Half-integer Quantum Hall Effect Research Articles

Evolution of microscopic localization in graphene in a magnetic field from scattering resonances to quantum dots

Graphene is a unique two-dimensional material with rich new physics and great promise for applications in electronic devices. Physical phenomena such as the half-integer quantum Hall effect and high carrier mobility are critically dependent on interactions with impurities/substrates and localization of Dirac fermions in realistic devices. We microscopically study these interactions using scanning tunneling spectroscopy (STS) of exfoliated graphene on a SiO2 substrate in an applied magnetic field. The magnetic field strongly affects the electronic behavior of the graphene; the states condense into welldefined Landau levels with a dramatic change in the character of localization. In zero magnetic field, we detect weakly localized states created by the substrate induced disorder potential. In strong magnetic field, the two-dimensional electron gas breaks into a network of interacting quantum dots formed at the potential hills and valleys of the disorder potential. Our results demonstrate how graphene properties are perturbed by the disorder potential; a finding that is essential for both the physics and applications of graphene.

Electronic transport properties of top-gated monolayer and bilayer graphene devices on SiC

ABSTRACTWe studied the electronic transport properties of monolayer and bilayer graphene in top-gated geometries. Monolayer and bilayer graphene were epitaxially grown by thermal decomposition of SiC. The half-integer quantum Hall effect under the gated environment was observed in monolayer graphene devices. The mobility of the monolayer and bilayer graphene devices showed distinct characteristics as a function of carrier density, which reflect their electronic structures. Strong temperature dependence at the charge neutrality point was observed in bilayer graphene devices, suggesting band gap opening.

Nobel Heroes of Graphene

2010 Novel Prize in physics has been awarded to “discovery of graphene” for its infinite potential applications utilizing the outstanding electrical, thermal, mechanical, optical, and chemical properties of graphene. Unfortunately, Prof. Philip Kim (Columbia Univ) who measured the half-integer quantum Hall effect for the first time together with Andre Geim and Konstantin Novosolev failed to get the prize. In this article, the personal backgrounds of the Nobel laureates and Prof. Kim will be introduced first, and then we will discuss the lessons from 2010 Nobel Prize in physics and what Korea needs to do to get the first Nobel Prize in science.

Growth of monolayer graphene on 8° off-axis 4H–SiC (000–1) substrates with application to quantum transport devices

Using high temperature annealing conditions with a graphite cap covering the C-face of an 8° off-axis 4H–SiC sample, large and homogeneous single epitaxial graphene layers have been grown. Raman spectroscopy shows evidence of the almost free-standing character of these monolayer graphene sheets, which was confirmed by magnetotransport measurements. We find a moderate p-type doping, high carrier mobility, and half integer quantum Hall effect typical of high quality graphene samples. This opens the way to a fully compatible integration of graphene with SiC devices on the wafers that constitute the standard in today’s SiC industry.

Roll-to-roll production of 30-inch graphene films for transparent electrodes

The outstanding electrical, mechanical and chemical properties of graphene make it attractive for applications in flexible electronics. However, efforts to make transparent conducting films from graphene have been hampered by the lack of efficient methods for the synthesis, transfer and doping of graphene at the scale and quality required for applications. Here, we report the roll-to-roll production and wet-chemical doping of predominantly monolayer 30-inch graphene films grown by chemical vapour deposition onto flexible copper substrates. The films have sheet resistances as low as approximately 125 ohms square(-1) with 97.4% optical transmittance, and exhibit the half-integer quantum Hall effect, indicating their high quality. We further use layer-by-layer stacking to fabricate a doped four-layer film and measure its sheet resistance at values as low as approximately 30 ohms square(-1) at approximately 90% transparency, which is superior to commercial transparent electrodes such as indium tin oxides. Graphene electrodes were incorporated into a fully functional touch-screen panel device capable of withstanding high strain.

