CHARGE DENSITY WAVES AND DETECTION TECHNIQUES

CHARGE DENSITY WAVES

AND DETECTION TECHNIQUES

Charles Mielke

Condensed Matter Physics (PHY401) Prof. Dr. Johan Chang

20 October, 2020

Competition Between CDW & SC

• Charge Density Waves (CDW’s) and superconductivity compete in YBa ₂ Cu ₃ O _6.67 (hole-doped, p=0.123)

• As a function of applied magnetic field

• As a function of hole-doping

• As a function of pressure

From H. Kim, Science 362 (2018)

But… How did they detect it?

• Hard X-ray scattering & tracking diffuse scattering

• Hard X-ray: refers to the energy regime of the beam

• Diffuse Scattering: best understood when compared to diffraction

• How to detect Charge Density Wave

From https://en.wikipedia.org/wiki/X-ray

Hard X-rays

• These beams are produced at synchrotrons or X-FEL (X- Ray Free Electron Laser)

• Accelerate electrons (LINAC)

• Focus them into small packets/a beam

• Accelerate (bend) them – release photons, in the X-ray regime

• Energy can be tuned

From P. Glatzel, MaMaSELF

Summer School Presentation

Single Crystal Diffraction

• Have a regularly repeating structure

• Incident photons interact with the electron clouds

• Can be scattered elastically or inelastically

(a) Quasicrystal (from en.wiktionary.org/wiki/quasicrystal) and

(b) (b) single crystals of pyrite, FeS

(from en.wikipedia.org/pyrite)

a b

Scattering

• Scattering vector q

• If incoming photons all have same k ₀ and are scattered in the same direction, then they can constructively interfere

• 2D structure, like a diffraction grating – get pattern of spots and dark areas

From Prof. F. Cámara,

Univ. Torino, 2. Elastic

Scattering

Diffraction Patterns

• When Bragg condition satisfied, crystal diffracts d sin(θ) = n λ

• Can determine structure from refinement of pattern

(a) Single crystal and (b) twinned crystal

a b

Charge Density Waves

• Periodic modulations in the density of charge, ie.

electron density.

• Normally have a periodic electron density, around atoms. Sometimes can move collectively

From J. Chang, Nature Physics 8 (2012)

Detecting Charge Density Waves

• Can also contribute to scattering

• Commensurate or incommensurate with the underlying structure

• Because they are a periodic charge density, can be detected by X-ray diffraction

• Also by neutron diffraction (because also associated with periodic

displacement in atomic positions [J. Chang 2012]), but the diffuse

scattering from CDW is ~10 million times less intense than Bragg

diffraction, only synchrotrons have high enough flux to be sensitive

Back to the studies: J. Chang, 2016

• Magnetic field to suppress SC

• At different temperatures

• Along different axes

• Identification of 3D CDW structure

appearing at B~15T [Chang 2016]

From J. Chang, Nature Comm. (2016)

Application of Pressure: Kim, 2018

• Similar effect to application of magnetic field, but more

intense

• Leads to stable long-range 3D CDW’s under application of modest strain

• 3D CDW forms even as the 2D mode strengthens – not at the cost of it

• 3D CDW forms even above T _c – so cannot be solely from

competition with SC

From H. Kim, Science 362 (2018)

Interplay between CDW & SC

• Complex interaction, many theories proposed –

• Mutually incompatible?

• Different manifestations of same pairing interaction?

• Different aspects of composite order parameter? [H. Kim 2018]

Thanks so much!!

• Questions?

From psi.ch/en

Strain as a Control Parameter

• Dependence with

strain application and temperature

From Kim, Science 362 (2018)