Quantum Hall states near the charge-neutral Dirac point in graphene

Third-order nonlinear Hall effect in a quantum Hall system

In two-dimensional systems, perpendicular magnetic fields can induce a bulk band gap and chiral edge states, which gives rise to the quantum Hall effect. The quantum Hall effect is characterized by zero longitudinal resistance (Rxx) and Hall resistance (Rxy) plateaus quantized to h/(υe2) in the linear response regime, where υ is the Landau level filling factor, e is the elementary charge and h is Planck's constant. Here we explore the nonlinear response of monolayer graphene when tuned to a quantum Hall state. We observe a third-order Hall effect that exhibits a nonzero voltage plateau scaling cubically with the probe current. By contrast, the third-order longitudinal voltage remains zero. The magnitude of the third-order response is insensitive to variations in magnetic field (down to ~5 T) and in temperature (up to ~60 K). Moreover, the third-order response emerges in graphene devices with a variety of geometries, different substrates and stacking configurations. We term the effect third-order nonlinear response of the quantum Hall state and propose that electron-electron interaction between the quantum Hall edge states is the origin of the nonlinear response of the quantum Hall state.

Honeycomb Electron Lattice Induced Dirac Fermion with Trigonal Warping in Bilayer Electrides

Emergent fermions arising from the excess electrons of electrides provide a new perspective for exploring semimetal states with unique Fermi surface geometries. In this study, a class of unique two-dimensional (2D) highly anisotropic Dirac fermions is designed using a sandwich structure. Based on the structural design and first-principles calculations, 2D electride MB (M = Ca/Sr, B = Cl/Br/I) is an ideal candidate material. The excess electrons of the bilayer MB could be stably localized in the interstitial cavities, constructing a natural zigzag honeycomb electron sublattice that further forms a Dirac fermion. Compared with traditional Dirac semimetals, 2D Dirac electrides exhibited rich physical properties: i) The Fermi surface shows trigonal warping in low-energy regions. In particular, the geometry of the Fermi surface determines the high anisotropy of the Fermi velocity. ii) A pair of Dirac fermions are protected by three-fold rotational symmetry and exhibit strong robustness. iii) Electride MB possesses a lower work function that strongly correlates with the surface area of the emission channel. Based on these properties, an electron-emitting device with multifunctional applications is fabricated. Therefore, this study provides an ideal platform for studying potential entanglement between structures, electrides, and topological states.

Phonon-mediated room-temperature quantum Hall transport in graphene

The quantum Hall (QH) effect in two-dimensional electron systems (2DESs) is conventionally observed at liquid-helium temperatures, where lattice vibrations are strongly suppressed and bulk carrier scattering is dominated by disorder. However, due to large Landau level (LL) separation (~2000 K at B = 30 T), graphene can support the QH effect up to room temperature (RT), concomitant with a non-negligible population of acoustic phonons with a wave-vector commensurate to the inverse electronic magnetic length. Here, we demonstrate that graphene encapsulated in hexagonal boron nitride (hBN) realizes a novel transport regime, where dissipation in the QH phase is governed predominantly by electron-phonon scattering. Investigating thermally-activated transport at filling factor 2 up to RT in an ensemble of back-gated devices, we show that the high B-field behaviour correlates with their zero B-field transport mobility. By this means, we extend the well-accepted notion of phonon-limited resistivity in ultra-clean graphene to a hitherto unexplored high-field realm.

