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Chirality02:25

Chirality

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Chirality is a term that describes the lack of mirror symmetry in an object. In other words, chiral objects cannot be superposed on their mirror images. For example, our feet are chiral, as the mirror image of the left foot, the right foot, cannot be superposed on the left foot.
Chiral objects exhibit a sense of handedness when they interact with another chiral object. For example, our left foot can only fit in the left shoe and not in the right shoe. Achiral objects — objects that have...
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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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In the study of the mechanics of materials, analyzing the behavior of prismatic members under opposing couples is crucial for understanding internal stress distributions, which are essential for structural design. When subjected to couples, a prismatic member experiences internal forces that maintain equilibrium. A couple, characterized by two equal and opposite forces, creates a moment but no resultant force. The internal forces at any section cut of the member must balance these external...
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Chirality is most prevalent in carbon-based tetrahedral compounds, but this important facet of molecular symmetry extends to sp3-hybridized nitrogen, phosphorus and sulfur centers, including trivalent molecules with lone pairs. Here, the lone pair behaves as a functional group in addition to the other three substituents to form an analogous tetrahedral center that can be chiral.
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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
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There is variation in the electrical conductivity of materials - metals, semiconductors, and insulators that are showcased with the help of the energy band diagrams.
Metals such as copper (Cu), zinc (Zn), or lead (Pb) have low resistivity and feature conduction bands that are either not fully occupied or overlap with the valence band, making a bandgap non-existent. This allows electrons in the highest energy levels of the valence band to easily transition to the conduction band upon gaining...
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Topological phase transitions and flat bands on an islamic lattice.

Journal of physics. Condensed matter : an Institute of Physics journalยท2023
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Related Experiment Video

Updated: Nov 12, 2025

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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C-symmetric Chern insulators.

Ying Han1, Ai-Lei He2

  • 1State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|March 15, 2021
PubMed
Summary

This study introduces methods to identify and analyze topological phase transitions in curved Chern insulators (CIs) on novel lattice geometries. Researchers explore CIs with n-fold rotational symmetry, advancing quantum Hall state research.

Keywords:
Chern insulatorsn-fold rotational symmetryquantum transportsreal-space Chern number

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Area of Science:

  • Condensed Matter Physics
  • Topological Materials Science
  • Quantum Phenomena

Background:

  • Chern insulators (CIs) are crucial for realizing quantum Hall states without magnetic fields.
  • Existing research on CIs has explored various curved lattices, including cone-like structures and fullerenes.
  • Identifying curved CIs and understanding their topological phase transitions (TPTs) remain underexplored areas.

Purpose of the Study:

  • To systematically investigate curved CIs with arbitrary n-fold rotational symmetry (Cn-symmetric CIs).
  • To explore topological phase transitions in these curved CIs.
  • To establish robust methods for identifying and characterizing curved CIs.

Main Methods:

  • Utilized a 'cutting and gluing' approach with disk geometry to construct Cn-symmetric CIs on cone-like and saddle-like lattices.
  • Proposed and applied two methods for calculating the real-space Chern number: Kitaev's formula and the local Chern marker.
  • Investigated TPTs by tuning parameters such as staggered flux and on-site mass.

Main Results:

  • Successfully identified Cn-symmetric CIs on curved lattices.
  • Demonstrated that chiral edge states, real-space Chern number, and quantized conductance are key identifiers for these curved CIs.
  • Characterized TPTs in curved CIs through parameter manipulation.

Conclusions:

  • The study provides a comprehensive framework for identifying and analyzing curved Chern insulators and their topological phase transitions.
  • The proposed methods offer new tools for exploring topological properties in curved material systems.
  • This work advances the understanding of topological states in non-Euclidean geometries.