phenomenon

charge density waves

Periodic modulations of electron density in materials, often persisting beyond order-disorder transitions.
20 related articles · 6 formulas

Description

Charge density waves are periodic modulations of electron density in certain crystalline materials, where the electrons organize into a standing wave pattern rather than being uniformly distributed. This phenomenon occurs in low-dimensional metals, such as layered compounds, and represents a collective quantum state of electrons. Charge density waves are often accompanied by a periodic distortion of the crystal lattice, and they can persist even when the material undergoes an order-disorder transition, making them a rich subject for studying quantum many-body physics.

History

Charge density waves were theoretically predicted by Rudolf Peierls in the 1930s, who showed that a one-dimensional metal is unstable against lattice distortion. The first experimental observations were made in the 1970s in layered transition-metal dichalcogenides like niobium diselenide.

How it works

In a charge density wave, the electron gas becomes unstable against a periodic modulation of its density, typically due to strong electron-phonon coupling or Fermi surface nesting. The electrons and the lattice distort together, creating a new ground state with a lower energy. This state has an energy gap at the Fermi level, turning the material into a semiconductor or insulator. The wave can be pinned by impurities or move under an applied electric field, leading to nonlinear transport phenomena.

In practice

Charge density waves are studied for potential applications in high-frequency oscillators, memory devices, and as model systems for understanding superconductivity and other quantum phenomena.

Fun fact

In some materials, charge density waves can move through the crystal like a 'sliding' state, carrying current without dissipation, similar to superconductivity but at higher temperatures.

Concept graph →

Formulas

$$\rho_{\rm GJ} = -\frac{\mathbf{\Omega} \cdot \mathbf{B}}{2\pi c}$$
Charge density required to screen electric field in pulsar magnetosphere.
What is in the formula
\rho_{\rm GJ}variableGoldreich-Julian charge density — charge density coulomb per cubic metre
\mathbf{\Omega}variableAngular velocity vector of the neutron star — angular velocity radian per second
\mathbf{B}variableMagnetic field vector — magnetic field tesla
cconstantUniversal constant, speed of light in vacuum — speed of light = 299792458 metre per second
2\piconstantMathematical constant, 2π — two pi = 6.283
\cdotoperatorScalar product of two vectors — dot product
ρ_{\rmgj}=-\frac{{ω}*{b}}{2πc} · 2606.03984v1
$$n(r) \propto r^{-\beta}$$
Density decreases with radius following a power law.
What is in the formula
nvariablenumber density — number density per metre cubed
rvariableradial distance — radius metre
βvariablepower-law index — power law index
∝operatoris proportional to — proportionality
n_h\proptor^{-β},\quadβ<2 · 2606.04711v1
$$p(\theta) = p_u(\phi) \left| \det \frac{\partial \phi}{\partial \theta} \right|$$
Transforms probability density under variable change.
What is in the formula
p(θ)variableProbability density in new variable θ — probability density
p_u(φ)variableProbability density in original variable φ — probability density
φvariableOriginal variable
θvariableNew variable
det(∂φ/∂θ)operatorScales the density to conserve probability mass — jacobian determinant
\hat{p}(θ|d)=p_u(f^{-1}(θ;c))|\det\frac{\partialf^{-1}(θ;c)}{\partialθ}| · 2607.04955
$$\omega_p = \sqrt{\frac{n e^2}{m \epsilon_0}}$$
Natural frequency of charge density oscillations.
What is in the formula
\omega_pvariableplasma angular frequency — angular frequency radian per second
nvariableelectron number density — number density per cubic metre
evariableelementary charge — electric charge coulomb
mvariableelectron mass — mass kilogram
\epsilon_0constantpermittivity of free space — vacuum permittivity = 8.8541878128e-12 farad per metre
\sqrt{}operatortakes the square root — square root
ħω_p\simeq2π\sqrt{w_mμ^{-1}a^3n_m(t)} · 2607.08826
$$S_I = 2eI$$
Shot noise power spectral density equals twice electron charge times current.
What is in the formula
S_Ivariablepower spectral density of current noise — power spectral density ampere squared per hertz
evariableelementary charge — elementary charge coulomb
Ivariableaverage electric current — electric current ampere
s_i=2ei · 2509.15983
$$J^{\mu\nu\alpha}(x) = x^{\mu} T^{\nu\alpha}(x) - x^{\nu} T^{\mu\alpha}(x)$$
Local density of angular momentum in flat spacetime.
What is in the formula
J^{\mu\nu\alpha}variableAngular momentum density tensor — angular momentum density kilogram per metre per second
x^{\mu}variableSpacetime coordinate — position metre
x^{\nu}variableSpacetime coordinate — position metre
T^{\nu\alpha}variableStress-energy tensor component — stress energy tensor joule per cubic metre
T^{\mu\alpha}variableStress-energy tensor component — stress energy tensor joule per cubic metre
j^{μνα}(x)=x^{μ}t^{να}(x)-x^{ν}t^{μα}(x) · 2605.13557v1

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