Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDistribution of resonance widths in localized tight-binding models
241
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We numerically analyze the distribution of scattering resonance widths in one- and quasi-one dimensional tight binding models, in the localized regime. We detect and discuss an algebraic decay of the distribution, similar, though not identical, to recent theoretical predictions.
rate research
Read More
We investigate the properties of PT-symmetric tight-binding models by considering both bounded and unbounded models. For the bounded case, we obtain closed form expressions for the corresponding energy spectra and we analyze the structure of eigenstates as well as their dependence on the gain/loss contrast parameter. For unbounded PT-lattices, we explore their scattering properties through the development of analytical models. Based on our approach we identify a mechanism that is responsible to the emergence of localized states that are entirely due to the presence of gain and loss. The derived expressions for the transmission and reflection coefficients allow one to better understand the role of PT-symmetry in energy transport problems occurring in such PT-symmetric tight-binding settings. Our analytical results are further exemplified via pertinent examples.
Artificial graphene consisting of honeycomb lattices other than the atomic layer of carbon has been shown to exhibit electronic properties similar to real graphene. Here, we reverse the argument to show that transport properties of real graphene can be captured by simulations using theoretical artificial graphene. To prove this, we first derive a simple condition, along with its restrictions, to achieve band structure invariance for a scalable graphene lattice. We then present transport measurements for an ultraclean suspended single-layer graphene pn junction device, where ballistic transport features from complex Fabry-Perot interference (at zero magnetic field) to the quantum Hall effect (at unusually low field) are observed and are well reproduced by transport simulations based on properly scaled single-particle tight-binding models. Our findings indicate that transport simulations for graphene can be efficiently performed with a strongly reduced number of atomic sites, allowing for reliable predictions for electric properties of complex graphene devices. We demonstrate the capability of the model by applying it to predict so-far unexplored gate-defined conductance quantization in single-layer graphene.
Maximally localized Wannier functions are localized orthogonal functions that can accurately represent given Bloch eigenstates of a periodic system at a low computational cost, thanks to the small size of each orbital. Tight-binding models based on the maximally localized Wannier functions obtained from different systems are often combined to construct tight-binding models for large systems such as a semi-infinite surface. However, the corresponding maximally localized Wannier functions in the overlapping region of different systems are not identical, and this discrepancy can introduce serious artifacts to the combined tight-binding model. Here, we propose two methods to seamlessly stitch two different tight-binding models that share some basis functions in common. First, we introduce a simple and efficient method: (i) finding the best matching maximally localized Wannier function pairs in the overlapping region belonging to the two tight-binding models, (ii) rotating the spin orientations of the two corresponding Wannier functions to make them parallel to each other, and (iii) making their overall phases equal. Second, we propose a more accurate and generally applicable method based on the iterative minimization of the difference between the Hamiltonian matrix elements in the overlapping region. We demonstrate our methods by applying them to the surfaces of diamond, GeTe, Bi$_2$Se$_3$, and TaAs. Our methods can be readily used to construct reliable tight-binding models for surfaces, interfaces, and defects.
If a localized quantum state in a tight-binding model with structural aperiodicity is subject to noisy evolution, then it is generally expected to result in diffusion and delocalization. In this work, it is shown that the localized phase of the kicked Aubry-Andre-Harper (AAH) model is robust to the effects of noisy evolution, for long times, provided that some kick is delivered once every time period. However, if strong noisy perturbations are applied by randomly missing kicks, a sharp dynamical transition from a ballistic growth phase at initial times to a diffusive growth phase for longer times is observed. Such sharp transitions are seen even in translationally invariant models. These transitions are related to the existence of flat bands, and using a 2-band model we obtain analytical support for these observations. The diffusive evolution at long times has a mechanism similar to that of a random walk. The time scale at which the sharp transition takes place is related to the characteristics of noise. Remarkably, the wavepacket evolution scales with the noise parameters. Further, using kick sequence modulated by a coin toss, it is argued that the correlations in the noise are crucial to the observed sharp transitions.
Graphene has proven to host outstanding mesoscopic effects involving massless Dirac quasiparticles travelling ballistically resulting in the current flow exhibiting light-like behaviour. A new branch of 2D electronics inspired by the standard principles of optics is rapidly evolving, calling for a deeper understanding of transport in large-scale devices at a quantum level. Here we perform large-scale quantum transport calculations based on a tight-binding model of graphene and the non-equilibrium Greens function method and include the effects of $p-n$ junctions of different shape, magnetic field, and absorptive regions acting as drains for current. We stress the importance of choosing absorbing boundary conditions in the calculations to correctly capture how current flows in the limit of infinite devices. As a specific application we present a fully quantum-mechanical framework for the 2D Dirac fermion microscope recently proposed by B{o}ggild $et, al.$ [Nat. Comm. 8, 10.1038 (2017)], tackling several key electron-optical effects therein predicted via semiclassical trajectory simulations, such as electron beam collimation, deflection and scattering off Veselago dots. Our results confirm that a semiclassical approach to a large extend is sufficient to capture the main transport features in the mesoscopic limit and the optical regime, but also that a richer electron-optical landscape is to be expected when coherence or other purely quantum effects are accounted for in the simulations.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
