What is a Charge Density Wave

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What is a Charge Density Wave?
Quasi-one-dimensional metal
Cool down ? Peierls Transition

• Electron density
• ?c ?/kF

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CDWs exhibit a collective charge transport mode

• CDW current Ic ? vc wave speed

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Physical Review 59, 928 (1941)

• "It is assumed that in the superconducting state
  there is a small periodic distortion of the
  lattice . . ." "The energy discontinuities
  produced by the zone structure yield a decrease
  in the energy of the electrons at the expense of
  the increase in energy of the lattice resulting
  from the distortion."

Proceedings of the Royal Society A223, 296 (1954)
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CDWs and Superconductors A Comparison
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Physical Review Letters 37, 602 (1976)
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CDW Materials
NbSe3
K0.3MoO3

• NbSe3 TP 145 K, 59 K (metallic at low T)
• K0.3MoO3 TP 180 K (semiconducting at low
  T)
• NbS3 TP 340 K

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CDWs are not Superconducting

• CDW motion is damped by interaction of phasons
  with single-particle excitations, and by phase
  slip.
• CDWs are pinned by their interaction with
  impurities and other lattice defects.

• In the presence of many impurities, the CDW
  adjusts its local phase ?(z) to maximize its
  impurity interaction energy.

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CDW Current (Velocity) - Electric Field Relation

• vc, Ic 0 for E
• ET 100 ?V/cm to 10 V/cm

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Effects of Pinning by Impurities

• Static CDW does not have long-range order.
• Lf phase-phase correlation length
• (analog of the Larkin length)
• CDW does not slide freely.
• ET threshold electric field for motion
• depinning field
• For E?ET, an elastic CDWs motion is periodic.

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Two types of pinning

• Local (strong) pinning
• CDW phase is pinned at each impurity site.
• ET ? ni, niimpurity concentration
• Existence of local pinning confirmed by X-ray
  white-line effect.
• Collective (weak) pinning
• CDW phase pinned by fluctuations in volumes
  containing many impurities
• ET ? ni2, L? ? 1/ni
• Existence of collective pinning confirmed by
  long X-ray CDW correlation lengths L?.
• ? Local and collective pinning can coexist

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ET versus impurity concentration in thick
Nb1-xTaxSe3 crystals
For both CDWs in NbSe3 ET ? ni2
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ET vs 1/thickness in Nb1-xTaxSe3
Collective Pinning ET ? ni2 3D ET ? ni/t
2D Thickness dependence due to cross-over
from 3D to 2D collective pinning when tX-ray diffraction.
Similar size effects observed for all
pinning-related properties.
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• ET is determined by collective pinning.
• Collective pinning energies 105 kBTP
• ? collective thermal creep negligible
• Length scale for collective pinning 10 ?m
• 104 ?c
• ? finite size effects important

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Coherent Voltage Oscillations ("Narrow-Band
Noise")

• Fundamental
• frequency
• fc vc/?c ? Icdc
• Q fc / ?fc
• up to 30,000

• CDW state evolves periodically as it interacts
  with impurities.
• ? CDW response is largely elastic

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Mode Locking (ac-dc Interference)

• V(t) Vdc Vac cos ?act
• DC Ic-V exhibits Shapiro steps, where internal
  frequency ?c ? Icdc locks to external frequency
  ?ac.
• On a step,
• ?c p/q ?ac,
• p, q integer

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• Memory Effects
• - single-particle resistance hysteresis
• - pulse-sign memory effect
• - pulse-duration memory effect (? SOC)
• Dielectric Properties
• ? 109 (!) at 1 kHz but lossy -(
• 103 at 1 GHz
• Electromechanical Properties
• ?Y/Y ? 1 , ?G/G ? 20 when CDW depins.
• Low-Temperature Properties
• broad distribution of relaxation times, aging
  effects, critical slowing down ?? electronic
  glass?

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Metal-Oxide-CDW FET (MOCFET)(Adelman et al.,
1994)
Channel NbSe3 or TaS3Channel length
100-800 ?mChannel area 10-3 - 1 ?m2Oxide
thickness 550 Å

• Gate voltage modulates channel charge density and
  collective current.

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CDW - CDW Tunneling
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Why are CDWs interesting?

• Physics of electrons in reduced dimensions
• Novel phase transition with pseudogap, large
  fluctuation effects
• Competes with other strongly-correlated ground
  states
• Unconventional density waves
• Novel electronic properties
• Possible applications in high-density memories
• Prototypical system for studying collective
  dynamics in the presence of quenched and thermal
  disorder
• Analogies with vortex lattices, Wigner crystals,
  interface dynamics in porous media, magnets,
  fracture, earthquakes