对57 nm宽GaAs量子阱中电子的磁输运测量表明，低朗道能级填充（$ν$）的相关电子态对电子电荷分布的对称性有显著的依赖性.在密度为$1.93 \times 10^{11}$ cm $^{-2}$时，当分布对称时，在填充$ν= 1/4$的偶数分母处观察到发展的分数量子霍尔态，但是当分布不对称时，分数量子霍尔态迅速消失。在较低的密度下，当我们使电荷分布不对称时，我们观察到围绕$ν= 1/5$分数量子霍尔态的绝缘相的快速增强。
英文摘要：
Magneto-transport measurements on electrons confined to a 57 nm-wide, GaAs quantum well reveal that the correlated electron states at low Landau level fillings ($ν$) display a remarkable dependence on the symmetry of the electron charge distribution. At a density of $1.93 \times 10^{11}$ cm$^{-2}$, a developing fractional quantum Hall state is observed at the even-denominator filling $ν= 1/4$ when the distribution is symmetric, but it quickly vanishes when the distribution is made asymmetric. At lower densities, as we make the charge distribution asymmetric, we observe a rapid strengthening of the insulating phases that surround the $ν= 1/5$ fractional quantum Hall state.
Moiré superlattices are excellent platforms to realize strongly correlated quantum phenomena, such as Mott insulation and superconductivity. In particular, recent research has revealed stripe phases and generalized Wigner crystals at fractional fillings of moiré superlattices. But these experiments have not focused on the influence of electronic crystallization on the excitonic and valleytronic properties of the superlattices. Here we report excitonic and valleytronic signatures of correlated states at fractional fillings in a WSe$_2$/WS$_2$ moiré superlattice. We observe reflection spectral m…
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…
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…
Moiré superlattices of van der Waals materials, such as twisted graphene and transitional metal dichalcogenides, have recently emerged as a fascinating platform to study strongly correlated states in two dimensions, thanks to the strong electron interaction in the moiré minibands. In most systems, the correlated states appear when the moiré lattice is filled by integer number of electrons per moiré unit cell. Recently, correlated states at fractional fillings of 1/3 and 2/3 holes per moiré unit cell has been reported in the WS2/WSe2 heterobilayer, hinting the long range nature of the electron …
Quantum particles on a lattice with competing long-range interactions are ubiquitous in physics. Transition metal oxides, layered molecular crystals and trapped ion arrays are a few examples out of many. In the strongly interacting regime, these systems often exhibit a rich variety of quantum many-body ground states that challenge theory. The emergence of transition metal dichalcogenide moiré heterostructures provides a highly controllable platform to study long-range electronic correlations. Here we report an observation of nearly two-dozen correlated insulating states at fractional fillings …
The ground state of two-dimensional electron systems (2DESs) at low Landau level filling factors ($ν\lesssim1/6$) has long been a topic of interest and controversy in condensed matter. Following the recent breakthrough in the quality of ultra-high-mobility GaAs 2DESs, we revisit this problem experimentally and investigate the impact of reduced disorder. In a GaAs 2DES sample with density $n=6.1\times10^{10}$ /cm$^2$ and mobility $μ=25\times10^6$ cm$^2$/Vs, we find a deep minimum in the longitudinal magnetoresistance ($R_{xx}$) at $ν=1/7$ when $T\simeq104$ mK. There is also a clear sign of a de…
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…
We introduce and analyze a model that sheds light on the interplay between correlated insulating states, superconductivity, and flavor-symmetry breaking in magic angle twisted bilayer graphene. Using a variational mean-field theory, we determine the normal-state phase diagram of our model as a function of the band filling. The model features robust insulators at even integer fillings, occasional weaker insulators at odd integer fillings, and a pattern of flavor-symmetry breaking at non-integer fillings. Adding a phonon-mediated inter-valley retarded attractive interaction, we obtain strong-cou…
The flat bands resulting from moiré superlattices in magic-angle twisted bilayer graphene (MATBG) and ABC-trilayer graphene aligned with hexagonal boron nitride (ABC-TLG/hBN) have been shown to give rise to fascinating correlated electron phenomena such as correlated insulators and superconductivity. More recently, orbital magnetism associated with correlated Chern insulators was found in this class of layered structures centered at integer multiples of n0, the density corresponding to one electron per moiré superlattice unit cell. Here we report the experimental observation of ferromagnetism …
Moiré heterostructures are rapidly emerging as a tunable platform to study correlated electronic phenomena. Discovery of exotic quantum phases in moiré systems requires novel probes of charge and spin order. Unlike detection schemes which average over several moiré cells, local sensors can provide richer information with greater sensitivity. We study a WSe$_2$/MoSe$_2$/WSe$_2$ heterotrilayer which hosts excitons and electrons in distinct moiré lattices, and show that localized dipolar excitons are sensitive proximity charge sensors, uncovering numerous correlated electronic states at fractiona…
Magic-angle twisted bilayer graphene (tBLG) has been studied extensively owing to its wealth of symmetry-broken phases, correlated Chern insulators, orbital magnetism, and superconductivity. In particular, the anomalous Hall effect (AHE) has been observed at odd integer filling factors ($ν=1$ and $3$) in a small number of tBLG devices, indicating the emergence of a zero-field orbital magnetic state with spontaneously broken time-reversal symmetry. However, the AHE is typically not anticipated at half filling ($ν=2$) owing to competing intervalley coherent states, as well as spin-polarized and …
