耦合到标量场的有质量Dirac系统中的量子谷霍尔效应

Spin and valley waves in Dirac semimetals with population imbalance

We find an intervalley wave collective mode in two- and three-dimensional Dirac semimetals in the presence of a valley population imbalance. The dispersion relation of this mode is gapless, proportional to the square of the wave vector at small frequencies, and inversely proportional to the electron-electron exchange interaction energy. The valley wave serves as an energy gain source for the external field, that generates the intervalley transitions. The spin wave analog is discussed for the case of a semimetal with nonequilibrium spin orientation.

六谷氢钝化硅（111）表面的量子量子霍尔效应

Integer quantum Hall effect on a six valley hydrogen-passivated silicon (111) surface

本文报道了在氢钝化的Si（111）表面与真空界面处的反型层中形成的二维电子系统的磁输运研究。在整数量子霍尔制度的测量表明，这些表面的预期六倍谷简并被打破，导致在不平等的占领的六个山谷和各向异性的电阻。我们假设Si表面的取向错误将谷态打破为三个不等间隔的对，但是奇数填充因子的观察很难与非相互作用电子理论相一致。

量子Hall系统中的向列谷序

Nematic Valley Ordering in Quantum Hall Systems

在具有自旋或赝自旋自由度的二维电子系统中，量子霍尔有序和自发破缺的“内部”对称性之间的相互作用引起了各种有趣的现象，包括新相、相变和拓扑激发。在这里，我们开发了一个理论的破缺对称量子霍尔态，适用于一类多谷系统，其中的对称性问题是一个点群元素，结合了空间旋转与置换的谷指数。色散关系的各向异性，通常存在于这样的系统中，有利于所有电子驻留在其中一个谷中的状态。在一个干净的系统中，谷“伪自旋”有序，或空间自旋有序，通过有限的温度转变发生。在弱无序系统中，形成了赝自旋极化域，这阻止了宏观谷和无序有序;然而，所得到的状态仍然渐近地表现出QHE。我们讨论了在有序和无序制度的输运性质，以及我们的研究结果的关系，最近的实验在铝。

Two-component parton fractional quantum Hall state in graphene

We study the $ν={\pm}1/2$ fractional quantum Hall states in graphene observed by Zibrov et al. [Nat. Phys. 14, 930 (2018)]. The parton construction is employed to provide a valley unpolarized trial wave function for these states. The lattice scale valley anisotropic terms in the Hamiltonian soften the repulsion between electrons in different valleys to favor the valley unpolarized state. The validity of our proposal is corroborated by numerical calculations.

石墨烯中的自旋-谷纠缠量子霍尔态

Spin-valley entangled quantum Hall states in graphene

本研究针对单层石墨烯双填充自旋-谷自由度的朗道能级，构建含多类相互作用与势场的模型，发现多种自发自旋-谷纠缠相及特殊的纠缠Kekulé反铁磁相，并量化了各相的纠缠程度。

Visualizing Broken Symmetry and Topological Defects in a Quantum Hall Ferromagnet

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic phases (QHFM), with broken spin or valley symmetry. Visualizing atomic scale electronic wavefunctions with scanning tunneling spectroscopy (STS), we resolve microscopic signatures of valley ordering in QHFM and fractional quantum Hall phases of graphene. At charge neutrality, we observe a field-tuned continuous quantum phase transition from a valley polarized state to an intervalley coherent state, with a Kekule distortion of its electronic density. Mapping …

Bulk quantum Hall effect of spin-valley-coupled Dirac fermions in a polar antiferromagnet BaMnSb$_2$

Unconventional features of relativistic Dirac/Weyl quasi-particles in topological materials are most evidently manifested in the 2D quantum Hall effect (QHE), whose variety is further enriched by their spin and/or valley polarization. Although its extension to three dimensions has been long-sought and inspired theoretical proposals, material candidates have been lacking. Here we have discovered valley-contrasting spin-polarized Dirac fermions in a multilayer form in bulk antiferromagnet BaMnSb$_2$, where the out-of-plane Zeeman-type spin splitting is induced by the in-plane inversion symmetry …

铋中Dirac谷的场致极化

Field-induced polarisation of Dirac valleys in bismuth

在特定晶格结构的存在下，电子被提供谷自由度。操纵谷简并是新兴研究领域的主题，主要集中在石墨烯中的电荷传输。在大块铋中，电子已知呈现三重谷简并和每个谷中的狄拉克色散。在这里，我们表明，由于其巨大的面内质量各向异性，沿三角轴的狄拉克电子流是非常敏感的面内磁场的取向。因此，可旋转的磁场可用作谷值阀，以调节每个谷值对总电导率的贡献。根据我们的测量，在很宽的温度和磁场范围内，单个谷载流子的电荷电导率可以超过总电导率的五分之四。在高温和低磁场下，这三个谷是可互换的，并且下面的晶格的三重对称性得到尊重。随着温度降低和/或磁场增加，这种对称性自发地丧失。后者可能是最近提出的谷-谷费米液态的实验表现。

Quantum Hall Valley Nematics

Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states: quantum Hall valley nematics. These phases of matter emerge when the formation of a topologically insulating quantum Hall state is accompanied by the spontaneous breaking of a point-group symmetry that combines a spatial rotation with a permutation of valley indices. The resulting orientational order is particularly sensitive to quenched disorder, while quantu…

Valley-Polarized Quantum Anomalous Hall State in Moiré MoTe$_2$/WSe$_2$ Heterobilayers

Moiré heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moiré bands in heterobilayer TMDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling $ν=2$ (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling $ν=1$ were observed in AB stacked moiré MoTe$_2$/WSe$_2$ heterobilayers. However, how the topologically nontrivial s…

手性叠层少层石墨烯体系中的自发量子霍尔态

Spontaneous Quantum Hall States in Chirally-stacked Few-Layer Graphene Systems

具有N >= 2的手性堆叠的N层石墨烯系统表现出各种不同的对称性破缺状态，其中来自不同自旋和谷的电荷密度贡献在层之间自发地转移。我们解释了这些国家是如何区分他们的电荷，自旋和谷霍尔电导率，他们的轨道磁化，和他们的边缘状态的属性。我们认为谷霍尔态每个自旋谷有[N/2]个边缘通道。