Topological insulating phases in mono and bilayer graphene
Alberto Cortijo, Adolfo G. Grushin, Maria A. H. Vozmediano
我们分析了单层和双层石墨烯中不同的二次相互作用对时间反演不变拓扑绝缘相的影响。我们利用有效作用形式主义，以确定不同的相互作用的陈西蒙斯系数的依赖性。
We analyze the influence of different quadratic interactions giving rise to time reversal invariant topological insulating phases in mono and bilayer graphene. We make use of the effective action formalism to determine the dependence of the Chern Simons coefficient on the different interactions.
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Insulating behavior in metallic bilayer graphene: Interplay between density inhomogeneity and temperature
我们研究了在环境中长程带电杂质诱导的电子空穴水坑存在下的双层石墨烯输运。我们解释的绝缘行为中观察到的温度依赖性的低迁移率双层石墨烯的导电性，使用分析统计理论，考虑到非平均场性质的运输在高度不均匀的密度和潜在的景观。我们发现，即使远离电荷中性点，由于系统中的随机局部激活间隙，水坑也可以诱导共存的金属和绝缘输运行为。
Thermopower of Interacting GaAs Bilayer Hole Systems in the Reentrant Insulating Phase near $ν=1$
我们报告相互作用的GaAs双层空穴系统的热电势测量。当两个层中的载流子密度相等时，这些系统在总填充因子$ν=1$下在量子霍尔态附近表现出重入绝缘相。我们的数据表明，随着温度的降低，热电势发散的绝缘阶段。这种行为表明在低温下能隙的打开，与钉扎维格纳固体的形成一致。我们提取了一个能隙和一个Wigner固体熔化相图。
We report on transport properties in dual-gated hexagonal boron nitride (hBN)/bilayer-graphene (BLG) superlattices. Here, BLG is nontwisted, i.e., plain. This paper focuses on the charge neutrality point (CNP) for a plain BLG. Under a perpendicular magnetic field, transitions between two insulating phases at the CNP are detected by varying a displacement field with the study on the resistance-temperature characteristics and the magnetoresistance. This work opens avenues for exploring the global phase diagram of the hBN/BLG superlattices beyond the CNP.
Coexistence of Topological and Normal Insulating Phases in Electro-Optically Tuned InAs/GaSb Bilayer Quantum Wells
本文通过光学和电学调谐InAs/GaSb双层量子阱，实验发现普通绝缘相与拓扑绝缘相可共存，并提出在体区构建平凡-拓扑绝缘界面的新电光调控方案。
Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene
扭曲双层石墨烯（TwBLG）是最简单的范德华异质结构之一，但它产生了一个复杂的电子系统，具有复杂的相互作用之间的摩尔物理和层间杂化效应。我们报告的高迁移率小角度TwBLG设备的电子输运测量显示在超晶格带边缘的绝缘状态的明确证据，与热激活间隙比理论预测的大几倍。此外，Shubnikov-de Haas振荡和紧束缚计算表明，能带结构由两个相交的费米轮廓，其交叉点是有效的未杂化。我们将此归因于大于莫尔波矢的动量转移的指数抑制层间跳跃振幅。
In this work the effects of impurity in various insulating phases of the twisted bilayer graphene (TBG) are studied. The well-accepted continuum model\cite{b} is employed and the local density of states (DOS) is calculated. It is found that insulating phases breaking different symmetries proposed in previous theories\cite{pa,op1,Lee_2019} are distinguishable via the number and properties of in-gap bound state peaks induced by impurities in local DOS. Insulating phases breaking the same previously proposed symmetries can be further classified by the remaining anti-unitary symmetries and disting…
We study a bilayer structure consisting of an antiferromagnetic insulator and a normal metal. An electron current is driven in the normal metal with direction parallel to the interface between the materials. Due to interfacial exchange coupling between the localized spins in the antiferromagnet and the itinerant electrons in the normal metal, a magnon current can then be induced in the antiferromagnet. Using an uncompensated antiferromagnetic interface, creating an asymmetry in the interfacial coupling to the two degenerate magnon modes, we find that it is possible to generate a magnon spin-cu…
