Real-Space Mapping of Local Subdegree Lattice Rotations in Low-Angle Twisted Bilayer Graphene.

In two-dimensional small-angle twisted bilayers, van der Waals (vdW) interlayer interaction introduces an atomic-scale reconstruction, which consists of a moiré-periodic network of local subdegree lattice rotations. However, real-space measurement of the subdegree lattice rotation requires extremely high spatial resolution, which is an outstanding challenge in an experiment. Here, a topmost small-period graphene moiré pattern is introduced as a magnifying lens to magnify sub-Angstrom lattice distortions in small-angle twisted bilayer graphene (TBG) by about 2 orders of magnitude. Local moiré periods of the topmost graphene moiré patterns and low-energy van Hove singularities of the system are spatially modified by the atomic-scale reconstruction of the underlying TBG, thus enabling real-space mapping of the networks of the subdegree lattice rotations both in structure and in electronic properties. Our results indicate that it is quite facile to study subdegree lattice rotation in vdW systems by measuring the periods of the topmost moiré superlattice.

Observation of Robust and Long-Ranged Superperiodicity of Electronic Density Induced by Intervalley Scattering in Graphene/Transition Metal Dichalcogenide Heterostructures.

Two-dimensional (2D) h-BN and transition metal dichalcogenides (TMDs) are widely used as substrates of graphene because they are insulating, atomically flat, and without dangling bonds. Usually, it is believed that such insulating substrates will not affect the electronic properties of graphene, especially when the moiré pattern generated between them is quite small. Here, we present a systematic study of the electronic properties of graphene/TMD heterostructures with the period of the moiré pattern <1 nm, and our results reveal an unexpected sensitivity of electronic properties in graphene to the 2D insulating substrates. We demonstrate that there is a robust and long-ranged superperiodicity of electronic density in graphene, which arises from the scattering of electrons between the two valleys of graphene in the graphene/TMD heterostructures. By using scanning tunneling microscope and spectroscopy, three distinct atomic-scale patterns of the electronic density are directly imaged in every graphene/TMD heterostructure.

Molecular Collapse States in Graphene/WSe_{2} Heterostructure Quantum Dots.

In relativistic physics, both atomic collapse in a heavy nucleus and Hawking radiation in a black hole are predicted to occur through the Klein tunneling process that couples particles and antiparticles. Recently, atomic collapse states (ACSs) were explicitly realized in graphene because of its relativistic Dirac excitation with a large "fine structure constant." However, the essential role of the Klein tunneling in the ACSs remains elusive in experiment. Here we systematically study the quasibound states in elliptical graphene quantum dots (GQDs) and two coupled circular GQDs. Bonding and antibonding molecular collapse states formed by two coupled ACSs are observed in both systems. Our experiments supported by theoretical calculations indicate that the antibonding state of the ACSs will change into a Klein-tunneling-induced quasibound state revealing deep connection between the ACSs and the Klein tunneling.

Magnetic-Field-Tunable Valley-Contrasting Pseudomagnetic Confinement in Graphene.

Introducing quantum confinement has uncovered a rich set of interesting quantum phenomena and allows one to directly probe the physics of confined (quasi-)particles. In most experiments, however, an electrostatic potential is the only available method to generate quantum dots in a continuous system to confine (quasi-)particles. Here we demonstrate experimentally that inhomogeneous pseudomagnetic fields in strained graphene can introduce exotic quantum confinement of massless Dirac fermions. The pseudomagnetic fields have opposite directions in the two distinct valleys of graphene. By adding and tuning real magnetic fields, the total effective magnetic fields in the two valleys are imbalanced. By that we realized valley-contrasting spatial confinement, which lifts the valley degeneracy and results in field-tunable valley-polarized confined states in graphene. Our results provide a new avenue to manipulate the valley degree of freedom.

Realizing Valley-Polarized Energy Spectra in Bilayer Graphene Quantum Dots via Continuously Tunable Berry Phases.

The Berry phase plays an important role in determining many physical properties of quantum systems. However, tuning the energy spectrum of a quantum system via Berry phase is comparatively rare because the Berry phase is usually a fixed constant. Here, we report the realization of an unusual valley-polarized energy spectra via continuously tunable Berry phases in Bernal-stacked bilayer graphene quantum dots. In our experiment, the Berry phase of electron orbital states is continuously tuned from about π to 2π by perpendicular magnetic fields. When the Berry phase equals π or 2π, the electron states in the two inequivalent valleys are energetically degenerate. By altering the Berry phase to noninteger multiples of π, large and continuously tunable valley-polarized energy spectra are realized. Our result reveals the Berry phase's essential role in valleytronics and the observed valley splitting, on the order of 10 meV at a magnetic field of 1 T, is about 100 times larger than Zeeman splitting for spin, shedding light on graphene-based valleytronics.