Benchmarking Noise and Dephasing in Emerging Electrical Materials for Quantum Technologies

As quantum technologies develop, a specific class of electrically conducting materials is rapidly gaining interest because they not only form the core quantum-enabled elements in superconducting qubits, semiconductor nanostructures, or sensing devices, but also the peripheral circuitry. The phase coherence of the electronic wave function in these emerging materials will be crucial when incorporated in the quantum architecture. The loss of phase memory, or dephasing, occurs when a quantum system interacts with the fluctuations in the local electromagnetic environment, which manifests in "noise" in the electrical conductivity. Hence, characterizing these materials and devices therefrom, for quantum applications, requires evaluation of both dephasing and noise, although there are very few materials where these properties are investigated simultaneously. Here, the available data on magnetotransport and low-frequency fluctuations in electrical conductivity are reviewed to benchmark the dephasing and noise. The focus is on new materials that are of direct interest to quantum technologies. The physical processes causing dephasing and noise in these systems are elaborated, the impact of both intrinsic and extrinsic parameters from materials synthesis and devices realization are evaluated, and it is hoped that a clearer pathway to design and characterize both material and devices for quantum applications is thus provided.

Coexistence of Canted Antiferromagnetism and Bond Order in ν=0 Graphene

Motivated by experimental studies of graphene in the quantum Hall regime, we revisit the phase diagram of a single sheet of graphene at charge neutrality. Because of spin and valley degeneracies, interactions play a crucial role in determining the nature of the ground state. We show that, generically within the Hartree-Fock approximation, in the regime of interest there is a region of coexistence between magnetic and bond orders in the phase diagram. We demonstrate this result both in continuum and lattice models, and argue that the coexistence phase naturally provides a possible explanation for unreconciled experimental observations on the quantum Hall effect in graphene.

Adsorption performance of modified graphene toward Ti: a first-principles investigation

In order to further explore the properties of graphene-reinforced matrix composites, the adsorption behaviors of intrinsic graphene, vacant defect graphene (VG), and Nd-doped graphene (Nd-doped) adsorbed with Ti were studied. The calculation results show that, compared with intrinsic graphene, the p-type doping and n-type doping are formed in the VG and Nd-doped, respectively. After the Ti adsorption of the above three adsorption systems, the stability of the VG and Nd-doped systems has been significantly improved. What's more, in optical performance, the absorption peaks and reflection peaks have different degrees of red-shift compared with the intrinsic graphene, indicating both adsorption and doping will change the spectral characteristics of graphene. Meanwhile, Ti adsorption can enhance absorption and reflection of graphene in the low-energy region. This study provides a novel method with the exploration of the new function of graphene for the better application of graphene-reinforced matrix composites in optoelectronic equipment in the future.

Carbon Nanomaterials for Electro-Active Structures: A Review

The use of electrically conductive materials to impart electrical properties to substrates for cell attachment proliferation and differentiation represents an important strategy in the field of tissue engineering. This paper discusses the concept of electro-active structures and their roles in tissue engineering, accelerating cell proliferation and differentiation, consequently leading to tissue regeneration. The most relevant carbon-based materials used to produce electro-active structures are presented, and their main advantages and limitations are discussed in detail. Particular emphasis is put on the electrically conductive property, material synthesis and their applications on tissue engineering. Different technologies, allowing the fabrication of two-dimensional and three-dimensional structures in a controlled way, are also presented. Finally, challenges for future research are highlighted. This review shows that electrical stimulation plays an important role in modulating the growth of different types of cells. As highlighted, carbon nanomaterials, especially graphene and carbon nanotubes, have great potential for fabricating electro-active structures due to their exceptional electrical and surface properties, opening new routes for more efficient tissue engineering approaches.

3D Graphene Materials: From Understanding to Design and Synthesis Control

Carbon materials, with their diverse allotropes, have played significant roles in our daily life and the development of material science. Following 0D C₆₀ and 1D carbon nanotube, 2D graphene materials, with their distinctively fascinating properties, have been receiving tremendous attention since 2004. To fulfill the efficient utilization of 2D graphene sheets in applications such as energy storage and conversion, electrochemical catalysis, and environmental remediation, 3D structures constructed by graphene sheets have been attempted over the past decade, giving birth to a new generation of graphene materials called 3D graphene materials. This review starts with the definition, classifications, brief history, and basic synthesis chemistries of 3D graphene materials. Then a critical discussion on the design considerations of 3D graphene materials for diverse applications is provided. Subsequently, after emphasizing the importance of normalized property characterization for the 3D structures, approaches for 3D graphene material synthesis from three major types of carbon sources (GO, hydrocarbons and inorganic carbon compounds) based on GO chemistry, hydrocarbon chemistry, and new alkali-metal chemistry, respectively, are comprehensively reviewed with a focus on their synthesis mechanisms, controllable aspects, and scalability. At last, current challenges and future perspectives for the development of 3D graphene materials are addressed.