We consider magic-angle twisted bilayer graphene (TBG) at filling $ν=+3$, where experiments have observed a robust quantized anomalous Hall effect. This has been attributed to the formation of a valley- and spin-polarized Chern insulating ground state that spontaneously breaks time-reversal symmetry, and is stabilized by a hexagonal boron nitride (hBN) substrate. We identify three different types of domain wall, and study their properties and energetic selection mechanisms via theoretical arguments and Hartree-Fock calculations adapted to deal with inhomogeneous moiré systems. We comment on th…
In this work, we calculate the optical response and the nonlinear Hall response of twisted bilayer graphene (TBG) in the insulating states. Different insulating states, including spin-valley polarized (SPVP) state, spin-polarized quantum Hall(SPQH) state, spin-polarized valley Hall (SPVH) state, and spin polarized Kramers-intervalley coherence (SPKIVC) state, are considered. We calculate the optical conductivity ($σ_{xx}$) of these four states and we find that the spin-valley polarized state shows a two-peak feature which is different from the other three states. In order to distinguish the ot…
Excitonic Instabilities and Insulating States in Bilayer Graphene
采用重整化群方法研究了双层石墨烯最近邻跃迁的竞争基态。在没有相互作用的情况下，该模型在半填充时的费米面由两个具有动量$\mathbf{K}$、$\mathbf{K}'$的节点组成，其中导带和价带彼此接触，产生半金属。由于在这两点附近的能量色散是二次的，具有完美的粒子-空穴对称性，如果存在带间相互作用，激子不稳定性是不可避免的。使用微扰重整化群分析的一个循环的水平，我们发现不同的竞争有序基态，包括铁磁性，超导性，自旋和电荷密度波态与有序矢量$\mathbf{Q}=\mathbf{K}-\mathbf{K}'$，激子绝缘体状态。此外，在激子绝缘相和铁磁相中发现了两个具有谷对称性破缺的态。这一分析有力地表明，双层石墨烯的基态应该是带隙的，除了超导性外，所有其他可能的基态都是绝缘的。
Quantum Transport and Field Induced Insulating States in Bilayer Graphene pnp Junctions
我们在高质量的双层石墨烯pnp结与悬浮顶栅进行输运测量。在磁场B=0时，我们证明了通过施加垂直电场的带隙打开，在260 mK时开/关比高达20，000。在带隙内，电导随着电场的增加以3个数量级的指数方式减小，并且可以通过具有栅极可调谐的状态密度、有效质量和局部化长度的可变范围跳跃来解释。在大B时，我们观察到具有分数值的量子霍尔电导，这是由差分掺杂区域之间的边缘态的平衡以及填充因子ν=0时绝缘态的存在引起的。我们的工作强调了双层石墨烯对于根本利益和技术应用的重要性。
Although much progress has been made on the physics of magic angle twisted bilayer graphene at integer fillings, little attention has been given to fractional fillings. Here we show that the three-peak structure of Wannier orbitals, dictated by the symmetry and topology of flat bands, facilitates the emergence of a novel state at commensurate fractional filling of $ν= n \pm 1/3$. We dub this state a "fractional correlated insulator". Specifically for the filling of $\pm 1/3$ electrons per moiré unit cell, we show that short-range interactions alone imply an approximate extensive entropy due to…
Relative weight of the inverse spin Hall and spin rectification effects for metallic Py,Fe/Pt and insulating YIG/Pt bilayers estimated by angular dependent spin pumping measurements
我们量化的相对重量的逆自旋霍尔和自旋整流效应发生在RF溅射多晶坡莫合金，分子束外延生长的外延铁和液相外延生长的钇铁石榴石双层系统与不同的封盖材料。为了将自旋整流信号与反自旋霍尔电压区分开，外部磁场在平面内旋转以利用主导效应的不同角度依赖性。我们证明，在坡莫合金的各向异性磁阻是自旋整流的主导来源，而在外延铁的异常霍尔效应也具有相当的强度。在钇铁石榴石/铂双层整流揭示了一个角度依赖性模仿自旋霍尔磁阻引起的各向异性磁阻。
