Nonlinear Landau Fan Diagram for Graphene Electrons Exposed to a Moiré Potential.

Due to Landau quantization, the conductance of two-dimensional electrons exposed to a perpendicular magnetic field exhibits oscillations that generate a fan of linear trajectories when plotted in the parameter space spanned by density and field. This fan looks identical, irrespective of the dispersion and field dependence of the Landau level energy. This is no surprise because the position of conductance minima depends solely on the level degeneracy that is linear in flux. The fractal energy spectrum that emerges within each Landau band when electrons are also exposed to a two-dimensional superlattice potential produces numerous additional oscillations, but they also create just linear fans for identical reasons. Here, we report conductance oscillations of graphene electrons exposed to a moiré potential that defy this general rule and form nonlinear trajectories in the density-field plane. We attribute this anomalous behavior to the simultaneous occupation of multiple minibands and magnetic breakdown-induced open orbits.

Reversible superdense ordering of lithium between two graphene sheets.

Many carbon allotropes can act as host materials for reversible lithium uptake1,2, thereby laying the foundations for existing and future electrochemical energy storage. However, insight into how lithium is arranged within these hosts is difficult to obtain from a working system. For example, the use of in situ transmission electron microscopy3-5 to probe light elements (especially lithium)6,7 is severely hampered by their low scattering cross-section for impinging electrons and their susceptibility to knock-on damage8. Here we study the reversible intercalation of lithium into bilayer graphene by in situ low-voltage transmission electron microscopy, using both spherical and chromatic aberration correction9 to enhance contrast and resolution to the required levels. The microscopy is supported by electron energy-loss spectroscopy and density functional theory calculations. On their remote insertion from an electrochemical cell covering one end of the long but narrow bilayer, we observe lithium atoms to assume multi-layered close-packed order between the two carbon sheets. The lithium storage capacity associated with this superdense phase far exceeds that expected from formation of LiC6, which is the densest configuration known under normal conditions for lithium intercalation within bulk graphitic carbon10. Our findings thus point to the possible existence of distinct storage arrangements of ions in two-dimensional layered materials as compared to their bulk parent compounds.

Ambipolar Superconductivity with Strong Pairing Interaction in Monolayer 1T'-MoTe2.

Gate tunable two-dimensional (2D) superconductors offer significant advantages in studying superconducting phase transitions. Here, we address superconductivity in exfoliated 1T'-MoTe2 monolayers with an intrinsic band gap of ∼7.3 meV using field effect doping. Despite large differences in the dispersion of the conduction and valence bands, superconductivity can be achieved easily for both electrons and holes. The onset of superconductivity occurs near 7-8 K for both charge carrier types. This temperature is much higher than that in bulk samples. Also the in-plane upper critical field is strongly enhanced and exceeds the BCS Pauli limit in both cases. Gap information is extracted using point-contact spectroscopy. The gap ratio exceeds multiple times the value expected for BCS weak-coupling. All of these observations suggest a strong enhancement of the pairing interaction.

Emerging perovskite monolayers.

The library of two-dimensional (2D) materials has been enriched over recent years with novel crystal architectures endowed with diverse exciting functionalities. Bulk perovskites, including metal-halide and oxide systems, provide access to a myriad of properties through molecular engineering. Their tunable electronic structure offers remarkable features from long carrier-diffusion lengths and high absorption coefficients in metal-halide perovskites to high-temperature superconductivity, magnetoresistance and ferroelectricity in oxide perovskites. Emboldened by the 2D materials research, perovskites down to the monolayer limit have recently emerged. Like other 2D species, perovskites with reduced dimensionality are expected to exhibit new physics and to herald next-generation multifunctional devices. In this Review, we critically assess the preliminary studies on the synthetic routes and inherent properties of monolayer perovskite materials. We also discuss how to exploit them for widespread applications and provide an outlook on the challenges and opportunities that lie ahead for this enticing class of 2D materials.

Single-spin resonance in a van der Waals embedded paramagnetic defect.

A plethora of single-photon emitters have been identified in the atomic layers of two-dimensional van der Waals materials1-8. Here, we report on a set of isolated optical emitters embedded in hexagonal boron nitride that exhibit optically detected magnetic resonance. The defect spins show an isotropic ge-factor of ~2 and zero-field splitting below 10 MHz. The photokinetics of one type of defect is compatible with ground-state electron-spin paramagnetism. The narrow and inhomogeneously broadened magnetic resonance spectrum differs significantly from the known spectra of in-plane defects. We determined a hyperfine coupling of ~10 MHz. Its angular dependence indicates an unpaired, out-of-plane delocalized π-orbital electron, probably originating from substitutional impurity atoms. We extracted spin-lattice relaxation times T1 of 13-17 µs with estimated spin coherence times T2 of less than 1 µs. Our results provide further insight into the structure, composition and dynamics of single optically active spin defects in hexagonal boron nitride.

