Nesting Wave Vector Research Articles

Two-Dimensional Spin-Peierls State With a Multimode Lattice Distortion

The effects of electron–electron (e–e) interactions on the two-dimensional (2D) Peierls state are discussed using the 2D Peierls–Hubbard model (2D PHM) in the limit of U ≫ t 0 , where U is the on-site e–e interaction parameter between up and down spin electrons and t 0 is the electron transfer integral between nearest neighbor sites. In this limit, the 2D PHM can be mapped onto the 2D spin-Peierls model (2D SPM) in which the effect of the lattice distortion is taken into account in the spin exchange interaction of the 2D Heisenberg model. As was demonstrated in a previous paper [J. Phys. Soc. Jpn. 69 (2000) 1769], the ground state of the 2D electron–lattice (e–l) system (the 2D 1/2-filled SSH model) is the so-called multimode Peierls state where the lattice distortion involves Fourier components with the nesting wave vector Q =(π/ a ,π/ a ), a being the lattice constant, and with those paralell to it. Using the exact diagonalization technique it is shown that the spin-Peierls transition with a mutlimode l...

Linear Response Theory Around a Localized Impurity in the Pseudogap Regime of an Anisotropic Superconductor

We compare and contrast the polarizability of a d-wave superconductor in the pseudogap regime, within the precursor pairing scenario (dPG), and of a d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Our study is motivated by STM imaging experiments around an isolated impurity, which may in principle distinguish between precursor pairing and dDW order in the pseudogap regime of the high-\(T_{c}\) superconductors. In both cases, the \({\bf q}\)-dependence of the polarizability is characterized by an azimuthal modulation, consistent with the d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave vector \({{\bf Q}}=(\pi,\pi)\), albeit imperfect, due to a nonzero value of the hopping ratio \(t^\prime /t\) in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also reflected by the \(({\bf q},\omega)\) dependence of the retarded polarizability.

2D Peierls state in a square lattice – Effect of anisotropy

In recent studies, we have shown that the lowest energy state in a 2D square lattice SSH-type model with a half-filled electronic band is not a simple Peierls state involving only distortions with the nesting wave vector Q but complicated multimode states involving distortions with various wave vectors parallel to Q and that there are many degenerate non-equivalent distortion patterns yielding the same ground state energy. In the present work we discuss the effect of anisotropy on these multimode Peierls states. It is indicated within the pertubational treatment combined with numerical calculations that the multimode states can survive as far as the anisotropy is small. Furthermore it is pointed out that the degeneracy can be lifted by the anisotropy. These studies will shed light on the understanding of the Peierls-like behaviors of 2D materials as layered organic conductors.

Sliding charge density wave in the monophosphate tungsten bronze(PO2)4(WO3)2mwith alternate stacking ofm=4andm=6WO3layers

The monophosphate tungsten bronzes $({\mathrm{PO}}_{2}{)}_{4}({\mathrm{WO}}_{3}{)}_{2m}$ form family of two-dimensional metals which exhibit charge density wave (CDW) instabilities. These materials are generally built by the regular stacking of $(a,b)$ layers in which chains made of segments of m ${\mathrm{WO}}_{6}$ octahedra directed along the $\mathbf{a}$ and $\mathbf{a}\ifmmode\pm\else\textpm\fi{}\mathbf{b}$ directions are delimited. Their electronic structure thus originates from quasi-one-dimensional (1D) bands located on these chains. As a consequence their Fermi surface (FS) exhibits large flat portions whose nesting gives rise to successive CDW instabilities. Here we present a structural study of the CDW instability of the $({\mathrm{PO}}_{2}{)}_{4}({\mathrm{WO}}_{3}{)}_{10}$ member formed by the alternate stacking of layers built with segments of $m=4$ and $m=6$ ${\mathrm{WO}}_{6}$ octahedra. Its ab initio electronic structure calculation shows that the FS of this member exhibits large flat portions which can be extremely well nested. Its best nesting wave vector accounts for the modulation wave vector stabilized by the CDW transition which occurs at 156 K. Because of the regular stacking of layers of different m values the FS is slightly split. The unusual thermal dependence of the x-ray satellite intensity provides evidence that the two types of layers become modulated at different temperature. This also leads to a slight thermal sliding of the CDW-nesting modulation wave vector, which can be accounted for within the framework of a Landau-Ginzburg theory. In addition, the observation of a global hysteresis in the thermal cycling of the satellite intensity, as well as the degradation of the interlayer order upon cooling, suggest the formation of a disordered lattice of dilute solitons. Such solitons allow to accomodate the charge transferred between the two types of layer. Finally the relevance of local charge transfers, at intergrowth defects, for example, to create pinned discommensurations that break the CDW coherence is emphasized in this whole family of bronzes.