The emergence of flat bands and correlated behaviors in 'magic angle' twisted bilayer graphene (tBLG) has sparked tremendous interest, though many aspects of the system are under intense debate. Here we report observation of both superconductivity and the Mott-like insulating state in a tBLG device with a twist angle of approximately 0.93, which is smaller than the magic angle by 15%. At an electron concentration of +/-5 electrons per moire unit cell, we observe a narrow resistance peak with an activation energy gap of approximately 0.1 meV, indicating the existence of an additional correlated…
The emergence of correlated insulating phases in magic-angle twisted bilayer graphene exhibits strong sample dependence. Here, we derive an Anderson theorem governing the robustness against disorder of the Kramers intervalley coherent (K-IVC) state, a prime candidate for describing the correlated insulators at even fillings of the moiré flat bands. We find that the K-IVC gap is robust against local perturbations, which are odd under $\mathcal{PT}$, where $\mathcal{P}$ and $\mathcal{T}$ denote particle-hole conjugation and time reversal, respectively. In contrast, $\mathcal{PT}$-even perturbati…
Stack of correlated insulating states in bilayer graphene kagome superlattice
本研究通过双层石墨烯kagome超晶格实现相关绝缘态堆叠，利用纳米图案化技术调控电子结构，揭示了强电子相互作用在扁平能带中的作用。
Gate-induced insulating state in bilayer graphene devices
由一层或几层石墨组成的石墨烯基材料用于集成电子器件的潜力源于这些系统中的大的室温载流子迁移率（约100%）。10，000 cm2/Vs）。然而，诸如场效应晶体管的电子器件的实现将需要借助于栅电极来控制甚至切断导电性，这由于本征材料中不存在带隙而变得困难。在这里，我们展示了绝缘状态的受控感应-具有大的导电性抑制-在双层石墨烯中，通过使用双栅极器件配置，允许垂直于平面施加电场。电阻对温度和电场的依赖性，以及在单层器件中没有任何影响，强烈表明栅极诱导的绝缘状态起源于最近预测的价带和导带之间的带隙的开放。
Quantum Hall Effect, Screening and Layer-Polarized Insulating States in Twisted Bilayer Graphene
我们研究了双栅扭曲双层石墨烯中的电子输运。尽管层之间的亚纳米接近，我们确定独立的贡献，从石墨烯朗道能级光谱的每一层的磁阻。我们证明，每一层的填充因子可以独立地控制通过双栅极，我们用它来诱导层之间的朗道能级交叉。通过分析朗道能级交叉的栅极依赖性，我们表征了有限的层间屏蔽，并提取原子间隔层之间的电容。在零填充因子下，我们观察到依赖于磁场和位移场的绝缘态，这表明存在层间耦合的反向传播边缘态。
We present a combined experimental and theoretical study of twisted double bilayer graphene with twist angles between 1° and 1.35°. Consistent with moiré band structure calculations, we observe insulators at integer moiré band fillings one and three, but not two. An applied transverse electric field separates the first moiré conduction band from neighbouring bands, and favors the appearance of correlated insulators at 1/4, 1/2, and 3/4 band filling. Insulating states at 1/4 and 3/4 band filling emerge only in a parallel magnetic field (B_{||}), whereas the resistance at half band filling is we…
Spontaneously gapped ground state in suspended bilayer graphene
由于自旋、谷和层对称性，双层石墨烯具有八倍简并性，从而允许由磁场或电场、由应变、或甚至由相互作用自发地诱导的大量对称性破缺状态。我们研究了清洁电流退火的悬浮双层石墨烯中的电输运。我们发现两种设备。在B1型双层膜中，八重零能朗道能级（LL）被部分提升到阈值场以上，揭示了电荷中性点（CNP）处的绝缘nu=0量子霍尔态。在B2型双层膜中，即使在零磁场下，LL提升也是完全的，并且在微分电导中也出现了一个能隙，表明是绝缘的自发破缺对称态。与B1不同的是，B2中的最小电导没有被指数抑制，而是保持有限，即使在大磁场中，其值G < e^2/h。我们建议，这一阶段的B2是绝缘的散装和约束的可压缩边缘状态。
