LOCAL HINDSIGHTS1956-8 summers @ Bell Labs: “everyone” was thereCM Theory exploding in all directions--one was transportI] Mult Scatt: Lax, Brueckner,…(sweeping dirt under the rug)II]Classic Boltzmann: Kohn-Luttinger PR108 (1957): 50pp, 10 appendices. The last Boltzmann treatment ?: then came Kubo.--but also-- iii] PWA cisport(name by LRW) the least of these Motivation: G Feher and ENDOR

ENDOR (the witch of)(Electron-Nuclear Double Resonance) slidesP R103, 500(1956) TO FIND NEW MATH, STUDY EXPERIMENT!Existing Theory: spin diffusion, Bloembergen (nuclear); Portis(electron); impurity band(Bardeen etc); Golden rule :

€

1/τ = Jij2 N(ω)

For electron exchange, for instance.

In every case, fails by many orders of magnitude: at low concentration, all spins are local, electrons, P and 29Si nuclei. (Ack

EA, DP)

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schematic of P donors in Si with 5%Si29 (S=1/2)

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EPR spectra as function of donor concentration

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Dig a “hole” at one field and study EPR as function of a low(NMR) frequency: each Si29retains its own frequency.

Good description of the situation in a surprising place: Can J Phys, 34, 1367, 1956: a discussion remark by D Pines on Mott’s famous paper on the Mott Transition! (A lesson in reading original sources). David discusses our puzzlement but properly does not mention my still speculative thoughts on localization.

Why do the frequencies remain stable for minutes if the electrons are hopping around according to Golden Rule!

What I’m going to do? Plagiarize! (“Lobachevsky”, via T Lehrer)Learn diagrams, self-energy sums from Dyson, Feynman via P Wolff; (turn them backwards--propagatorlocator); learn about stat. of non-repeating paths from Hammersley via c Herring, who reads everything, (and the idea of critical conc--H’s percolation, just invented); and I can use sums on singular distributions, self-plagiarized from own line-shape work, going back to Russian school (Markov, Kolmogorov?)

So voila! “proof” that localized regimeBut of course not rigorous for any real system because of interactions. The system I study is strictly linear. The great advantage of experiment--I was sure it was true, anyhow! Never had a moment’s doubt.

20 years interlude to beginto convince the “young fogies”What happened while I wasn’t looking?Mostly Mott: tied loc to conductivity theory: Ioffe-Regel 1960 said l< impossibleMott ‘61: minimum metallic conductivity (e2/h)kF

-1

(observed 1914 by WFG Swann!! on Bi films)Note QUANTUM UNIT “von Klitzing”=e2/h

2 other suitable names: Landauer, conductance of transmitting channel (of great importance to modern theory); Thouless, crit conductance of 2D metal.1978 “Ill-condensed Matter” Les Houches summer school

1979: Localization redux!

Ramakrishnan, visiting prof; Elihu Abrahams; Asst Prof Don Licciardello from team of L & Thouless; and PWA: Gang of IV! Idea suggested by L&T: one-parameter scaling of

g=conductance in units of e2/h

vs size L: =d(lng)/dlnL

Second idea (Rama and El): first correction in 1/g from crossed diagrams (that came from old Langer paper--plagiarize again!)

The era of weak localization!

PRL42, 633

dec ‘78

PRL42, 633

dec ‘78

Experiment rears its head againGerry Dolan and Doug Osheroff were trying to makethin films into 1D wires to test Thouless’ predictions about 1D.

But their I vs V curves were never quite straight(trust DDO to always sight along a “straight” line)

lnL elastic and LTpVp’

PRL 43, 714 and 718 (apr 79) GIII=Abrahams, Rama and PWA.And then the floodgates were open. The field theorists could play to their hearts’ content.

“Well, In my country,” said alice, still panting a little, “you would generally get to somehere else, if you ran very fast for a long time, as we’ve been doing”. “A slow sort of country!”, said the queen. “Now here, it takes all the running you can do, to stay in the same

place.”