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arXiv:cond-mat/0208121

Pseudogaps due to sound modes: from incommensurate charge density waves to semiconducting wires

S. Brazovskiǐ, Sergey I. Matveenko

Published Aug 6, 2002• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/0208121

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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.
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.
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.
The theory of Wilson's solitary-wave acoustic polaron motion is generalized to include the effects of quantum fluctuations and the non-adiabatic behaviour of the electron-phonon coupling. The polaron dynamics are described quantum mechanically in terms of master equations for the electronic variables. As a final result, it emerges that due to the considered quantum effects for v<<c (v=polaron velocity, c=sound velocity) the polaron behaviour is determined by the well-known semiclassical non-linear Schrodinger equation, whereas for v<c the polaron motion is overdamped but shows by no means a divergent behaviour as obtained in semiclassical theories. In addition, for v=c the phonon cloud around the electron disappears and the electron motion becomes diffusive.
A semiclassical method is presented for tunneling of self-trapped states in many-body systems with electrons and phonons. An overcomplete set of Slater determinants, lattice coordinates, and lattice momenta is used to represent a functional integral. Stationary phase equations are solved numerically without any constraint on the dynamics of electrons and phonons, i.e., without the use of the adiabatic approximation. To evaluate transition amplitudes, we integrate over small fluctuations in both electronic and phonon degrees of freedom, keeping their time order correctly. This method can be applied to general electron-phonon systems is and useful when self-trapped states have complex structures in charge or spin densities and lattice displacements. The effective hopping strength is calculated for a self-trapped kink in the commensurate charge-density-wave state in one dimension. At strong coupling in the Holstein and attractive Hubbard models, where tunneling involves effectively a single tightly bound bipolaron, this method reproduces previous analytic results. New results are obtained at intermediate coupling where the kink is extended over a couple of lattice sites and for models with both electron-electron and electron-phonon interactions.
The effects of doping on a one-dimensional wire in a charge density wave state are studied using the density-matrix renormalization group method. We show that for a finite number of extra electrons, the ground state becomes conducting but the particle density along the wire corresponds to a charge density wave with an incommensurate+ wave number determined by the filling. We find that the absence of the translational invariance can be discerned even in the thermodynamic limit as long as the number of doping electrons is finite. The Luttinger liquid behavior is reached only for a finite change in the electron filling factor, which for an infinite wire corresponds to the addition of an infinite number of electrons. In addition to the half filled insulating Mott state and the conducting states, we find evidence for subgap states at fillings different from half filling by a single electron or hole. Finally, we show that by coupling our system to a quantum dot, one can have a discontinuous dependence of its population on the applied gate voltage in the thermodynamic limit, similar to the one predicted for a Luttinger liquid without umklapp processes.
We have studied one dimensional acoustic phonon linearly coupled to the electron density. The phonon spectrum is linear with cutoff at the Debye frequency, it is straightforward modification of three dimensional optical phonons. Phonon field results in substituting the dynamical coupling for the screened coulomb interaction. We have shown that the electron-phonon coupling quantitatively changed the phase diagram of Luttinger liquid with a single impurity. The existence of slow and fast polaron modes with different weights in different regimes resulted in different renormalization group flow for a weak scatterer and a weak tunneling link. The resulting phase diagram depending on the parameters of the problem, regimes corresponding to purely metallic or purely insulating behavior and an intermediate regime with two stable fixed points and one unstable, finite conductance fixed point. we have found that the direction of renormalization group flow change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. The obtained results were found in good agreement with previously obtained results.