Friday, 15 August 2014

quantum mechanics - Collective modes of charge density wave


The question is about collective modes of charge density waves, i.e., amplitude and phase fluctuations δ,ϕ of the order parameter Δ(x,t)=(Δ0+δ)eiϕ.


I read on p.1 of this paper that amplitude mode and phason mode can be expressed using the phonon normal coordinate Qq±2kF respectively as (2kF is the density wave vector) 12(Qq+2kF±Qq2kF).

But how to obtain this result? It's not quite obvious to me.


I also found in another review paper (p. 1135, eq(3.1)) the following. To the lowest order in the fluctuations δ,ϕ, the amplitude mode corresponds to Δ2kF+Δ2kF=2Δ0+2δ and the phason mode corresponds to Δ2kFΔ2kF=2Δ0Δϕ. But I don't find a clear definition of Δ2kF in the paper. Still it's not clear how this is obtained.




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