arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1111.2592cond-mat.supr-con
收藏

涡旋态准粒子半Dirac节标度性质

Pnictide Half-Dirac Nodal Quasiparticle Scaling Properties in Vortex State

Imam Makhfudz

摘要:

本文研究了具有“半狄拉克”节点的磷族元素化物准粒子在磁场作用下涡旋态的标度性质。通过计算态密度,我们的目标是在涡旋态中找到最近几个工作在非涡旋态中预测的非Simon-Lee标度的形式。通过对Bogoliubov-de Genne哈密顿量的精确对角化和有限尺寸标度,我们发现在没有磁场的情况下,一个$N(E)\sim \sqrt{E}$幂律与分析预测一致。我们首先研究了无涡旋的均匀磁场的假设情况,然后通过用超流速度和Berry规范场表示BdG哈密顿量来适当地处理磁场诱导的涡旋晶格。这两种计算结果是一致的。定量分析了各向异性色散对涡旋晶格标度性质的影响,并从非涡旋态的尺度分析中发现,涡旋晶格间距将标度为$d'_y\sim s^{-η}d'_x $,其中$1/2\leq η\leq1$和$s\sim H^2/3$与$η=1/2$相比.一个非常重要的预测也作出了上限值的“异常尺寸”$δ$的状态密度与磁场的标度,我们发现是$δ\leq1/2$,一个数量,不能确定由以前的纯分析工作和数量,可以通过实验测量。

英文摘要:

In this work we investigate the scaling properties of quasiparticles of Pnictide with "half-Dirac" node under magnetic field in vortex state. By computing the density of states, we aim to find in vortex state the form of non-Simon-Lee scaling predicted for such system by several recent works in non-vortex state. We find by exact diagonalization of the Bogoliubov-de Genne Hamiltonian and finite size scaling a $N(E)\sim \sqrt{E}$ power law in the case without magnetic field which agrees with analytical prediction. We consider the vortex state by first studying the hypothetical situation of uniform magnetic field without vortices and then we properly treat the magnetic field-induced vortex lattice by expressing the BdG Hamiltonian in terms of superfluid velocity and Berry's gauge fields. The two calculations are shown to agree with each other. We then analyze quantitatively, the effects of anisotropic dispersion to the scaling properties of vortex lattice and show that the vortex lattice spacings will scale as $d'_y\sim s^{-η}d'_x $ where $1/2\leq η\leq1$ and $s\sim H^2/3$ as compared to $η=1/2$ from dimensional scaling analysis of non-vortex state. A very crucial prediction is also made on an upper bound to the value of 'anomalous dimension' $δ$ of density of states scaling with magnetic field which we find to be $δ\leq1/2$, a quantity that could not be determined conclusively by previous purely analytical works and a quantity that can be measured experimentally.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