- #1
Yiping
- 7
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In one dimensional electron gas in charge density wave phase, as I know , the density of electrons will be periodic. The order parameter of charge density wave is written as
[tex]O_{CDW}(x)=\sum_s\psi_{L,s}^{\dagger}(x)\psi_{R,s}(x)[/tex]
For Luttinger model, the \psi is the Fermion annihilation field operator.
I am not very familiar with Luttinger liquid, I try to understand why the order parameter of CDW would be written in this form. If I try to construct an order parameter for CDW by myself, I would guess the Fourier transform of electron density will be a feature for CDW, but I don't know the periodicity of the CDW. If the order parameter is correct, for CDW with any periodicity, I should find that <O_{CDW}>=1. I am not able to construct such order parameter by myself.
I can't understand why the order parameter will be the summation of
[tex]\psi_{L,s}^{\dagger}(x)\psi_{R,s}(x)[/tex]
, it seems odd for me. Creating a right-moving electron and destroy a left-moving electron?
[tex]O_{CDW}(x)=\sum_s\psi_{L,s}^{\dagger}(x)\psi_{R,s}(x)[/tex]
For Luttinger model, the \psi is the Fermion annihilation field operator.
I am not very familiar with Luttinger liquid, I try to understand why the order parameter of CDW would be written in this form. If I try to construct an order parameter for CDW by myself, I would guess the Fourier transform of electron density will be a feature for CDW, but I don't know the periodicity of the CDW. If the order parameter is correct, for CDW with any periodicity, I should find that <O_{CDW}>=1. I am not able to construct such order parameter by myself.
I can't understand why the order parameter will be the summation of
[tex]\psi_{L,s}^{\dagger}(x)\psi_{R,s}(x)[/tex]
, it seems odd for me. Creating a right-moving electron and destroy a left-moving electron?