Vicenta Sánchez

Exact results of the Kubo conductivity in macroscopic Fibonacci systems: a renormalization approach

Abstract In this work, the Kubo–Greenwood formula is used to investigate the electrical conduction in macroscopic Fibonacci lattices within a single-band tight-binding model. This investigation is carried out by means of a renormalization method, which allows the iterative evaluation of the products of the Green’s function in an exact way. The results of d.c. conductivity show an extremely fine band structure and a periodic oscillating pattern in the neighborhood of the transparent state. The a.c. conductivity of these transparent states as a function of the frequency shows a regular oscillating behavior, whose maximums decay following an inverse power law. Furthermore, the d.c. conduction in two-dimensional Fibonacci superlattices reveals a smooth dependence on the Fermi energy location and finally the transition from one- into two-dimensional conductivity is also analyzed.

Improving the ballistic AC conductivity through quantum resonance in branched nanowires

Frequency-dependent electrical conductivity is studied by means of the Kubo-Greenwood formula and a real-space renormalization plus convolution method. An analytical solution of the alternating current (AC) conductivity is found for periodic chains. In this article, we report enhancements to this ballistic AC conductivity when periodically or quasiperiodically placed Fano-Anderson impurities are introduced to an otherwise periodic chain, which is connected to two semi-infinite periodic leads at its ends. Moreover, the temperature effects on these resonant AC conducting states are remarkably different in periodic and in quasiperiodic systems. Finally, such enhancement is further analysed in branched nanowires with a small cross section.

RESONANT AC CONDUCTING SPECTRA IN QUASIPERIODIC SYSTEMS

Based on the Kubo-Greenwood formula, a renormalization plus convolution method is developed to investigate the frequency-dependent electrical conductivity of quasiperiodic systems. This method combines the convolution theorem with the real-space renormalization technique which is able to address multidimensional systems with 1024 atoms. In this article, an analytical evaluation of the Kubo-Greenwood formula is presented for the ballistic ac conductivity in periodic chains. For quasiperiodic Fibonacci lattices connected to two semi-infinite periodic leads, the electrical conductivity, is calculated by using the renormalization method and the results show that at several frequencies, their ac conductivities could be larger than the ballistic ones. This fact might be related to the resonant scattering process in quasiperiodic systems. Finally, calculations made in segmented Fibonacci nanowires reveal that this improvement to the ballistic ac conductivity via quasiperiodicity is also present in multidimensional systems.

Improving Thermoelectric Properties of Nanowires Through Inhomogeneity

Inhomogeneity in nanowires can be present in the cross-section and/or by breaking the translational symmetry along the nanowire. In particular, the quasiperiodicity introduces an unusual class of electronic and phononic transport with a singular continuous eigenvalue spectrum and critically localized wave functions. In this work, the thermoelectricity in periodic and quasiperiodically segmented nanobelts and nanowires is addressed within the Boltzmann formalism by using a real-space renormalization plus convolution method developed for the Kubo–Greenwood formula, in which tight-binding and Born models are, respectively, used for the calculation of electric and lattice thermal conductivities. For periodic nanowires, we observe a maximum of the thermoelectric figure-of-merit (ZT) in the temperature space, as occurred in the carrier concentration space. This maximum ZT can be improved by introducing into nanowires periodically arranged segments and an inhomogeneous cross-section. Finally, the quasiperiodically segmented nanowires reveal an even larger ZT in comparison with the periodic ones.

Resonant thermoelectric transport in atomic chains with Fano defects

Atomic clusters attached to a low-dimensional system, called Fano defects, produce rich wave interferences. In this work, we analytically found an enhanced thermoelectric figure-of-merit (ZT) in periodic atomic chains with Fano defects, compared to those without such defects. We further study self-assembled DNA-like systems with periodic and quasiperiodically placed Fano defects by using a real-space renormalization method developed for the Kubo-Greenwood formula, in which tight-binding and Born models are respectively used for the electric and lattice thermal conductivities. The results reveal that the quasiperiodicity could be another ZT-improving factor, whose long-range disorder inhibits low-frequency acoustic phonons insensitive to local defects.

Electronic transport in multidimensional Fibonacci lattices

In this article, the Kubo-Greenwood formula is used to investigate the electronic transport behaviour in macroscopic systems by means of an exact renormalization method. The convolution technique is employed in the analysis of two-dimensional Fibonacci lattices. The dc electrical conductance spectra of multidimensional systems exhibit a quantized behaviour when the electric field is applied along a periodically arranged atomic direction, and it becomes a devils stair if the perpendicular subspace of the system is quasiperiodic. The spectrally averaged conductance shows a power-law decay as the system length grows, neither constant as in periodic systems nor exponential decays occurred in randomly disordered lattices, revealing the critical localization nature of the eigenstates in quasicrystals. Finally, the ac conductance along periodic and quasiperiodic directions is compared with the optical conductivity measured in decagonal quasicrystals.

A real-space renormalization approach to the Kubo–Greenwood formula in mirror Fibonacci systems

An exact real-space renormalization method is developed to address the electronic transport in mirror Fibonacci chains at a macroscopic scale by means of the Kubo-Greenwood formula. The results show that the mirror symmetry induces a large number of transparent states in the dc conductivity spectra, contrary to the simple Fibonacci case. A length scaling analysis over ten orders of magnitude reveals the existence of critically localized states and their ac conduction spectra show a highly oscillating behaviour. For multidimensional quasiperiodic systems, a novel renormalization plus convolution method is proposed. This combined renormalization + convolution method has shown an extremely elevated computing efficiency, being able to calculate electrical conductance of a three-dimensional non-crystalline solid with 10 30 atoms. Finally, the dc and ac conductances of mirror Fibonacci nanowires are also investigated, where a quantized dc-conductance variation with the Fermi energy is found, as observed in gold nanowires.

Fractal quantization of the electrical conductance in quasiperiodic systems

In this work, the Kubo-Greenwood formula is used to investigate the electronic transport in multidimensional macroscopic quasiperiodic lattices within the tight-binding model. This investigation is carried out by means of a novel renormalization method and the convolution technique. The dc electrical conductance of two-dimensional (2D) periodic systems shows uniform steps in units of 2e 2 /h, as observed in 2D electron-gas experiments, and a fractal distribution of these steps is found when the atoms in perpendicular direction to the applied electric field are quasiperiodically ordered. The spectral integral of these conductances presents a strong dependence on the imaginary part of energy in the Greens function, contrary to the case of density of states.

Electrical conductivity and localization in quasiperiodic lattices

Abstract The electrical conductivity of Fibonacci lattices at zero temperature is studied by means of Kubo and Landauer formalisms, in which a tight-binding Hamiltonian of the system is considered. The localization of the eigenstates is quantified by using the participation ratio and the Lyapunov exponent. The results show a close behavior between the dc conductivity and the Lyapunov exponent. In addition, the effects of the boundary conditions on the ac conductivity are also analyzed in detail.