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arXiv 1804.01547cond-mat.str-el
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狄拉克和外尔半金属拓扑相变中具有无限各向异性的量子临界性

Quantum Criticalities with Infinite Anisotropy in Topological Phase Transitions between Dirac and Weyl Semi-metals

SangEun Han, Gil Young Cho, Eun-Gook Moon

备注：
Published at PRB (Phys. Rev. B 98, 085149 (2018)), Main text: 18 pages, 2 table, 5 figures, Supplementary Material: 12 pages, 1 figure
发表信息：
Phys. Rev. B 98, 085149 (2018)
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摘要：

我们研究了由狄拉克和外尔半金属之间的拓扑相变激发的与分裂节点费米点相关的量子相变。狄拉克半金属中的狄拉克点可以通过打破晶格对称性或时间反演对称性分裂成两个外尔点，并且Lifshitz转变通常用于描述相变。在这里，我们表明，Lifshitz描述是根本不正确的QPT分裂节点费米点。我们认为，费米子之间的相关性，序参量，和长程库仑相互作用{必须}从一开始就纳入。我们发现的最显著的相关效应之一是物理量的{ \it无限各向异性}，这在Lifshitz跃迁中是不可能出现的。利用标准重整化群（RG）方法，在三维空间中发现了两种随Dirac点（$N_f$）数目变化的无限各向异性量子临界态.对于$N_f = 1$，费米子速度与序参量激发速度的比值沿狄拉克点分裂方向变得普适（$\sqrt{2}-1$）。对于$N_f >1$，我们发现费米子在所有方向上都比序参量激发快。我们的RG分析是完全控制的事实，即序参量和费米子的波动是在上临界尺寸，因此，我们的稳定的不动点证明存在弱耦合量子临界无限各向异性。

英文摘要：

We study quantum phase transitions (QPTs) associated with splitting nodal Fermi points, motivated by topological phase transitions between Dirac and Weyl semi-metals. A Dirac point in Dirac semi-metals may be split into two Weyl points by breaking a lattice symmetry or time reversal symmetry, and the Lifshitz transition is commonly used to describe the phase transitions. Here, we show that the Lifshitz description is fundamentally incorrect in QPTs with splitting nodal Fermi points. We argue that correlations between fermions, order parameter, and the long range Coulomb interaction { must} be incorporated from the beginning. One of the most striking correlation effects we find is {\it infinite anisotropy} of physical quantities, which cannot appear in a Lifshitz transition. By using the standard renormalization group (RG) method, two types of infinitely anisotropic quantum criticalities are found in three spatial dimensions varying with the number of the Dirac points ($N_f$). For $N_f = 1$, the ratio of the fermion velocity to the velocity of order parameter excitations becomes universal ($\sqrt{2}-1$) along the Dirac point splitting direction . For $N_f >1$, we find that fermions are parametrically faster than order parameter excitations in all directions. Our RG analysis is fully controlled by the fact that order parameter and fermion fluctuations are at the upper critical dimension, and thus our stable fixed points demonstrate the presence of weakly coupled quantum criticalities with infinite anisotropy.

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