论文标题
Luttinger液体中状态的隧道密度与超导体接近：非本地相互作用的影响
Tunneling density of states in Luttinger Liquid in proximity to a superconductor: Effect of non-local interaction
论文作者
论文摘要
最近的一项研究表明，与预期的抑制相比，在Luttinger液体（LL）中的隧道密度（TDOS）中，可能具有增强功能，该隧道密度仅由非局部密度相互作用驱动。同样，众所周知，靠近超导体（SC）的LL显示出零能量极限的连接附近TDOS的增强。在本文中，我们研究了SC-LL结附近TDO中的非局部密度密度相互作用和超导相关性的相互作用，在此，LL可能在整数或分数量子霍尔状态的边缘实现。我们表明，由于连接处的超导相关性，可以在适当选择非局部相互作用参数的情况下扩大了LL量子线（QW）中的TDOS增强，这可以通过弱相互作用限制中的巧妙代数表达来证明。我们还表明，在包含局部和非本地相互作用的完整参数状态下，通过“超导”边界条件和“无渗透率保存”边界条件的LL连接的增强型TDO区域（在Phys。B104，045402（20221）中进行了互斥。我们表明，这一事实可以从理论的超导和非责任领域之间建立的对称关系来理解。我们比较接近诱导的对电势和TDOS的依赖性是与交界处的距离$ x $的函数。 We demonstrate that the dependence of the spatial power law exponent for the `TDOS(x)/TDOS(x -> 0)' and the `pair-potential(x)/pair-potential(x -> 0)' are distinct function of the various local and non-local interaction parameters, which implies that the TDOS enhancement can not be directly attributed to the proximity induced pair potential in the LL.
A recent study have shown that it is possible to have enhancement, in contrast to an expected suppression, in tunneling density of states (TDOS) in a Luttinger liquid (LL) which is solely driven by the non-local density-density interactions. Also, it is well known that a LL in proximity to a superconductor (SC) shows enhancement in TDOS in the vicinity of the junction in the zero energy limit. In this paper, we study the interplay of nonlocal density-density interaction and superconducting correlations in the TDOS in the vicinity of the SC-LL junction, where the LL maybe realized on the edge of an integer or a fractional quantum Hall state. We show that the TDOS enhancement in a LL quantum wire (QW) due to superconducting correlation at the junction can be farther amplified in presence of appropriate choice of non-local interaction parameters, which is demonstrated through a neat algebraic expression in the weak interaction limit. We also show that, in the full parameter regime comprising both the local and the non-local interaction, the region of enhanced TDOS for LL junction with "superconducting" boundary condition and that of "non-superconducting charge conserving" boundary condition (discussed in Phys. Rev. B 104, 045402 (2021)) are mutually exclusive. We show that this fact can be understood in terms of symmetry relation established between the superconducting and non-superconducting sectors of the theory. We compare the dependence of the proximity induced pair potential and TDOS as a function of distance $x$ from the junction. We demonstrate that the dependence of the spatial power law exponent for the `TDOS(x)/TDOS(x -> 0)' and the `pair-potential(x)/pair-potential(x -> 0)' are distinct function of the various local and non-local interaction parameters, which implies that the TDOS enhancement can not be directly attributed to the proximity induced pair potential in the LL.
