A new perspective of the Green's function in a boundary value problem as the only eigenstate in an auxiliary formulation is introduced. In this treatment, the Green's function can be perceived as a defect state in the presence of a $δ$-function potential, the height of which depends on the Green's function itself. This approach is illustrated in one-dimensional and two-dimensional Helmholtz equation problems, with an emphasis on systems that are open and have a non-Hermitian potential. We then draw an analogy between the Green's function obtained this way and a chiral edge state circumventing a defect in a topological lattice, which shines light on the local minimum of the Green's function at the source position.
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 scaling recursive Green's function formalism that allows us to treat large systems quantum-mechanically. The electronic structure of the CNT is described by a density-functional-based tight-binding model. We determine the influence of the defects on the transmission function for a given defect density by statistical analysis. We show that the system is in t…
We derive an improved version of the recursive Green's function formalism (RGF), which is a standard tool in the quantum transport theory. We consider the case of disordered quasi one-dimensional materials where the disorder is applied in form of randomly distributed realistic defects, leading to partly periodic Hamiltonian matrices. The algorithm accelerates the common RGF in the recursive decimation scheme, using the iteration steps of the renormalization decimation algorithm. This leads to a smaller effective system, which is treated using the common forward iteration scheme. The computatio…
The Green functions play a big role in the calculation of the local density of states of the carbon nanostructures. We investigate their nature for the variously oriented and disclinated graphene-like surface. Next, we investigate the case of a small perturbation generated by two heptagonal defects and from the character of the local density of states in the border sites of these defects we derive their minimal and maximal distance on the perturbed cylindrical surface. For this purpose, we transform the given surface into a chain using the Haydock recursion method. We will suppose only the nea…
Zigzag phosphorene nanoribbons have quasi-flat band edge modes entirely detached from the bulk states. We analytically study the electronic transport through such edge states in the presence of a localized defect for semi-infinite and finite ribbons. Using the tight-binding model, we derive analytical expressions for the Green's function and transmission amplitude of both pristine and defective nanoribbons. We find that the transmission of both semi-infinite and finite ribbons is sensitive to the location of a single impurity defect with respect to the edge. By the presence of an impurity on t…
We present a detailed theoretical analysis of the electronic and optical properties of c-plane InGaN/GaN quantum well structures with In contents ranging from 5% to 25%. Special attention is paid to the relevance of alloy induced carrier localization effects to the green gap problem. Studying the localization length and electron-hole overlaps at low and elevated temperatures, we find alloy-induced localization effects are crucial for the accurate description of InGaN quantum wells across the range of In content studied. However, our calculations show very little change in the localization effe…
The boundary effects affecting the Hamiltonian for the nanocone with curvatureinduced spin orbit coupling were considered and the corresponding electronic structure was calculated. These boundary effects include the spin orbit coupling, the electron mass acquisition and the Coulomb interaction. Different numbers of the pentagonal defects in the tip were considered. The Green function approach into the second order was used for getting more precise results in the case of the spin orbit coupling.
We present an efficient numerical approach for treating ballistic quantum transport across devices described by tight binding (TB) Hamiltonians designated to systems with localized potential defects. The method is based on the wave function matching approach, Lippmann-Schwinger equation (LEQ) and the scattering matrix formalism. We show that the number of matrix elements of the Green's function to be evaluated for the unperturbed system can be essentially reduced by projection of the time reversed scattering wave functions on LEQ which radically improves the speed and lowers the memory consump…
In this work the conducting properties of graphene lattice with a particular concentration of defect (5\% and 10\%) has been studied. The real space block recursion method introduced by Haydock et al. has been used in presence of the random distribution of defects in graphene. This Green function based method is found more powerful than the usual reciprocal based methods which need artificial periodicity. Different resonant states appear because of the presence of topological and local defects are studied within the framework of Green function.
