Chandra Varma wrote a cursory piece Mott Physics, Mixed Valence, Oxygen Valence, in Lithium ion batteries at the Journal Club for the Condensed Matter Physics. He pointed out that these batteries use some materials involving cobaltate [CoO2] layers similar to those in superconducting sodium cobaltate. Furthermore, insights are being gained from ARPES.
But, I struggled to see the way forward for any significant involvement of quantum many-body theorists. The most useful connection was the figure below in the article that Chandra reviews.
I would think that LDA+DMFT calculations would be ideal for addressing whether these cartoon pictures are correct. One question will be the role of Hund's rule coupling.
The Economist had an article about Tesla motors which makes electric cars and is really trying to develop the lithium battery technology further. The company stock capitalisation is now half that of General Motors! But GM sells as many cars in one day as Tesla sells in six months!
Tesla CEO, Elon Musk has a physics background [he dropped out of an applied physics Ph.D at Stanford] and there is an interesting interview with him in APS News.
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