Articles
Publication Date: 2024
Physica Scripta (00318949)99(8)
In this paper, we investigate the Kane-Mele model and endeavor to demonstrate, through analytical calculations, how the presence of topological edge states influences the RKKY interaction. We illustrate that the effect diminishes as one moves away from the edges. To facilitate our analytical approach, we initially utilize a one-dimensional wire exhibiting linear dispersion for each spin as an approximation to the Kane-Mele model. We examine its impact on the RKKY interaction. Subsequently, we establish a correspondence between the edge states of the Kane-Mele model and a one-dimensional quantum wire model, wherein the coupling strength diminishes with increasing distance from the edges. Finally, we compare the analytical results with numerical findings obtained using the Landauer-Buttiker formulation. © 2024 IOP Publishing Ltd.
Publication Date: 2024
Physical Review B (24699950)109(2)
The quantization of conductance in the presence of nonmagnetic point defects is a consequence of topological protection and the spin-momentum locking of helical edge states in two-dimensional topological insulators. This protection ensures the absence of backscattering of helical edge modes in the quantum Hall phase of the system. However, in this paper, we focus on exploring an approach to spoil such conductance quantization. We propose that a linear arrangement of (nonmagnetic) on-site impurities can effectively cause deviations from the conductance quantization of the edge states in the Kane-Mele model. To investigate this phenomenon, we consider an armchair ribbon containing a line defect spanning its width. Utilizing the tight-binding model and nonequilibrium Green's function method, we calculate the transmission coefficient of the system. Our results reveal a suppression of conductance at energies near the lower edge of the bulk gap for positive on-site potentials. To further comprehend this behavior, we perform analytical calculations and discuss the formation of an impurity channel. This channel arises due to the overlap of in-gap bound states, linking the bottom edge of the ribbon to its top edge, consequently facilitating backscattering. Our explanation is supported by the analysis of the local density of states at sites near the position of impurities. © 2024 American Physical Society.
Publication Date: 2024
Physica Scripta (00318949)99(6)
We examine an armchair bilayer phosphorene connected to two leads, one hot and one cold, on both sides, investigating the thermoelectric properties of this system with periodic vacancies along the armchair direction and at the center of the nanoribbon. Initially, we analytically demonstrate that the creation of a vacancy results in the generation of a localized state around it. Subsequently, we illustrate that the presence of periodic vacancies leads to the formation of a new energy band in the energy bandstructure. Our calculations reveal that by varying the distance between vacancies, one can tune the width of the corresponding transmission channel, the generated electric power, and the thermoelectric efficiency. © 2024 IOP Publishing Ltd.
Although one of the most important and intriguing features of the topological insulators is the presence of edge states, the closed-form expressions for the edge states of some famous topological models are still lacking. Here, we focus on the Kane-Mele model with and without Rashba spin-orbit coupling as a well-known model to describe a two-dimensional version of the Z2 topological insulator to study the properties of its edge states analytically. By considering the tight-binding model on a honeycomb lattice with zigzag boundaries and introducing a perturbative approach, we derive explicit expressions for the wave functions, energy dispersion relations, and the spin rotations of the (generic) helical edge states. To this end, we first map the edge states of the ribbon geometry into an effective two-leg ladder model with momentum-dependent energy parameters. Then, we split the Hamiltonian of the system into an unperturbed part and a perturbation. The unperturbed part has a flat-band energy spectrum and can be solved exactly, which allows us to consider the remaining part of the Hamiltonian perturbatively. The resulting energy dispersion relation within the first-order perturbation, surprisingly, is in excellent agreement with the numerical spectra over a very wide range of wave numbers. Our perturbative framework also allows deriving an explicit form for the rotation of the spins of the momentum edge states in the absence of axial spin symmetry due to the Rashba spin-orbit interaction. © 2023 American Physical Society.