The recently observed superconductivity in twisted bilayer graphene emerges from insulating states believed to arise from electronic correlations. While there have been many proposals to explain the insulating behaviour, the commensurability at which these states appear suggests that they are Mott insulators. Here we focus on the insulating states with $\pm 2$ electrons or holes with respect to the charge neutrality point. We show that the theoretical expectations for the Mott insulating states are not compatible with the experimentally observed dependence on temperature and magnetic field if,…
Theory of integer quantum Hall effect in insulating bilayer graphene
提出了量子化磁场作用下绝缘双层石墨烯（BLG）的变分基态。由于塞曼耦合，全带隙BLG中的层反铁磁（LAF）序参量被投影到自旋易平面上，同时铁磁序沿磁场方向发展，并可通过交换作用进一步增强.激活间隙的$ν=0$霍尔状态，然后显示一个交叉从二次线性缩放与磁场，因为它变得更强，我获得了极好的协议与最近的实验与现实的强度为铁磁相互作用。LAF阶的一个分量，平行于外部磁场，在填充$ν=\pm 2$时产生额外的不可压缩霍尔态，而BLG中的远程跳跃产生$ν=\pm 1$霍尔态。LAF的顺序在倾斜磁场中的演变，缩放的间隙在$ν=2$，外部电场对各种霍尔高原的影响，和不同的可能层次的分数量子霍尔状态的突出显示。
We review analytical and numerical studies of correlated insulating states in twisted bilayer graphene, focusing on real-space lattice models constructions and their unbiased quantum many-body solutions. We show that by constructing localized Wannier states for the narrow bands, the projected Coulomb interactions can be approximated by interactions of cluster charges with assisted nearest neighbor hopping terms. With the interaction part only, the Hamiltonian is $SU(4)$ symmetric considering both spin and valley degrees of freedom. In the strong coupling limit where the kinetic terms are negle…
We propose that the electronic structure of twisted bilayer graphene (TBG) can be understood as Dirac fermions coupled with opposite pseudo magnetic fields generated by the moiré pattern. The two low-energy flat bands from each monolayer valley originate from the two zeroth pseudo Landau levels of Dirac fermions under such opposite effective magnetic fields, which have opposite sublattice polarizations and carry opposite Chern numbers $\pm1$, giving rise to helical edge states in the gaps below and above the low-energy bulk bands near the first magic angle. We argue that small Coulomb interact…
Quantum Hall Effect and Quantum Point Contact in Bilayer-Patched Epitaxial Graphene
我们研究了外延单层石墨烯双层夹杂物通过磁输运测量和扫描门显微镜在低温下。我们发现，双层夹杂物可以是金属或绝缘的初始和门控载流子密度的依赖。金属双层作为边缘电流的等电位短路，而紧密间隔的绝缘双层引导电子在单层收缩，这是局部门控使用扫描门探针的流动。
Quantum Oscillation in Excitonic Insulating Electron-Hole Bilayer
本文用Hartree Fock平均场理论研究激子绝缘电子-空穴双层中层间电容的量子振荡，揭示其源于电子/空穴朗道能级形成的激子，并发现强磁场会破坏激子序参量，使系统变为两个独立量子霍尔液体。
Topological confinement in bilayer graphene
我们研究了一种新型的一维手征态，它可以通过静电横向限制在双层石墨烯（BLG）中产生。这些状态出现在隔离经历相反的门控极性的绝缘区域的畴壁上。虽然这些状态类似于传统的孤子零模，但它们的性质是由不寻常的手性BLG准粒子定义的。零模分支的数目由绝缘BLG态的拓扑真空电荷确定。我们讨论了如何这些手征状态可以体现实验，并强调其相关性谷电子学。
Twisting two layers into a magic angle (MA) of ~1.1° is found essential to create low energy flat bands and the resulting correlated insulating, superconducting, and magnetic phases in twisted bilayer graphene (TBG). While most of previous works focus on revealing these emergent states in MA-TBG, a study of the twist angle dependence, which helps to map an evolution of these phases, is yet less explored. Here, we report a magneto-transport study on one non-magic angle TBG device, whose twist angle θ changes from 1.25° at one end to 1.43° at the other. For θ=1.25°, we observe an emergence of to…
