Wavefunctions in graphene artificial atoms reveal giant orbital magnetic moments.

We examine graphene quantum dots in back-gated devices on hexagonal boron nitride (hBN) and visualize their merger using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy. These dots are formed by the combination of nanoscale potential wells created by pulsing the voltage of an STM tip above charged defects in the hBN underlayer, and strong magnetic fields gapping the density of states, which add insulating rings in the potential wells. Control of the charge state is achieved via the back gate and sample bias voltages, and the position of the STM tip which serves as a mobile top gate. The individual quantum dots present a distinct phenomenology of single-electron charging due to multiple Landau levels crossing the Fermi energy concentrically. Here, we study side by side pairs of these quantum dots via STM, where we observe a tunable interdot coupling and mergeability. Specifically, with increasing charge filling, the quantum dots formed by electrons belonging to one Landau level merge into a single quantum dot, while the electrons in the next-higher Landau level remain spatially separated into two charge pockets. Using the probe tip as a multifunction tool, we visualize the evolution, growth, and merger of this unique double quantum dot system as a function of tip position and gate voltages.

The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded and brought into focus the concept of topological order in physics. The topologically protected quantum Hall edge states are of crucial importance to the QH effect but have been measured with limited success. The QH edge states in graphene take on an even richer role as 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 but has eluded spatial measurements. In this report, we map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of $\nu=0,\pm 1$ across the quantum Hall edge boundary using atomic force microscopy (AFM). Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moir\'e superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.

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. Extensive benchmarking measurements were performed using superconductor-insulator-superconductor tunnel junctions, with Josephson tunneling as a noise metering detector. After extensive testing and optimization, we have achieved less than 8 μeV instrument resolving capability for tunneling spectroscopy, which is 5-10 times better than previous instrument reports and comparable to the quantum and thermal limits set by the operating temperature at 10 mK.

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. By changing the charge density and the magnetic field we can tune continuously between single- and double-concentric LL QD systems within the same potential well. In the concentric QD regime, single-electron charging peaks of the two dots intersect, displaying a characteristic avoidance pattern. At moderate fields, we observe an unconventional avoidance pattern that differs significantly from that observed in capacitively coupled double-QD systems. We find that we can reproduce in detail this anomalous avoidance pattern within the framework of the electrostatic double-QD model by replacing the capacitive interdot coupling with a phenomenological charge-counting system in which charges in the inner concentric dot are counted in the total charge of both islands. The emergence of such strange forms of interdot coupling in a single potential well, together with the ease of producing such charge pockets in graphene and other two-dimensional (2D) materials, reveals an intriguing testbed for the confinement of 2D electrons in customizable potentials.

In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological nature of one-dimensional (1D) bound states localized at step edges of the [001] surface of a topological crystalline insulator (TCI) Pb$_{0.7}$Sn$_{0.3}$Se, both theoretically and experimentally. We show that the topological stability of the step edge states arises from an emergent particle-hole symmetry of the surface low-energy physics, and demonstrate the experimental signatures of the particle-hole symmetry breaking. We also reveal the effects of an external magnetic field on the 1D bound states. Our work suggests the possibility of similar topological step edge modes in other topological materials with a rocks-salt structure.

The path from a Mott insulating phase to high temperature superconductivity encounters a rich set of unconventional phenomena involving the insulator-to-metal transition (IMT) such as emergent electronic orders and pseudogaps that ultimately affect the condensation of Cooper pairs. A huge hindrance to understanding the origin of these phenomena in the curates is the difficulty in accessing doping levels near the parent state. Recently, the J$_{eff}$=1/2 Mott state of the perovskite strontium iridates has revealed intriguing parallels to the cuprates, with the advantage that it provides unique access to the Mott transition. Here, we exploit this accessibility to study the IMT and the possible nearby electronic orders in the electron-doped bilayer iridate (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$. Using spectroscopic imaging scanning tunneling microscopy, we image the La dopants in the top as well as the interlayer SrO planes. Surprisingly, we find a disproportionate distribution of La in these layers with the interlayer La being primarily responsible for the IMT, thereby revealing the distinct site-dependent effects of dopants on the electronic properties of bilayer systems. Furthermore, we discover the coexistence of two electronic orders generated by electron doping: a unidirectional electronic order with a concomitant structural distortion; and local resonant states forming a checkerboard-like pattern trapped by La. This provides evidence that multiple charge orders may exist simultaneously in Mott systems, even with only one band crossing the Fermi energy.

