Essay: Quantum Hall Effect and the New International System of Units.

On 20 May 2019 the International System of Units will switch over to a new, globally accepted set of definitions based on constants of nature. The quantum Hall effect, discovered 39 years ago, plays an essential role in this development and will now contribute to a new definition of the kilogram. Ironically, the title of publication in Physical Review Letters that introduced the quantum Hall effect is, in hindsight, inaccurate in view of the revised units [K. von Klitzing, G. Dorda, and M. Pepper, New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance, Phys. Rev. Lett. 45, 494 (1980)PRLTAO0031-900710.1103/PhysRevLett.45.494].

A cascade of phase transitions in an orbitally mixed half-filled Landau level.

Half-filled Landau levels host an emergent Fermi liquid that displays instability toward pairing, culminating in a gapped even-denominator fractional quantum Hall ground state. While this pairing may be probed by tuning the polarization of carriers in competing orbital and spin degrees of freedom, sufficiently high quality platforms offering such tunability remain few. We explore the ground states at filling factor ν = 5/2 in ZnO-based two-dimensional electron systems through a forced intersection of opposing spin branches of Landau levels taking quantum numbers N = 1 and 0. We reveal a cascade of phases with distinct magnetotransport features including a gapped phase polarized in the N = 1 level and a compressible phase in N = 0, along with an unexpected Fermi liquid, a second gapped, and a strongly anisotropic nematic-like phase at intermediate polarizations when the levels are near degeneracy. The phase diagram is produced by analyzing the proximity of the intersecting levels and highlights the excellent reproducibility and controllability that ZnO offers for exploring exotic fractionalized electronic phases.

Anomalous Interlayer Transport of Quantum Hall Bilayers in the Strongly Josephson-Coupled Regime.

We investigate Josephson coupling in a closely spaced quantum Hall bilayer. Reduction of the interlayer barrier from the widely used values of 10-12 nm to the present one of 8 nm leads to qualitatively different interlayer transport properties. The breakdown of interlayer coherence can be spatially confined in regions that are smaller than the device size. Such a spatial inhomogeneity depends crucially on the Josephson-coupling strength and can be removed by adding an in-plane magnetic field of about 0.5 T. At higher in-plane fields, the interlayer tunneling I-V curve develops unexpected overshoot features. These results challenge current theoretical understanding and suggest that our bilayer system has entered a previously unexplored regime.

Erratum: Signatures for Wigner Crystal Formation in the Chemical Potential of a Two-Dimensional Electron System [Phys. Rev. Lett. 113, 076804 (2014)].

This corrects the article DOI: 10.1103/PhysRevLett.113.076804.

Probing the microscopic structure of the stripe phase at filling factor 5/2.

A prominent manifestation of the competition between repulsive and attractive interactions acting on different length scales is the self-organized ordering of electrons in a stripelike fashion in material systems such as high-T_{c} superconductors. Such stripe phases are also believed to occur in two-dimensional electron systems exposed to a perpendicular magnetic field, where they cause a strong anisotropy in transport. The addition of an in-plane field even enables us to expel fractional quantum Hall states, to the benefit of such anisotropic phases. An important example represents the disappearance of the 5/2 fractional state. Here, we report the use of nuclear magnetic resonance spectroscopy to probe the electron density distribution of this emergent anisotropic phase. A surprisingly strong spatial density modulation was found. The observed behavior suggests a stripe pattern with a period of 2.6±0.6 magnetic lengths and an amplitude as large as 20% relative to the total density.

Signatures for Wigner crystal formation in the chemical potential of a two-dimensional electron system.

We investigate the evolution of the chemical potential of a two-dimensional electron system (2DES) as a function of density at a fixed magnetic field. By using a bilayer system, changes in the chemical potential of one 2DES are determined from the density variation induced in the second, nearby 2DES. At high magnetic fields around a filling factor of ν=1 or ν=2, the chemical potential jump associated with the condensation in a quantum Hall state exhibits two anomalies symmetrically located around these integer filling factors. They are attributed to the formation of a 2D Wigner crystal of quasiparticles.

Transconductance fluctuations as a probe for interaction-induced quantum Hall states in graphene.

