Exact solution for the general Peierls-Fröhlich chain with disorder

Kopietz

2000

Phys. Rev. B

In the pseudogap regime of one-dimensional incommensurate Peierls systems, fluctuations of the phase of the order parameter prohibit the emergence of long-range order and generate a finite correlation length. For classical phase fluctuations, we present exact results for the average electronic density of states, the mean localization length, the electronic specific heat and the spin susceptibility at low temperatures. Our results for the susceptibility give a good fit to experimental data.

“…3, we show the exact inverse localization length ℓ −1 (ω) given in Eq. (11) for several values of g. For g ≫ 1 we obtain the following approximations:…”

mentioning

confidence: 91%

Classical phase fluctuations in incommensurate Peierls chains

Kopietz

2000

Phys. Rev. B

“…In general, one has to rely on approximations to calculate ρ(ω) or its disorder average ρ(ω) , but in special limits exact results are available. Besides the trivial case where V (x) and ∆(x) are constant, the exact ρ(ω) can be obtained by various methods [5][6][7] in the white noise limit ξ → 0, ∆ s → ∞, with ∆ 2 s ξ → const. For real ∆(x) and V (x) = 0 the average DOS is known to exhibit, for sufficiently small ∆ av , a Dyson singularity [8] at ω = 0.…”

mentioning

confidence: 99%

Exact numerical calculation of the density of states of the fluctuating gap model

Kopietz

1999

Phys. Rev. B

We develop a powerful numerical algorithm for calculating the density of states ρ(ω) of the fluctuating gap model, which describes the low-energy physics of disordered Peierls and spin-Peierls chains. We obtain ρ(ω) with unprecedented accuracy from the solution of a simple initial value problem for a single Riccati equation. Generating Gaussian disorder with large correlation length ξ by means of a simple Markov process, we present a quantitative study of the behavior of ρ(ω) in the pseudogap regime. In particular, we show that in the commensurate case and in the absence of forward scattering the pseudogap is overshadowed by a Dyson singularity below a certain energy scale ω * , which we explicitly calculate as a function of ξ.

“…The treatment of the general case is similar but more awkward than the Ovchinnikov and Erikhman limit because instead of a linear differential equation of second order one has to face a linear differential equation of fourth order. The equations to determine the integrated DOS and the localization length are, however, the same as those derived by Hayn and Mertsching using the method of supersymmetry [26] so that we recover their general results which also include the incommensurate case which we will discuss afterwards.…”

Section: The White Noise Limitmentioning

confidence: 70%

“…Although the ultraviolet cutoff E 0 was introduced here in the sum over Matsubara frequencies instead of as a cutoff in the momentum integral, expanding Eqs. (26) and (27) in the regime bjDj ( 1, we get the usual Ginzburg-Landau functional,…”

Section: Generalized Ginzburg-landau Functionalmentioning

confidence: 99%

Fluctuation effects in disordered Peierls systems

2001

Ann. Phys.

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.