Valley Polarization and Inversion in Strained Graphene via Pseudo-Landau Levels, Valley Splitting of Real Landau Levels, and Confined States.

It is quite easy to control spin polarization and the spin direction of a system via magnetic fields. However, there is no such direct and efficient way to manipulate the valley pseudospin degree of freedom. Here, we demonstrate experimentally that it is possible to realize valley polarization and valley inversion in graphene by using both strain-induced pseudomagnetic fields and real magnetic fields. Pseudomagnetic fields, which are quite different from real magnetic fields, point in opposite directions at the two distinct valleys of graphene. Therefore, the coexistence of pseudomagnetic fields and real magnetic fields leads to imbalanced effective magnetic fields at two distinct valleys of graphene. This allows us to control the valley in graphene as conveniently as the electron spin. In this work, we report a consistent observation of valley polarization and inversion in strained graphene via pseudo-Landau levels, splitting of real Landau levels, and valley splitting of confined states using scanning tunneling spectroscopy. Our results highlight a pathway to valleytronics in strained graphene-based platforms.

Tunable Lattice Reconstruction, Triangular Network of Chiral One-Dimensional States, and Bandwidth of Flat Bands in Magic Angle Twisted Bilayer Graphene.

The interplay between interlayer van der Waals interaction and intralayer lattice distortion can lead to structural reconstruction in slightly twisted bilayer graphene (TBG) with the twist angle being smaller than a characteristic angle θ_{c}. Experimentally, the θ_{c} is demonstrated to be very close to the magic angle (θ≈1.08°). Here we address the transition between reconstructed and unreconstructed structures of the TBG across the magic angle by using scanning tunneling microscopy (STM). Our experiment demonstrates that both structures are stable in the TBG around the magic angle. By using a STM tip, we show that the two structures can be changed to each other and a triangular network of chiral one-dimensional states hosted by domain boundaries can be switched on and off. Consequently, the bandwidth of the flat band, which plays a vital role in the emergent strongly correlated states in the magic angle TBG, is tuned. This provides an extra control knob to manipulate the exotic electronic states of the TBG near the magic angle.

Visualizing a single wavefront dislocation induced by orbital angular momentum in graphene.

Phase singularities are phase-indeterminate points where wave amplitudes are zero, which manifest as phase vertices or wavefront dislocations. In the realm of optical and electron beams, the phase singularity has been extensively explored, demonstrating a profound connection to orbital angular momentum. Direct local imaging of the impact of orbital angular momentum on phase singularities at the nanoscale, however, remains challenging. Here, we study the role of orbital angular momentum in phase singularities in graphene, particularly at the atomic level, through scanning tunneling microscopy and spectroscopy. Our experiments demonstrate that the scatterings between different orbital angular momentum states, which are induced by local rotational symmetry-breaking potentials, can generate additional phase singularities, and result in robust single-wavefront dislocations in real space. Our results pave the way for exploring the effects of orbital degree of freedom on quantum phases in quasiparticle interference processes.

Spectroscopic Evidence for a Spin- and Valley-Polarized Metallic State in a Nonmagic-Angle Twisted Bilayer Graphene.

In the magic-angle twisted bilayer graphene (MA-TBG), strong electron-electron (e-e) correlations caused by the band-flattening lead to many exotic quantum phases such as superconductivity, correlated insulator, ferromagnetism, and quantum anomalous Hall effects, when its low-energy van Hove singularities (VHSs) are partially filled. Here our high-resolution scanning tunneling microscope and spectroscopy measurements demonstrate that the e-e correlation in a nonmagic-angle TBG with a twist angle θ = 1.49° still plays an important role in determining its electronic properties. Our most interesting observation on that sample is when one of its VHSs is partially filled, the one associated peak in the spectrum splits into four peaks. Simultaneously, the spatial symmetry of electronic states around the split VHSs is broken by the e-e correlation. Our analysis based on the continuum model suggests that such a one-to-four split of the VHS originates from the formation of an interaction-driven spin-valley-polarized metallic state near the VHS, which is a symmetry-breaking phase that has not been identified in the MA-TBG or in other systems.