Peierls transition in two-dimensional metallic monophosphate tungsten bronzes

Abstract The two-dimensional metallic bronzes made of ReO3-type layers of MoO6 or WO6 octahedra present quasi-one-dimensional (1D) electronic structures along three directions of preferential overlap of the t2g transition metal orbitals. They exhibit a Peierls instability towards the formation of charge density waves (CDW) at the 2kF critical wave vector allowing to nest simultaneously the Fermi surfaces associated to two quasi-1D band structures out of three. The Peierls transition is achieved through a periodic lattice distortion (PLD), that we analyse, in the present work, for the monophosphate tungsten bronzes. The Peierls critical temperature decreases in presence of disorder, which breaks the electron–hole pairs forming the CDW condensate, and in presence of misfit between the PLD wave vector and the 2kF nesting wave vector. The pair breaking effect accounts for the drop of the Peierls transition in the NaxP4W12O44 (x

Superconducting gap symmetry from repulsive interactions in the spin-singlet state

We obtained the superconducting gap equation in terms of the effective T-scattering matrix. We considered the gap symmetry in both singlet and triplet states as well as in charge and spin channels. We show that the superconducting gap for the repulsive interactions in the spin-singlet state exists in the charge channel only, and the gap has s-wave symmetry (ℓ=0, where ℓ is the orbital quantum number of a pair) or d-wave (ℓ=2) symmetry. We also show that in the 2D case, the strongly anisotropic s-wave gap might have nodes in the direction of the nesting wave vector and may resemble the d x 2− y 2 gap symmetry. We show that there is a gap for the attractive interactions in the spin channel only. Such a gap indicates the phase transition into superfluid state which is similar to liquid 3He. The gap due to pairing instability for the attractive interactions in the spin channel has p-wave symmetry (ℓ=1) for the spin-triplet state with m s=±1 or p-wave symmetry (ℓ=1) for the spin-triplet state with m s=0.

The gap symmetry in the Hubbard model

The gap symmetry for both the attractive (U<0) and repulsive (U> 0) Hubbard models has been studied. The gap symmetry in both singlet and triplet channels as well as in charge and spin channels is considered. It is shown that the gap for the attractive Hubbard model exists in the spin channel only, and has s-wave symmetry (ℓ = 0, where ℓ is the orbital momentum) for the spin-triplet state of p-wave symmetry (ℓ = 1) for the spin-singlet state with j = s + ℓ = 1, the total spin and orbital quantum number of a pair. The attractive Hubbard model describes superfluidity in the spin-channel and is an adequate model for liquid 3He as shown. However, for the repulsive Hubbard model the gap exists in the charge channel only and has s-wave (ℓ = 0) or d-wave (ℓ = 2) symmetry for the spin-angle state. The repulsive Hubbard model describes superconductivity in the charge channel. It is also shown that in the 2D case the strongly anisotropic s-wave gap has nodes in the direction of the nesting wave vector resembling the d x− y 2-wave symmetry.

Peierls Distortion in Two-Dimensional Tight-Binding Model

The Peierls distortions in a two-dimensional electron-lattice system described by a Su-Schrieffer-Heeger type model extended to two-dimensions are numerically studied for a square lattice. The electronic band is just half-filled and the nesting vector is ($\pi/a$, $\pi/a$) with $a$ the lattice constant. In contrast to the previous understanding on the Peierls transition in two dimensions, the distortions which are determined so as to minimize the total energy of the system involve not only the Fourier component with the nesting wave vector but also many other components with wave vectors parallel to the nesting vector. It is found that such unusual distortions contribute to the formation of gap in the electronic energy spectrum by indirectly (in the sense of second order perturbation) connecting two states having wave vectors differing by the nesting vector from each other. Analyses for different system sizes and for different electron-lattice coupling constants indicate that the existence of such distortions is not a numerical artifact. It is shown that the gap of the electronic energy spectrum is finite everywhere over the Fermi surface.

