半满朗道能级上的费米液体有波梅兰丘克不稳定性吗？
Does a Fermi liquid on a half-filled Landau level have Pomeranchuk instabilities?
摘要：
本文提出了半填充朗道能级的费米面自发形变理论（填充因子形式为$ν=2n+1/2$）。我们假设半满的水平是在一个可压缩的，费米液体状态与圆形费米表面。朗道能级投影通过修改的有效电子-电子相互作用被合并，并且在Hartree-Fock近似内描述所得到的能带结构。我们在理论中调节了红外发散，并探测了费米面通过Pomeranchuk不稳定性变形的内在趋势。我们发现，相应的磁化率从来没有发散，虽然系统是渐近不稳定的$n \to \infty$限制。
英文摘要：
We present a theory of spontaneous Fermi surface deformations for half-filled Landau levels (filling factors of the form $ν=2n+1/2$). We assume the half-filled level to be in a compressible, Fermi liquid state with a circular Fermi surface. The Landau level projection is incorporated via a modified effective electron-electron interaction and the resulting band structure is described within the Hartree-Fock approximation. We regulate the infrared divergences in the theory and probe the intrinsic tendency of the Fermi surface to deform through Pomeranchuk instabilities. We find that the corresponding susceptibility never diverges, though the system is asymptotically unstable in the $n \to \infty$ limit.
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