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.

Disorder induced power-law gaps in an insulator-metal Mott transition.

A correlated material in the vicinity of an insulator-metal transition (IMT) exhibits rich phenomenology and a variety of interesting phases. A common avenue to induce IMTs in Mott insulators is doping, which inevitably leads to disorder. While disorder is well known to create electronic inhomogeneity, recent theoretical studies have indicated that it may play an unexpected and much more profound role in controlling the properties of Mott systems.

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.

Interplay of orbital effects and nanoscale strain in topological crystalline insulators.

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.

An on/off Berry phase switch in circular graphene resonators.

The phase of a quantum state may not return to its original value after the system's parameters cycle around a closed path; instead, the wave function may acquire a measurable phase difference called the Berry phase. Berry phases typically have been accessed through interference experiments. Here, we demonstrate an unusual Berry phase-induced spectroscopic feature: a sudden and large increase in the energy of angular-momentum states in circular graphene p-n junction resonators when a relatively small critical magnetic field is reached.

Helical Level Structure of Dirac Potential Wells.

In graphene and other massless two-dimensional Dirac materials, Klein tunneling compromises electron confinement, and momentum-space contours can be assigned a Berry phase which is either zero or π. Consequently, in such systems the energy spectrum of circular potential wells exhibits an interesting discontinuity as a function of magnetic field : for a given angular momentum the ladder of eigen-resonances is split at an energy-dependent critical field . Here we show that introducing a mass term Δ in the Hamiltonian bridges this discontinuity in such a way that states below are adiabatically connected to states above whose principal quantum number differs by unity depending on the sign of Δ.

Strain engineering Dirac surface states in heteroepitaxial topological crystalline insulator thin films.

The unique crystalline protection of the surface states in topological crystalline insulators has led to a series of predictions of strain-generated phenomena, from the appearance of pseudo-magnetic fields and helical flat bands to the tunability of Dirac surface states by strain that may be used to construct 'straintronic' nanoswitches. However, the practical realization of this exotic phenomenology via strain engineering is experimentally challenging and is yet to be achieved. Here, we have designed an experiment to not only generate and measure strain locally, but also to directly measure the resulting effects on Dirac surface states.

Nanoscale determination of the mass enhancement factor in the lightly doped bulk insulator lead selenide.

Bismuth chalcogenides and lead telluride/selenide alloys exhibit exceptional thermoelectric properties that could be harnessed for power generation and device applications. Since phonons play a significant role in achieving these desired properties, quantifying the interaction between phonons and electrons, which is encoded in the Eliashberg function of a material, is of immense importance. However, its precise extraction has in part been limited due to the lack of local experimental probes.

Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators.

The tunability of topological surface states and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In the newly discovered topological crystalline insulators (TCIs), theory predicts that the Dirac node is protected by a crystalline symmetry and that the surface state electrons can acquire a mass if this symmetry is broken. Recent studies have detected signatures of a spontaneously generated Dirac gap in TCIs; however, the mechanism of mass formation remains elusive.

Observation of Dirac node formation and mass acquisition in a topological crystalline insulator.

In topological crystalline insulators (TCIs), topology and crystal symmetry intertwine to create surface states with distinct characteristics. The breaking of crystal symmetry in TCIs is predicted to impart mass to the massless Dirac fermions. Here, we report high-resolution scanning tunneling microscopy studies of a TCI, Pb(1-x)Sn(x)Se that reveal the coexistence of zero-mass Dirac fermions protected by crystal symmetry with massive Dirac fermions consistent with crystal symmetry breaking.

Imaging the evolution of metallic states in a correlated iridate.

The Ruddlesden-Popper series of iridates (Srn+1IrnO3n+1) have been the subject of much recent attention due to the anticipation of emergent phenomena arising from the cooperative action of spin-orbit-driven band splitting and Coulomb interactions. However, an ongoing debate over the role of correlations in the formation of the charge gap and a lack of understanding of the effects of doping on the low-energy electronic structure have hindered experimental progress in realizing many of the predicted states. Using scanning tunnelling spectroscopy we map out the spatially resolved density of states in Sr3Ir2O7 (Ir327).