Explicit derivation of the chiral and generic helical edge states for the Kane-Mele model: Closed expressions for the wave function, dispersion relation, and spin rotation

Rahmati, Fatemeh; Amini, Mohsen; Soltani, Mehdi; Mozhgan, Sadeghizadeh,

doi:10.1103/physrevb.107.205408

Cited by 5 publications

(5 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Additionally, the influence of y k ( ) on the Green's function is examined in figures 3 and 4(a). As evident, the Green's function remains non-zero and nearly constant on the first zigzag (indicating a good second approximation in equation (13), while it suddenly tends to zero on the second zigzag, supporting the analytical results from reference [67].…”

Section: Calculation Of Edge States Of Kane-mele Model and Calculatio...supporting

confidence: 70%

“…To precisely determine α, numerical solutions are essential for the given equation. However, rather than directly solving this equation, we shift our focus to the group velocity = » This assumption aligns seamlessly with our numerical results [67], ensuring a robust correspondence.…”

Section: Calculation Of Edge States Of Kane-mele Model and Calculatio...mentioning

confidence: 53%

“…Finally, we compare the analytical results with the numerical results. To calculate the Green's function as well as the α and v f coefficients, one can utilize the results from the reference [67]. It presents an analytical method to obtain highly accurate dispersion and edge-state wavefunction results.…”

Section: Calculation Of Edge States Of Kane-mele Model and Calculatio...mentioning

confidence: 99%

“…As established in articles [67] and [68], the exploration of edge states within the Haldane model necessitates a departure from the conventional approach seen in the graphene model. Unlike the direct mapping characteristic of the graphene model, associating each wave vector k x with an SSH chain, the Haldane model requires a conceptualization resembling an SSH ladder.…”

Section: Calculation Of Edge States Of Kane-mele Model and Calculatio...mentioning

confidence: 99%

See 3 more Smart Citations

Analytical and numerical calculation of the effect of edge states of the Kane-Mele model on the RKKY interaction

Alsayyid,

Ahmadi,

Soltani

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

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.

show abstract

Section: Calculation Of Edge States Of Kane-mele Model and Calculatio...supporting

confidence: 70%

Section: Calculation Of Edge States Of Kane-mele Model and Calculatio...mentioning

confidence: 53%

Section: Calculation Of Edge States Of Kane-mele Model and Calculatio...mentioning

confidence: 99%

Section: Calculation Of Edge States Of Kane-mele Model and Calculatio...mentioning

confidence: 99%

See 2 more Smart Citations

Analytical and numerical calculation of the effect of edge states of the Kane-Mele model on the RKKY interaction

Alsayyid,

Ahmadi,

Soltani

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…This model is known to exhibit edge states within the energy gap, making it an ideal system for exploring the characteristics and behaviors of these edge states. The explicit form of the edge states in the considered model remained elusive until very recently that the successful determination of the edge state wave functions for the zigzag ribbon configuration is reported 25 . In this study, by focusing on the armchair geometry, we specifically target the unique features associated with the edge states in this type of termination.…”

Section: Introductionmentioning

confidence: 99%

Rigorous analysis of the topologically protected edge states in the quantum spin Hall phase of the armchair ribbon geometry

Mozhgan

Soltani

Amini

2023

Sci Rep

Self Cite

View full text Add to dashboard Cite

Studying the edge states of a topological system and extracting their topological properties is of great importance in understanding and characterizing these systems. In this paper, we present a novel analytical approach for obtaining explicit expressions for the edge states in the Kane-Mele model within a ribbon geometry featuring armchair boundaries. Our approach involves a mapping procedure that transforms the system into an extended Su–Schrieffer–Heeger model, specifically a two-leg ladder, in momentum space. Through rigorous derivation, we determine various analytical properties of the edge states, including their wave functions and energy dispersion. Additionally, we investigate the condition for topological transition by solely analyzing the edge states, and we elucidate the underlying reasons for the violation of the bulk-edge correspondence in relatively narrow ribbons. Our findings shed light on the unique characteristics of the edge states in the quantum spin Hall phase of the Kane–Mele model and provide valuable insights into the topological properties of such systems.

show abstract

Design and control of topological Fano resonance in Kane-Mele nanoribbons for sensing applications

Jalilvand,

Soltani,

Noorinejad

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

The concept of topological Fano resonance, characterized by an ultrasharp asymmetric line shape, is a promising candidate for robust sensing applications due to its sensitivity to external parameters and immunity to structural disorder. In this study, the vacancy-induced topological Fano resonance in a nanoribbon made up of a hexagonal lattice with armchair sides is examined by introducing several on-site vacancies, which are deliberately created at regular distances, along a zigzag chain that stretches across the width of the ribbon. The presence of the on-site vacancies can create localized energy states within the electronic band structure, leading tothe formation of an impurity band, which can result in Fano resonance phenomena by forming a conductivity channel between the edge modes on both armchair sides of the ribbon. Consequently, an ultracompact tunable on-chip integrated topologicalFano resonance derived from the graphene-based nanomechanical phononic crystals is proposed. The Fano resonance arises from the interference between topologically protected even and odd edge modes at the interface between trivial and nontrivialinsulators in a nanoribbon structure governed by the Kane-Mele model describing the quantum spin Hall e®ect in hexagonal lattices. The simulation of the topological Fano resonance is performed analytically using the Lippmann-Schwinger scatteringformulation. One of the advantages of the present study is that the related calculations are carried out analytically, and in addition to the simplicity and directness, it reproduces the results obtained from the Landauer-BÄuttiker formulation very well bothquantitatively and qualitatively. The ¯ndings open up possibilities for the design of highly sensitive and accurate robust sensors for detecting extremely tiny forces, masses, and spatial positions.

show abstract

Explicit derivation of the chiral and generic helical edge states for the Kane-Mele model: Closed expressions for the wave function, dispersion relation, and spin rotation

Cited by 5 publications

References 28 publications

Analytical and numerical calculation of the effect of edge states of the Kane-Mele model on the RKKY interaction

Analytical and numerical calculation of the effect of edge states of the Kane-Mele model on the RKKY interaction

Rigorous analysis of the topologically protected edge states in the quantum spin Hall phase of the armchair ribbon geometry

Design and control of topological Fano resonance in Kane-Mele nanoribbons for sensing applications

Contact Info

Product

Resources

About