Incompatibility of BCS pairing and the Peierls distortion in linear chain systems

We have solved the coupled gap equations for a one dimensional electron gas which can undergo both a Peierls insulating and a BCS superconducting transition. We find that, except for a very special case, (i) only one of the order parameters can be non-vanishing and (ii) there is only one critical temperature. We conclude that, independent of the pairing interaction strength, if the Peierls transition occurs, there can be no BCS superconductivity, and conversely.     

The superconducting transition in coupled linear chain systems

The superconducting transition and the critical fluctuations of a model system that can pass continuously from one-dimension to three-dimensions are investigated. The transition is brought about by a variable coupling between families of linear chains. First, a Bose lattice-gas is considered, and the Bose-Einstein transition temperature T_BE is calculated as a function of the coupling strength. Second, the temperature T_oz at which the fluctuations in the gap parameter equal the average gap parameter is calculated as a function of the coupling, and is found to behave in a similar way to T_BE. Both these temperatures go continuously to zero as the system becomes one-dimensional while T_c calculated in mean-field theory does not vanish in this limit.It is found that for coupling parameters believed to be characteristic of some superconductors possessing the A-15 crystal structure, such as Nb₃Sn, the system is essentially three-dimensional (3D) as far as superconducting properties are concerned; but critical fluctuations may be somewhat enhanced, in particular when the electronic density of states is not very large.     

The dynamic Peierls instability

The ‘effective field’ model of the Peierls transition in one-dimensional metals is shown to have a dynamic instability in the presence of a large electric field. The behavior is analogous to laser action, and has a critical temperature above that of the static instability.     

SLIM-a formalism for linear coupled systems

A SLIM formalism to deal with a general, linearly coupled accelerator lattice is summarized. Its application to a wide range of accelerator calculations is emphasized.     

Instanton in disordered Peierls systems

We study disordered Peierls systems described by the fluctuating gap model. We show that the typical electron states with energies lying deep inside the pseudogap are localized near large disorder fluctuations (instantons), which have the form of a soliton-antisoliton pair. Using the “saddle-point” method we obtain the average density of states and the average optical absorption coefficient at small energy.     

Photoinduced instability and semiconductor-metal phase transition in a Peierls system

A microscopic theory of the appearance of electron-phonon instability and a semiconductor-metal phase transition away from thermodynamic equilibrium in a Peierls system upon the optical excitation of electron-hole pairs is devised. An equation which specifies the dependence of the order parameter of the phase transition and the uniquely related gap width in the electron spectrum, on the concentration n of conduction-band electrons is obtained. The critical concentration n=n _c, above which the semiconductor phase of the system is unstable toward the transition to the metallic state, is calculated. A comparison with an experiment on the irradiation of a substrate-supported vanadium dioxide film by a laser pulse is made. Fiz. Tverd. Tela (St. Petersburg) 40, 2113–2118 (November 1998)     

Localization lengths in disordered Peierls systems

We have studied the influence of bond- and site-type impurities on the ground state properties of one-dimensional Peierls systems. Using a functional integral formalism with both commuting and anticommuting variables we have calculated the averaged Green's function which determines the electronic density of states and localization length (Thouless formula). Some limiting cases can be solved analytically. To apply our model to doped polymers we derive the connection between doping concentration and disorder strengths D_j. For illustration we present the results with parameters appropriate for polyacetylene.     

Charge density wave in graphene: Magnetic-field-induced Peierls instability

We suggest that a magnetic-field-induced Peierls instability accounts for the recent experiment of Zhang et al. in which unexpected quantum Hall plateaus were observed at high magnetic fields in graphene on a substrate. This Peierls instability leads to an out-of-plane lattice distortion resulting in a charge density wave (CDW) on sublattices A and B of the graphene honeycomb lattice. We also discuss alternative microscopic scenarios proposed in the literature and leading to a similar CDW ground state in graphene.     

