Quantum spin Hall phase in honeycomb nanoribbons with two different atoms: edge shape effect to bulk-edge correspondence

Kondo, Kenji; Ito, Ryo

doi:10.1088/2399-6528/ab1c67

Cited by 5 publications

(3 citation statements)

References 51 publications

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“…In such cases, where the width of the ribbon is small enough for the edge modes to overlap, the system may not exhibit distinct edge states within the bulk energy gap. This deviation from the bulk-edge correspondence highlights the importance of considering the size and geometry of the system when studying topological properties which was studied before numerically 26 and is addressed here analytically.…”

Section: Resultsmentioning

confidence: 88%

“…This breakthrough provides us with a valuable opportunity to delve into the detailed analysis of these edge states and their intriguing properties. By leveraging this newfound understanding, we aim to identify the topological transition point as well as the origin of the bulk-edge correspondence violation for relatively narrow ribbons 26 .…”

Section: Introductionmentioning

confidence: 99%

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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

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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.

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Section: Resultsmentioning

confidence: 88%

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

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“…Many researchers have paid much attention to topological materials [1][2][3][4][5][6][7][8][9] and topological phenomena [10][11][12][13][14][15] from the viewpoint of their application to spintronics devices. [16][17][18][19][20] Weyl semimetals (WSMs) are one kind of topological materials, which are studied extensively due to peculiar transport properties originating from the chiral anomaly.…”

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confidence: 99%

General formula of chiral anomaly for type-I and type-II Weyl semimetals

Morishima

Kondo

2021

Applied Physics Letters

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Weyl semimetals (WSMs) are classified into type-I and type-II, depending on the magnitudes of the inclination of Weyl cones. It is known that these WSMs show negative longitudinal magnetoresistance originating from chiral anomaly. Moreover, we have recently revealed that type-II WSMs show positive longitudinal magnetoresistance originating from chiral anomaly. The negative longitudinal magnetoresistance in type-I WSMs can be explained utilizing the conventional formula of the chiral anomaly, which does not have the term related to the inclination of the Weyl cones. However, we cannot explain both the positive and the negative longitudinal magnetoresistance in type-II WSMs utilizing it. Therefore, in this paper, we derive the general formula including the term related to the inclination of the Weyl cones in order to explain straightforwardly the positive and the negative longitudinal magnetoresistance in type-II WSMs. Also, we consider both cases where a pair of the Weyl cones are tilted in the same direction (positive tilt chirality) and toward (or against) each other (negative tilt chirality) in order to investigate the influence of the direction to which the Weyl cones are tilted. As a result, we find that in the negative tilt chirality, the general formula is strongly affected by the inclination. These results suggest that we can estimate whether the WSMs show the positive or the negative longitudinal magnetoresistance using the general formula from the information of their tilt chirality and the magnitudes of the inclination of the Weyl cones.

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A comparison of magnetoconductivities between type-I and type-II Weyl semimetals

Morishima

Kondo

2021

Journal of Applied Physics

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It is well known that Weyl semimetals (WSMs) are classified into two types of type-I and type-II depending on whether or not they have electron and hole pockets. Also, these WSMs have peculiar transport properties such as negative longitudinal magnetoresistance and planar Hall effect because of a chiral anomaly. In this paper, however, we show that the chiral anomaly can cause positive longitudinal magnetoresistance in type-II WSMs. Here, we investigate longitudinal and transverse magnetoconductivities of time reversal symmetry broken type-I and type-II WSMs using a tight-binding model. The model allows us to describe both types of type-I and type-II WSMs by tuning parameters, and it has two Weyl points that are separated along the kx-direction. The numerical calculations of these conductivities are performed using the Boltzmann equation including the Berry curvature. It is found that longitudinal magnetoconductivities in the x-direction can have both positive and negative values depending on the magnitude of the inclination of a Weyl cone. This is because the zeroth Landau energy-level becomes either a hole-like one or an electron-like one depending on the magnitude of the inclination of the Weyl cone in type-II WSMs. These results imply that we can make a high MR-ratio device using type-II WSMs by tuning the inclination of their cones if it is possible to change their energy bands by the application of electric field and so on.

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Quantum spin Hall phase in honeycomb nanoribbons with two different atoms: edge shape effect to bulk-edge correspondence

Cited by 5 publications

References 51 publications

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

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

General formula of chiral anomaly for type-I and type-II Weyl semimetals

A comparison of magnetoconductivities between type-I and type-II Weyl semimetals

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