Flat electronic bands, characteristic of magic-angle twisted bilayer graphene (TBG), host a wealth of correlated phenomena. Early theoretical considerations suggested that, at the magic angle, the Dirac velocity vanishes and the entire width of the moiré bands becomes extremely narrow. Yet, this scenario contradicts experimental studies that reveal a finite Dirac velocity as well as bandwidths significantly larger than predicted. Here we use spatially resolved spectroscopy in finite and zero magnetic fields to examine the electronic structure of moiré bands and their intricate connection to co…
Van der Waals (vdW) heterostructures are an emergent class of metamaterials comprised of vertically stacked two-dimensional (2D) building blocks, which provide us with a vast tool set to engineer their properties on top of the already rich tunability of 2D materials. One of the knobs, the twist angle between different layers, plays a crucial role in the ultimate electronic properties of a vdW heterostructure and does not have a direct analog in other systems such as MBE-grown semiconductor heterostructures. For small twist angles, the moiré pattern produced by the lattice misorientation create…
Tuning correlated states of twisted mono-bilayer graphene with proximity-induced spin-orbit coupling
Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；Technische Universität München（慕尼黑工业大学）；University of Geneva（日内瓦大学）；Leiden University（莱顿大学）；University of Stuttgart（斯图加特大学）
Mirror-symmetric magic-angle twisted trilayer graphene (MATTG) hosts flat electronic bands close to zero energy, and has been recently shown to exhibit abundant correlated quantum phases with flexible electrical tunability. However studying these phases proved challenging as these are obscured by intertwined Dirac bands. In this work, we demonstrate a novel spectroscopy technique, that allows to quantify the energy gaps and Chern numbers of the correlated states in MATTG by driving band crossings between Dirac cone Landau levels and the energy gaps in the flat bands. We uncover hard correlated…
The dominance of Coulomb interactions over kinetic energy of electrons in narrow, non-trivial moiré bands of magic-angle twisted bilayer graphene (TBG) gives rise to a variety of correlated phases such as correlated insulators, superconductivity, orbital ferromagnetism, Chern insulators and nematicity. Most of these phases occur at or near an integer number of carriers per moiré unit cell. Experimental demonstration of ordered states at fractional moiré band-fillings at zero applied magnetic field $B$, is a challenging pursuit. In this letter, we report the observation of states near half-inte…
The fractional quantum Hall effect (FQHE) is extensively studied, but the explanation for Hall plateau widths and excitation energy gaps remains elusive. We study the effective theory of FQHE built upon experimental inputs of Hall current distribution, edge dynamics, and many-body correlations. We argue that correlated composites of integer spin, comprising electrons and their images, localized at the edge of the incompressible strip are the basic transport entity. We show in the lowest Landau level that Zeeman interactions of these composites produce all odd denominator plateaus and effective…
We create laterally large and low disorder quantum well based quantum dots to study single electron additions to two dimensional electron systems (2DES). Electrons tunnel into these dots across an AlGaAs tunnel barrier from a single $n+$ electrode. Using single-electron capacitance spectroscopy in a dilution refrigerator, we identify capacitance peaks for the addition of the first electron to a dot and record subsequent peaks in the addition spectrum up to occupancies of thousands of electrons. Here, we report two remarkable phenomena that occur in the filling factor range $ν=2$ to $ν=5$ while…
Recent experiments on magic-angle twisted bilayer graphene have discovered correlated insulating behavior and superconductivity at a fractional filling of an isolated narrow band. In this paper we show that magic-angle bilayer graphene exhibits another hallmark of strongly correlated systems --- a broad regime of $T-$linear resistivity above a small, density dependent, crossover temperature--- for a range of fillings near the correlated insulator. We also extract a transport "scattering rate", which satisfies a near Planckian form that is universally related to the ratio of $(k_BT/\hbar)$. Our…
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。
Van der Waals moiré materials have emerged as a highly controllable platform to study the electronic correlation phenomena. In particular, robust correlated insulating states have recently been discovered at both integer and fractional filling factors of the semiconductor moiré systems. Here, we reveal the thermodynamic properties of these states by measuring the gate capacitance of MoSe2/WS2 moiré superlattices. We observe a series of incompressible states for filling factor 0 - 8 and anomalously large capacitance (nearly 60% above the device's geometrical capacitance) in the intervening comp…
Using acoustic method we study dependences of transverse AC conductance, $σ(ω)$, on magnetic field, temperature and the amplitude of AC electric field in a wide (75 nm) quantum well (QW) structure focusing on the vicinity of the filling factor $ν=1/2$. Measurements are performed in the frequency domain 30-307 MHz and in the temperature domain 20-500 mK. Usually, in wide QW structures closely to $ν=1/2$ the fractional quantum Hall effect (FQHE) regime is realized at some parameters of the sample. However, in our structure, at $ν=1/2$ it is a compressible state corresponding to gas of composite …
