We investigate the stability of a quadratic band-crossing point (QBCP) in 2D fermionic systems. At the non-interacting level, we show that a QBCP exists and is topologically stable for a Berry flux $\pm 2π$, if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable free-fermion QBCP is marginally unstable to {\em arbitrarily weak} short-range repulsive interactions. We consider both spinless and spin-1/2 fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nematic-spin-nematic phase.
A nematic superconductor can in principle support a vestigial order phase above its superconducting transition temperature, with rotational symmetry spontaneously broken while remain nonsuperconducting. We examine the condition for this vestigial nematic order to occur, within a Ginzburg-Landau theory with order parameter fluctuations included. Contrary to prior theoretical results, we found that this vestigial order actually requires very stringent conditions to be met: the material must be sufficiently deep in the nematic regime (i.e. far away from the boundary separating the nematic and chi…
We investigate nematic quantum phase transitions in two different Dirac fermion models. The models feature twofold and fourfold, respectively, lattice rotational symmetries that are spontaneously broken in the ordered phase. Using negative-sign-free quantum Monte Carlo simulations and an $ε$-expansion renormalization group analysis, we show that both models exhibit continuous phase transitions. In contrast to generic Gross-Neveu dynamical mass generation, the quantum critical regime is characterized by large velocity anisotropies, with fixed-point values being approached very slowly. Hence bot…
A parity-breaking electronic nematic phase transition in the spin-orbit coupled metal Cd$_2$Re$_2$O$_7$
强的电子相互作用可以驱动金属系统向各种众所周知的电子破碎相发展，但是具有强自旋轨道耦合的相关金属的不稳定性直到最近才开始被探索。利用空间分辨二次谐波光学各向异性测量方法，我们发现了金属烧绿石Cd $_2$ Re $_2$ O $_7$中物质的多极双相.像以前发现的电子双极相，这种多极相自发地打破旋转对称性，同时保持平移不变性。然而，它具有在空间反演下为奇数的显着性质，这仅在存在自旋轨道耦合的情况下才允许。通过研究多极子序参量的临界行为，我们发现它驱动Cd $_2$ Re $_2$ O $_7$在200开尔文附近的热相变，并诱导宇称破缺晶格畸变作为二级序。
Thermodynamic evidence for nematic superconductivity in Cu$_x$Bi$_2$Se$_3$
非常规超导的特征在于宏观超导波函数的自发对称性破缺，以及规范对称性破缺，例如相对于基本晶格对称性的旋转对称性破缺。特别是，超导性与自发的旋转对称性破缺的波函数振幅，从而在体的性质，尚未报告以前，是有趣的，可以被称为“双”超导性的类比，以双液晶相。在这里，基于比热测量的单晶Cu $_x$ Bi $_2$ Se $_3$精确的磁场方向控制下，我们报告的热力学证据的超导性，即，明确的双重对称行为的三角晶格。结果表明，实现了一个“奇宇称”的状态，只有宏观量子凝聚体和不同的液晶中的双态。结果也证实了Cu $_x$ Bi $_2$ Se $_3$的拓扑非平凡超导电性。
Emergent XY electronic nematicity in iron-based superconductors
电子向列性是一种自发破坏旋转对称性的相关态，在几种分层量子材料中观察到。与它们的液晶对应物相比，双折射指向矢通常不能指向任意方向（XY向列），而是被晶体锁定在离散方向（伊辛向列），导致在过渡上方的强烈各向异性波动。在这里，我们报告的观察，通过弹性电阻测量，在空穴掺杂的Ba $_{1-x}$ Rb $_{x}$ Fe $_{2}$ As $_{2}$铁基超导体的近各向同性XY的波动。而对于$x=0$，双折射指向矢沿着四面体晶格的面内对角线指向，对于$x=1$，它沿着水平轴和垂直轴指向。值得注意的是，对于中间掺杂，这两个不可还原的Curie-Weiss通道的磁化率显示出相当的Curie-Weiss行为，从而揭示了一个接近XY-Curie-state。这开辟了一条新的途径来评估这种难以捉摸的电子量子液晶态，它是一个候选人主机独特的现象不存在于伊辛-伊辛的情况下。
Electronic nematicity in iron pnictide materials is coupled to both the lattice and the conducting electrons, which allows both structural and transport observables to probe nematic fluctuations and the order parameter. Here we combine simultaneous transport and x-ray diffraction measurements with in-situ tunable strain (elasto-XRD) to measure the temperature dependence of the shear modulus and elastoresistivity above the nematic transition and the spontaneous orthorhombicity and resistivity anisotropy below the nematic transition, all within a single sample of $Ba(Fe_{0.96}Co_{0.04})_{2} As_{…
As in between liquid and crystal phases lies a nematic liquid crystal, which breaks rotation with preservation of translation symmetry, there is a nematic superfluid phase bridging a superfluid and a supersolid. The nematic order also emerges in interacting electrons and has been found to largely intertwine with multi-orbital correlation in high-temperature superconductivity, where Ising nematicity arises from a four-fold rotation symmetry $C_4$ broken down to $C_2$. Here we report an observation of a three-state ($\mathbb{Z}_3$) quantum nematic order, dubbed "Potts-nematicity", in a system of…
In the vicinity of a quantum critical point, quenched disorder can lead to a quantum Griffiths phase, accompanied by an exotic power-law scaling with a continuously varying dynamical exponent that diverges in the zero-temperature limit. Here, we investigate a nematic quantum critical point in the iron-based superconductor FeSe$_{0.89}$S$_{0.11}$ using applied hydrostatic pressure. We report an unusual crossing of the magnetoresistivity isotherms in the non-superconducting normal state which features a continuously varying dynamical exponent over a large temperature range. We interpret our resu…
Uniaxial-strain Control of Nematic Superconductivity in Sr$_{x}$Bi$_2$Se$_3$
向列相态的特征在于没有平移有序的旋转对称性破缺。近年来，人们发现了超导能隙自发地提升晶格转动对称性的超导现象。然而，配对机制和机制决定的取向仍然没有得到解决。第一步是通过施加外部破缺磁场来证明向列性的控制，以确定耦合到晶格的符号和强度。在这里，我们报告的第一次控制的超导性的Sr $_x$ Bi $_2$ Se $_3$，通过外部施加的单轴应力的取向。亚结构域的抑制表明，它是$Δ_{4y}$状态，是最有利的压缩下沿基础Bi-Bi键。这些结果提供了一个不可避免的一步，了解独特的拓扑超导电性的微观起源。