Correlated Insulating States in Twisted Double Bilayer Graphene Enhanced by Interfacial Effect on CrOCl
研究在CrOCl衬底上扭曲双双层石墨烯的关联绝缘态，通过超高磁场输运测量发现电荷转移导致半填充因子处增强的关联绝缘态，揭示界面电荷相关效应影响，为操控关联态提供新途径。
Role of density imbalance in an interacting bilayer hole system
研究了零隧穿极限下GaAs空穴双层膜的相互作用。当层具有相等的密度，我们观察到一个相位相干双层量子霍尔（QH）状态在总填充因子$ν=1$，两侧的绝缘相在附近的填充物，这表明形成钉扎，双层维格纳晶体。当我们将电荷从一层转移到另一层时，绝缘相消失，而令人惊讶的是，$ν=1$ QH态变得更强。同时，一个明显的滞后发展的纵向磁阻在较高的填充，一阶量子相变的指示。
Topological origin of subgap conductance in insulating bilayer graphene
基于石墨烯的系统的边缘具有不寻常的电子性质，源自与电子波函数的伪旋量特征相关联的非平凡拓扑结构。这些性质与传统系统中薛定谔方程所描述的电子没有类似之处，导致了许多惊人现象的预测，如门可调铁磁性和谷选择性输运。然而，在大多数情况下，预计预测的现象不会在强烈的结构和化学无序的影响下幸存下来，这些结构和化学无序必然会影响真实石墨烯器件的边缘。在这里，我们提出了一个理论研究的本征低能态在边缘的静电间隙双层石墨烯（BLG），并发现边缘模式的贡献，现实设备的电导仍然是相当大的，即使是高度不完美的边缘。这种边缘电导占主导地位的批量贡献，如果静电诱导的间隙是足够大的，并在最近的运输和光学光谱实验中所作的看似相互矛盾的观察帐户。我们的研究结果说明了鲁棒性的现象，其起源是植根于电子能带结构的拓扑结构，即使在没有特定的保护机制。
Evidence of topological Kondo insulating state in MoTe2/WSe2 moiré bilayers
本文在MoTe2/WSe2莫尔双层中实验证实了二维拓扑近藤绝缘态，通过构建近藤耦合的Mott绝缘体与巡游能带，观察到低温绝缘体体态与螺旋边缘态，为莫尔材料中可调拓扑近藤物理研究开辟了新途径。
Interaction-driven (quasi-) insulating ground states of gapped electron-doped bilayer graphene
本文在电子掺杂双层石墨烯中发现了一系列由自旋和谷序驱动的新型关联相，这些相表现出非线性电流-偏压行为和绝缘性温度依赖，被归因于电荷或自旋密度波态及Wigner晶体，与已知Stoner相共存形成复杂相图。
Moiré Mott correlated mosaics in twisted bilayer 1T-TaS$_2$
研究通过扭折双层1T-TaS₂的堆叠依赖性绝缘间隙，揭示了莫尔图案诱导的马赛克超晶格，具有局部磁矩和非磁性绝缘区域的竞争。
An unconventional insulating phase and a superconducting phase were recently discovered in the twisted bilayer graphene [Y. Cao et al, Nature {\bf 556}, 80; {\bf 556}, 43 (2018)], but the relevant low-energy electronic states have not been clearly identified yet. In this work, I show that the interlayer hopping induces a spatially modulated Dirac mass term in the continuum Hamiltonian, and leads to a low-energy band formed by Dirac zero modes in the moiré superlattice. This moiré band becomes extremely flat and thus strongly correlated as the Dirac velocity vanishes at the magic angle, and ent…
Inhomogenous electronic structure, transport gap, and percolation threshold in disordered bilayer graphene
计算了猝灭电荷杂质存在下无带隙和带隙无序双层石墨烯的非均匀实空间电子结构。对于有间隙的双层石墨烯，我们发现，对于当前的实验条件下，屏蔽的无序势的波动的幅度的顺序是（或往往大于）的固有间隙$Δ$诱导的垂直电场的应用。我们计算了交叉化学势，$Δ_{\rm cr}$，将绝缘状态与其中双层石墨烯样品的面积的不到一半是绝缘的绝缘状态分开。我们发现，目前的实验大多是在与$Δ_{\rm cr}<<Δ$的澄清制度。与$Δ$相比，$Δ_{\rm cr}$的巨大抑制为理论带隙$Δ$和实验提取的传输带隙之间的大差异提供了可能的解释。
When bilayer graphene is rotationally faulted to an angle $θ\approx 1.1^\circ$, theory predicts the formation of a flat electronic band and correlated insulating, superconducting, and ferromagnetic states have all been observed at partial band filling. The proximity of superconductivity to correlated insulators has suggested a close relationship between these states, reminiscent of the cuprates where superconductivity arises by doping a Mott insulator. Here, we show that superconductivity can appear without correlated insulating states. While both superconductivity and correlated insulating be…