Magneto-transport properties of gapped graphene

Based on the Kubo formula, we have studied the electron transport properties of a gappedgraphene in the presence of a strong magnetic field. By solving the Dirac equation, we findthat the Landau level spectra in two valleys differ from each other in that then = 0 level inthe K valley is located at top of the valence band, whereas it is at the bottom of the conduction band in theK′ valley. Thus, in an individual valley, the symmetry between conduction and valencebands is broken by the presence of a magnetic field. By using the self-consistentBorn approximation to treat the long range potential scattering, we formulate thediagonal and the Hall conductivities in terms of the Green function. To performthe numerical calculation, we find that a large bandgap can suppress thequantum Hall effect, owing to the enhancement of the bandgap squeezing thespacing between the low-lying Landau levels. On the other hand, if the bandgap isnot very large, the odd integer quantum Hall effect experimentally, observed inthe gapless graphene, remains in the gapped one. However, such a result doesnot indicate the half integer quantum Hall effect in an individual valley of thegapped graphene. This is because the heights of the Hall plateaux in either valleycan be continuously tuned by the variation of the bandgap. More interestingly,we find that the height of the diagonal conductivity peak corresponding to then = 0 Landau level is independent of the bandgap if the scattering is not very strong. In the weakscattering limit, we demonstrate analytically that such a peak takes a universal valuee2/(hπ), regardless of the bandgap.

Large‐Yield Preparation of High‐Electronic‐Quality Graphene by a Langmuir–Schaefer Approach

Graphene was discovered less than five years ago and proved the existence of pure two-dimensional systems, thought physically impossible in the past. It appeared very quickly that this exceptionalmaterial showedmany outstanding properties. Since electrons and holes in graphene have potential for high carrier mobilities, this novel material has become an exciting new playground for physicists; properties such as the halfinteger quantum Hall effect at room temperature, spin transport, high elasticity, electromechanicalmodulation, and ferromagnetism all contribute to the fame of graphene. Since the first experiments conducted five years ago on micromechanically cleaved graphite (the renowned but lowyield adhesive tape method), the growing appeal of graphene’s properties has focused much of the research attention towards the conception of a reliable method for large-scale production. Recent advances using chemical vapor deposition and successful transfer of the prepared films to arbitrary substrates brought impressive results in terms of crystalline quality of the layers and consequent electrical and mechanical properties. Notwithstanding these results, truly controllable singleor multilayer large-scale deposition is still a pressing issue and a method for depositing high-quality graphene at variable coverage on an arbitrary surface is not yet available. Moreover, for practical application or simply for fundamental research purposes, good adhesion of graphene to the substrate is of great importance.

Half integer quantum Hall effect in high mobility single layer epitaxial graphene

The quantum Hall effect, with a Berry’s phase of π is demonstrated here on a single graphene layer grown on the C-face of 4H silicon carbide. The mobility is ∼20 000 cm2/V⋅s at 4 K and 15 000 cm2/V⋅s at 300 K despite contamination and substrate steps. This is comparable to the best exfoliated graphene flakes on SiO2 and an order of magnitude larger than Si-face epitaxial graphene monolayers. These and other properties indicate that C-face epitaxial graphene is a viable platform for graphene-based electronics.

Synthesis of isotopically-labeled graphite films by cold-wall chemical vapor deposition and electronic properties of graphene obtained from such films

We report the synthesis of isotopically-labeled graphite films on nickel substrates by using cold-wall chemical vapor deposition (CVD). During the synthesis, carbon from 12C- and 13C-methane was deposited on, and dissolved in, a nickel foil at high temperature, and a uniform graphite film was segregated from the nickel surface by cooling the sample to room temperature. Scanning and transmission electron microscopy, micro-Raman spectroscopy, and X-ray diffraction prove the presence of a graphite film. Monolayer graphene films obtained from such isotopically-labeled graphite films by mechanical methods have electron mobility values greater than 5000 cm2·V−1·s−1 at low temperatures. Furthermore, such films exhibit the half-integer quantum Hall effect over a wide temperature range from 2 K to 200 K, implying that the graphite grown by this cold-wall CVD approach has a quality as high as highly oriented pyrolytic graphite (HOPG). The results from transport measurements indicate that 13C-labeling does not significantly affect the electrical transport properties of graphene.

Graphene: The New Two‐Dimensional Nanomaterial

Every few years, a new material with unique properties emerges and fascinates the scientific community, typical recent examples being high-temperature superconductors and carbon nanotubes. Graphene is the latest sensation with unusual properties, such as half-integer quantum Hall effect and ballistic electron transport. This two-dimensional material which is the parent of all graphitic carbon forms is strictly expected to comprise a single layer, but there is considerable interest in investigating two-layer and few-layer graphenes as well. Synthesis and characterization of graphenes pose challenges, but there has been considerable progress in the last year or so. Herein, we present the status of graphene research which includes aspects related to synthesis, characterization, structure, and properties.