Odd Integer Quantum Hall States with Interlayer Coherence in Twisted Bilayer Graphene.

We report on the quantum Hall effect in two stacked graphene layers rotated by 2°. The tunneling strength among the layers can be varied from very weak to strong via the mechanism of magnetic breakdown when tuning the density. Odd-integer quantum Hall physics is not anticipated in the regime of suppressed tunneling for balanced layer densities, yet it is observed. We interpret this as a signature of Coulomb interaction induced interlayer coherence and Bose-Einstein condensation of excitons that form at half filling of each layer. A density imbalance gives rise to reentrant behavior due to a phase transition from the interlayer coherent state to incompressible behavior caused by simultaneous condensation of both layers in different quantum Hall states. With increasing overall density, magnetic breakdown gains the upper hand. As a consequence of the enhanced interlayer tunneling, the interlayer coherent state and the phase transition vanish.

Two-Dimensional Quantum Hall Effect and Zero Energy State in Few-Layer ZrTe5.

Topological matter plays a central role in today's condensed matter research. Zirconium pentatelluride (ZrTe5) has attracted attention as a Dirac semimetal at the boundary of weak and strong topological insulators (TI). Few-layer ZrTe5 is anticipated to exhibit the quantum spin Hall effect due to topological states inside the band gap, but sample degradation inflicted by ambient conditions and processing has so far hampered the fabrication of high quality devices. The quantum Hall effect (QHE), serving as the litmus test for 2D systems to be considered of high quality, has not been observed so far. Only a 3D variant on bulk was reported. Here, we succeeded in preserving the intrinsic properties of thin films lifting the carrier mobility to ∼3500 cm2 V-1 s-1, sufficient to observe the integer QHE and a bulk band gap related zero-energy state. The magneto-transport results offer evidence for the gapless topological states within this gap.

Highly Polarized Single Photons from Strain-Induced Quasi-1D Localized Excitons in WSe2.

Single photon emission from localized excitons in two-dimensional (2D) materials has been extensively investigated because of its relevance for quantum information applications. Prerequisites are the availability of photons with high purity polarization and controllable polarization orientation that can be integrated with optical cavities. Here, deformation strain along edges of prepatterned square-shaped substrate protrusions is exploited to induce quasi-one-dimensional (1D) localized excitons in WSe2 monolayers as an elegant way to get photons that fulfill these requirements. At zero magnetic field, the emission is linearly polarized with 95% purity because exciton states are valley hybridized with equal shares of both valleys and predominant emission from excitons with a dipole moment along the elongated direction. In a strong field, one valley is favored and the linear polarization is converted to high-purity circular polarization. This deterministic control over polarization purity and orientation is a valuable asset in the context of integrated quantum photonics.

Quasiparticle Tunneling across an Exciton Condensate.

The bulk properties of the bilayer quantum Hall state at total filling factor one have been intensively studied in experiment. Correlation induced phenomena such as Josephson-like tunneling and zero Hall resistance have been reported. In contrast, the edge of this bilayer state remains largely unexplored. Here, we address this edge physics by realizing quasiparticle tunneling across a quantum point contact. The tunneling manifests itself as a zero bias peak that grows with decreasing temperature. Its shape agrees quantitatively with the formula for weak quasiparticle tunneling frequently deployed in the fractional quantum Hall regime in single layer systems, consistent with theory. Interestingly, we extract a fractional charge of only a few percent of the free electron charge, which may be a signature of the theoretically predicted leakage between the chiral edge and the bulk mediated by gapless excitations.

Probing Exfoliated Graphene Layers and Their Lithiation with Microfocused X-rays.

X-ray diffraction is measured on individual bilayer and multilayer graphene single-crystals and combined with electrochemically induced lithium intercalation. In-plane Bragg peaks are observed by grazing incidence diffraction. Focusing the incident beam down to an area of about 10 µm × 10 µm, individual flakes are probed by specular X-ray reflectivity. By deploying a recursive Parratt algorithm to model the experimental data, we gain access to characteristic crystallographic parameters of the samples. Notably, it is possible to directly extract the bi/multilayer graphene c-axis lattice parameter. The latter is found to increase upon lithiation, which we control using an on-chip peripheral electrochemical cell layout. These experiments demonstrate the feasibility of in situ X-ray diffraction on individual, micron-sized single crystallites of few- and bilayer two-dimensional materials.

