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Related Concept Videos

Chirality02:25

Chirality

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...
Prochirality02:05

Prochirality

The concept of prochirality leads to the nomenclature of the individual faces of a molecule and plays a crucial role in the enantioselective reaction. It is a concept where two or more achiral molecules react to produce chiral products. A typical process is the reaction of an achiral ketone to generate a chiral alcohol. Here, the achiral reactant reacts with an achiral reducing agent, sodium borohydride, to generate an equimolar mixture of the chiral enantiomers of the product. For example, an...
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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.
A consequence of chirality is the need for enantiomeric resolution. While this is theoretically possible for all...
Chirality in Nature02:30

Chirality in Nature

Chirality is the most intriguing yet essential facet of nature, governing life’s biochemical processes and precision. It can be observed from a snail shell pattern in a macroscopic world to an amino acid, the minutest building block of life. Most of the snails around the world have right-coiled shells because of the intrinsic chirality in their genes. All the amino acids present in the human body exist in an enantiomerically pure state, except for glycine - the sole achiral amino acid. The...
Molecules with Multiple Chiral Centers02:25

Molecules with Multiple Chiral Centers

Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are...
Fischer Projections02:18

Fischer Projections

Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines. While...

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Anomalous chiral Fermi surfaces.

Ismail Zahed1

  • 1Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA. zahed@tonic.physics.sunysb.edu

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

A geometric argument reveals a Wess-Zumino-Witten (WZW) term in Fermi surfaces with Berry curvature. This leads to chiral anomalies in fermionic currents, while fermion number is conserved due to paired Berry curvatures.

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Area of Science:

  • Condensed matter physics
  • High-energy physics
  • Quantum field theory

Background:

  • Berry curvature in condensed matter systems.
  • Wess-Zumino-Witten (WZW) terms in quantum field theory.
  • Chiral anomalies and their physical implications.

Purpose of the Study:

  • To provide a geometrical argument for the emergence of a WZW term in a Fermi surface threaded by Berry curvature.
  • To investigate the implications of the gauged WZW term in the presence of external fields.
  • To discuss anomalous currents and temperature corrections in fermionic fluids.

Main Methods:

  • Geometrical arguments.
  • Analysis of gauged WZW terms.
  • Low-temperature fermionic fluid dynamics.

Main Results:

  • Emergence of a WZW term from Berry curvature in Fermi surfaces.
  • Chiral anomaly in fermionic current at the Fermi surface edge.
  • Conservation of fermion number due to paired Berry curvatures.
  • Discussion of anomalous vector and axial currents.
  • Identification of a potential link between temperature correction to chiral vortical effect and gravitational anomaly.

Conclusions:

  • The study establishes a geometric origin for WZW terms in systems with Berry curvature.
  • Chiral anomalies are a direct consequence of these terms in the presence of external fields.
  • Fermion number conservation is maintained through the paired nature of Berry curvatures.
  • The findings offer insights into anomalous transport phenomena and potential connections to gravitational anomalies.