Energy gaps and a zero-field quantum Hall effect in graphene by strain engineering

Owing to the fact that graphene is just one atom thick, it has been suggested that it might be possible to control its properties by subjecting it to mechanical strain. New analysis indicates not only this, but that pseudomagnetic behaviour and even zero-field quantum Hall effects could be induced in graphene under realistic amounts of strain. Among many remarkable qualities of graphene, its electronic properties attract particular interest owing to the chiral character of the charge carriers, which leads to such unusual phenomena as metallic conductivity in the limit of no carriers and the half-integer quantum Hall effect observable even at room temperature1,2,3. Because graphene is only one atom thick, it is also amenable to external influences, including mechanical deformation. The latter offers a tempting prospect of controlling graphene’s properties by strain and, recently, several reports have examined graphene under uniaxial deformation4,5,6,7,8. Although the strain can induce additional Raman features7,8, no significant changes in graphene’s band structure have been either observed or expected for realistic strains of up to ∼15% (refs 9, 10, 11). Here we show that a designed strain aligned along three main crystallographic directions induces strong gauge fields12,13,14 that effectively act as a uniform magnetic field exceeding 10 T. For a finite doping, the quantizing field results in an insulating bulk and a pair of countercirculating edge states, similar to the case of a topological insulator15,16,17,18,19,20. We suggest realistic ways of creating this quantum state and observing the pseudomagnetic quantum Hall effect. We also show that strained superlattices can be used to open significant energy gaps in graphene’s electronic spectrum.

Origin of spatial charge inhomogeneity in graphene

In an ideal graphene sheet charge carriers behave as two-dimensional (2D) Dirac fermions governed by the quantum mechanics of massless relativistic particles. This has been confirmed by the discovery of a half-integer quantum Hall effect in graphene flakes placed on a SiO2 substrate. The Dirac fermions in graphene, however, are subject to microscopic perturbations that include topographic corrugations and electron density inhomogeneities (i.e. charge puddles). Such perturbations profoundly alter Dirac fermion behavior, with implications for their fundamental physics as well as for future graphene device applications. Here we report a new technique of Dirac point mapping that we have used to determine the origin of charge inhomogeneities in graphene. We find that fluctuations in graphene charge density are not caused by topographical corrugations, but rather by charge-donating impurities below the graphene. These impurities induce unexpected standing wave patterns due to supposedly forbidden back-scattering of Dirac fermions. Such wave patterns can be continuously modulated by electric gating. Our observations provide new insight into impurity scattering of Dirac fermions and the microscopic mechanisms limiting electronic mobility in graphene.

Fabrication of graphene nanoribbon by local anodic oxidation lithography using atomic force microscope

We conducted local anodic oxidation (LAO) lithography in single-layer, bilayer, and multilayer graphenes using tapping-mode atomic force microscope. The width of insulating oxidized area depends systematically on the number of graphene layers. An 800-nm-wide bar-shaped device fabricated in single-layer graphene exhibits the half-integer quantum Hall effect. We also fabricated a 55-nm-wide graphene nanoribbon (GNR). The conductance of the GNR at the charge neutrality point was suppressed at low temperature, which suggests the opening of an energy gap due to lateral confinement of charge carriers. These results show that LAO lithography is an effective technique for the fabrication of graphene nanodevices.

Large-scale pattern growth of graphene films for stretchable transparent electrodes

Problems associated with large-scale pattern growth of graphene constitute one of the main obstacles to using this material in device applications. Recently, macroscopic-scale graphene films were prepared by two-dimensional assembly of graphene sheets chemically derived from graphite crystals and graphene oxides. However, the sheet resistance of these films was found to be much larger than theoretically expected values. Here we report the direct synthesis of large-scale graphene films using chemical vapour deposition on thin nickel layers, and present two different methods of patterning the films and transferring them to arbitrary substrates. The transferred graphene films show very low sheet resistance of approximately 280 Omega per square, with approximately 80 per cent optical transparency. At low temperatures, the monolayers transferred to silicon dioxide substrates show electron mobility greater than 3,700 cm(2) V(-1) s(-1) and exhibit the half-integer quantum Hall effect, implying that the quality of graphene grown by chemical vapour deposition is as high as mechanically cleaved graphene. Employing the outstanding mechanical properties of graphene, we also demonstrate the macroscopic use of these highly conducting and transparent electrodes in flexible, stretchable, foldable electronics.

