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Tomonaga-Luttinger liquid (TLL) theory is a canonical formalism used to describe one-dimensional (1D) metals, where the low energy physics is determined by collective bosonic excitations. In this work, we present a theoretical model to…

Although the Tomonaga-Luttinger liquid exhibits spin-charge separation and the electron is not an elementary excitation of the system, nevertheless an effective electronic dispersion may be defined by the frequency-dependent peak in the…

We propose and study the properties of a non-linear electrodynamics that emerges inspired on the physics of Dirac materials. This new electrodynamic model is an extension of the one-loop corrected non-linear effective Lagrangian computed in…

Optical dispersion spectra at energies up to 30 eV play a vital role in understanding the chirality-dependent van der Waals London dispersion interactions of single wall carbon nanotubes (SWCNTs). We use one-electron theory based…

We study the effect of resonant scatterers on the local density of states in a rectangular graphene setup with metallic leads. We find that the density of states in a vicinity of the Dirac point acquires a strong position dependence due to…

Motivated by a recent first principles prediction of an anisotropic cubic Dirac semi-metal in a real material Tl(TeMo)$_3$, we study the behavior of electrons tunneling through a potential barrier in such systems. To clearly investigate…

Carbon nanotubes are a good realization of one-dimensional crystals where basic science and potential nanodevice applications merge. Defects are known to modify the electrical resistance of carbon nanotubes. They can be present in as-grown…

The complete energy expression of a deformed single-walled carbon nanotube (SWNT) is derived in the continuum limit from the local density approximation model proposed by Lenosky {\it et al.} \lbrack Nature (London) {\bf 355}, 333…

The aim of this habilitation thesis is to present recent results, obtained during the period 2012-2017, related to interaction effects in condensed matter physics systems such as planar Dirac liquids, e.g., graphene and graphene-like…

Tomonaga-Luttinger-liquid theory is formulated for metallic carbon nanotubes with open boundaries. Both cases of single- and multi-wall nanotubes are discussed. Based on this theory, spatial variation of the charge density from an edge is…

An interacting one-dimensional (1D) electron system is predicted to behave very differently than its higher-dimensional counterparts. Coulomb interactions strongly modify the properties away from those of a Fermi liquid, resulting in a…

Understanding Dirac-like Fermions has become an imperative in modern condensed matter sciences: all across its research frontier, from graphene to high T$_c$ superconductors to the topological insulators and beyond, various electronic…

A comprehensive theory of electron spin resonance (ESR) for a Luttinger liquid (LL) state of correlated metals is presented. The ESR measurables such as the signal intensity and the line-width are calculated in the framework of Luttinger…

We study the transport properties of defective single-walled armchair carbon nanotubes (CNTs) on a mesoscopic length scale. Monovacancies and divancancies are positioned randomly along the CNT. The calculations are based on a fast, linearly…

Interactions between electrons in solids are often behind exciting novel effects such as ferromagnetism, antiferromagnetism and superconductivity. All these phenomena break away from the single-electron picture, instead having to take into…

The concept of topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin-orbit coupled materials, some classes of…

Using bosonization we derive the dc conductance G(L,T) of an interacting quantum wire with good contacts including current relaxing backscattering and Umklapp processes. Our result yields the dependence of the conductance on length L and…

Scattering of a 2D Dirac electrons on a rectangular matrix potential barrier is considered using the formalism of spinor transfer matrices. It is shown, in particular, that in the absence of the mass term, the Klein tunneling is not…

We revisited the influence of electron-electron scattering on the resistivity of a two-dimensional system with linear spectrum. In conventional systems with parabolic spectrum, where Umklapp scattering is either prohibited or ineffective…

Two-dimensional (2D) massless Dirac electrons appear on a surface of three-dimensional topological insulators. The conductivity of such a 2D Dirac electron system is studied for strong topological insulators in the case of the Fermi level…