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The Hall Effect

The Hall Effect

Edwin H. Hall, in the year 1879, devised an experiment that could be used to identify the polarity of the predominant charge carriers in a conducting material. From a historical perspective, this experiment was the first to demonstrate that the charge carriers in most metals are negative.

Valence Bond Theory

Valence Bond Theory

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...

The Pauli Exclusion Principle

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

Atomic Nuclei: Nuclear Spin State Overview

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Spin–Spin Coupling: Three-Bond Coupling (Vicinal Coupling)

Vicinal or three-bond coupling is commonly observed between protons attached to adjacent carbons. Here, nuclear spin information is primarily transferred via electron spin interactions between adjacent C‑H bond orbitals. This generally favors the antiparallel arrangement of spins, so 3J values are usually positive.
The extent of coupling depends on the C‑C bond length, the two H‑C‑C angles, any electron-withdrawing substituents, and the dihedral angle between the involved orbitals. The...

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Related Experiment Video

Updated: May 29, 2026

All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics

All-electronic Nanosecond-resolved Scanning Tunneling Microscopy: Facilitating the Investigation of Single Dopant Charge Dynamics

Published on: January 19, 2018

Quantum spin Hall effect in silicene and two-dimensional germanium.

Cheng-Cheng Liu¹, Wanxiang Feng, Yugui Yao

¹Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences, China.

Physical Review Letters

|September 10, 2011

Summary

Silicene and germanium exhibit a quantum spin Hall effect (QSHE) due to spin-orbit coupling, with predicted observable band gaps at accessible low temperatures. These 2D materials offer potential for future electronic applications.

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Area of Science:

Condensed Matter Physics
Materials Science
Quantum Chemistry

Background:

Exploration of two-dimensional (2D) materials beyond graphene for novel electronic properties.
Understanding the role of spin-orbit coupling in determining electronic band structure and topology.
Investigating the potential for realizing topological quantum phenomena in low-buckled honeycomb structures.

Purpose of the Study:

To investigate the spin-orbit opened energy gap and band topology in silicene and 2D germanium.
To demonstrate the realization of the quantum spin Hall effect (QSHE) in silicene.
To predict the QSHE observability and band gap tunability in silicene and germanium.

Main Methods:

Utilized first-principles calculations to analyze electronic structures.
Employed adiabatic continuity and direct calculation of the Z(2) topological invariant to confirm topological nontriviality.
Investigated the effects of pressure strain on the band gap.

Main Results:

Silicene exhibits topologically nontrivial electronic structures, enabling the quantum spin Hall effect (QSHE).
Predicted a spin-orbit band gap of 1.55 meV in silicene, significantly higher than graphene, observable at low temperatures.
Identified a band gap of 23.9 meV in 2D germanium, exceeding liquid nitrogen temperatures, due to spin-orbit coupling.

Conclusions:

Silicene and 2D germanium are promising candidates for realizing the quantum spin Hall effect.
The predicted band gaps are experimentally accessible, suggesting potential for spintronic applications.
Spin-orbit coupling plays a crucial role in opening significant band gaps in these 2D materials.