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

• URL: http://arxiv.org/abs/2306.03690v1
• Date: Tue, 6 Jun 2023 14:00:25 GMT
• Title: Rigorous analysis of the topologically protected edge states in the quantum spin Hall phase of the armchair ribbon geometry
• Authors: Mozhgan Sadeghizadeh, Morteza Soltani, and Mohsen Amini
• Abstract summary: We present a novel analytical approach for obtaining explicit expressions for the edge states in the Kane-Mele model. We determine various analytical properties of the edge states, including their wave functions and energy dispersion. Our findings shed light on the unique characteristics of the edge states in the quantum spin Hall phase of the Kane-Mele model.
• Score: 1.2999413717930817
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Exploring Topological Boundary Effects through Quantum Trajectories in Dissipative SSH Models [0.0]
  We investigate the topological properties of the Su-Schrieffer-Heeger (SSH) model under dissipative dynamics using the quantum trajectory approach. Our study explores the preservation or breakdown of topological edge states, particularly focusing on the effects of symmetry-preserving and symmetry-breaking dissipations.
  arXiv  Detail & Related papers  (2024-11-08T16:22:39Z)
• Quantum geometry in many-body systems with precursors of criticality [0.0]
  We analyze the geometry of the ground-state manifold in parameter-dependent many-body systems with quantum phase transitions (QPTs) We elucidate the role of diabolic points in the formation of first-order QPTs, showing that these isolated geometric singularities represent seeds generating irregular behavior of geodesics in finite systems.
  arXiv  Detail & Related papers  (2024-11-06T15:06:05Z)
• Real-space detection and manipulation of topological edge modes with ultracold atoms [56.34005280792013]
  We demonstrate an experimental protocol for realizing chiral edge modes in optical lattices. We show how to efficiently prepare particles in these edge modes in three distinct Floquet topological regimes. We study how edge modes emerge at the interface and how the group velocity of the particles is modified as the sharpness of the potential step is varied.
  arXiv  Detail & Related papers  (2023-04-04T17:36:30Z)
• Softening of Majorana edge states by long-range couplings [77.34726150561087]
  Long-range couplings in the Kitaev chain is shown to modify the universal scaling of topological states close to the critical point. We prove that the Majorana states become increasingly delocalised at a universal rate which is only determined by the interaction range.
  arXiv  Detail & Related papers  (2023-01-29T19:00:08Z)
• 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 [1.2999413717930817]
  We focus on the Kane-Mele model with and without Rashba spin-orbit coupling as a well-known model. We derive explicit expressions for the wave functions, energy dispersion relations, and the spin rotations of the (generic) helical edge states. 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.
  arXiv  Detail & Related papers  (2022-12-22T07:41:11Z)
• Edge states, Majorana fermions and topological order in superconducting wires with generalized boundary conditions [0.0]
  We study the properties of one-dimensional topological superconductors under the influence of generic boundary conditions. In particular, we investigate the resilience of the long-distance, edge-to-edge quantum mutual information and squashed entanglement.
  arXiv  Detail & Related papers  (2022-07-04T14:05:03Z)
• Accessing the topological Mott insulator in cold atom quantum simulators with realistic Rydberg dressing [58.720142291102135]
  We investigate a realistic scenario for the quantum simulation of such systems using cold Rydberg-dressed atoms in optical lattices. We perform a detailed analysis of the phase diagram at half- and incommensurate fillings, in the mean-field approximation. We furthermore study the stability of the phases with respect to temperature within the mean-field approximation.
  arXiv  Detail & Related papers  (2022-03-28T14:55:28Z)
• Bridging the gap between topological non-Hermitian physics and open quantum systems [62.997667081978825]
  We show how to detect a transition between different topological phases by measuring the response to local perturbations. Our formalism is exemplified in a 1D Hatano-Nelson model, highlighting the difference between the bosonic and fermionic cases.
  arXiv  Detail & Related papers  (2021-09-22T18:00:17Z)
• A supervised learning algorithm for interacting topological insulators based on local curvature [6.281776745576886]
  We introduce a supervised machine learning scheme that uses only the curvature function at the high symmetry points as input data. We show that an artificial neural network trained with the noninteracting data can accurately predict all topological phases in the interacting cases. Intriguingly, the method uncovers a ubiquitous interaction-induced topological quantum multicriticality.
  arXiv  Detail & Related papers  (2021-04-22T18:00:00Z)
• Self-consistent theory of mobility edges in quasiperiodic chains [62.997667081978825]
  We introduce a self-consistent theory of mobility edges in nearest-neighbour tight-binding chains with quasiperiodic potentials. mobility edges are generic in quasiperiodic systems which lack the energy-independent self-duality of the commonly studied Aubry-Andr'e-Harper model.
  arXiv  Detail & Related papers  (2020-12-02T19:00:09Z)
• Probing chiral edge dynamics and bulk topology of a synthetic Hall system [52.77024349608834]
  Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension. We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
  arXiv  Detail & Related papers  (2020-01-06T16:59:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.