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.     

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.     

Effects of long range Coulomb interaction on the Peierls instability

The Peierls instability is studied for a one-dimensional tight-binding model of conduction electrons in the half-filled case. The long range Coulomb interaction as well as the electron-phonon coupling are taken into account. It is found that the Peierls distortion is hindered by the long wavelength charge fluctuations due to the Coulomb interaction.     

On the instability of the one-dimensional Peierls insulator in uniform electric field

Behaviour of the quasi-one-dimensional Peierls insulator (PI) with a doubled lattice period (of the trans-polyacetylene type) is studied in the uniform electric field The electric field polarizes the insulator thus decreasing the gap Δ in the quasiparticle spectrum and creates by tunnelling charge carriers pairs. Depending on the field strength direct creation of soliton-antisoliton pairs or electron-hole pairs (e-h) takes place. The (e-h) pairs deform the lattice forming polarons. For the cis-type polyacetylene the superinsulator phase with soliton confinement exists. The latter is characterized by a great number of soliton-antisoliton quantum levels. Because of the charges generation the process of insulator-to-metal transition becomes continuous.     

Superconductivity and Peierls instability in coupled linear chain systems

We study the superconducting transition temperature (T_c) and the Peierls instability temperature (T_p) using Eliashberg type equations for both T_c and T_p self consistently with finite interchain coupling. We show that T_c > T_p below a critical electron-phonon coupling constant which depends on the bare phonon frequency. This determines an upper bound on T_c so that for higher transition temperatures T_p > T_c and superconductivity is unlikely. Higher values of T_c are possible if the interchain coupling is increased above a critical value where the Peierls instability is suppressed.     

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.     

Peierls transitions in semimetallic one dimensional charge transfer salts

Peierls transitions in one dimensional charge transfer salts in which both donor and acceptor molecules have even valency such as TTF-TCNQ have been studied. Transitions involving macroscopic occupation of phonon states of wavevector $\text{k}{}_{\mathrm{<mtext>F</mtext>}}\text{(TTF)}\text{+ k}{}_{\mathrm{<mtext>F</mtext>}}\text{(TCNQ)}\text{=}\text{1}\text{2}\text{G}$ and |k_F(TTF) ? k_F (TCNQ)| can occur as well as transitions of wavevector 2k_F(TTF) [and 2k_F(TCNQ)].     

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)     

Symmetry-breaking phase transition without a Peierls instability in conducting monoatomic chains

The one-dimensional (1D) model system Au/Ge(001), consisting of linear chains of single atoms on a surface, is scrutinized for lattice instabilities predicted in the Peierls paradigm. By scanning tunneling microscopy and electron diffraction we reveal a second-order phase transition at 585 K. It leads to charge ordering with transversal and vertical displacements and complex interchain correlations. However, the structural phase transition is not accompanied by the electronic signatures of a charge density wave, thus precluding a Peierls instability as origin. Instead, this symmetry-breaking transition exhibits three-dimensional critical behavior. This reflects a dichotomy between the decoupled 1D electron system and the structural elements that interact via the substrate. Such substrate-mediated coupling between the wires thus appears to have been underestimated also in related chain systems.     

Bose-Fermi mixtures in one dimension

We analyze the phase stability and the response of a mixture of bosons and spin-polarized fermions in one dimension (1D). Unlike in 3D, phase separation happens for low fermion densities. The dynamics of the mixture at low energy is independent of the spin-statistics of the components, and the modes are essentially undamped.     

Delocalization transition in one dimension

Singular extended states among random system localized states are proved to be a general rule. When a Fermi energy coincides with the extended state energy, a residual resistance becomes proportional to the square of the system length.     

Tan relations in one dimension

We derive exact relations that connect the universal C/k⁴-decay of the momentum distribution at large k with both thermodynamic properties and correlation functions of two-component Fermi gases in one dimension with contact interactions. The relations are analogous to those obtained by Tan in the three-dimensional case and are derived from an operator product expansion of the one- and two-particle density matrix. They extend earlier results by Olshanii and Dunjko (2003) [24] for the bosonic Lieb–Liniger gas. As an application, we calculate the pair distribution function at short distances and the dimensionless contact in the limit of infinite repulsion. The ground state energy approaches a universal constant in this limit, a behavior that also holds in the three-dimensional case. In both one and three dimensions, a Stoner instability to a saturated ferromagnet for repulsive fermions with zero range interactions is ruled out at any finite coupling.     

Continuous measures in one dimension

Families of unimodal maps satisfying

1. T _λ: [?1,1]?[?1,1] withT(±1)=?1 and |T _λ ^′ (1)|>1.
2. T _λ(x) isC ² inx ² and λ, and symmetric inx.
3. T ₀(0)=0,T ₁(0)=1 with \(\frac{d}{{d\lambda }}\) T _λ(0)>0

are considered. The results of Guckenheimer (1982) are extended to show that there is a positive measure of λ for whichT _λ has a finite absolutely continuous invariant measure. The appendix contains general theorems for the existence of such measures for some markov maps of the interval.