Physics 361 Problem Set 6 due November 18, 2009 P6.1 Peierls instability http://www.pas.rochester.edu/ ∼ stte/phy521S08/hw4.html The weak interactions between electrons and ions can make a spontaneous symmetry breaking in otherwise simple lattice of identical atoms such as the one in the top ﬁgure above. If the atoms interact via a smooth potential, the distortion shown in the bottom picture (like any other lattice distortion) costs an energy E L proportional to δx 2 . Such a distortion also aﬀects the electrons. Rudolf Peierls (http://en.wikipedia.org/wiki/Rudolf Peierls) noticed that if there is a single nearly-free electron per atom, the distortion above decreases the electron energy by an amount proportional to δx p , where the exponent p ≤ 2. This means that the total energy can be lowered by increasing the distortion from zero, so that the distortion can happen spontaneously. This “Peierls distortion” is seen in certain real three-dimesional solids. a) When
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This note was uploaded on 03/02/2010 for the course PHYSICS 336 taught by Professor Pucker during the Spring '10 term at King's College London.