallic nanocohesion using a simple jellium model. Universal force oscillations of order´F͞l F are predicted in metallic nanostructures exhibiting conductance quantization, where l F is the Fermi wavelength. Our results are in quantitative agreement with the recent pioneering experiment of Rubio, Agraït, and Vieira [2], who measured simultaneously the force and conductance during the formation and rupture of an atomic-scale Au contact. Similar experimental results have been obtained independently by Stalder and Dürig [3].Quantum-size effects on the mechanical properties of metallic systems have previously been observed in ultrasmall metal clusters [4], which exhibit enhanced stability for certain magic numbers of atoms. These magic numbers have been rather well explained in terms of a shell model based on the jellium approximation [4]. The success of the jellium approximation in these closed nanoscopic systems motivates its application to open (infinite) systems, which are the subject of interest here. We investigate the conducting and mechanical properties of a nanoscopic constriction connecting two macroscopic metallic reservoirs. The natural framework in which to investigate such an open system is the scattering approach developed by Landauer [5] and Büttiker [6]. Here, we extend the formalism of Ref.[6], which describes electrical conduction, to describe the mechanical properties of a confined electron gas as well.For definiteness, we consider a constriction of length L in an infinitely long cylindrical wire of radius R, as shown in Fig. 1. We neglect electron-electron interactions, and assume the electrons to be confined along the z axis by a hard-wall potential at r r͑z͒. This model is considerably simpler than a self-consistent jellium calculation [4], but should suffice to capture the essential physics of the problem. Outside the constriction, the Schrödinger equation ...

A time-dependent equation for the interlayer phase differences is derived for Josephson-coupled layered superconductors. It generalizes the sine-Gordon equation for the phase in a standard Josephson junction to the case of multilayer systems. Vhth the help of this equation, the dispersion of a collective mode is found at low temperatures. In highly anisotropic systems the gap in the spectrum of this mode lies below the superconducting gap and is suppressed strongly by a magnetic Geld parallel to the layers. The effect of this mode on the dielectric function and speci6c heat is calculated.For a Josephson junction formed by two bulk superconductors the time-dependent phase difFerence satisfies the well-known sine-Gordon equation, 2 which describes the full dynamics of the junction. The corresponding equation for multilayer systems of Josephson-coupled layerss of atomic thickness (high-T, superconductors, organic layered superconductors, artificial superlattices of YBazCus07 5/PrBa2Cus07 5 type) has only been derived for the static limit.As pointed out by Doniach and Inui,~the problem here is to account properly for the screened Coulomb repulsion which determines the kinetic energy of the phase variables.In the following, using Maxwell's equations and the Josephson relation, we derive the equation for the timedependent phase differences for Josephson-coupled multilayer systems.We then calculate the dispersion of the collective mode corresponding to coupled phase and charge variations at low temperatures T. This plasma mode lies well below the superconducting gap in highly anisotropic materials and affects low-energy properties of high-T superconductors.We study the behavior of this mode in a magnetic field parallel to the layers and derive its contributions to the dielectric function and the specific heat at low T for the Meissner and the high-field regimes.We consider a multilayer system within the Lawrence-Doniach model. The z axis is chosen perpendicular to the layers (along the c axis). Let us denote by P"(r,t) the phase of the superconducting order parameter at position r = (2:, y) in layer n and at time t. The magnetic field B(r, z, t) = curlA(r, z, t) is oriented along the layers, and the electric field is given by E(r, z, t) = -(I/c)BA(r, z, t)/Bt, where we have chosen the gauge with zero scalar potential. The Maxwell equations read epV E(r, z, t) = 4mp(r, z, t), c rluB(r, z, t) = -' ' +j(r, z, t), ep BE(r, z, t) 4n'. c Bt c where ep is the high-frequency dielectric constant and p(r, z) is the three-dimensional (3D) charge density. To proceed, we need constitutive equations relating the current density to the superconducting order parameter. We assume that the frequencies u of phase variations are well below the superconducting gap b, /h, so that the modulus of the order parameter is constant in space and time.Then the current density component parallel to the layers in layer n, averaged over the periodicity length s, is given by s(n+1/2) J"(r) =dzj(r, z) a(n -1/2) VP"(r) + A"(r)where A /, is the penetration...

