A honeycomb lattice system has four types of Dirac electrons corresponding to the spin and valley degrees of freedom. We consider a state that contains only one type of massless electrons and three types of massive ones, which we call the single Dirac-cone state. We analyze quantum Hall (QH) effects in this state. We make a detailed investigation of the Chern and spin-Chern numbers. We make clear the origin of unconventional QH effects discovered in graphene. We also show that the single Dirac-cone state may have arbitrary large spin-Chern numbers in magnetic field. Such a state will be generated in antiferromagnetic transition-metal oxides under electric field or silicene with antiferromagnetic order under electric field.
Theory anticipates that the in-plane px, py orbitals in a honeycomb lattice lead to new and potentially useful quantum electronic phases. So far, p orbital bands were only realized for cold atoms in optical lattices and for light and exciton-polaritons in photonic crystals. For electrons, in-plane p orbital physics is difficult to access since natural electronic honeycomb lattices, such as graphene and silicene, show strong s-p hybridization. Here, we report on electronic honeycomb lattices prepared on a Cu(111) surface in a scanning tunneling microscope that, by design, show (nearly) pure orb…
Vortex magnetic structure in artificial honeycomb lattice provides a unique platform to explore emergent properties due to the additional Berry phase curvature imparted by chiral magnetization to circulating electrons via direct interaction. We argue that while the perpendicularly-aligned magnetic component leads to the quantized flux of monopole at the center of the Berry sphere, the in-plane vortex circulation of magnetization gives rise to unexpected non-trivial topological Berry phase due to the gauge field transformation. The unprecedented effect signifies the importance of vector potenti…
We theoretically investigate the transport of magnon orbitals in a honeycomb antiferromagnet. We find that the magnon orbital Berry curvature is finite even without spin-orbit coupling and thus the resultant magnon orbital Hall effect is an intrinsic property of the honeycomb antiferromagnet rooted only in the exchange interaction and the lattice structure. Due to the intrinsic nature of the magnon orbital Hall effect, the magnon orbital Nernst conductivity is estimated to be orders of magnitude larger than the predicted values of the magnon spin Nernst conductivity that requires finite spin-o…
Muffin-tin methods have been instrumental in the design of honeycomb lattices that show, in contrast to graphene, separated s and in-plane p bands, a p orbital Dirac cone, and a p orbital flat band. Recently, such lattices have been experimentally realized using the 2D electron gas on Cu(111). A possible next avenue is the introduction of spin-orbit coupling to these systems. Intrinsic spin-orbit coupling is believed to open topological gaps, and create a topological flat band. Although Rashba coupling is straightforwardly incorporated in the muffin-tin approximation, intrinsic spin-orbit coup…
Geometrically frustrated materials, such as spin ice or kagome lattice, are known to exhibit exotic Hall effect phenomena due to spin chirality. We explore Hall effect mechanism in an artificial honeycomb spin ice of Nd--Sn element using Hall probe and polarized neutron reflectivity measurements. In an interesting observation, a strong enhancement in Hall signal at relatively higher temperature of $T$ $\sim$ 20 K is detected. The effect is attributed to the planar Hall effect due to magnetic moment configuration in spin ice state in low field application. In the antiferromagnetic state of neod…
Intrinsic spin-Hall accumulation in honeycomb lattices: Band structure effects
用Landauer-Keldysh方法计算了二维蜂窝晶格上的局域自旋和电荷密度。通过经验紧束缚方法，我们展示了如何现实的能带结构可以带入LKF。取Bi（111）表面，其上存在强表面态和Rashba自旋轨道耦合[Phys. Rev. Lett. 93，046403（2004）]，作为数值示例，我们在其上示出了典型的本征自旋霍尔累积（ISHA）图案。随后分析了双端纳米结构样品中自旋和电荷输运的费米能量依赖性。通过改变E_{F}，我们表明，ISHA模式是近各向同性（自由电子类），只有当E_{F}是接近带底，是敏感/不敏感的E_{F}的低/高的偏压制度与这样的E_{F}。当E_{F}远离能带底部时，能带结构效应因此进入ISHA图案并且输运方向变得显著。
We study geometrical responses of magnons driven by a temperature gradient in frustrated spin systems. While Dzyaloshinskii-Moriya (DM) interactions are usually incorporated to obtain geometrically nontrivial magnon bands, here we investigate thermal Hall responses of magnons that do no rely on the DM interactions. Specifically, we focus on frustrated spin systems with sublattice degrees of freedom and show that a nonzero Berry curvature requires breaking of an effective $PT$ symmetry. According to this symmetry consideration, we study the $J_1$-$J_2$-$J_2^\prime$ Heisenberg models on a honeyc…
Compression dramatically changes the transport and localization properties of graphene. This is intimately related to the change of symmetry of the Dirac cone when the particle hopping is different along different directions of the lattice. In particular, for a critical compression, a semi-Dirac cone is formed with massless and massive dispersions along perpendicular directions. Here we show direct evidence of the highly anisotropic transport of polaritons in a honeycomb lattice of coupled micropillars implementing a semi-Dirac cone. If we optically induce a vacancy-like defect in the lattice,…
In this paper we propose the precise Wigner-Weyl calculus for the lattice models defined on the honeycomb lattice. We construct two symbols of operators: the $\mathscr{B}$-symbol, which is similar to the symbol introduced by F. Buot, and the $W$ (or, Weyl) symbol. The latter possesses the set of useful properties. These identities allow us to use it in physical applications. In particular, we derive topological expression for the Hall conductivity through the Wigner transformed Green function. This expression may be used for the description of quantum Hall effect in the systems with artificial…
At nonlinear orders in the electric field, the vanishing of the Hall conductivity does not prevent the nonlinear component of the current from being transverse for selected field directions. We study electrons on $\mathcal{C}_{3v}$-symmetric honeycomb lattice for which the Hall conductivity vanishes at first and second order. Nevertheless, the second-order current component is transverse for fields perpendicular to the three mirror lines. The $\mathcal{C}_{3v}$ symmetry constrains the first-order and second-order conductivity tensors to have only one independent component each, which we calcul…
Magnon spin Hall systems could hardly show experimentally observable particle and thermal transport phenomena intrinsically due to the spin cancellation. Here we demonstrated that the magnon spin Hall systems can exhibit magnon Nernst effect and thermal Hall effect under external magnetic field by considering two typical systems, i.e. the antiferromagnetically (AFM) coupled bilayer honeycomb ferromagnets and monolayer collinear honeycomb antiferromagnet. The both systems experience magnetic phase transitions from AFM phase to a field-polarized phase via a spin-flop (SF) phase or directly. In b…
The possibility of dissipationless chiral edge states without the need of an external magnetic field in the quantum anomalous Hall effect (QAHE) offers a great potential in electronic/spintronic applications. The biggest hurdle for the realization of a room-temperature magnetic Chern insulator is to find a structurally stable material with a sufficiently large energy gap and Curie temperature that can be easily implemented in electronic devices. This work based on first-principle methods shows that a single atomic layer of V2O3 with honeycomb-kagome (HK) lattice is structurally stable with a s…
