Nature of the many-body excitations in a quantum wire: Theory and experiment
Nature of the many-body excitations in a quantum wire: Theory and experiment
复制标题
量子线中多体激发的本质：理论与实验
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
D. Ritchie
中科院分区：
文献类型：
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作者：
O. Tsyplyatyev;A. Schofield;Y. Jin;M. Moreno;W. K. Tan;A. Anirban;C. Ford;J. Griffiths;I. Farrer;G. Jones;D. Ritchie
低能量相互作用的一维系统的自然激发是卢廷格液体的流体动力学模式，受到线性色散的洛伦兹不变性的保护。我们表明，除了低能量之外，二次色散降低了伽利略的对称性，多体激发的主要特征变成了层次结构：费米子（无自旋）动态相关函数的计算表明，激发的光谱权重与
右
2
/
L
2
， 在哪里
右
是与相互作用相关的长度尺度
L
是系统长度。因此，只有少量的激发在能量动量平面上的代表性区域中携带主要光谱功率。我们详细分析了谱函数，并表明第一级（最强）激发形成具有抛物线色散的模式，就像重整化的单粒子一样。第二级激励对第一级模式产生奇异的幂律线形状，并在光谱边缘产生多个幂律。我们通过计算所有能量尺度的局部态密度（从线性到非线性，再到高于化学势能），说明了低能路廷格液体的交叉。为了测试这个模型，我们进行了实验来测量来自/到 GaAs 异质结构内形成的导线的电子（具有自旋的费米子）的动量分辨隧道效应。我们在低能量下观察到良好解析的自旋电荷分离，具有可观的相互作用强度，并且在较高能量下仅观察到第一级模式的抛物线色散。我们发现了一种类似于二级激发的结构，它在高动量下迅速消失，与这里的理论预测一致。
The natural excitations of an interacting one-dimensional system at low energy are the hydrodynamic modes of a Luttinger liquid, protected by the Lorentz invariance of the linear dispersion. We show that beyond low energies, where the quadratic dispersion reduces the symmetry to Galilean, the main character of the many-body excitations changes into a hierarchy: calculations of dynamic correlation functions for fermions (without spin) show that the spectral weights of the excitations are proportional to powers of
R
2
/
L
2
, where
R
is a length-scale related to interactions and
L
is the system length. Thus only small numbers of excitations carry the principal spectral power in representative regions on the energy-momentum planes. We have analyzed the spectral function in detail and have shown that the first-level (strongest) excitations form a mode with parabolic dispersion, like that of a renormalized single particle. The second-level excitations produce a singular power-law line shape to the first-level mode and multiple power laws at the spectral edge. We have illustrated a crossover to a Luttinger liquid at low energy by calculating the local density of states through all energy scales: from linear to nonlinear, and to above the chemical potential energies. In order to test this model, we have carried out experiments to measure the momentum-resolved tunneling of electrons (fermions with spin) from/to a wire formed within a GaAs heterostructure. We observe a well-resolved spin-charge separation at low energy with appreciable interaction strength and only a parabolic dispersion of the first-level mode at higher energies. We find a structure resembling the second-level excitations, which dies away rapidly at high momentum in line with the theoretical predictions here.