We review recent advances in the theoretical modelling of n-conjugated polymers. Our emphasis is on quasi-one-dimensional n-electron models that include both electron-phonon and electron-electron interactions. We use the widely studied Peierls-Hubbard Hamiltonian as a prototype model, since this contains both the pure electron-phonon (Hiickel and SSH) limits and the pure electronelectron (Hubbard and PPP) limits. We attempt to present an integrated perspective by explaining the essential concepts in both chemical language (valence bonds, resonance, bond alternation defects, etc.) and solid-state physics terms (band structure, localized states, broken symmetry, solitons). We argue that modelling n-conjugated polymers is a true many-electron problem requiring advanced techniques that give reliable answers to precise questions, especially for excited states. Among the techniques we discuss are mean-field, perturbative, and variational approximations for infinite polymer chains and (numerically) exact computations (Lanczos and quantum Monte Carlo methods) for finite chains (oligomers). We compare critically the theoretical results obtained by these various methods with experimental observations, in particular with optical spectroscopy and nuclear magnetic resonance, both for the archetypal nconjugated system polyacetylene and for other conjugated polymers including polydiacetylenes and poly thiophene. Our goal is to find a model consistent with the broad range of experimental data. This analysis establishes that electronphonon and electron-electron interactions are likely to be of equal importance in determining the properties of these materials. Hence neither the Hiickel/SSH nor the PPP/Hubbard models are sufficient for a complete description of the observed behaviour of n-conjugated polymers. We add an analysis of factors that go beyond the idealized models, including disorder, inter-chain coupling and quantum lattice fluctuations, and conclude with a brief discussion of the dopinginduced insulator-metal transition and of the possible mechanisms of charge transport.

A variational ground state of the repulsive Hubbard model on a square lattice is investigated numerically for an intermediate coupling strength (U = 8t) and for moderate sizes (from 6 × 6 to 10 × 10). Our ansatz is clearly superior to other widely used variational wave functions. The results for order parameters and correlation functions provide new insight for the antiferromagnetic state at half filling as well as strong evidence for a superconducting phase away from half filling.PACS numbers: 71.10. Fd,74.20.Mn, The Hubbard model plays a key role in the analysis of correlated electron systems, and it is widely used for describing quantum antiferromagnetism, the Mott metalinsulator transition and, ever since Anderson's suggestion [1], superconductivity in the layered cuprates. Several approximate techniques have been developed to determine the various phases of the two-dimensional Hubbard model. For very weak coupling, the perturbative Renormalization Group extracts the dominant instabilities in an unbiased way, namely antiferromagnetism at half filling and d-wave superconductivity for moderate doping [2,3]. Quantum Monte Carlo simulations have been successful in extracting the antiferromagnetic correlations at half filling [4,5], but in the presence of holes the numerical procedure is plagued by the fermionic minus sign problem [6]. This problem appears to be less severe in dynamic cluster Monte Carlo simulations, which exhibit a clear tendency towards d-wave superconductivity for intermediate values of U [7].Variational techniques address directly the ground state and thus offer an alternative to quantum Monte Carlo simulations, which are limited to relatively high temperatures. Previous variational wave functions include mean-field trial states from which configurations with doubly occupied sites are either completely eliminated (full Gutzwiller projection) [8,9,10] or at least partially suppressed [11]. Recently, more sophisticated wave functions have been proposed, which include, besides the Gutzwiller projector, non-local operators related to charge and spin densities [12,13]. Our own variational wave function is based on the idea that for intermediate values of U the best ground state is a compromise between the conflicting requirements of low potential energy (small double occupancy) and low kinetic energy (delocalization). It is known that the addition of an operator involving the kinetic energy yields an order of magnitude improvement of the ground state energy with respect to a wave function with a Gutzwiller projector alone [14]. In this letter, we show that such an additional term allows us to draw an appealing picture of the ground state, both at half filling and as a function of doping (some preliminary results have been published [15,16]).In its most simple form, the 2D Hubbard model is composed of two terms,Ĥ = tT + UD , witĥHere c † iσ creates an electron at site i with spin σ, the summation is restricted to nearest-neighbor sites and n iσ = c † iσ c iσ . We consider a square lattice with peri...

We study the interplay of electron-electron interactions and Rashba spin-orbit coupling in one-dimensional ballistic wires. Using the renormalization group approach we construct the phase diagram in terms of Rashba coupling, Tomonaga-Luttinger stiffness and backward scattering strength. We identify the parameter regimes with a dynamically generated spin gap and show where the Luttinger liquid prevails. We also discuss the consequences for the operation of the Datta-Das transistor.