Density functional theory is applied to study the mechanism of the Stone-Wales defect formation in pure and nitrogen-doped dodecahedral C$_{20}$ fullerenes. The molecular structures of initial and defected cages as well as transition states dividing them are obtained. Depending on the number of nitrogen atoms and their relative position in the cage, Stone-Wales defect is formed through the single additional intermediate state or directly. The activation energy barrier of the defect formation reduces from 4.93 eV in pure C$_{20}$ to 2.98 eV in single-doped C$_{19}$N, and reaches $\sim$ 2 eV und…
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 revea…
Using density functional theory and non-equilibrium Greens function technique, we performed theoretical investigations on the structural and transport properties of zigzag silicene nanoribbons with Stone-Wales defect. The calculated formation energy is significantly lower than that of graphene and silicene, which implies the high stability of such defect in SiNRs. Negative differential resistance can be observed within certain bias voltage range in both perfect and SW defected SiNRs. In order to elucidate the mechanism the NDR behavior,the transmission spectra and molecular projected self-cons…
Using the non-equilibrium Keldysh Green's function formalism, we investigate the effect of defects on the electronic structure and transport properties of two-dimensional topological insulators (TI). We demonstrate how the spatial flow of charge changes between the topologically protected edge and bulk states and show that elastically and inelastically scattering defects that preserve the time reversal symmetry of the TI lead to qualitatively different effects on the TI's local electronic structure and its transport properties. Moreover, we show that the recently predicted ability to create hi…
Magnetic properties of a single vacancy in graphene is a relevant and still much discussed problem. The experimental results point to a clearly detectable magnetic defect state at the Fermi energy, while calculations based on density functional theory (DFT) yield widely varying results for the magnetic moment, in the range of $μ=1.04-2.0$ $μ_{B}$. We present a multi-tool \textit{ab initio} theoretical study of the same defect, using two simulation protocols for a defect in a crystal (cluster and periodic boundary conditions) and different DFT functionals - bare and hybrid DFT, mixing a fractio…
We describe a method and its implementation for calculating electronic structure and electron transport without approximating the structure using periodic super-cells. This effectively removes spurious periodic images and interference effects. Our method is based on already established methods readily available in the non-equilibrium Green function formalism and allows for non-equilibrium transport. We present examples of a N defect in graphene, finite voltage bias transport in a point-contact to graphene, and a graphene-nanoribbon junction. This method is less costly, in terms of CPU-hours, t…
We analyze the screening of an external Coulomb charge in gapless graphene cone, which is taken as a prototype of a topological defect. In the subcritical regime, the induced charge is calculated using both the Green's function and the Friedel sum rule. The dependence of the polarization charge on the Coulomb strength obtained from the Green's function clearly shows the effect of the conical defect and indicates that the critical charge itself depends on the sample topology. Similar analysis using the Friedel sum rule indicates that the two results agree for low values of the Coulomb charge bu…
Magnetic properties of a single vacancy in graphene is a relevant and still unsolved problem. The experimental results point to a clearly detectable magnetic defect state at the Fermi energy, while several calculations based on density functional theory (DFT) yield widely varying results for the magnetic moment, in the range of $μ=1.04-2.0$ $μ_{B}$. We present a multi-tool \textit{ab initio} theoretical study of the same defect, using two simulation protocols for a defect in a crystal (cluster and periodic boundary conditions) and different DFT functionals - bare and hybrid DFT, mixing a fract…
Being a flexible wide band gap semiconductor, hexagonal boron nitride (h-BN) has great potential for technological applications like efficient deep ultraviolet light sources, building block for two-dimensional heterostructures and room temperature single photon emitters in the ultraviolet and visible spectral range. To enable such applications, it is mandatory to reach a better understanding of the electronic and optical properties of h-BN and the impact of various structural defects. Despite the large efforts in the last years, aspects such as the electronic band gap value, the exciton bindin…
Amorphous solids show surprisingly universal behaviour at low temperatures. The prevailing wisdom is that this can be explained by the existence of two-state defects within the material. The so-called standard tunneling model has become the established framework to explain these results, yet it still leaves the central question essentially unanswered -- what are these two-level defects? This question has recently taken on a new urgency with the rise of superconducting circuits in quantum computing, circuit quantum electrodynamics, magnetometry, electrometry and metrology. Superconducting circu…
The renormalization-decimation algorithm (RDA) of López Sancho et al. is used in quantum transport theory to calculate bulk and surface Green's functions. We derive an improved version of the RDA for the case of very long quasi one-dimensional unit cells (in transport direction). This covers not only long unit cells but also supercell-like calculations for structures with disorder or defects. In such large systems, short-range interactions lead to sparse real-space Hamiltonian matrices. We show how this and a corresponding subdivision of the unit cell in combination with the decimation techniq…
Point defects in solids such as vacancy and dopants often cause large thermal resistance. Because the lattice site occupied by a point defect has a much smaller size than phonon wavelengths, the scattering of thermal acoustic phonons by point defects in solids has been widely assumed to be the Rayleigh scattering type. In contrast to this conventional perception, using an ab initio Green's function approach, we show that the scattering by point defects in PbTe and GeTe exhibits Mie scattering characterized by a weaker frequency dependence of the scattering rates and highly asymmetric scatterin…
Interaction of waves with point and line defects are usually described by $δ$-function potentials supported on points or lines. In two dimensions, the scattering problem for a finite collection of point defects or parallel line defects is exactly solvable. This is not true when both point and parallel line defects are present. We offer a detailed treatment of the scattering problem for finite collections of point and parallel line defects in two dimensions. In particular, we perform the necessary renormalization of the coupling constants of the point defects, introduce an approximation scheme …