Transport measurements normally provide a macroscopic, averaged view of the sample so that disorder prevents the observation of fragile interaction-induced states. Here, we demonstrate that transconductance fluctuations in a graphene field effect transistor reflect charge localization phenomena on the nanometer scale due to the formation of a dot network which forms near incompressible quantum states. These fluctuations give access to fragile broken symmetry and fractional quantum Hall states even though these states remain hidden in conventional magnetotransport quantities.

Electronic transport in two stacked graphene monolayers.

We report on interlayer and lateral electronic transport measurements in two stacked graphene monolayers which have separate electrical contacts. The current-voltage characteristic across the two layers shows linear Ohmic behavior at zero magnetic field. At high magnetic fields, sequences of quantum Hall plateaus of the overlap region with filling factors 4, 8, and 12 are observed which can be explained by equilibration of the edge channel potentials of the individual graphene layers. An anomaly is observed at total filling factors ±2 in the overlap region. The I-V characteristic for interlayer transport turns nonlinear, and the Hall signal vanishes, indicating a magnetic field induced electrical decoupling of the two graphene layers.

Quantum Hall effect in twisted bilayer graphene.

We address the quantum Hall behavior in twisted bilayer graphene transferred from the C face of SiC. The measured Hall conductivity exhibits the same plateau values as for a commensurate Bernal bilayer. This implies that the eightfold degeneracy of the zero energy mode is topologically protected despite rotational disorder as recently predicted. In addition, an anomaly appears. The densities at which these plateaus occur show a magnetic field dependent offset. It suggests the existence of a pool of localized states at low energy, which do not count towards the degeneracy of the lowest band Landau levels. These states originate from an inhomogeneous spatial variation of the interlayer coupling.

Hot phonons in an electrically biased graphene constriction.

Phonon-carrier interactions can have significant impact on device performance. They can be probed by measuring the phonon lifetime, which reflects the interaction strength of a phonon with other quasi-particles, in particular charge carriers as well as its companion phonons. The carrier phonon and phonon-phonon contributions to the phonon lifetime can be disentangled from temperature-dependent studies. Here, we address the importance of phonon-carrier interactions in Joule-heated graphene constrictions in order to contribute to the understanding of energy dissipation in graphene-based electronic devices. We demonstrate that gapless graphene grants electron-phonon interactions uncommon significance in particular at low carrier density. In conventional semiconductors, the band gap usually prevents the decay of phonons through electron-hole generation and also in metals or other semimetals the Fermi temperature is excessively large to enter the regime where electron-phonon coupling plays such a dominant role as in graphene in the investigated phonon temperature regime from 300 to 1600 K.

Dispersion of the excitations of fractional quantum Hall States.

The rich correlation physics in two-dimensional (2D) electron systems is governed by the dispersion of its excitations. In the fractional quantum Hall regime, excitations involve fractionally charged quasi particles, which exhibit dispersion minima at large momenta referred to as rotons. These rotons are difficult to access with conventional techniques because of the lack of penetration depth or sample volume. Our method overcomes the limitations of conventional methods and traces the dispersion of excitations across momentum space for buried systems involving small material volume. We used surface acoustic waves, launched across the 2D system, to allow incident radiation to trigger these excitations at large momenta. Optics probed their resonant absorption. Our technique unveils the full dispersion of such excitations of several prominent correlated ground states of the 2D electron system, which has so far been inaccessible for experimentation.

Four-terminal magneto-transport in graphene p-n junctions created by spatially selective doping.

In this paper, we describe a graphene p-n junction created by chemical doping. We find that chemical doping does not reduce mobility in contrast to top-gating. The preparation technique has been developed from systematic studies about influences on the initial doping of freshly prepared graphene. We investigated the removal of adsorbates by vacuum treatment, annealing, and compensation doping using NH(3). Hysteretic behavior is observed in the electric field effect due to dipolar adsorbates like water and NH(3). Finally we demonstrate spatially selective doping of graphene using patterned PMMA. Four-terminal transport measurements of the p-n devices reveal edge channel mixing in the quantum hall regime. Quantized resistances of h/e(2), h/3e(2) and h/15e(2) can be observed as expected from theory.