Spin-Split Band Hybridization in Graphene Proximitized with α-RuCl3 Nanosheets.

Proximity effects induced in the two-dimensional Dirac material graphene potentially open access to novel and intriguing physical phenomena. Thus far, the coupling between graphene and ferromagnetic insulators has been experimentally established. However, only very little is known about graphene's interaction with antiferromagnetic insulators. Here, we report a low-temperature study of the electronic properties of high quality van der Waals heterostructures composed of a single graphene layer proximitized with α-RuCl3. The latter is known to become antiferromagnetically ordered below 10 K. Shubnikov-de Haas oscillations in the longitudinal resistance together with Hall resistance measurements provide clear evidence for a band realignment that is accompanied by a transfer of electrons originally occupying the graphene's spin degenerate Dirac cones into α-RuCl3 band states with in-plane spin polarization. Left behind are holes in two separate Fermi pockets, only the dispersion of one of which is distorted near the Fermi energy due to spin selective hybridization with these spin polarized α-RuCl3 band states. This interpretation is supported by our density functional theory calculations. An unexpected damping of the quantum oscillations as well as a zero-field resistance upturn close to the Néel temperature of α-RuCl3 suggest the onset of additional spin scattering due to spin fluctuations in the α-RuCl3.

Charge Inversion and Topological Phase Transition at a Twist Angle Induced van Hove Singularity of Bilayer Graphene.

van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes, and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neighboring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with conventional gating. Here we have addressed magnetotransport when the chemical potential crosses the twist angle induced VHS in twisted bilayer graphene. A topological phase transition is experimentally disclosed in the abrupt conversion of electrons to holes or vice versa, a loss of a nonzero Berry phase and distinct sequences of integer quantum Hall states above and below the singularity.

Structural Attributes and Photodynamics of Visible Spectrum Quantum Emitters in Hexagonal Boron Nitride.

Newly discovered van der Waals materials like MoS2, WSe2, hexagonal boron nitride (h-BN), and recently C2N have sparked intensive research to unveil the quantum behavior associated with their 2D structure. Of great interest are 2D materials that host single quantum emitters. h-BN, with a band gap of 5.95 eV, has been shown to host single quantum emitters which are stable at room temperature in the UV and visible spectral range. In this paper we investigate correlations between h-BN structural features and emitter location from bulk down to the monolayer at room temperature. We demonstrate that chemical etching and ion irradiation can generate emitters in h-BN. We analyze the emitters' spectral features and show that they are dominated by the interaction of their electronic transition with a single Raman active mode of h-BN. Photodynamics analysis reveals diverse rates between the electronic states of the emitter. The emitters show excellent photo stability even under ambient conditions and in monolayers. Comparing the excitation polarization between different emitters unveils a connection between defect orientation and the h-BN hexagonal structure. The sharp spectral features, color diversity, room-temperature stability, long-lived metastable states, ease of fabrication, proximity of the emitters to the environment, outstanding chemical stability, and biocompatibility of h-BN provide a completely new class of systems that can be used for sensing and quantum photonics applications.

Erratum: Signatures for Wigner Crystal Formation in the Chemical Potential of a Two-Dimensional Electron System [Phys. Rev. Lett. 113, 076804 (2014)].

This corrects the article DOI: 10.1103/PhysRevLett.113.076804.

Fractional Quantum Hall States in Bilayer Graphene Probed by Transconductance Fluctuations.

We have investigated fractional quantum Hall (QH) states in Bernal-stacked bilayer graphene using transconductance fluctuation measurements. A variety of odd-denominator fractional QH states with νQH → νQH + 2 symmetry, as previously reported, are observed. However, surprising is that also particle-hole symmetric states are clearly resolved in the same measurement set. We attribute their emergence to the reversal of orbital states in the octet level scheme induced by a strong local charge imbalance, which can be captured by the transconductance fluctuations. Also the even-denominator fractional QH state at filling -1/2 is observed. However, contrary to a previous study on a suspended graphene layer [ Ki et al. Nano Lett. 2014, 14 , 2135 ], the particle-hole symmetric state at filling 1/2 is detected as well. These observations suggest that the stability of both odd and even denominator fractional QH states is very sensitive to local transverse electric fields in bilayer graphene.

Probing the microscopic structure of the stripe phase at filling factor 5/2.

