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.Comment: To be published in J.Phys.:Condensed Matte

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.Comment: Istituto Nazionale di Fisica della Materia - Dipartimento di Matematica e Fisica, Istituto Nazionale di Fisica della Materia Universita' di Camerino, 62032 Camerino, Ital

Helix untwisting and bubble formation in circular DNA

The base pair fluctuations and helix untwisting are examined for a circular molecule. A realistic mesoscopic model including twisting degrees of freedom and bending of the molecular axis is proposed. The computational method, based on path integral techniques, simulates a distribution of topoisomers with various twist numbers and finds the energetically most favorable molecular conformation as a function of temperature. The method can predict helical repeat, openings loci and bubble sizes for specific sequences in a broad temperature range. Some results are presented for a short DNA circle recently identified in mammalian cells.Comment: The Journal of Chemical Physics, vol. 138 (2013), in pres

Path Integral Method for DNA Denaturation

The statistical physics of homogeneous DNA is investigated by the imaginary time path integral formalism. The base pair stretchings are described by an ensemble of paths selected through a macroscopic constraint, the fulfillement of the second law of thermodynamics. The number of paths contributing to the partition function strongly increases around and above a specific temperature $T^*_c$ whereas the fraction of unbound base pairs grows continuosly around and above $T^*_c$. The latter is identified with the denaturation temperature. Thus, the separation of the two complementary strands appears as a highly cooperative phenomenon displaying a smooth crossover versus $T$. The thermodynamical properties have been computed in a large temperature range by varying the size of the path ensemble at the lower bound of the range. No significant physical dependence on the system size has been envisaged. The entropy grows continuosly versus $T$ while the specific heat displays a remarkable peak at $T^*_c$. The location of the peak versus $T$ varies with the stiffness of the anharmonic stacking interaction along the strand. The presented results suggest that denaturation in homogeneous DNA has the features of a second order phase transition. The method accounts for the cooperative behavior of a very large number of degrees of freedom while the computation time is kept within a reasonable limit.Comment: Physical Review E 2009 in pres

Thermodynamic properties of Holstein polarons and the effects of disorder

The ground state and finite temperature properties of polarons are studied considering a two-site and a four-site Holstein model by exact diagonalization of the Hamiltonian. The kinetic energy, Drude weight, correlation functions involving charge and lattice deformations, and the specific heat have been evaluated as a function of electron-phonon (e-ph) coupling strength and temperature. The effects of site diagonal disorder on the above properties have been investigated. The disorder is found to suppress the kinetic energy and the Drude weight, reduces the spatial extension of the polaron, and makes the large-to-small polaron crossover smoother. Increasing temperature also plays similar role. For strong coupling the kinetic energy arises mainly from the incoherent hopping processes owing to the motion of electrons within the polaron and is almost independent of the disorder strength. From the coherent and incoherent contributions to the kinetic energy, the temperature above which the incoherent part dominates is determined as a function of e-ph coupling strength.Comment: 17 pages. 17 figure

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.Comment: 6 pages, 3 figures, to appear in J.Phys.:Condensed Matter {PACS: 63.10.+a, 63.20.Dj, 71.38.+i

J-factors of short DNA molecules

The propensity of short DNA sequences to convert to the circular form is studied by a mesoscopic Hamiltonian method which incorporates both the bending of the molecule axis and the intrinsic twist of the DNA strands. The base pair fluctuations with respect to the helix diameter are treated as path trajectories in the imaginary time path integral formalism. The partition function for the sub-ensemble of closed molecules is computed by imposing chain ends boundary conditions both on the radial fluctuations and on the angular degrees of freedom. The cyclization probability, the J-factor, proves to be highly sensitive to the stacking potential, mostly to its nonlinear parameters. We find that the J-factor generally decreases by reducing the sequence length ( N ) and, more significantly, below N = 100 base pairs. However, even for very small molecules, the J-factors remain sizeable in line with recent experimental indications. Large bending angles between adjacent base pairs and anharmonic stacking appear as the causes of the helix flexibility at short length scales.Comment: The Journal of Chemical Physics - May 2016 ; 9 page

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 $\omega_{\pi}/J$, $\omega_{\pi}$ 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 $\omega_{\pi}\sim \sqrt{2}J$.Comment: To be published in Phys.Rev.B - 3 figure

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.Comment: To be published in J.Phys.:Condensed Matte

Polarons and slow quantum phonons

We describe the formation and properties of Holstein polarons in the entire parameter regime. Our presentation focuses on the polaron mass and radius, which we obtain with an improved numerical technique. It is based on the combination of variational exact diagonalization with an improved construction of phonon states, providing results even for the strong coupling adiabatic regime. In particular we can describe the formation of large and heavy adiabatic polarons. A comparison of the polaron mass for the one and three dimensional situation explains how the different properties in the static oscillator limit determine the behavior in the adiabatic regime. The transport properties of large and small polarons are characterized by the f-sum rule and the optical conductivity. Our calculations are approximation-free and have negligible numerical error. This allows us to give a conclusive and impartial description of polaron formation. We finally discuss the implications of our results for situations beyond the Holstein model.Comment: Final version, 10 pages, 10 figure