A quantum ruler for orbital magnetism in moiré quantum matter.

For almost a century, magnetic oscillations have been a powerful "quantum ruler" for measuring Fermi surface topology. In this study, we used Landau-level spectroscopy to unravel the energy-resolved valley-contrasting orbital magnetism and large orbital magnetic susceptibility that contribute to the energies of Landau levels of twisted double-bilayer graphene. These orbital magnetism effects led to substantial deviations from the standard Onsager relation, which manifested as a breakdown in scaling of Landau-level orbits.

Edge channels of broken-symmetry quantum Hall states in graphene visualized by atomic force microscopy.

The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded the concept of topological order in physics bringing into focus the intimate relation between the "bulk" topology and the edge states. The QH effect in graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials. However, the broken-symmetry edge states have eluded spatial measurements.

Tuning single-electron charging and interactions between compressible Landau level islands in graphene.

Interacting and tunable quantum dots (QDs) have been extensively exploited in condensed matter physics and quantum information science. Using a low-temperature scanning tunneling microscope (STM), we both create and directly image a new type of coupled QD system in graphene, a highly interacting quantum relativistic system with tunable density. Using detailed scanning tunneling spectroscopy (STS) measurements, we show that Landau quantization inside a potential well enables novel electron confinement via the incompressible strips between partially filled Landau levels (LLs), forming isolated and concentric LL QDs.

Achieving μeV tunneling resolution in an in-operando scanning tunneling microscopy, atomic force microscopy, and magnetotransport system for quantum materials research.

Research in new quantum materials requires multi-mode measurements spanning length scales, correlations of atomic-scale variables with a macroscopic function, and spectroscopic energy resolution obtainable only at millikelvin temperatures, typically in a dilution refrigerator. In this article, we describe a multi-mode instrument achieving a μeV tunneling resolution with in-operando measurement capabilities of scanning tunneling microscopy, atomic force microscopy, and magnetotransport inside a dilution refrigerator operating at 10 mK. We describe the system in detail including a new scanning probe microscope module design and sample and tip transport systems, along with wiring, radio-frequency filtering, and electronics.

Interaction-driven quantum Hall wedding cake-like structures in graphene quantum dots.

Quantum-relativistic matter is ubiquitous in nature; however, it is notoriously difficult to probe. The ease with which external electric and magnetic fields can be introduced in graphene opens a door to creating a tabletop prototype of strongly confined relativistic matter. Here, through a detailed spectroscopic mapping, we directly visualize the interplay between spatial and magnetic confinement in a circular graphene resonator as atomic-like shell states condense into Landau levels.