But it moves! (charge density wave in a metal)
In a metal, the electron density is highly uniform. The equilibrium positions of the ions form a perfectly periodic lattice (top part of figure). Variations of the electron density (local regions of high or low densities) cost a lot of Coulomb energy, so they are strongly suppressed. In quasi-one- and two-dimensional metals, however, static modulations of the density are stable under certain conditions. In a large class of transition metal-chalcogenides (for example NbSe2, NbSe3, TaS2, TaS3), and in 'blue bronze' K0.3MoO3, the electron gas and the ion lattice spontaneously develop a periodic modulation (bottom part of figure) when the temperature decreases below a critical transition temperature Tp ('p' for Peierls). The modulation of the electron density is called a charge density wave (CDW).
The periodic distortion of the ion lattice creates a super-unit cell which reduces slightly the kinetic energy of the highest energy electrons (a quantum effect). This gain increases in importance as the temperature decreases. Below Tp, the gain is large enough to offset the cost of distorting the lattice and the Coulomb energy cost. The charge density wave is an example of a cooperative state in which the ionic lattice and electron gas both develop a distortion to lower the total free energy of the sample. Before experiments appeared in the 70's, there was a lot of theoretical discussion about whether the CDW would move in an electric field. Since the trough of the wave (in red) can be placed anywhere without changing the total energy, the CDW may slide freely. In an electric field, it could conduct an electric current, and possibly even superconduct!
In 1976, the first example of a sliding CDW was discovered in the compound NbSe3, and recognized as such in 1977 (it moves, but does not superconduct). However, it sings! For reasons that are still rather unclear, as the CDW slides in the applied electric field, it emits an electrical note whose pitch (frequency) is proportional to its velocity. The note is rich in overtones. Harmonics of the fundamental up to the 10th have been recorded. To sense the note, one simply connects the voltage probes on the sample to an oscilloscope (or better, a spectrum analyzer). The electric potential has a tiny ac component that oscillates at the pitch frequency with a train of overtones.
A similar voltage oscillation also occurs in a type II superconductor when the vortex lattice (in an applied field) is made to flow by a large applied current (in this context, the pitch is called the washboard frequency). This was demonstrated in the 70's by Fiory in niobium. In the cuprates the only demonstration reported is by Harris et al., Phys. Rev. Lett. 74, 3684 (1995); J. Low Temp. Phys. 105, 877 (1996).
Charge density waves seem to be enjoying a comeback. They are candidate, competing states ('stripes') in the Quantum Hall Effect system (at high Landau filling) and in underdoped, cuprate superconductors.
For the earlier CDW work on chalcogenides, see
N.P. Ong and P. Monceau, "Anomalous transport properties of a linear-chain metal: NbSe3", Phys. Rev. B 16, 3443 (1977).
N.P. Ong, J.W. Brill, J.C. Eckert, J.W. Savage, S.K. Khanna and R.B. Somoano, "Effect of Impurities on the anomalous transport properties of NbSe3", Phys. Rev. Lett. 42, 811 (1979).
Can. Jnl. Phys. 60, 757 (1982),
N.P. Ong, G. Verma and K. Maki, " Vortex array model for charge-density-wave conduction noise", Phys. Rev. Lett. 52, 663 (1984).
N.P. Ong, C.B. Kalem and J.C. Eckert, "Quantised voltage jumps in the charge-density-wave conduction noise in TaS3.", Phys. Rev. B 30, 2902 (1984).
In a metal, the electron density is highly uniform. The equilibrium positions of the ions form a perfectly periodic lattice (top part of figure). Variations of the electron density (local regions of high or low densities) cost a lot of Coulomb energy, so they are strongly suppressed. In quasi-one- and two-dimensional metals, however, static modulations of the density are stable under certain conditions. In a large class of transition metal-chalcogenides (for example NbSe2, NbSe3, TaS2, TaS3), and in 'blue bronze' K0.3MoO3, the electron gas and the ion lattice spontaneously develop a periodic modulation (bottom part of figure) when the temperature decreases below a critical transition temperature Tp ('p' for Peierls). The modulation of the electron density is called a charge density wave (CDW).
The periodic distortion of the ion lattice creates a super-unit cell which reduces slightly the kinetic energy of the highest energy electrons (a quantum effect). This gain increases in importance as the temperature decreases. Below Tp, the gain is large enough to offset the cost of distorting the lattice and the Coulomb energy cost. The charge density wave is an example of a cooperative state in which the ionic lattice and electron gas both develop a distortion to lower the total free energy of the sample. Before experiments appeared in the 70's, there was a lot of theoretical discussion about whether the CDW would move in an electric field. Since the trough of the wave (in red) can be placed anywhere without changing the total energy, the CDW may slide freely. In an electric field, it could conduct an electric current, and possibly even superconduct!
In 1976, the first example of a sliding CDW was discovered in the compound NbSe3, and recognized as such in 1977 (it moves, but does not superconduct). However, it sings! For reasons that are still rather unclear, as the CDW slides in the applied electric field, it emits an electrical note whose pitch (frequency) is proportional to its velocity. The note is rich in overtones. Harmonics of the fundamental up to the 10th have been recorded. To sense the note, one simply connects the voltage probes on the sample to an oscilloscope (or better, a spectrum analyzer). The electric potential has a tiny ac component that oscillates at the pitch frequency with a train of overtones.
A similar voltage oscillation also occurs in a type II superconductor when the vortex lattice (in an applied field) is made to flow by a large applied current (in this context, the pitch is called the washboard frequency). This was demonstrated in the 70's by Fiory in niobium. In the cuprates the only demonstration reported is by Harris et al., Phys. Rev. Lett. 74, 3684 (1995); J. Low Temp. Phys. 105, 877 (1996).
Charge density waves seem to be enjoying a comeback. They are candidate, competing states ('stripes') in the Quantum Hall Effect system (at high Landau filling) and in underdoped, cuprate superconductors.
For the earlier CDW work on chalcogenides, see
N.P. Ong and P. Monceau, "Anomalous transport properties of a linear-chain metal: NbSe3", Phys. Rev. B 16, 3443 (1977).
N.P. Ong, J.W. Brill, J.C. Eckert, J.W. Savage, S.K. Khanna and R.B. Somoano, "Effect of Impurities on the anomalous transport properties of NbSe3", Phys. Rev. Lett. 42, 811 (1979).
Can. Jnl. Phys. 60, 757 (1982),
N.P. Ong, G. Verma and K. Maki, " Vortex array model for charge-density-wave conduction noise", Phys. Rev. Lett. 52, 663 (1984).
N.P. Ong, C.B. Kalem and J.C. Eckert, "Quantised voltage jumps in the charge-density-wave conduction noise in TaS3.", Phys. Rev. B 30, 2902 (1984).
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