We consider the superconducting and Mott-insulating states for the twisted bilayer graphene, modeled as two narrow-band system of electrons with appreciable intraatomic Coulomb interactions. The interaction induces kinetic exchange which leads to real-space, either triplet- or singlet-spin pairing, in direct analogy to heavy-fermions and high-temperature superconductors. By employing the statistically-consistent Gutzwiller method, we construct explicitly the phase diagram as a function of electron concentration for the spin-triplet $d_{x^2 - y^2}+id_{xy}$ paired case, as well as determine the …
Microwave spectroscopic studies of the bilayer electron solid states at low Landau filling in a wide quantum well
在分数量子霍尔效应（Fractional Hall effect，简称FHE）系列的低朗道填充因子$(ν)$终端，二维电子系统（2DES）呈现出一种绝缘相，这种绝缘相被理解为钉扎维格纳固体的一种形式。在这里，我们使用微波光谱探测过渡到绝缘体的宽量子阱（WQW）的样品，可以支持单层或双层状态取决于其总的载流子密度，$n$。我们发现绝缘体表现出共振，这是双层固体的特征。共振还揭示了一对过渡内的固体，这是不可访问的直流传输测量。随着$n$被更深地偏置到双层固体区域，共振以特定强度增长，并且绝缘体内的跃迁消失。这些行为暗示了绝缘相作为液体和固体组分的乳液的图像。
For two decades, two-dimensional carbon species, including graphene, have been the core of research in pursuing next-generation logic applications beyond the silicon technology. Yet the opening of a gap in a controllable range of doping, whilst keeping high conductance outside of this gapped state, has remained a grand challenge in them thus far. Here we show that, by bringing Bernal-stacked bilayer graphene in contact with an anti-ferromagnetic insulator CrOCl, a strong insulating behavior is observed in a wide range of positive total electron doping $n_\mathrm{tot}$ and effective displacemen…
Magic-angle twisted bilayer graphene (TBG), with rotational misalignment close to 1.1$^\circ$, features isolated flat electronic bands that host a rich phase diagram of correlated insulating, superconducting, ferromagnetic, and topological phases. The origins of the correlated insulators and superconductivity, and the interplay between them, are particularly elusive. Both states have been previously observed only for angles within $\pm0.1^\circ$ from the magic-angle value and occur in adjacent or overlapping electron density ranges; nevertheless, it is still unclear how the two states are rela…
Excitonic insulators and superfluidity in 2D bilayers without external fields
本文通过从头计算结合平均场BCS理论，在二维Janus范德华双层中发现了16种无需外场即可实现内禀激子绝缘态并具有超流性质的材料，揭示了层间杂化、自旋轨道耦合与介电屏蔽之间的竞争机制。
The experimentally observed correlated insulating states and quantum anomalous Hall (QAH) effect in twisted bilayer graphene (TBG) have drawn significant attention. However, up to date, the specific mechanisms of these intriguing phenomena are still open questions. Using a fully unrestricted Hartree-Fock variational method, we have explained the correlated insulating states and QAH effects at various integer fillings of the flat bands in TBG. Our results indicate that states breaking flavor (valley and spin) symmetries are energetically favored at all integer fillings. In particular, the corre…