Observation of Half-Integer Quantum Hall Effect in Single-Layer Graphene Using Pulse Magnet

We report on the magnetotransport measurement on a single-layer graphene in pulsed magnetic fields up to B = 53 T. With either electron- or hole-type charge carriers, the Hall resistance R H is quantized into R H = ( h / e 2 )ν -1 with ν= ±2, ±6, and ±10, which demonstrates the observation of a half-integer quantum Hall effect (QHE). At B = 50 T, the half-integer QHE is even observed at room temperature in spite of a conventional carrier mobility µ= 4000 cm 2 V -1 s -1 .

Carbon-Encapsulated Magnetic Nanoparticles Based on Fe, Mn, and Cr for Spintronics Applications

Carbon-based nanostructured materials are the promising candidates for future applications in novel electronics. Unique flexibility in sp-hybridization of carbon valences orbitals results in different stable carbon allotropic forms, affinity for bonding with other atoms and gives nearly ten million different chemical compounds, with the potential use in miniaturized electronics. Carbon nanotube transistors and logic gates, conducting carbonbased polymers have been already demonstrated. Graphite is one of the candidates for future electronics – single layers of graphite (so called graphene) forms two dimensional materials and show many interesting physical properties in the presence of magnetic field like half integer quantum Hall effect, electron– hole degeneracy and vanishing carrier mass near the point of charge neutrality. Intercalation of graphite with various elements yields charge-transfer compounds which may be consider as an analog of semiconductor doping. In this communication we propose to integrate ferromagnetic nano-materials with several graphene layers in so-called carbon-encapsulated magnetic nanoparticles (CEMNPs). Such hybrid structures posses interesting chemical and physical properties. The carbon shell protects the encapsulated crystallites from the oxidation and further agglomeration. On the other hand magnetic field from the core nanomagnet should influence on graphite band electrons. Morphology of nanosized Mn, Fe and Cr-based CEMNPs was studied by transmission electron microscopy. Magnetic properties of encapsulated Mn, Fe and Cr (and their carbides) were studied by means of SQUID magnetometry. The nanometer-sized particles showed superparamagnetic behavior at high temperatures, similar for Mn, Fe and Cr, while at low temperatures different behavior was observed, depending on composition of magnetic cores. For Fe-based CEMNPs Mossbauer spectroscopy was used to investigate chemical composition. Clear evidence of the presence of α-Fe and metastable γ-Fe phase was found.

GRAPHENE IN EXTREMELY HIGH MAGNETIC FIELDS

We have studied the quantum Hall (QH) effect in two-dimensional electrons and holes in high quality graphene samples in strong magnetic fields up to 45 T. A distinctive half-integer QH effect is discovered at high magnetic fields, with QH plateaus appearing at filling factors ν = ±4(|n| + 1/2), where n is the Landau level (LL) index. This finding is consistent with theoretical predictions. In addition, in the extreme magnetic quantum limit with magnetic fields up to 45 T, we observe LL splittings in graphene at filling factors ν = 0,±1,±4. Further detailed investigation shows that the presence of the ν = 0,±1 QH states indicates the n = 0 LL at the charge neutral Dirac point splits into four sublevels, lifting both the sublattice and the spin degeneracy, while the QH states at ν = ±4 can be attributed to lifting of the spin degeneracy of the n = ±1 LLS.

Experimental observation of the quantum Hall effect and Berry's phase in graphene

When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron-hole degeneracy and vanishing carrier mass near the point of charge neutrality. Indeed, a distinctive half-integer quantum Hall effect has been predicted theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction--a consequence of the exceptional topology of the graphene band structure. Recent advances in micromechanical extraction and fabrication techniques for graphite structures now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.

An Open Letter to the Next Generation

S as an undergraduate student and ending as a department head, I had a career in physics that spanned approximately a half century. While, on the whole, I enjoyed my various roles as student, professor, and department head, I suppose a reviewer of a proposal I wrote got it right when he said I had had a relatively undistinguished career. Then why you may wonder, should you listen to me? For one thing, I think my career was fun. Physics is so interesting that I believe it is rewarding at whatever level you can perform. My teaching often energized me; I wrote papers that interested me, if few others; and I met many interesting people. However, I wish I had maximized my opportunities. Obviously, because I had a long, uninterrupted physics career, I must have done a few things right. But that is another story. Retirement has given me time for introspection, and I think I have figured out a few reasons why I was not more successful. Such insights are of little use to me now, but perhaps they may be helpful to some of the younger generation.