| Peierls transition | |
|---|---|
| Name | Peierls transition |
| Fields | Condensed Matter Physics, Quantum Mechanics |
| Description | A phase transition in one-dimensional electronic systems |
Peierls transition
The Peierls transition is a fundamental concept in Quantum Physics, describing a phase transition that occurs in one-dimensional electronic systems. This transition is named after the British physicist Rudolf Peierls, who first proposed the idea in the 1950s. The Peierls transition is significant in the context of Quantum Physics because it explains how a one-dimensional metal can become an insulator at low temperatures, due to the formation of a charge density wave.
Peierls Transition The Peierls transition is a type of phase transition that occurs in one-dimensional electronic systems, such as nanowires or molecular chains. This transition is characterized by the formation of a charge density wave, which is a periodic modulation of the electronic charge density. The Peierls transition is driven by the interaction between the electrons and the lattice vibrations, also known as phonons. This interaction leads to a distortion of the lattice, which in turn affects the electronic properties of the system. Researchers at institutions like Stanford University and MIT have made significant contributions to the understanding of the Peierls transition.
in Quantum Physics The Peierls transition is rooted in the principles of Quantum Mechanics and Condensed Matter Physics. The concept of a charge density wave is closely related to the idea of a Bloch wave, which is a wave function that describes the behavior of electrons in a periodic potential. The Peierls transition can be understood in terms of the Fermi-Dirac statistics, which describe the behavior of fermions, such as electrons, in a many-body system. Theoretical models, such as the Hubbard model and the Peierls-Hubbard model, have been developed to describe the behavior of electrons in one-dimensional systems and to study the Peierls transition. These models have been applied to systems like graphene and carbon nanotubes.
The theoretical framework for the Peierls transition is based on the concept of a mean-field theory, which is a type of approximation that is used to describe the behavior of a many-body system. The mean-field theory is used to describe the interaction between the electrons and the lattice vibrations, and to calculate the energy of the system. The Peierls transition can be described using the Landau theory of phase transitions, which provides a framework for understanding the behavior of a system near a phase transition. Researchers at institutions like Harvard University and University of California, Berkeley have developed theoretical models to describe the Peierls transition.
The one-dimensional chain model is a simple model that is used to study the Peierls transition. This model consists of a chain of atoms, each of which is connected to its neighbors by a spring. The electrons in the chain are described using a tight-binding model, which is a type of approximation that is used to describe the behavior of electrons in a periodic potential. The one-dimensional chain model has been used to study the behavior of systems like polyacetylene and trans-polyacetylene. The model has also been applied to systems like quantum wires and nanotubes.
Experimental observations of the Peierls transition have been made in a variety of systems, including nanowires, molecular chains, and quasi-one-dimensional materials. These observations have been made using a range of experimental techniques, including X-ray diffraction, electron diffraction, and optical spectroscopy. The Peierls transition has been observed in systems like KCP (K2Pt(CN)4Br0.3·3H2O) and TTF-TCNQ (tetrathiafulvalene-tetracyanoquinodimethane). Researchers at institutions like University of Oxford and University of Cambridge have made significant contributions to the experimental study of the Peierls transition.
The Peierls transition has significant implications for our understanding of quantum systems. The transition is an example of a quantum phase transition, which is a type of phase transition that occurs at zero temperature. The Peierls transition is also an example of a non-equilibrium phase transition, which is a type of phase transition that occurs in a system that is not in equilibrium. The study of the Peierls transition has implications for our understanding of other quantum systems, such as superconductors and superfluids. Researchers at institutions like Los Alamos National Laboratory and Argonne National Laboratory have studied the implications of the Peierls transition for quantum systems.
The Peierls transition is related to other quantum phenomena, such as superconductivity and magnetism. The transition is also related to the concept of a Mott insulator, which is a type of insulator that arises from the interaction between electrons. The Peierls transition has been studied in relation to other quantum phase transitions, such as the quantum Hall effect and the superfluid-insulator transition. Researchers at institutions like University of Chicago and Princeton University have studied the relationship between the Peierls transition and other quantum phenomena. The study of the Peierls transition has also been influenced by the work of researchers like Philip Warren Anderson and Walter Kohn.