Density functional theory methods are applied to investigate the properties of the new superconductor $β$-YbAlB$_4$ and its polymorph $α$-YbAlB$_4$. We utilize the generalized gradient approximation + Hubbard U (GGA+U) approach with spin-orbit(SO) coupling to approximate the effects of the strong correlations due to the open $4f$ shell of Yb. We examine closely the differences in crystal bonding and symmetry of $β$-YbAlB$_4$ and $α$-YbAlB$_4$. The in-plane bonding structure amongst the dominant itinerant electrons in the boron sheets is shown to differ significantly. Our calculations indicate that, in both polymorphs, the localized 4$f$ electrons hybridize strongly with the conduction sea when compared to the related materials YbRh$_{2}$Si$_{2}$ and YbB$_{2}$. Comparing $β$-YbAlB$_4$ to the electronic structure of related crystal structures indicates a key role of the 7-member boron coordination of the Yb ion in $β$-YbAlB$_4$ in producing its enhanced Kondo scale and superconductivity. The Kondo scale is shown to depend strongly on the angle between the B neighbors and the Yb ion, relative to the $x-y$ plane, which relates some of the physical behavior to structural characteristics.
在Yb基周期晶体如YbRh $_2$ Si $_2$和$β$ -YbAlB $_4$中观察到的非常规量子临界现象一直是强关联电子系统的中心问题之一。在准晶体Yb $_{15}$ Au $_{51}$ Al $_{34}$中发现了共同的临界性，其在至少高达$P=1.5$ GPa的压力下令人惊讶地持续存在。在准晶体中发现了$T/H$标度，其中磁化率可以表示为温度$T$与磁场$H$之比的单一标度函数，这与在$β$ -YbAlB $_4$中观察到的标度基本相同.最近，在压力下，甚至在近似晶体Yb $_{14}$ Au $_{51}$ Al $_{35}$中也观察到了$T/H$标度以及共临界性。Yb的临界价涨落理论对这些引人注目的现象给出了统一的自然解释。
Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院理论固体物理研究所）；Institute for Quantum Materials and Technology, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）
Multiple lattice instabilities resolved by magnetic-field and disorder sensitivities in cubic paramagnetic phase of the orbital-degenerate frustrated spinel MgV$_2$O$_4$
超声波速度测量的轨道简并沮丧尖晶石MgV $_2$ O $_4$中进行的高纯度的单晶，表现出连续的结构和反铁磁相变，并在无序引入的单晶，表现出自旋玻璃样的行为。测量结果表明，两种类型的不寻常的温度依赖性的弹性模量共存的立方顺磁相，这是解决了磁场和无序的敏感性：巨大的居里型软化与温度降低，和凹的温度依赖性的特征最小值。这些弹性异常表明晶格的耦合共存的轨道涨落和轨道自旋耦合激发。
Peierls-type structural phase transition in a crystal induced by magnetic breakdown
我们预言了准二维电子系统在强磁场中的一种新的相变，即密度波的稳定化，它将二维开放费米面转变为周期性的大口袋链，它们之间的距离很小。电子在包围这些口袋的相邻闭合轨道之间的量子隧穿将电子光谱转换成一组极窄的能带和带隙，这降低了总电子能量，从而导致磁击穿诱导密度波（MBIDW）基态。我们发现，这种DW不稳定性有一些定性不同的性质相比，类似DW的Peierls型不稳定性。E. G. MBIDW相变的临界温度随着反向磁场的变化以一种特殊的方式出现和消失。
