R. C. Ashoori

Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals Heterostructure

Graphene, Gapped and Butterflied The remarkable transport properties of graphene, such as the high electron mobility, make it a promising material for electronics. However, unlike semiconductors such as silicon, graphenes electronic structure lacks a band gap, and a transistor made out of graphene would not have an “off” state. Hunt et al. (p. 1427, published online 16 May; see the Perspective by Fuhrer) modulated the electronic properties of graphene by building a heterostructure consisting of a graphene flake resting on hexagonal boron nitride (hBN), which has the same honeycomb structure as graphene, but consists of alternating boron and nitrogen atoms instead of carbons. The natural mismatch between the graphene and hBN lattices led to a moire pattern with a large wavelength, causing the opening of a band gap, the formation of an elusive fractional quantum Hall state, and, at high magnetic fields, a fractal phenomenon in the electronic structure called the Hofstadter butterfly. A band gap is observed in a monolayer graphene–hexagonal boron nitride heterostructure. [Also see Perspective by Fuhrer] van der Waals heterostructures constitute a new class of artificial materials formed by stacking atomically thin planar crystals. We demonstrated band structure engineering in a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally aligned hexagonal boron nitride substrate. The spatially varying interlayer atomic registry results in both a local breaking of the carbon sublattice symmetry and a long-range moiré superlattice potential in the graphene. In our samples, this interplay between short- and long-wavelength effects resulted in a band structure described by isolated superlattice minibands and an unexpectedly large band gap at charge neutrality. This picture is confirmed by our observation of fractional quantum Hall states at ±53 filling and features associated with the Hofstadter butterfly at ultrahigh magnetic fields.

Coexistence of magnetic order and two-dimensional superconductivity at LaAlO3/SrTiO3 interfaces

Lanthanum aluminate and strontium titanate are insulators, but when you bring them together, the interface between them becomes a two-dimensional superconductor. Even more surprising, magnetometry and transport measurements show that this superconducting state coexists with magnetic order.

Very Large Capacitance Enhancement in a Two-Dimensional Electron System

Electron correlation effects at the interface of two metal oxides lead to a lower chemical potential and enhance capacitance. Increases in the gate capacitance of field-effect transistor structures allow the production of lower-power devices that are compatible with higher clock rates, driving the race for developing high-κ dielectrics. However, many-body effects in an electronic system can also enhance capacitance. Onto the electron system that forms at the LaAlO3/SrTiO3 interface, we fabricated top-gate electrodes that can fully deplete the interface of all mobile electrons. Near depletion, we found a greater than 40% enhancement of the gate capacitance. Using an electric-field penetration measurement method, we show that this capacitance originates from a negative compressibility of the interface electron system. Capacitance enhancement exists at room temperature and arises at low electron densities, in which disorder is strong and the in-plane conductance is much smaller than the quantum conductance.Novel electronic systems forming at oxide interfaces comprise a class of new materials with a wide array of potential applications. A high mobility electron system forms at the LaAlO3/SrTiO3 interface and, strikingly, both superconducts and displays indications of hysteretic magnetoresistance[1– 5]. An essential step for device applications is establishing the ability to vary the electronic conductivity of the electron system by means of a gate. We have fabricated metallic top gates above a conductive interface to vary the electron density at the interface. By monitoring capacitance and electric field penetration, we are able to tune the charge carrier density and establish that we can completely deplete the metallic interface with small voltages. Moreover, at low carrier densities, the capacitance is significantly enhanced beyond the geometric capacitance for the structure. In the same low density region, the metallic interface overscreens an external electric field. We attribute these observations to a negative compressibility of the electronic system at the interface. Similar phenomena have been observed previously in semiconducting two-dimensional electronic systems [6–12]. The observed compressibility result is consistent with the interface containing a system of mobile electrons in two dimensions [13, 15].

Subsurface charge accumulation imaging of a quantum Hall liquid

The unusual properties of two-dimensional electron systems that give rise to the quantum Hall effect have prompted the development of new microscopic models for electrical conduction. The bulk properties of the quantum Hall effect have also been studied experimentally using a variety of probes including transport,, photoluminescence,, magnetization and capacitance, measurements. However, the fact that two-dimensional electron systems typically exist some distance (about 1,000 Å) beneath the surface of the host semiconductor has presented an important obstacle to more direct measurements of microscopic electronic structure in the quantum Hall regime. Here we introduce a cryogenic scanning-probe technique—‘subsurface charge accumulation’ imaging—that permits very high resolution examination of systems of mobile electrons inside materials. We use this technique to image directly the nanometre-scale electronic structures that exist in the quantum Hall regime.

Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state

Low-dimensional electronic systems have traditionally been obtained by electrostatically confining electrons, either in heterostructures or in intrinsically nanoscale materials such as single molecules, nanowires and graphene. Recently, a new method has emerged with the recognition that symmetry-protected topological (SPT) phases, which occur in systems with an energy gap to quasiparticle excitations (such as insulators or superconductors), can host robust surface states that remain gapless as long as the relevant global symmetry remains unbroken. The nature of the charge carriers in SPT surface states is intimately tied to the symmetry of the bulk, resulting in one- and two-dimensional electronic systems with novel properties. For example, time reversal symmetry endows the massless charge carriers on the surface of a three-dimensional topological insulator with helicity, fixing the orientation of their spin relative to their momentum. Weakly breaking this symmetry generates a gap on the surface, resulting in charge carriers with finite effective mass and exotic spin textures. Analogous manipulations have yet to be demonstrated in two-dimensional topological insulators, where the primary example of a SPT phase is the quantum spin Hall state. Here we demonstrate experimentally that charge-neutral monolayer graphene has a quantum spin Hall state when it is subjected to a very large magnetic field angled with respect to the graphene plane. In contrast to time-reversal-symmetric systems, this state is protected by a symmetry of planar spin rotations that emerges as electron spins in a half-filled Landau level are polarized by the large magnetic field. The properties of the resulting helical edge states can be modulated by balancing the applied field against an intrinsic antiferromagnetic instability, which tends to spontaneously break the spin-rotation symmetry. In the resulting canted antiferromagnetic state, we observe transport signatures of gapped edge states, which constitute a new kind of one-dimensional electronic system with a tunable bandgap and an associated spin texture.

PERIODIC AND APERIODIC BUNCHING IN THE ADDITION SPECTRA OF QUANTUM DOTS

We study electron addition spectra of quantum dots in a broad range of electron occupancies starting from the first electron. Spectra for dots containing <200 electrons reveal a surprising feature. Electron additions are not evenly spaced in gate voltage. Rather, they group into bunches. With increasing electron number the bunching evolves from occurring randomly to periodically at about every fifth electron. The periodicity of the bunching and features in electron tunneling rates suggest that the bunching is associated with electron additions into spatially distinct regions within the dots.

High-resolution spectroscopy of two-dimensional electron systems

Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunnelling, yield measurements of the ‘single-particle’ density of states spectrum of a system. This density of states is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy, and is among the most fundamental and directly calculable quantities in theories of highly interacting systems. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect, has proved difficult to probe spectroscopically. Here we present an improved version of time-domain capacitance spectroscopy that allows us to measure the single-particle density of states of a 2DES with unprecedented fidelity and resolution. Using the method, we perform measurements of a cold 2DES, providing direct measurements of interesting correlated electronic effects at energies that are difficult to reach with other techniques; these effects include the single-particle exchange-enhanced spin gap, single-particle lifetimes in the quantum Hall system, and exchange splitting of Landau levels not at the Fermi surface.

Localization in artificial disorder: two coupled quantum dots

Using single electron capacitance spectroscopy, we study electron additions in quantum dots containing two potential minima separated by a shallow barrier. Analysis of the addition spectra in the magnetic field allows us to distinguish between electrons delocalized over the entire dot and those localized in either of the potential minima. We demonstrate that a high magnetic field abruptly splits up a low-density droplet into two smaller fragments, each residing in a potential minimum. An unexplained cancellation of electron repulsion between electrons in these fragments gives rise to paired electron additions.

Single-electron transistor as a charge sensor for semiconductor applications

We describe the use of aluminum single-electron transistors (SETs) to measure, with extremely high sensitivity, the fluctuation of charge in semiconductor quantum dots. Our method of fabricating SETs results in excellent reliability and reproducibility.

Imaging Transport Resonances in the Quantum Hall Effect

We use a scanning capacitance probe to image transport in the quantum Hall system. Applying a dc bias voltage to the tip induces a ring-shaped incompressible strip (IS) in the 2D electron system (2DES) that moves with the tip. At certain tip positions, short-range disorder in the 2DES creates a quantum dot island in the IS. These islands enable resonant tunneling across the IS, enhancing its conductance by more than 4 orders of magnitude. The images provide a quantitative measure of disorder and suggest resonant tunneling as the primary mechanism for transport across ISs.