论文标题
在两个sublattices存在下，BCS超流体的集体激发
Collective excitations of a BCS superfluid in the presence of two sublattices
论文作者
论文摘要
我们考虑一种通用的哈密顿量，适用于以两点为基础的晶格描述均匀的BCS超流体，并在零温度下研究其集体激发。为此，我们首先为配对波动提供了有效的高斯动作，然后为相位内戈德石和不相同的Leggett模式提取低能分散关系，以及相应的振幅（即所谓的Higgs）。我们发现，虽然金石模式在零动量下是无处不在的，并且一般而言传播，但leggett模式只有通过足够强的相互作用而无法阻止。此外，我们表明，除了由Bloch带的能量控制的常规贡献外，Goldstone Mode的速度还具有几何贡献，该几何贡献受Bloch状态的量子度量张量的控制。我们的结果表明，当前者对狭窄或平坦的频段变得可忽略时，后者的贡献主导了速度。
We consider a generic Hamiltonian that is suitable for describing a uniform BCS superfluid on a lattice with a two-point basis, and study its collective excitations at zero temperature. For this purpose, we first derive an effective-Gaussian action for the pairing fluctuations, and then extract the low-energy dispersion relations for the in-phase Goldstone and out-of-phase Leggett modes along with the corresponding amplitude (i.e., the so-called Higgs) ones. We find that while the Goldstone mode is gapless at zero momentum and propagating in general, the Leggett mode becomes undamped only with sufficiently strong interactions. Furthermore, we show that, in addition to the conventional contribution that is controlled by the energy of the Bloch bands, the velocity of the Goldstone mode has a geometric contribution that is governed by the quantum metric tensor of the Bloch states. Our results suggest that the latter contribution dominates the velocity when the former one becomes negligible for a narrow- or a flat-band.
