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Valence Bond Theory

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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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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

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Related Experiment Video

Updated: Jan 12, 2026

Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

Published on: July 24, 2015

Spin-Orbit-Driven Quarter Semimetals in Rhombohedral Graphene.

Jing Ding^1,2, Hanxiao Xiang^1,2, Naitian Liu^1,2

¹Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science, Westlake University, Hangzhou, 310030, China.

Advanced Materials (Deerfield Beach, Fla.)

|November 5, 2025

Summary

Researchers observed quarter semimetals in multilayer graphene by adding spin-orbit coupling (SOC). This opens new avenues for exploring semimetal properties, correlations, and topology in advanced materials.

Keywords:

anomalous Hall effect graphene semimetal spin–orbit coupling strong correlations topology

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Area of Science:

Condensed Matter Physics
Materials Science

Background:

Semimetals possess unique electronic properties due to coexisting electrons and holes.
Rhombohedral multilayer graphene exhibits trigonal warping, creating a semimetallic state near the Fermi surface.

Purpose of the Study:

To investigate the emergence of quarter semimetals in rhombohedral multilayer graphene.
To explore the effects of spin-orbit coupling (SOC) on the electronic and topological properties of this material.

Main Methods:

Introduction of spin-orbit coupling (SOC) via WSe2 proximity.
Measurement of Hall resistance and longitudinal resistance.
Analysis of anomalous Hall effect and temperature dependence.

Main Results:

Observation of quarter semimetal phase characterized by vanished Hall resistance and parabolic longitudinal resistance.
Spontaneous symmetry breaking and time-reversal symmetry breaking induced by SOC.
Nonmonotonic temperature dependence of anomalous Hall resistance due to polarized electron-hole coexistence.
Phase transition from quarter semimetals to Chern insulators under magnetic fields.

Conclusions:

Rhombohedral multilayer graphene with SOC is a promising platform for studying strong correlations and topology in semimetals.
The findings provide insights into the interplay of electronic correlations, topology, and symmetry breaking in novel quantum materials.