Suppression of biquadratic coupling at the Cr Néel temperature in Fe/Cr(001) superlattices (invited) (abstract)

We present the effects of antiferromagnetic (AF) order of the Cr spacers in Fe/Cr(001) superlattices on the interlayer coupling of the Fe layers. AF order of the Cr spacers is suppressed for layer thicknesses less than 42 Å. For ≳42 Å of Cr, the Néel temperature (TN) increases rapidly and asymptotically approaches the bulk value for thick Cr spacers as characterized by a transition-temperature shift exponent λ=1.4±0.3. Neutron diffraction confirms both the AF order of the Cr layers in superlattices with 62, 100, and 200 Å thick Cr layers, and the existence of the incommensurate, transverse spin-density-wave magnetic structure whose nesting wave vector is equal to that of bulk Cr. The AF ordering of the Cr results in anomalies in a variety of magnetic properties, including the interlayer coupling, remanent magnetization, coercivity, and magnetoresistance. Most strikingly, the 90° or ‘‘biquadratic’’ coupling of the Fe layers observed for T≳TN is suppressed below TN as confirmed by polarized neutron reflectivity. This behavior can be understood in terms of the combination of finite-size and spin frustration effects at rough Fe/Cr interfaces.

Neutron diffraction and reflectivity studies of the Cr Néel transition in Fe/Cr (001) superlattices

The effects on the interlayer coupling of the Cr Néel transition is studied in Fe/Cr(001) superlattices. The Néel transition is suppressed for Cr layer thickness < 42 Å. For > 42 Å of Cr, the Néel temperature T N initially increases rapidly and then asymptotically approaches its bulk value with a three-dimensional transition-temperature shift exponent value of λ = 1.4 ± 0.3. Neutron diffraction confirms both the Cr antiferromagnetic order and the existence of the incommensurate, transverse spin density wave whose nesting wave vector is the same as that of bulk Cr. The ordering of the Cr dramatically alters the coupling of the Fe layers. The biquadratic Fe interlayer coupling observed for T > T N vanishes below T N as confirmed by polarized neutron reflectivity. The behavior can be understood in terms of finite-size and spin frustration effects at rough Fe-Cr interfaces.

Phase diagram for charge-density waves in a magnetic field

The influence of an external magnetic field on a quasi one-dimensional system with a charge density wave (CDW) instability is treated within the random phase approximation which includes both CDW and spin density wave correlations. We show that the CDW is sensitive to both orbital and Pauli effects of the field. In the case of perfect nesting, the critical temperature decreases monotonously with the field, and the wave vector of the instability starts to shift above some critical value of magnetic field. Depending on the ratio between the spin and charge coupling constants and on the direction of the applied magnetic field, the wave vector shift is either parallel ($CDW_x$ order) or perpendicular ($CDW_y$ order) to the most conducting direction. The $CDW_x$ order is a field dependent linear combination of the charge and spin density waves and is sensible only to the Pauli effect. The wave vector shift in $CDW_y$ depends on the interchain coupling, but the critical temperature does not. This order is affected by the confinement of the electronic orbits. By increasing the relative strength of the orbital effect with respect to the Pauli effect, one can destroy the $CDW_y$, establishing either a $CDW_x$, or a $CDW_0$ (corresponding to perfect nesting wave vector). We also show that by increasing the imperfect nesting parameter, one passes from the regime where the critical temperature decreases with the field to the regime where it is initially enhanced by the orbital effect and eventually suppressed by the Pauli effect. For a bad nesting, the quantized phases of the field-induced CDW appear.

Chemical pressure and charge-density waves in rare-earth tritellurides.