A prominent manifestation of the competition between repulsive and attractive interactions acting on different length scales is the self-organized ordering of electrons in a stripelike fashion in material systems such as high-T_{c} superconductors. Such stripe phases are also believed to occur in two-dimensional electron systems exposed to a perpendicular magnetic field, where they cause a strong anisotropy in transport. The addition of an in-plane field even enables us to expel fractional quantum Hall states, to the benefit of such anisotropic phases. An important example represents the disappearance of the 5/2 fractional state. Here, we report the use of nuclear magnetic resonance spectroscopy to probe the electron density distribution of this emergent anisotropic phase. A surprisingly strong spatial density modulation was found. The observed behavior suggests a stripe pattern with a period of 2.6±0.6 magnetic lengths and an amplitude as large as 20% relative to the total density.

Signatures for Wigner crystal formation in the chemical potential of a two-dimensional electron system.

We investigate the evolution of the chemical potential of a two-dimensional electron system (2DES) as a function of density at a fixed magnetic field. By using a bilayer system, changes in the chemical potential of one 2DES are determined from the density variation induced in the second, nearby 2DES. At high magnetic fields around a filling factor of ν=1 or ν=2, the chemical potential jump associated with the condensation in a quantum Hall state exhibits two anomalies symmetrically located around these integer filling factors. They are attributed to the formation of a 2D Wigner crystal of quasiparticles.

Precise Characterization of a Waveguide Fiber Interface in Silicon Carbide.

Spin-active optical emitters in silicon carbide are excellent candidates toward the development of scalable quantum technologies. However, efficient photon collection is challenged by undirected emission patterns from optical dipoles, as well as low total internal reflection angles due to the high refractive index of silicon carbide. Based on recent advances with emitters in silicon carbide waveguides, we now demonstrate a comprehensive study of nanophotonic waveguide-to-fiber interfaces in silicon carbide. We find that across a large range of fabrication parameters, our experimental collection efficiencies remain above 90%. Further, by integrating silicon vacancy color centers into these waveguides, we demonstrate an overall photon count rate of 181 kilo-counts per second, which is an order of magnitude higher compared to standard setups. We also quantify the shift of the ground state spin states due to strain fields, which can be introduced by waveguide fabrication techniques. Finally, we show coherent electron spin manipulation with waveguide-integrated emitters with state-of-the-art coherence times of T 2 ∼ 42 µs. The robustness of our methods is very promising for quantum networks based on multiple orchestrated emitters.

Fractional quantum Hall phase transitions and four-flux states in graphene.

Graphene and its multilayers have attracted considerable interest because their fourfold spin and valley degeneracy enables a rich variety of broken-symmetry states arising from electron-electron interactions, and raises the prospect of controlled phase transitions among them. Here we report local electronic compressibility measurements of ultraclean suspended graphene that reveal a multitude of fractional quantum Hall states surrounding filling factors ν=-1/2 and -1/4. Several of these states exhibit phase transitions that indicate abrupt changes in the underlying order, and we observe many additional oscillations in compressibility as ν approaches -1/2, suggesting further changes in spin and/or valley polarization. We use a simple model based on crossing Landau levels of composite fermions with different internal degrees of freedom to explain many qualitative features of the experimental data. Our results add to the diverse array of many-body states observed in graphene and demonstrate substantial control over their order parameters.

Atom-by-atom observation of grain boundary migration in graphene.

Grain boundary (GB) migration in polycrystalline solids is a materials science manifestation of survival of the fittest, with adjacent grains competing to add atoms to their outer surfaces at each other's expense. This process is thermodynamically favored when it lowers the total GB area in the sample, thereby reducing the excess free energy contributed by the boundaries. In this picture, a curved boundary is expected to migrate toward its center of curvature with a velocity proportional to the local radius of boundary curvature (R). Investigating the underlying mechanism of boundary migration in a 3D material, however, has been reserved for computer simulation or analytical theory, as capturing the dynamics of individual atoms in the core region of a GB is well beyond the spatial and temporal resolution limits of current characterization techniques. Here, we similarly overcome the conventional experimental limits by investigating a 2D material, polycrystalline graphene, in an aberration-corrected transmission electron microscope, exploiting the energy of the imaging electrons to stimulate individual bond rotations in the GB core region. The resulting morphological changes are followed in situ, atom-by-atom, revealing configurational fluctuations that take on a time-averaged preferential direction only in the presence of significant boundary curvature, as confirmed by Monte Carlo simulations. Remarkably, in the extreme case of a small graphene grain enclosed within a larger one, we follow its shrinkage to the point of complete disappearance.