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DTSTAMP:20261019T213739Z
LAST-MODIFIED:20210402T172254Z
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URL:http://physics.bu.edu/internal/events/show/2425
SUMMARY:POINT SINGULARITIES IN TWO AND THREE DIMENSIONAL BANDS
DESCRIPTION:Featuring Anirudh Chandrasekaran\, Boston University\, Physics 
	Department\n\nPart of the PhD Final Oral Exams.\n\nAlthough band theory is 
	about a century old\, it remains relevant today as a tool for the treatment
	 of electrons in solids. The confluence of mathematical ideas like geometry
	 and topology with band theory has proven to be a ripe avenue for research 
	in the past few decades. The importance of Fermi surface geometry\, especia
	lly in con- junction with electronic correlation\, has been well recognized
	. One particular thread in this direction is probing the occurrence of non-
	trivial Fermi surface geometry\, and its influence on macroscopic propertie
	s of materials.  A notable example of exotic Fermi surface geometry arises 
	from singular points of the dispersion\, and these have been known since 19
	53. The investigation into these was reignited recently\, culminating in th
	e work presented in this thesis. In this dissertation\, I investigate two b
	road categories of singular points in bands. At a singular point\, either t
	he dispersion or the Fermi surface fail to be smooth. This may cause distin
	ct signatures in transport and spectroscopic properties when the singular p
	oint occurs close to the Fermi level. In the two dimensional setting\, I cl
	assify using catastrophe theory\, the point singularities arising from high
	er order saddles of the dispersion.  These are the more exclusive cousins o
	f the regular van Hove saddle that cause\, among other things\, a power law
	 divergence in the density of states. The role of lattice symmetries in aid
	ing or pre- venting the occurrence of these singularities is also carefully
	 explored. In the case of three dimensional bands\, I investigate the spect
	roscopic properties of the nodal point singularity\, arising from a linear 
	band crossing. In particular\, I determine the distinct signature of nodal 
	points in the analytic\, momentum resolved\, joint density of states (JDOS)
	 and the numerically calculated resonant inelastic x-ray scattering (RIXS) 
	spectrum\, within the fast collision approximation that ignores core hole e
	ffects. The results presented here will be the stepping stone towards a car
	eful future calculation\, incorporating the potential edge singularity effe
	cts through core hole potential. Such a calculation may be directly compara
	ble with ongoing experiments.
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STATUS:CONFIRMED
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