The discovery of flat bands with non-trivial band topology in magic angle twisted bi-layer graphene (MATBG) has provided a unique platform to study strongly correlated phe-nomena including superconductivity, correlated insulators, Chern insulators and magnetism. A fundamental feature of the MATBG, so far unexplored, is its high magnetic field Hof-stadter spectrum. Here we report on a detailed magneto-transport study of a MATBG de-vice in external magnetic fields of up to B = 31 T, corresponding to one magnetic flux quan-tum per moiré unit cell Φ0. At Φ0, we observe a re-entrant correlated insu…
We use the DMRG to study the correlated electron states favored by the Coulomb interaction projected onto the narrow bands of twisted bilayer graphene within a spinless one-valley model. The Hilbert space of the narrow bands is constructed from a pair of hybrid Wannier states with opposite Chern numbers. Depending on the parameters in the BM model, the DMRG in this basis determines the ground state at one particle per unit cell to be either QAH state or a state with no Hall effect which is nearly a product state. Based on this form, we then apply the variational method to study their competiti…
Microwave spectroscopy within the Landau filling ($ν$) range of the integer quantum Hall effect (IQHE) has revealed pinning mode resonances signifying Wigner solids (WSs) composed of quasi-particles or -holes. We study pinning modes of WSs in wide quantum wells (WQWs) for $ 0.8\leν\le1.2$, varying the density, $n$, and tilting the sample by angle $θ$ in the magnetic field. Three distinct WS phases are accessed. One phase, S1, is phenomenologically the same as the WS observed in the IQHEs of narrow QWs. The second phase, S2, exists at $ν$ further from $ν=1$ than S1, and requires a sufficiently …
Twisted bilayer graphene (TBG) is remarkable for its topological flat bands, which drive strongly-interacting physics at integer fillings, and its simple theoretical description facilitated by the Bistritzer-MacDonald Hamiltonian, a continuum model coupling two Dirac fermions. Due to the large moiré unit cell, TBG offers the unprecedented opportunity to observe reentrant Hofstadter phases in laboratory-strength magnetic fields near $25$T. This Letter is devoted to magic angle TBG at $2π$ flux where the magnetic translation group commutes. We use a newly developed gauge-invariant formalism to d…
Charge imprinting biases topology of correlated insulator in hBN-aligned rhombohedral multilayer graphene
University of Chinese Academy of Sciences（中国科学院大学）；Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院理论科学 kavli 研究所）；ShanghaiTech University（上海科技大学）；Liaoning Academy of Materials（辽宁省材料研究院）
Spin-flip excitations in a quantum Hall electron system at fixed filling factor nu=2 are modelled and studied under conditions of a strong Coulomb interaction when the `Landau level mixing' is a dominant factor determining the excitation energy. The `one-exciton' approach used for the purely electronic excitations in question allows us to describe the Stoner transition from the unpolarized/paramgnet state to the polarized/ferromagnet one. The theoretical results are compared with the available experimental data.
Transition metal dichalcogenide (TMD) moiré heterostructures provide an ideal platform to explore the extended Hubbard model1 where long-range Coulomb interactions play a critical role in determining strongly correlated electron states. This has led to experimental observations of Mott insulator states at half filling2-4 as well as a variety of extended Wigner crystal states at different fractional fillings5-9. Microscopic understanding of these emerging quantum phases, however, is still lacking. Here we describe a novel scanning tunneling microscopy (STM) technique for local sensing and manip…
We demonstrate memory devices based on proton doping and re-distribution in perovskite nickelates (RNiO3, {R=Sm,Nd}) that undergo filling-controlled Mott transition. Switching speeds as high as 30 ns in two-terminal devices patterned by electron-beam lithography is observed. The state switching speed reported here are 300X greater than what has been noted with proton-driven resistance switching to date. The ionic-electronic correlated oxide memory devices also exhibit multi-state non-volatile switching. The results are of relevance to use of quantum materials in emerging memory and neuromorphi…
Two dimensional materials and their heterostructures constitute a promising platform to study correlated electronic states as well as many body physics of excitons. Here, we present experiments that unite these hitherto separate efforts and show how excitons that are dynamically screened by itinerant electrons to form exciton-polarons, can be used as a spectroscopic tool to study interaction-induced incompressible states of electrons. The MoSe$_2$/hBN/MoSe$_2$ heterostructure that we study exhibits a long-period Moiré superlattice as evidenced by coherent-hole tunneling mediated avoided crossi…
Stripe phases, in which the rotational symmetry of charge density is spontaneously broken, occur in many strongly correlated systems with competing interactions. One representative example is the copper-oxide superconductors, where stripe order is thought to be relevant to the mechanism of high-temperature superconductivity. Identifying and studying the stripe phases in conventional strongly correlated systems are, however, challenging due to the complexity and limited tunability of these materials. Here we uncover stripe phases in WSe2/WS2 moiré superlattices with continuously gate-tunable ch…
