Solid State Physics Lecture Notes, Lecture notes of Solid State Physics

Download Solid State Physics Lecture Notes and more Lecture notes Solid State Physics in PDF only on Docsity!

PHYS 545 Solid State Physics

Lecture 13

Spring 2017, Purdue University

Prof. Yong P. Chen

Phonon Density of States; Van Hove Singularities; Scattering & Diffraction

1

ZM Chap. 2

Debye model : acoustic phonons

High T limit:

(limit to acoustic phonon, so n=1)

Low T limit:

Debye wavenumber

(Debye sphere)

Wigner-Seitz radius

when velocity (slope) v q

“critical point” or van Hove “singularities” (VHS)

[sth diverges… D(v) or its derivative..]

Van Hove Theorem

“topological features in the bands”

VHS at:

(all ’s negative)

(band) (band)

(all ’s positive)

(2 ’s negative, one positive – “saddle point”)

(3D)

(2D)

Topological Objects in Condensed Matter

=532nm

R.He & T-F. Chung/QMD et al., Nano Lett’

(cf also Zettl’12;Park’12..)

L. Van Hove

Phys. Rev. 1953

Fermi Surface

zeolites/MOF/

porous/polymers.. Vortex (fluids, superfluids & superconductors) (^) Magnetic skrmions

Real-space

k-space (^) Van Hove singularity

cf. topological classification by

Zhao & Wang PRL’

MRS-Bulletin’

g is reciprocal lattice vector

Quantum Theory of Diffraction

Different types of diffractions (beams)

see different kinds of potential V

(sensitive to different information/order)

• Neutrons
• Spin-polarized neutrons
• Electrons
• Light (X-rays)..

(neutron scattering, measure [besides phonons] magnetic order, magnons…)