arXiv subjects

Marco Zoli

Publications and source records attributed to Marco Zoli.

51 records · Page 3Linked to original sources

arXiv2005

Non Local Electron-Phonon Correlations in a Dispersive Holstein Model

Due to the dispersion of optical phonons, long range electron-phonon correlations renormalize downwards the coupling strength in the Holstein model. We evaluate the size of this effect both in a linear chain and in a square lattice for a time averaged {\it e-ph} potential, where the time variable is introduced according to the Matsubara formalism. Mapping the Holstein Hamiltonian onto the time scale we derive the perturbing source current which appears to be non time retarded. This property permits to disentangle phonon and electron coordinates in the general path integral for an electron coupled to dispersive phonons. While the phonon paths can be integrated out analytically, the electron path integrations have to be done numerically. The equilibrium thermodynamic properties of the model are thus obtained as a function of the electron hopping value and of the phonon spectrum parameters. We derive the {\it e-ph} corrections to the phonon free energy and show that its temperature derivatives do not depend on the {\it e-ph} effective coupling hence, the Holstein phonon heat capacity is strictly harmonic. A significant upturn in the low temperature total heat capacity over $T$ ratio is attributed to the electron hopping which largely contributes to the action.

cond-mat.mtrl-sci↗

arXiv2005

Path Integral of the Two Dimensional Su-Schrieffer-Heeger Model

The equilibrium thermodynamics of the two dimensional Su-Schrieffer-Heeger Model is derived by means of a path integral method which accounts for the variable range of the electronic hopping processes. While the lattice degrees of freedom are classical functions of time and are integrated out exactly, the electron particle paths are treated quantum mechanically. The free energy of the system and its temperature derivatives are computed by summing at any $T$ over the ensemble of relevant particle paths which mainly contribute to the total partition function. In the low $T$ regime, the {\it heat capacity over T} ratio shows un upturn peculiar of a glassy like behavior. This feature is more sizeable in the square lattice than in the linear chain as the overall hopping potential contribution to the total action is larger in higher dimensionality.

cond-mat.stat-mech↗

arXiv2004

Phonon Thermodynamics versus Electron-Phonon Models

Applying the path integral formalism we study the equilibrium thermodynamics of the phonon field both in the Holstein and in the Su-Schrieffer-Heeger models. The anharmonic cumulant series, dependent on the peculiar source currents of the {\it e-ph} models, have been computed versus temperature in the case of a low energy oscillator. The cutoff in the series expansion has been determined, in the low $T$ limit, using the constraint of the third law of thermodynamics. In the Holstein model, the free energy derivatives do not show any contribution ascribable to {\it e-ph} anharmonic effect. We find signatures of large {\it e-ph} anharmonicities in the Su-Schrieffer-Heeger model mainly visible in the temperature dependent peak displayed by the phonon heat capacity.

cond-mat.stat-mech↗

arXiv2004

Polaron Crossover in Molecular Solids

An analytical variational method is applied to the molecular Holstein Hamiltonian in which the dispersive features of the dimension dependent phonon spectrum are taken into account by a force constant approach. The crossover between a large and a small size polaron is monitored, in one, two and three dimensions and for different values of the adiabatic parameter, through the behavior of the effective mass as a function of the electron-phonon coupling. By increasing the strength of the inter-molecular forces the crossover becomes smoother and occurs at higher {\it e-ph} couplings. These effects are more evident in three dimensions. We show that our Modified Lang-Firsov method starts to capture the occurence of a polaron self-trapping transition when the electron energies become of order of the phonon energies. The self-trapping event persists in the fully adiabatic regime. At the crossover we estimate polaron effective masses of order $\sim 5 - 40$ times the bare band mass according to dimensionality and value of the adiabatic parameter. Modified Lang-Firsov polaron masses are substantially reduced in two and three dimensions. There is no self-trapping in the antiadiabatic regime.

cond-mat.supr-con↗

arXiv2003

Path Integral Computation of Phonon Anharmonicity

The partition function of an oscillator disturbed by a set of electron particle paths has been computed by a path integral method which permits to evaluate at any temperature the relevant cumulant terms in the series expansion. The time dependent source current peculiar of the semiclassical Su-Schrieffer-Heeger model induces large electron-phonon anharmonicities on the phonon subsystem. As a main signature of anharmonicity the phonon heat capacity shows a peak whose temperature location strongly varies with the strength of the {\it e-ph} coupling. High energy oscillators are less sensitive to anharmonic perturbations.

cond-mat.soft↗

arXiv2003

Particle Path Correlations in a Phonon Bath

The path integral formalism is applied to derive the full partition function of a generalized Su-Schrieffer-Heeger Hamiltonian describing a particle motion in a bath of oscillators. The electronic correlations are computed versus temperature for some choices of oscillators energies. We study the perturbing effect of a time averaged particle path on the phonon subsystem deriving the relevant temperature dependent cumulant corrections to the harmonic partition function and free energy. The method has been applied to compute the total heat capacity up to room temeperature: a low temperature upturn in the heat capacity over temperature ratio points to a glassy like behavior ascribable to a time dependent electronic hopping with variable range in the linear chain.

cond-mat.mtrl-sci↗

arXiv2003

Path Integral Description of a Semiclassical Su-Schrieffer-Heeger Model

The electron motion along a chain is described by a continuum version of the Su-Schrieffer-Heeger Hamiltonian in which phonon fields and electronic coordinates are mapped onto the time scale. The path integral formalism allows us to derive the non local source action for the particle interacting with the oscillators bath. The method can be applied for any value of the {\it e-ph} coupling. The path integral dependence on the model parameters has been analysed by computing the partition function and some thermodynamical properties from $T= 1K$ up to room temperature. A peculiar upturn in the low temperature {\it heat capacity over temperature} ratio (pointing to a glassy like behavior) has been ascribed to the time dependent electronic hopping along the chain.