Raman spectra of epitaxial graphene on SiC and of epitaxial graphene transferred to SiO2.

Raman spectra were measured for mono-, bi-, and trilayer graphene grown on SiC by solid state graphitization, whereby the number of layers was preassigned by angle-resolved ultraviolet photoemission spectroscopy. It was found that the only unambiguous fingerprint in Raman spectroscopy to identify the number of layers for graphene on SiC(0001) is the line width of the 2D (or D*) peak. The Raman spectra of epitaxial graphene show significant differences as compared to micromechanically cleaved graphene obtained from highly oriented pyrolytic graphite crystals. The G peak is found to be blue-shifted. The 2D peak does not exhibit any obvious shoulder structures, but it is much broader and almost resembles a single-peak even for multilayers. Flakes of epitaxial graphene were transferred from SiC onto SiO2 for further Raman studies. A comparison of the Raman data obtained for graphene on SiC with data for epitaxial graphene transferred to SiO2 reveals that the G peak blue-shift is clearly due to the SiC substrate. The broadened 2D peak however stems from the graphene structure itself and not from the substrate.

Developments in the quantum Hall effect.

The most important applications of the quantum Hall effect (QHE) are in the field of metrology. The observed quantization of the resistance is primarily used for the reproduction of the SI unit ohm, but is also important for high precision measurements of both the fine structure constant and the Planck constant. Some current QHE research areas include the analysis of new electron-electron correlation phenomena and the development of a more complete microscopic picture of this quantum effect. Recently, scanning force microscopy (SFM) of the potential distribution in QHE devices has been used to enhance the microscopic understanding of current flow in quantum Hall systems. This confirms the importance of the theoretically predicted stripes of compressible and incompressible electronic states close to the boundary of the QHE devices.

Tunable subpicosecond optoelectronic transduction in superlattices of self-assembled ErAs nanoislands.

In applications as diverse as fibre-optic communications and time-domain or terahertz spectroscopy, researchers are keen on ultrafast optoelectronic transducers that can be tailored to specific needs. The molecular beam epitaxy of photoconductors composed of equidistant layers of self-assembled ErAs-islands in a III-V semiconductor matrix, which act as efficient non-radiative carrier capture sites, enables this flexibility. Here, photocurrent autocorrelation techniques are applied to metal-semiconductor-metal photodetectors patterned on ErAs:GaAs superlattices. The experiments demonstrate that the electrical response speed can be conveniently tuned over at least two orders of magnitude starting from 190 fs by increasing the thickness of the GaAs spacer separating adjacent ErAs layers. The same concept is applied to the narrower bandgap InGaAs matrix. We demonstrate an electron lifetime of approximately 1 ps for this material. This brings closer the prospect of implementing terahertz technology at the important optical communication wavelengths of 1.3 and 1.55 microm.

Zero-resistance states induced by electromagnetic-wave excitation in GaAs/AlGaAs heterostructures.

The observation of vanishing electrical resistance in condensed matter has led to the discovery of new phenomena such as, for example, superconductivity, where a zero-resistance state can be detected in a metal below a transition temperature T(c) (ref. 1). More recently, quantum Hall effects were discovered from investigations of zero-resistance states at low temperatures and high magnetic fields in two-dimensional electron systems (2DESs). In quantum Hall systems and superconductors, zero-resistance states often coincide with the appearance of a gap in the energy spectrum. Here we report the observation of zero-resistance states and energy gaps in a surprising setting: ultrahigh-mobility GaAs/AlGaAs heterostructures that contain a 2DES exhibit vanishing diagonal resistance without Hall resistance quantization at low temperatures and low magnetic fields when the specimen is subjected to electromagnetic wave excitation. Zero-resistance-states occur about magnetic fields B = 4/5 Bf and B = 4/9 Bf, where Bf = 2pifm*/e,m* is the electron mass, e is the electron charge, and f is the electromagnetic-wave frequency. Activated transport measurements on the resistance minima also indicate an energy gap at the Fermi level. The results suggest an unexpected radiation-induced, electronic-state-transition in the GaAs/AlGaAs 2DES.