Collective modes near a Pomeranchuk instability in two dimensions
Collective modes near a Pomeranchuk instability in two dimensions
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DOI：
10.1103/physrevresearch.1.033134
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发表时间：
2019-08
影响因子：
4.2
通讯作者：
A. Klein;D. Maslov;L. Pitaevskiĭ;A. Chubukov
中科院分区：
文献类型：
--
作者：
A. Klein;D. Maslov;L. Pitaevskiĭ;A. Chubukov
我们考虑费米液体的集体激发。对于角动量的每一个值，我们研究了具有朗道参数的电荷(C)和自旋(S)通道中纵向和横向集体模的演化，从正的{F_L^{c(S)}}开始，一直到{F_L^{c(S)}=-1的波美兰丘克跃迁。在每种情况下，我们都确定了一个临界零声模，它的速度在波美兰丘克不稳定性时为零。对于$F_L^{c(S)}<；-1$，该模位于基态不稳定的上频半平面。在干净的费米液体中，临界模可以是纯弛豫的，也可以是几乎传播的，这取决于L的宇称和响应函数是纵向的还是横向的。这些差异导致在初始微扰后序参数的不同类型的时间演化。对于与自旋电流或电荷电流重合的$L=1$序参数，出现了一种特殊情况。在这种情况下，临界模的残余在波美兰丘克相变时消失了。然而，临界模可以在距相变任意距离处被识别，并且仍然位于$F_1^{c(S)}<；-1$的高频半平面内。电荷/自旋电流有序参数的唯一特点是它的时间演化比其他有序参数在更长的尺度上发生。我们还分析了远离临界点的集体模，发现在多层黎曼曲面上，模随着{F_L^{c(S)}}$而演化。对于$F_L^{c(S)}$的特定间隔，模或者移动到非物理黎曼片上，或者停留在物理片上，但远离实频率轴。在这种情况下，模式不会在相应敏感度的虚部产生峰值。
We consider collective excitations of a Fermi liquid. For each value of the angular momentum $l$, we study the evolution of longitudinal and transverse collective modes in the charge (c) and spin (s) channels with the Landau parameter $F_l^{c(s)}$, starting from positive $F_l^{c(s)}$ and all the way to the Pomeranchuk transition at $F_l^{c(s)} = -1$. In each case, we identify a critical zero-sound mode, whose velocity vanishes at the Pomeranchuk instability. For $F_l^{c(s)} < -1$, this mode is located in the upper frequency half-plane, which signals an instability of the ground state. In a clean Fermi liquid the critical mode may be either purely relaxational or almost propagating, depending on the parity of $l$ and on whether the response function is longitudinal or transverse. These differences lead to qualitatively different types of time evolution of the order parameter following an initial perturbation. A special situation occurs for the $l = 1$ order parameter that coincides with the spin or charge current. In this case the residue of the critical mode vanishes at the Pomeranchuk transition. However, the critical mode can be identified at any distance from the transition, and is still located in the upper frequency half-plane for $F_1^{c(s)} < -1$. The only peculiarity of the charge/spin current order parameter is that its time evolution occurs on longer scales than for other order parameters. We also analyze collective modes away from the critical point, and find that the modes evolve with $F_l^{c(s)}$ on a multi-sheet Riemann surface. For certain intervals of $F_l^{c(s)}$, the modes either move to an unphysical Riemann sheet or stay on the physical sheet but away from the real frequency axis. In that case, the modes do not give rise to peaks in the imaginary parts of the corresponding susceptiblities.