Superconductivity often occurs close to broken-symmetry parent states and is especially common in doped magnetic insulators. When twisted close to a magic relative orientation angle near 1 degree, bilayer graphene has flat moire superlattice minibands that have emerged as a rich and highly tunable source of strong correlation physics, notably the appearance of superconductivity close to interaction-induced insulating states. Here we report on the fabrication of bilayer graphene devices with exceptionally uniform twist angles. We show that the reduction in twist angle disorder reveals insulatin…
Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene
在电荷中性点（CNP）处的双层石墨烯（BLG）对电子相互作用非常敏感，并且预期经历相变进入具有自发破缺对称性的状态。通过系统地研究大量的单栅和双栅双层石墨烯（BLG）器件，我们发现绝缘状态只出现在具有高迁移率和低非本征掺杂的器件中。这种绝缘状态有一个相关的转变温度Tc~ 5 K和能隙~3 meV，从而强烈建议一个缺口破坏对称性状态，被破坏的非常弱的无序。到本征对称性破缺态的跃迁可以通过无序、面外电场或载流子密度来调谐。
Orientation-tunable correlated Chern insulating states in chiral twisted double bilayer graphene proximitized by WSe2
通过理论计算和输运测量，发现石墨烯与WSe2的扭转角调控Ising和Rashba自旋轨道耦合的平衡，从而决定关联陈绝缘体的拓扑性质。
We present a simple model that we believe captures the key aspects of the competition between superconducting and insulating states in twisted bilayer graphene. Within this model, the superconducting phase is primary, and arises at generic fillings, but is interrupted by the insulator at commensurate fillings. Importantly, the insulator forms because of electron-electron interactions, but the model is agnostic as to the superconducting pairing mechanism, which need not originate with electron-electron interactions. The model is composed of a collection of crossed one-dimensional quantum wires …
Stacking boundaries and transport in bilayer graphene
原始的双层石墨烯在某些情况下表现为具有几meV的传输间隙的绝缘体。这种行为已被解释为多体关联引起的内在电子不稳定性的结果。然而，有趣的是，一些具有类似迁移率的样品表现出良好的金属性质，具有$2e^2/h$量级的最小电导率。在这里，我们提出了一个解释这种二分法，这是无关的电子相互作用，而不是基于可逆的形成堆叠域（“孤子”）之间的边界。我们认为，使用数值分析，以前推断的多体绝缘状态的标志性特征可以解释为散射域之间的边界具有不同的堆叠顺序（AB和BA）。此外，我们提出的实验证据，加强我们的解释，金属和绝缘制度之间的可逆切换悬浮双层时，受到热循环或高电流退火。
Generation and detection of pure valley current by electrically induced Berry curvature in bilayer graphene
谷值是非耗散电子器件的有用自由度，因为即使在绝缘材料中也可以流动的谷值电流不伴随电子电流。我们使用双栅双层石墨烯的霍尔棒几何形状，以电控制破缺的反转对称性或Berry曲率以及载流子密度，以产生和检测纯谷电流。我们发现一个大的非局部电阻和立方标度之间的非局部电阻和局部电阻率在绝缘制度在零磁场和70 K的纯谷电流的证据。在零电导率的极限中的谷电流的电控制允许谷电流从电场的非耗散感应，并且因此为非耗散电子学的进步提供了显著贡献。
The combination of field tunable bandgap, topological edge states, and valleys in the band structure, makes insulating bilayer graphene a unique localized system, where the scaling laws of dimensionless conductance g remain largely unexplored. Here we show that the relative fluctuations in ln g with the varying chemical potential, in strongly insulating bilayer graphene (BLG) decay nearly logarithmically for channel length up to L/$ξ$ ${\approx}$ 20, where $ξ$ is the localization length. This 'marginal' self averaging, and the corresponding dependence of <ln g> on L, suggest that transport in …
Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene
双层石墨烯（BLG）中的平带对层之间的电场E \bot敏感，并放大了电子-电子相互作用效应，从而使BLG成为新的二维（2D）电子物理学的有吸引力的平台[1-5]。理论[6-16]已经提出了各种有趣的对称性破缺态的可能性，其中一些以自发质量间隙为特征，当电子密度处于载流子中性点（CNP）时。理论上提出的双层石墨烯中的间隙[6，7，10]类似于粒子物理学中对称性破坏产生的质量[17，18]，并产生大的动量空间Berry曲率[8，19]，伴随着自发的量子霍尔效应[7-9]。尽管最近的实验[20-23]提供了令人信服的证据，证明BLG中CNP附近存在强的电子相关性，但由于缺乏直接的光谱测量，很难确定间隙的存在。在这里，我们提出了运输测量在超净双栅BLG，使用源漏偏置作为光谱工具，以解决在CNP的间隙为2毫电子伏。间隙可以通过13 mV/nm的电场E \bot \sim闭合，但随着磁场B单调增加，在间隙上方具有明显的粒子-空穴不对称性，从而提供BLG中的基态的第一映射。
