非完全自旋极化复合费米海的费米波矢
Fermi wave vector for the non-fully spin polarized composite-fermion Fermi sea
摘要：
在半满朗道最低能级处的完全自旋极化复合费米子（CF）费米海具有一个费米波矢$k^*_{\rm F}=\sqrt{4πρ_e}$，其中$ρ_e$是电子或复合费米子的密度，支持复合费米子之间的相互作用可以微扰处理的观点.远离$ν=1/2$，对于$ν<1/2$，该区域被认为与$k^*_{\rm F}=\sqrt{4πρ_e}$一致，但是对于$ν>1/2$，该区域被认为与$k^*_{\rm F}=\sqrt{4πρ_h}$一致，其中$ρ_h$是最低朗道能级中的空穴密度。这一结果与最低朗道能级的粒子-空穴对称性一致。本文研究了自旋单重态CF费米海（CFFS）在$ν=1/2$的费米波矢，其中不考虑粒子-空穴对称性。利用微观CF理论，我们发现对于自旋单重态CFFS，上下自旋CFFS在$ν=1/2$的费米波矢与$k^{*\uparrow,\downarrow}_{\rm F}=\sqrt{4πρ^{\uparrow,\downarrow}_e}$一致，其中$ρ^{\uparrow}_e=ρ^{\downarrow}_e=ρ_e/2$，这意味着复合费米子之间的剩余相互作用对非完全自旋极化CFFS也不会引起非微扰修正.我们的结果支持了这样一个自然的猜想：对于任意自旋极化，CF费米波矢由$k^{*\uparrow}_{\rm F}=\sqrt{4πρ^{\uparrow}_e}$和$k^{*\downarrow}_{\rm F}=\sqrt{4πρ^{\downarrow}_e}$给出。
英文摘要：
The fully spin polarized composite fermion (CF) Fermi sea at half filled lowest Landau level has a Fermi wave vector $k^*_{\rm F}=\sqrt{4πρ_e}$, where $ρ_e$ is the density of electrons or composite fermions, supporting the notion that the interaction between composite fermions can be treated perturbatively. Away from $ν=1/2$, the area is seen to be consistent with $k^*_{\rm F}=\sqrt{4πρ_e}$ for $ν<1/2$ but $k^*_{\rm F}=\sqrt{4πρ_h}$ for $ν>1/2$, where $ρ_h$ is the density of holes in the lowest Landau level. This result is consistent with particle-hole symmetry in the lowest Landau level. We investigate in this article the Fermi wave vector of the spin-singlet CF Fermi sea (CFFS) at $ν=1/2$, for which particle-hole symmetry is not a consideration. Using the microscopic CF theory, we find that for the spin-singlet CFFS the Fermi wave vectors for up and down spin CFFSs at $ν=1/2$ are consistent with $k^{*\uparrow,\downarrow}_{\rm F}=\sqrt{4πρ^{\uparrow,\downarrow}_e}$, where $ρ^{\uparrow}_e=ρ^{\downarrow}_e=ρ_e/2$, which implies that the residual interactions between composite fermions do not cause a non-perturbative correction for non-fully spin polarized CFFS either. Our results suggest the natural conjecture that for arbitrary spin polarization the CF Fermi wave vectors are given by $k^{*\uparrow}_{\rm F}=\sqrt{4πρ^{\uparrow}_e}$ and $k^{*\downarrow}_{\rm F}=\sqrt{4πρ^{\downarrow}_e}$.
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