Non-perturbative analysis of impurity effects on the Kubo conductivity of nano to macroscopic structures
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MRS Advances © 2016 Materials Research Society DOI: 10.1557/adv.2016.3
Non-perturbative analysis of impurity effects on the Kubo conductivity of nano to macroscopic structures Vicenta Sánchez1, Fernando Sánchez1, Carlos Ramírez1 and Chumin Wang2 1 Departamento de Física, Facultad de Ciencias, Universidad Nacional Autónoma de México, Apartado Postal 70-542, 04510 D.F. México 2 Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Apartado Postal 70-360, 04510 D.F. México ABSTRACT The presence of impurities in solids is a source of many interesting effects, particularly relevant in the conductivity, optical properties and specific heat. For instance, in nano-electronics these effects could be useful to develop molecular devices such as novel computer architectures, chemical and biomedical sensors. However, the inclusion of impurities breaks the translational symmetry, restricting the systems that can be addressed theoretically in an exact way to those of few atoms. In this work, we present an alternative way to study the electrical conductance in real-space by means of a renormalization plus convolution method applied on the KuboGreenwood formula for multidimensional systems of macroscopic size with site and bond impurities. The results show that the spectral average of conductivity depends strongly on the location of site and bond impurities in periodic chains. Particularly, when the distance between impurities follows the Fibonacci sequence, we find that the spectral average falls following a power law as the number of atoms in the system grows. Finally, we analyze the impurity effects on the conductance spectra of periodic core-shell nanowires with a macroscopic length and periodic and quasiperiodically located impurities. INTRODUCTION The study of quantum effects caused by impurities in nanostructured materials has been a field with increasing activity during the last decades in order to improve existing technologies [1]. Such nanostructured materials are especially sensible to the location of impurities, creating novel behaviors which could be employed to improve the efficiency of devices by, for example, increasing velocity, reducing power consumption, and making them more portable [2-4]. Some of the more interesting quantum effects of nanomaterials surge from aperiodic arrangements of their components, which could convert a material into a conductor or isolator. For instance, the single-walled carbon nanotubes can exhibit metallic or semiconducting properties, depending on the arrangement of constituent carbon atoms. Moreover, recent developments in synthesis techniques allow building materials according to a proposed design, making easier to verify theoretical predictions [5, 6]. The knowledge of transport properties of a material is particularly important for applications in nano-electronics [7, 8]. However, due to the inclusion of impurities, which breaks the translational symmetry, their study should be performed in real space. This fact restricts exact theoretical investiga
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