We report the results of transmission electron microscopy on the layered rare-earth tritellurides R${\mathrm{Te}}_{3}$ (R=La,Sm,Gd,Tb,Dy,Ho,Er,Tm). Through electron diffraction we have identified superlattice reflections indicating the presence of incommensurate distortions, consistent with sinusoidal atomic displacements in the square Te sheets. The superlattice wave vector corresponds to the maximal Fermi-surface nesting wave vector determined from extended H\uckel tight-binding band calculations. The charge-density wave (CDW) is stable under the volume decrease obtained by substituting the heavier rare earths, and the distortion wave vector scales with the lattice parameters across the rare-earth series. Our results indicate that the rare-earth tritellurides host small-amplitude Fermi-surface-driven distortions. We find no evidence for substantial deviation from sinusoidal atomic displacements, in contrast to the large commensurate distortions and ordered vacancy structures found in other rare-earth polychalcogenide phases. Our observations establish the rare-earth polychalcogenides as a family of CDW hosts in which a variety of structural distortions occur with variation of chalcogen type and stoichiometry, despite a very simple but universal chalcogen sheet band structure.

Giant magnetoresistance in f-electron systems

Various types of mechanisms for giant magnetoresistance, in particular for f-electron systems, are critically reviewed. First, the most typical prototype of the nesting-type magnetic ordering in the heavy-rare-earth metals is reviewed. Both negative and positive magnetoresistances are expected for the resistivities, parallel and perpendicular to the nesting wave vector, respectively. Then, the most typical negative magnetoresistance due to impurity states is studied on Eu chalcogenides with chalcogen vacancies or with trivalent rare-earth impurities substituting Eu atoms. In the former, the change from the singlet to the triplet for the trapped pair electrons is the main origin. In both cases magnetic polarons play important roles. For low-carrier-density systems in the metallic region ferromagnetic ordering is induced; the resistivity then has a peak at a temperature near above Tc due to a critical scattering resulting a negative magnetoresistance. Narrow-gap semiconductors and low-carrier semimetals are also typical materials to show exotic giant magnetoresistance. Various other cases including valence fluctuating systems are also studied.

Optical properties and Fermi-surface nesting in superconducting oxides.

Fermi-surface nesting is found to modify the electron-electron scattering and therefore yields an unusual variation of the optical reflectivity. At long wavelengths a Drude form of the dielectric function is derived with a relaxation rate for a nested Fermi liquid (NFL) that is linear in frequency for \ensuremath{\omega}&gt;T. The corresponding Drude mass is also frequency and temperature dependent. Remarkably good fits to the reflectivity of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$, ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8}$, and ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ are achieved using an on-site Coulomb interaction of intermediate strength. The static limit for the NFL conductivity is compatible with the temperature-dependent resistivity of the high-temperature superconductors. Self-energy and vertex corrections yield a long-wavelength susceptibility that is much weaker and different in structure from the response at the nesting wave vector Q, and the distinctions are relevant to the Raman spectrum. In cases of imperfect nesting, a crossover to conventional Fermi-liquid behavior is possible at a temperature ${\mathit{T}}^{\mathrm{*}}$ determined by the quasiparticle orbits. Predictions for the optical response as a function of chemical composition are discussed, with attention to the anomalous resistivity of ${\mathrm{Nd}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$.

Nested-Fermi-liquid theory.

The susceptibility and quasiparticle self-energy are found to exhibit anomalous behavior in nested-Fermi-liquid (NFL) systems that have nearly parallel sections of the Fermi surface. Electron-electron scattering yields damping much stronger than the conventional electron-gas result and predicts a linear temperature variation of the resistivity. The susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathrm{NFL}}^{\mathrm{\ensuremath{''}}}$(q,\ensuremath{\omega}) for nested fermions is calculated at q\ensuremath{\simeq}Q, where Q is a typical nesting wave vector. The NFL susceptibility is linear in frequency up to a crossover region near \ensuremath{\omega}\ensuremath{\simeq}4T where a saturation to a constant value occurs. The above features, as well as various theoretical constraints, are highly sensitive to the strength of the electron-electron coupling and to the degree of nesting. The relevance of the NFL results to superconducting oxides is briefly examined, with emphasis on the resistivity and the photoemission data, which supports the calculated damping \ensuremath{\Gamma}(\ensuremath{\omega}&gt;T)\ensuremath{\simeq}\ensuremath{\alpha}\ensuremath{\omega} with an intermediate on-site Coulomb coupling.