The Peierls instability in one-dimensional conductors with arbitrary bandfilling

Mean field calculations of the Peierls instability have been carried out for arbitrary bandfilling both in the case of free electrons as well as for the tightbinding approximation. New expressions for Δ(0) and T_p are derived which change the experimentally derived λ to a more reasonable value. Δ(0)/k_BT_p may differ significantly from the BCS value 1.76 in the tightbinding approximation.     

Fluctuation effects in disordered Peierls systems

We review the density of states (DOS) and related quantities of quasi one‐dimensional disordered Peierls systems in which fluctuation effects of a backscattering potential play a crucial role. The low‐energy behavior of non‐interacting fermions which are subject to a static random backscattering potential will be described by the strictly one‐dimensional fluctuating gap model (FGM). Recently, the FGM has also been used to explain the pseudogap phenomenon in high‐T_c superconductors. We develop a non‐perturbative method which allows for a simultaneous calculation of the DOS and inverse localization length for an arbitrary given disorder potential by solving a simple initial value problem. In the white noise limit, we recover all known results by solving a Fokker‐Planck equation. For the physically interesting case of finite correlation lengths, we use analytical and numerical methods to show that a complex order parameter leads to a suppression of the DOS, i.e. a pseudogap, and that for a real order parameter this pseudogap is overshadowed by a singularity in the DOS. We will also consider the case of classical phase fluctuations which applies to low temperatures where amplitude fluctuations are frozen out. For this regime we present analytic results for the DOS, the inverse localization length, the specific heat, and the Pauli susceptibility.     

Modulation instability in systems of coupled waves with nonlinearity dispersion

Conditions for the appearance of modulation instability of an optical wave packet formed by one or two unidirectional strongly interacting waves are studied taking into account the influence of the temporal dispersion of a nonlinear response of the medium on this process. The regions of values of the frequency, input radiation intensity, and dispersion parameters in which the wave perturbations are increased are found. It is shown that the initial conditions for excitation of optical fibers of this type significantly affect the dynamics of the modulation instability.     

Superconductivity in heavy-Fermion systems

DeHaas-van Alphen experiments have established the character of the heavy mass: an enhancement factor of 15 to 40 from f-electron many-body effects occurs in the quasi-particle mass, and the band mass is comparable to 10 m_e or less. From this, we show that “Migdal's theorem” holds in superconductivity theory for heavy-Fermion systems. The mass-renormalization alone, in combination with the usual coulomb and phonon-mediated interactions (in compounds that are the same except for absence of f-electrons), cannot cause the heavy-Fermion superconductivity to occur. Some kind of “Kondo boson” interaction peculiar to the heavy-Fermion metal must therefore definitely occur.     

Magnetic field dependence of the Peierls instability in one-dimensional conductors

We show that an applied magnetic field will suppress the Peierls instability in one-dimensional conductors. The effect is big enough to be observable. In sufficiently strong fields the transition between the metallic and insulating state is due to the condensation of a phonon with wave vectorq≠2p _F, but close to 2p _F. The role of spinorbit interactions is also discussed.     

Superconductivity in ordering systems

We analyse the behaviour of 2-order parameter systems (where one subsystem is superconducting) in constant external ordering fields and find the spatial distribution of the order parameters.The authors would like to thank Prof. B. T.Matthias and Prof. T. L.Birman for useful discussions.     

Imperfect nesting and Peierls instability for a two-dimensional tight-binding model

Based on a half-filled two-dimensional tight-binding model with nearest-neighbour and next nearest-neighbour hopping the effect of imperfect Fermi surface nesting on the Peierls instability is studied at zero temperature. Two dimerization patterns corresponding to a phonon vector (π,π) are considered. It is found that the Peierls instability will be suppressed with an increase of next nearest-neighbour hopping which characterizes the nesting deviation. First and second order transitions to a homogeneous state are possible. The competition between the two dimerized states is discussed. Received 22 December 2000