We study electronic, charge, and magnetic properties of twisted bilayer graphene with fillings $2\leq n\leq 6$ per moire unit cell within the recently introduced formulation of extended dynamical mean-field theory (E-DMFT) for two-sublattice systems. We use previously obtained hopping parameters between the states, described by Wannier functions, centered at the lattice spots of AB and BA stacking, and the long-range Coulomb interaction, obtained within cRPA analysis. We show that account of spin exchange between AB and BA nearest neighbour spots is crucial to introduce charge and spin correla…
Strongly Interacting Phases in Twisted Bilayer Graphene at the Magic Angle
通过无限制大规模Hartree-Fock计算，研究魔角扭曲双层石墨烯在整数填充下的强相互作用绝缘相，发现铁磁态、量子反常霍尔效应及亚晶格对称性破缺，证明了大规模晶格计算对确定基态的重要性。
Insulating state in tetralayers reveals an even-odd interaction effect in multilayer graphene
不存在分隔价带和导带的能隙使得石墨烯及其多层的低能电子性质对电子-电子相互作用敏感。例如，在双层中，相互作用预计会在电荷中性处打开一个间隙，将系统变成绝缘体，正如实验所观察到的那样。在单层和（伯纳尔堆叠）三层中，相互作用虽然仍然很重要，但没有同样剧烈的影响，这些系统在低温下保持导电。可以预期的是，对于较厚的多层膜，相互作用效应变得较弱，其行为最终应该收敛到石墨的行为。在这里，我们通过研究Bernal堆叠的四层石墨烯（4LG）的情况表明，这种期望并不符合现实。我们揭示了一个强大的绝缘状态的发生在一个狭窄的范围内的载流子密度周围的电荷中性，预期从单粒子能带结构的行为不兼容。这种现象类似于在双层中观察到的现象，但是更强的电导抑制使得4LG中的绝缘状态在更高的温度下可见。为了解释我们的研究结果，我们提出了一个自然的泛化的相互作用驱动的，双分子层的破缺状态。这一概括也解释了从实验中出现的不同厚度的Bernal堆叠层中相互作用的系统奇偶效应，并对多层到石墨的交叉有影响。
Interface states in bilayer graphene and valleytronics
我们研究了导电和绝缘双层石墨烯（BLG）之间的界面附近的状态，并表明它们具有非常不寻常的特性，在传统系统中没有类似的。此外，属于BLG的布里渊区中的两个独立谷的状态显示出对比的性质，其允许相对更容易的实验实现谷电子学中期望的各种基于谷的功能，而不需要任何复杂的技术。
Electronic transmission through AB-BA domain boundary in bilayer graphene
我们研究了电子在分隔AB和BA堆叠区的双层石墨烯上通过畴界的传输。利用有效连续介质模型，计算了几种特定边界结构的电子透射几率随电子能量和入射角的变化。透射率强烈地依赖于边界的晶体学方向，也依赖于内部的原子构型。在低能量下，取决于结构，边界是绝缘的或高度透明的。在绝缘情况下，当费米能增加到一定程度时，透射率急剧上升，表明通过边界的电流可以由场效应控制。平行于Z字形方向的边界在两个不同的谷之间通常具有不同的传输特性，并且这使得能够在特定配置中产生谷极化电流。我们表明，这些特征可以定性地解释的横向动量守恒的位置依赖的能带结构在中间区域。
Negative electronic compressibility in charge islands in twisted bilayer graphene
本文利用扭转双层石墨烯中自然形成的电荷岛，通过库仑振荡测量电容，在相关绝缘态和能带绝缘态附近观测到负电子压缩性，并验证其与载流子间距成正比，最终归因于维格纳晶化。
Electron-electron interactions play an important role in graphene and related systems and can induce exotic quantum states, especially in a stacked bilayer with a small twist angle. For bilayer graphene where the two layers are twisted by a "magic angle", flat band and strong many-body effects lead to correlated insulating states and superconductivity. In contrast to monolayer graphene, the band structure of untwisted bilayer graphene can be further tuned by a displacement field, providing an extra degree of freedom to control the flat band that should appear when two bilayers are stacked on t…
Spontaneous charge-ordered state in Bernal-stacked bilayer graphene
本文提出Bernal堆叠双层石墨烯中存在由层间范德瓦尔斯相互作用与波纹协同诱导的自发电荷有序绝缘态，可解释电阻随栅极电场非单调变化及能隙闭合重开现象。
Electron Tunneling in Monolayer and Bilayer Graphene
利用全紧束缚模型研究了单层和双层石墨烯晶格中电子隧穿势垒的行为。重点讨论了共振隧穿特性和谷间散射几率。结果表明，单层和双层石墨烯的垂直入射透射概率表现出不同的性质。计算结果表明，石墨烯体系中的谷电子可以通过改变外电势的结构参数来检测、产生和控制。
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