For electrons confined to two dimensions at Landau level filling ν = 2, the relative strength of the interaction is conventionally measured through the parameter rs which is the inter-particle distance measured in units of the Bohr radius aB ≡ ¯h2/me2, m is the band mass of electrons.
rs=(πρ)-1/2/aB
where ρ is the two-dimensional density of electrons.
The interaction strength is enhanced relative to the kinetic energy as the system becomes more dilute, i.e., as rs increases. It has been predicted that as rs is increased, the electron liquid eventually becomes spontaneously spin polarized with a gain in the exchange energy, ultimately becoming a Wigner crystal at rs≈ 37.
Now, my question is how can we vary the density parameter rs theoretically for ν = 2 IQHE state?
I have attached the related paper in which it was done, but I could not find my answer. Please, help me out.
As stated, rs depends only on the density-so to vary it means to vary the density; nothing more and nothing less.
Not like that Sir (Stam Nicolis), as here Landau level filling ν = 2 so, density is fixed. Density cannot be varied.
The filling fraction is distinct from the density, that's all. It's the assumption that the density is fixed, that's not valid. More precisely, the density of states is not the same as the charge density.
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