AI 中文总结
研究通过掺杂分数陈绝缘体获得金属相和超导相的统一框架，基于部分子构造，探讨色反对称配对、希格斯场等产生的超导和金属相情况，还讨论了化学势调谐转变及所需费米子。
AI 中文摘要
我们为通过掺杂具有陈数\(C = 1/3\)的分数陈绝缘体（FCI）而得到的金属相和超导相建立了一个统一框架。从部分子构造\(c(\mathbf r)=f_1(\mathbf r)f_2(\mathbf r)f_3(\mathbf r)\)出发，低能理论具有\(SU(3)_{\mathrm{gauge}}\times SU(3)_{\mathrm{valley}}\)对称性，并且由电荷为\(-e/3\)的空穴子\(\psi_{ab}\)形成九个费米面口袋，其中\(a\)和\(b\)标记颜色和能谷。将空穴子视为夸克，可将此问题与高能物理中的色超导联系起来。色反对称配对产生一类角动量\(L = 3n\)且手征中心荷\(c_- = m/2\)（\(m\)为奇数）的电荷\(2e\)超导体。因此，电荷为\(-e/3\)的任意子气体可直接进入超导相而无需束缚。粒子 - 空穴色 - 能谷希格斯场产生两个具有一个或三个口袋的\(Z_3\)正交金属，分别作为\(SU(3)_{\mathrm{valley}}\)的单重态或三重态变换。具有三个相同口袋的\(U(1)^2\)空穴子金属可保持三角晶格空间群，同时将出现的能谷对称性降低到\(S_3\)。其配对不稳定性包括一个带隙的电荷\(2e\) \(f - if\)超导体和一个无带隙的电荷\(2e\)正交超导体，其\(\langle cc\rangle = 0\)且在\(\Gamma\)处有一个博戈留波夫费米面。最后，我们讨论了从FCI到超导的化学势调谐转变的可能性，并认为如果转变保持完整的出现的\(SU(3)_v\)对称性，则可能需要所有九个费米子。
英文摘要
We develop a unified framework for metallic and superconducting phases obtained by doping a fractional Chern insulator (FCI) with $C=1/3$. Starting from the parton construction $c(\mathbf r)=f_1(\mathbf r)f_2(\mathbf r)f_3(\mathbf r)$, the low-energy theory has $SU(3)_{\mathrm{gauge}}\times SU(3)_{\mathrm{valley}}$ symmetry and nine Fermi pockets formed by charge-$-e/3$ holons $ψ_{ab}$, where $a$ and $b$ label color and valley. Viewing the holons as quarks connects this problem to color superconductivity in high-energy physics. Color-antisymmetric pairing produces a class of charge-$2e$ superconductors with angular momentum $L=3n$ and chiral central charge $c_-=m/2$, where $m$ is odd. Thus a gas of charge-$e/3$ anyons can enter a superconducting phase directly without binding. Particle--hole color--valley Higgs fields instead produce two $Z_3$ orthogonal metals with one or three pockets, transforming respectively as a singlet or triplet of $SU(3)_{\mathrm{valley}}$. A $U(1)^2$ holon metal with three identical pockets can preserve the triangular-lattice space group while reducing the emergent valley symmetry down to $S_3$. Its pairing instabilities include a gapped charge $2e$ $f-if$ superconductor and a gapless charge-$2e$ orthogonal superconductor with $\langle cc\rangle=0$ and a Bogoliubov Fermi surface at $Γ$. Finally, we discuss the possibility of a chemical-potential-tuned transition from the FCI to superconductivity and argue that all nine fermions may be required if the transition preserves the full emergent $SU(3)_v$ symmetry.
Comments5+7 pages
