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Journal de Physique IV (Proceedings)

Theory of pseudogaps in charge density waves in application to photo electron spectroscopy

Sergey I. Matveenko, S. Brazovskiǐ

Published Nov 1, 2002• 0 citations
Publisher

Abstract

For a one-dimensional electron-phonon system we consider the photon absorption involving electronic excitations within the pseudogap energy range. Within the adiabatic approximation for the electron - phonon interactions these processes are described by ronlinear configurations of an instanton type. We calculate the subgap absorption as it can be observed by means of photo electron or tunneling spectroscopies. In details we consider systems with gapless modes: 1D semiconductors with acoustic phonons and incommensurate charge density waves. We found that below the free particle edge the pseudogap starts with the exponential decrease of transition rates changing to a power law deeply within the pseudogap, near the absolute edge.

DOI
10.1051/jp4:20020358

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For a one-dimensional electron-phonon system we consider the photon absorption involving electronic excitations within the pseudogap energy range. Within the adiabatic approximation for the electron - phonon interactions these processes are described by ronlinear configurations of an instanton type. We calculate the subgap absorption as it can be observed by means of photo electron or tunneling spectroscopies. In details we consider systems with gapless modes: 1D semiconductors with acoustic phonons and incommensurate charge density waves. We found that below the free particle edge the pseudogap starts with the exponential decrease of transition rates changing to a power law deeply within the pseudogap, near the absolute edge.
We consider pseudogap effects for electrons interacting with gapless modes. We study both generic 1D semiconductors with acoustic phonons and incommensurate charge density waves. We calculate the subgap absorption as it can be observed by means of the photo electron or tunneling spectroscopy. Within the formalism of functional integration and the adiabatic approximation, the probabilities are described by nonlinear configurations of an instanton type. Particularities of both cases are determined by the topological nature of stationary excited states (acoustic polarons or amplitude solitons) and by presence of gapless phonons which change the usual dynamics to the regime of the quantum dissipation. Below the free particle edge the pseudogap starts with the exponential (stretched exponential for gapful phonons) decrease of transition rates. Deeply within the pseudogap they are dominated by a power law, in contrast with nearly exponential law for gapful modes.
The adiabatic Holstein-Hubbard model describes electrons on a chain with step a interacting with themselves (with coupling U) and with a classical phonon field ${\ensuremath{\varphi}}_{x}$ (with coupling \ensuremath{\lambda}). There is Peierls instability if the electronic ground-state energy $F(\ensuremath{\varphi})$ as a functional of ${\ensuremath{\varphi}}_{x}$ has a minimum which corresponds to a periodic function with period $\ensuremath{\pi}{/p}_{F},$ where pF{p}_{F}pF​ is the Fermi momentum. We consider ${p}_{F}/\ensuremath{\pi}a$ irrational so that the charge-density wave is incommensurate with the chain. We prove in a rigorous way in the spinless case, when \ensuremath{\lambda}, U are small and $U/\ensuremath{\lambda}$ large, that (a) when the electronic interaction is attractive U<0U<0U<0 there is no Peierls instability and (b) when the interaction is repulsive U>0U>0U>0 there is Peierls instability in the sense that our convergent expansion for $F(\ensuremath{\varphi}),$ truncated at second order has a minimum which corresponds to an analytical and $\ensuremath{\pi}{/p}_{F}$ periodic ${\ensuremath{\varphi}}_{x}.$ Such a minimum is found solving an infinite set of coupled self-consistent equations, one for each of the infinite Fourier modes of ${\ensuremath{\varphi}}_{x}.$
A 2D model of the pseudogap state is considered on the basis of the scenario of strong electron scattering by short-range-order fluctuations of the “dielectric” (antiferromagnetic or charge density wave) type. A system of recurrence relations is constructed for a one-particle Green’s function and the vertex part, describing the interaction of electrons with an external field. This system takes into account all Feynman diagrams for electron scattering at short-range-order fluctuations. The results of detailed calculations of optical conductivity are given for various geometries (topologies) of the Fermi surface, demonstrating both the effects of pseudogap formation in the electron spectrum and the localization effects. The obtained results are in qualitative agreement with experimental data for underdoped HTSC cuprates.
We present a detailed numerical study of the one-dimensional Holstein model with a view to understanding the self-trapping process of electrons or excitons in crystals with short-range particle-lattice interactions. Applying a very efficient variational Lanczos method, we are able to analyze the ground-state properties of the system in the weak- and strong-coupling, adiabatic and nonadiabatic regimes on lattices large enough to eliminate finite-size effects. In particular, we obtain the complete phase diagram and comment on the existence of a critical length for self-trapping in finite (closed) one-dimensional systems. In order to characterize large and small polaron states we calculate self-consistently the lattice distortions and the particle-phonon correlation functions. In the strong-coupling case, two distinct types of small polaron states are shown to be possible according to the relative importance of static displacement field and dynamic polaron effects. Special emphasis is on the intermediate-coupling regime, which we also study by means of direct diagonalization, preserving the full dynamics and quantum nature of phonons. The crossover from large to small polarons shows up in a strong decrease of the kinetic energy accompanied by a substantial change in the optical absorption spectra. We show that our numerical results in all important limiting cases reveal excellent agreement with both analytical perturbation theory predictions and very recent density matrix renormalization group data.
The evolution of the role of lattice vibrations in the formation of the pseudogap state in strongly correlated electron systems has been investigated concerning changes in the electron-phonon coupling parameters and the concentration of doped charge carriers. We apply the polaronic version of the generalized tight-binding method to analyze the band structure of a realistic multiband two-dimensional model that incorporates the electron-lattice contributions of both Holstein and Peierls types. It has been demonstrated that the emergence of polaronic effects begins with the modulation of spectral function intensity. However, within a specific region of the phase diagram, a significant transformation of the electron band structure and pseudogap state occurs. It results from coherent polaron excitations that create a partially flat band near the Fermi level. This process leads to a change in the topology of the Fermi surface and the emergence of corresponding features in the density of states.
Studies of Hamiltonians modeling electron-electron (e-e) and electron-phonon (e-ph) coupling have been fundamental in capturing the novel ordering seen in many quasi-one-dimensional condensed matter systems. Extending such studies to quasi-two-dimensional (2D) systems is of great current interest, as e-ph couplings are predicted to play a major role in the stabilization or enhancement of novel phases in 2D material systems. In this work, we study model systems that describe the interplay between the Hubbard coupling and the phonon modes in the Holstein and Su-Schrieffer-Heeger (SSH) Hamiltonians using the functional renormalization group. For both types of e-ph couplings, we find the predicted charge density wave phases in competition with antiferromagnetic ordering. As the system is doped, the transition shifts, with both orders showing incommensurate peaks. We compare the evolution of the quasiparticle weight for the Holstein model with that of the SSH model as the systems transition from antiferromagnetic to charge-ordered ground states. Finally, we calculate the self-energy of the phonon and capture the impact of charge ordering on the phonon modes.