The path from a Mott insulating phase to high temperature superconductivity encounters a rich set of unconventional phenomena involving the insulator-to-metal transition (IMT) such as emergent electronic orders and pseudogaps that ultimately affect the condensation of Cooper pairs. A huge hindrance to understanding the origin of these phenomena in the curates is the difficulty in accessing doping levels near the parent state. Recently, the J_eff=1/2 Mott state of the perovskite strontium iridates has revealed intriguing parallels to the cuprates, with the advantage that it provides unique access to the Mott transition. Here, we exploit this accessibility to study the IMT and the possible nearby electronic orders in the electron-doped bilayer iridate (Sr_1-xLa_x)_3Ir_2O_7. Using spectroscopic imaging scanning tunneling microscopy, we image the La dopants in the top as well as the interlayer SrO planes. Surprisingly, we find a disproportionate distribution of La in these layers with the interlayer La being primarily responsible for the IMT, thereby revealing the distinct site-dependent effects of dopants on the electronic properties of bilayer systems. Furthermore, we discover the coexistence of two electronic orders generated by electron doping: a unidirectional electronic order with a concomitant structural distortion; and local resonant states forming a checkerboard-like pattern trapped by La. This provides evidence that multiple charge orders may exist simultaneously in Mott systems, even with only one band crossing the Fermi energy.

The path from a Mott insulating phase to high temperature superconductivity encounters a rich set of unconventional phenomena involving the insulator-to-metal transition (IMT), such as emergent electronic orders and pseudogaps, that ultimately affect the condensation of Cooper pairs. A huge hindrance to understanding the origin of these phenomena is the difficulty in accessing doping levels near the parent state. The J eff = 1/2 Mott state of the perovskite strontium iridates has revealed intriguing parallels to the cuprates, with the advantage that it provides unique access to the Mott transition. Here, we exploit this accessibility to study the IMT and the possible nearby electronic orders in the electron-doped bilayer iridate (Sr 1 − x La x ) 3 Ir 2 O 7 . Using spectroscopic imaging scanning tunneling microscopy, we image the La dopants in the top as well as the interlayer SrO planes. Surprisingly, we find a disproportionate distribution of La between these layers with the interlayer La being primarily responsible for the IMT. This reveals the distinct site-dependent effects of dopants on the electronic properties of bilayer systems. Electron doping also results in charge reordering. We find unidirectional electronic order concomitant with the structural distortion known to exist in this system. Intriguingly, similar to the single layer iridate, we also find local resonant states forming a checkerboard-like pattern trapped by La. This suggests that multiple charge orders may exist simultaneously in Mott systems, even with only one band crossing the Fermi energy.

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. We directly observe the development of a "wedding cake"-like structure of concentric regions of compressible-incompressible quantum Hall states, a signature of electron interactions in the system. Solid-state experiments can, therefore, yield insights into the behavior of quantum-relativistic matter under extreme conditions.

Orbital degrees of freedom can have pronounced effects on the fundamental properties of electrons in solids. In addition to influencing bandwidths, gaps, correlation strength and dispersion, orbital effects have been implicated in generating novel electronic and structural phases. Here we show how the orbital nature of bands can result in non-trivial effects of strain on band structure. We use scanning-tunneling microscopy to study the effects of strain on the electronic structure of a heteroepitaxial thin film of a topological crystalline insulator, SnTe. By studying the effects of uniaxial strain on the band structure we find a surprising effect where strain applied in one direction has the most pronounced influence on the band structure along the perpendicular direction. Our theoretical calculations indicate that this effect arises from the orbital nature of the conduction and valence bands. Our results imply that a microscopic model capturing strain effects must include a consideration of the orbital nature of bands.