cond-mat.soft↗

arXiv2002

Spectral Properties of the Su-Schrieffer-Heeger Model

We present a study of the one dimensional Su-Schrieffer-Heeger model Hamiltonian by a diagrammatic perturbative method in the weak electron-phonon coupling regime. Exact computation of both the charge carrier effective mass and the electron spectral function shows that electrons are good quasiparticles in the adiabatic and antiadiabatic limits but novel features emerge in the intermediate regime, where the phonons and the electrons compare on the energy scale. Together with a sizeable mass enhancement we observe, in the latter regime, a spread of the spectral weight (among several transition peaks) associated with an increased relevance of multiphonons contributions at larger {\it e-ph} couplings. Accordingly electrons cease to be the good quasiparticles and an onset of polaron formation is favoured.

cond-mat.mtrl-sci↗

arXiv2002

Dimensionality Effects on the Su-Schrieffer-Heeger Model

A low order diagrammatic study of the dimension dependent Su-Schrieffer-Heeger model Hamiltonian in the weak electron-phonon coupling regime is presented. Exact computation of both the charge carrier effective mass and the electron spectral function shows that electrons are good quasiparticles in the antiadiabatic limit but new features emerge in the adiabatic and intermediate regime, where the phonons and the electrons compare on the energy scale. Here we find: i) a sizeable mass enhancement over the bare band value, ii) the appearance of many transition peaks in the band bottom spectral function together with a growing loss of spectral weight at larger {\it e-ph} couplings. The onset of a polaronic state is favoured in two dimensions.

cond-mat.supr-con↗

arXiv2002

Mass Renormalization in the Su-Schrieffer-Heeger Model

This study of the one dimensional Su-Schrieffer-Heeger model in a weak coupling perturbative regime points out the effective mass behavior as a function of the adiabatic parameter $ω_π/J$, $ω_π$ is the zone boundary phonon energy and $J$ is the electron band hopping integral. Computation of low order diagrams shows that two phonons scattering processes become appreciable in the intermediate regime in which zone boundary phonons energetically compete with band electrons. Consistently, in the intermediate (and also moderately antiadiabatic) range the relevant mass renormalization signals the onset of a polaronic crossover whereas the electrons are essentially undressed in the fully adiabatic and antiadiabatic systems. The effective mass is roughly twice as much the bare band value in the intermediate regime while an abrupt increase (mainly related to the peculiar 1D dispersion relations) is obtained at $ω_π\sim \sqrt{2}J$.

cond-mat.supr-con↗

arXiv2001

Resistivity peculiarities in systems with lattice distortions

We study a molecular lattice Hamiltonian in which polaronic charge carriers interact with non linear potentials provided by local atomic fluctuations between two equilibrium sites. The path integral formalism is applied to select the class of atomic oscillations which mainly contributes to the partition function and the electrical resistivity is computed in a number of representative cases. Non metallic resistivity behaviors are found at temperatures above $\simeq 100K$.

cond-mat.stat-mech↗

arXiv2001

Polaron self-trapping in a honeycomb net

Small polaron behavior in a two dimensional honeycomb net is studied by applying the strong coupling perturbative method to the Holstein molecular crystal model. We find that small optical polarons can be mobile also if the electrons are strongly coupled to the lattice. Before the polarons localize and become very heavy, there is infact a window of {\it e-ph} couplings in which the polarons are small and have masses of order $\simeq 5 - 50$ times the bare band mass according to the value of the adiabaticity parameter. The 2D honeycomb net favors the mobility of small optical polarons in comparison with the square lattice.

cond-mat.supr-con↗

arXiv2001

Non Metallic Transport in Molecular Solids versus Dimensionality

Path integral techniques and Green functions formalism are applied to study the (time) temperature dependent scattering of a polaronic quasiparticle by a local anharmonic potential in a bath of diatomic molecules. The electrical resistivity has been computed in any molecular lattice dimensionality for different values of electron-phonon coupling and intermolecular forces. A broad resistivity peak with non metallic behavior at temperatures larger than $\simeq 100K$ is predicted by the model for sufficiently strong polaron-local potential coupling strengths. This peculiar behavior, ascribed to purely structural effects, is favoured in low dimensionality.

cond-mat.stat-mech↗

arXiv2001

Path integrals approach to resisitivity anomalies in anharmonic systems

Different classes of physical systems with sizeable electron-phonon coupling and lattice distortions present anomalous resistivity behaviors versus temperature. We study a molecular lattice Hamiltonian in which polaronic charge carriers interact with non linear potentials provided by local atomic fluctuations between two equilibrium sites. We study a molecular lattice Hamiltonian in which polaronic charge carriers interact with non linear potentials provided by local atomic fluctuations between two equilibrium sites. A path integral model is developed to select the class of atomic oscillations which mainly contributes to the partition function and the electrical resistivity is computed in a number of representative cases. We argue that the common origin of the observed resistivity anomalies lies in the time retarded nature of the polaronic interactions in the local structural instabilities.

cond-mat.supr-con↗

arXiv2000

Mass enhancement in narrow band systems

A perturbative study of the Holstein Molecular Crystal Model which accounts for lattice structure and dimensionality effects is presented. Antiadiabatic conditions peculiar of narrow band materials and an intermediate to strong electron-phonon coupling are assumed. The polaron effective mass depends crucially in all dimensions on the intermolecular coupling strengths which also affect the size of the lattice deformation associated with the small polaron formation.

cond-mat.supr-con↗