Charge Density Wave: Difference between revisions
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Introduction | ==Introduction== | ||
Charge Density Wave (CDW) is a spatial modulation of the conduction electron density in a metal and an associated modulation of the lattice atom positions. In the relation to the symmetry breaking, CDW is a broken symmetry state of metals brought by the electron-phonon interactions whose ground states are the coherent superposition of electron-hole pairs, and it displays spatial variation. | Charge Density Wave (CDW) is a spatial modulation of the conduction electron density in a metal and an associated modulation of the lattice atom positions. In the relation to the symmetry breaking, CDW is a broken symmetry state of metals brought by the electron-phonon interactions whose ground states are the coherent superposition of electron-hole pairs, and it displays spatial variation. | ||
CDW states was first discussed by Frohlich in 1954 and by Peierls in 1955. The latter pointed out that a one-dimensional metal coupled to the underlying lattice is not stable at low temperatures. The ground state of the coupled electron-phonon system is characterized by a gap in the single-particle excitation spectrum and by a collective mode formed by electron-hole pairs involving a wave vector <math>q = 2k_F \!</math> with the charge density <math>\rho(\vec{r})=\rho_0 + \rho_1 cos(2\vec{k_F} \cdot \vec{r}+\phi)</math>, where <math>\rho_0 \!</math> is the unperturbed electron density of the metal and the condensate is called the charge density wave. As with the superconductivity, CDW has a complex order parameter <math>\Delta e^{i\phi} \!</math> with the magnitude of <math>\Delta \!</math> determines the size of the electronic gap and the amplitude <math>\delta u \!</math> of the atomic displacements. The phase <math>\phi \!</math> determines the position of the CDW relative to the underlying lattice. | CDW states was first discussed by Frohlich in 1954 and by Peierls in 1955. The latter pointed out that a one-dimensional metal coupled to the underlying lattice is not stable at low temperatures. The ground state of the coupled electron-phonon system is characterized by a gap in the single-particle excitation spectrum and by a collective mode formed by electron-hole pairs involving a wave vector <math>q = 2k_F \!</math> with the charge density <math>\rho(\vec{r})=\rho_0 + \rho_1 cos(2\vec{k_F} \cdot \vec{r}+\phi)</math>, where <math>\rho_0 \!</math> is the unperturbed electron density of the metal and the condensate is called the charge density wave. As with the superconductivity, CDW has a complex order parameter <math>\Delta e^{i\phi} \!</math> with the magnitude of <math>\Delta \!</math> determines the size of the electronic gap and the amplitude <math>\delta u \!</math> of the atomic displacements. The phase <math>\phi \!</math> determines the position of the CDW relative to the underlying lattice. | ||
==Materials== | |||
CDW primarily exists in the low-dimensional metals, that is metals whose Fermi surfaces exhibit high anisotropy (metal is defined as an object in which the Fermi surface exists). This anisotropy is the answer to the question why the conductivity along one axis is higher than it is in any other axis, hence although the material itself appears to be 3 dimensional, the conductivity exist only on a certain plane or a certain axis. The materials are typically conducting polymers, or also known as synthetic metals. | |||
As a simple picture of how the CDW comes into the system, let's consider a thought experiment about making a polyacetylene out of polyethylene. | |||
Revision as of 13:59, 24 November 2010
Introduction
Charge Density Wave (CDW) is a spatial modulation of the conduction electron density in a metal and an associated modulation of the lattice atom positions. In the relation to the symmetry breaking, CDW is a broken symmetry state of metals brought by the electron-phonon interactions whose ground states are the coherent superposition of electron-hole pairs, and it displays spatial variation.
CDW states was first discussed by Frohlich in 1954 and by Peierls in 1955. The latter pointed out that a one-dimensional metal coupled to the underlying lattice is not stable at low temperatures. The ground state of the coupled electron-phonon system is characterized by a gap in the single-particle excitation spectrum and by a collective mode formed by electron-hole pairs involving a wave vector with the charge density , where is the unperturbed electron density of the metal and the condensate is called the charge density wave. As with the superconductivity, CDW has a complex order parameter with the magnitude of determines the size of the electronic gap and the amplitude of the atomic displacements. The phase determines the position of the CDW relative to the underlying lattice.
Materials
CDW primarily exists in the low-dimensional metals, that is metals whose Fermi surfaces exhibit high anisotropy (metal is defined as an object in which the Fermi surface exists). This anisotropy is the answer to the question why the conductivity along one axis is higher than it is in any other axis, hence although the material itself appears to be 3 dimensional, the conductivity exist only on a certain plane or a certain axis. The materials are typically conducting polymers, or also known as synthetic metals.
As a simple picture of how the CDW comes into the system, let's consider a thought experiment about making a polyacetylene out of polyethylene.