Superconductivity and spin-density waves in heavy-fermion systems.

Starting from a Kondo-lattice-type description, superconductivity and spin-density-wave coexistence is studied in the heavy-fermion systems. It is shown that the coexistence is energetically stable only in the presence of a supplementary ${\ensuremath{\Delta}}_{Q}$ superconducting order parameter connected to the $〈{a}_{k,\ensuremath{-}\ensuremath{\sigma}}{a}_{\ensuremath{-}k\ensuremath{-}Q,\ensuremath{\sigma}}〉$-type average, where $Q$ is the nesting wave vector.

Possible superconductivity in nearly antiferromagnetic itinerant fermion systems.

Strong spin fluctuations arising in itinerant fermion systems close to a magnetic instability may induce or inhibit superconductivity depending on the nesting wave vector ${\mathrm{q}}_{0}$ for which the instability occurs. If \ensuremath{\Vert}${\mathrm{q}}_{0}$\ensuremath{\Vert} is small but finite, triplet pairing is favored and singlet pairing is suppressed as efficiently as in nearly ferromagnetic systems (${q}_{0}$=0). If \ensuremath{\Vert}${\mathrm{q}}_{0}$\ensuremath{\Vert} is large, there is a repulsive contribution from backward scattering by which triplet as well as singlet pairings are strongly depressed. The cases of ${\mathrm{UPt}}_{3}$, ${\mathrm{CePb}}_{3}$, and some organic compounds are considered.

Cascade of field induced spin density wave phases in quasi one dimensional conductors

We discuss first the spin susceptibility of a non interacting two-dimensional electron gas with open Fermi surface under perpendicular magnetic field. Orbital motion induces a drastic change in the wave vector dependence of the susceptibility : it exhibits a series of peaks at wave vectors which obey a quantized condition. When the Fermi surface is not perfectly nested, each of these peaks becomes in turn the absolute maximum ; at large fields the latter corresponds to the perfect nesting wave vector. The magnitude of each peak diverges logarithmically at low temperatures. As a result, an interacting two dimensional electron gas with zero field metallic ground state exhibits a cascade of field induced phase transitions. The Metal-Spin-Density Wave (SDW) transition line is second order. It is a succession of segments, each of which is labelled by a quantum number which also labels each SDW sub-phase at lower T. The SDW wave vector varies with the field within each SDW sub-phase so as to satisfy the quantization condition. Transitions between sub-phases are weakly first order. This theory describes well the observed transitions at intermediate field (H ≲ 8 T) in the (TMTSF) 2X salts. If in these systems, the electron-electron interaction favours longitudinal nesting, the latter is stable at high fields, but a nesting wave vector with large transverse component is more stable at low fields, so that a strongly first order transition between the two types of nesting occurs at intermediate fields. The Hall effect data in the (TMTSF) 2X salts is examined in the light of existing theories.

Shift of the SDW Wave Vector in the Transient Region in the Anisotropic 2D Hubbard Model

A variational procedure shows that two new types of spin density wave (SDW) ground states appear successively in the titled system modeling the Bechgaard salts, when the transverse transfer energy increases around its upper bound imposed for the usual SDW state having the so far known best nesting wave vector. From this value the wave vectors of the new states are appreciably shifted, entailing uncompensated carrier pockets of the size found in the Shubnikov-de Haas experiments. An analytic expression clarifying the situation of the starting-point of the shift shows that the shift is sensitive to details of the system.

Self-consistent band structure calculation of chromium: pressure influence

The band structures of both paramagnetic and antiferromagnetic phases were calculated in the framework of local density (or spin density) approximations of the exchange-correlation potential. In order to compute the antiferromagnetic phase of Cr the perfect nesting model was assumed. These calculations were performed as a function of the lattice parameter and also self-consistently using the linear hybridised KKR method. The ground-state and quasi-particle properties are discussed in comparison with the suitable experimental data. The pressure dependence of the magnetic moment, the nesting wave vector, the antiferromagnetic gap and the Fermi surface extremal cross sections are also discussed.