Quantum-dot assisted spectroscopy of degeneracy-lifted Landau levels in graphene

Energy spectroscopy of strongly interacting phases requires probes which minimize screening while retaining spectral resolution and local sensitivity. Here, we demonstrate that such probes can be realized using atomic sized quantum dots bound to defects in hexagonal Boron Nitride tunnel barriers, placed at nanometric distance from graphene. With dot energies capacitively tuned by a planar graphite electrode, dot-assisted tunneling becomes highly sensitive to the graphene excitation spectrum. The spectra track the onset of degeneracy lifting with magnetic field at the ground state, and at unoccupied excited states, revealing symmetry-broken gaps which develop steeply with magnetic field - corresponding to Landé g factors as high as 160. Measured up to B = 33 T, spectra exhibit a primary energy split between spin-polarized excited states, and a secondary spin-dependent valley-split. Our results show that defect dots probe the spectra while minimizing local screening, and are thus exceptionally sensitive to interacting states.

Valley and Zeeman Splittings in Multilayer Epitaxial Graphene Revealed by Circular Polarization Resolved Magneto-infrared Spectroscopy

Circular-polarization-resolved magneto-infrared studies of multilayer epitaxial graphene (MEG) are performed using tunable quantum cascade lasers in high magnetic fields up to 17.5 T. Landau level (LL) transitions in the monolayer and bilayer graphene inclusions of MEG are resolved, and considerable electron-hole asymmetry is observed in the extracted electronic band structure. For monolayer graphene, a four-fold splitting of the n = 0 to n = 1 LL transition is evidenced and attributed to the lifting of the valley and spin degeneracy of the zeroth LL and the broken electron-hole symmetry. The magnetic field dependence of the splitting further reveals its possible mechanisms. The best fit to experimental data yields effective g-factors, g_VS^* = 6.7 and g_ZS^* = 4.8, for the valley and Zeeman splittings, respectively.

Electronic Compressibility of Magic-Angle Graphene Superlattices

We report the first electronic compressibility measurements of magic-angle twisted bilayer graphene. The evolution of the compressibility with carrier density offers insights into the interaction-driven ground state that have not been accessible in prior transport and tunneling studies. From capacitance measurements, we determine the chemical potential as a function of carrier density and find the widths of the energy gaps at fractional filling of the moiré lattice. In the electron-doped regime, we observe unexpectedly large gaps at quarter- and half-filling and strong electron-hole asymmetry. Moreover, we measure a ∼35  meV minibandwidth that is much wider than most theoretical estimates. Finally, we explore the field dependence up to the quantum Hall regime and observe significant differences from transport measurements.

First-Principles Investigation of Adsorption of Ag on Defected and Ce-doped Graphene

To enhance the wettability between Ag atoms and graphene of graphene-reinforced silver-based composite filler, the adsorption behavior of Ag atoms on graphene was studied by first-principles calculation. This was based on band structure analysis, both p-type doping and n-type doping form, of the vacancy-defected and Ce-doped graphene. It was verified by the subsequent investigation on the density of states. According to the charge transfer calculation, p-type doping can promote the electron transport ability between Ag atoms and graphene. The adsorption energy and population analysis show that both defect and Ce doping can improve the wettability and stability of the Ag-graphene system. Seen from these theoretical calculations, this study provides useful guidance for the preparation of Ag-graphene composite fillers.

Inter-Landau-level Andreev Reflection at the Dirac Point in a Graphene Quantum Hall State Coupled to a NbSe_{2} Superconductor

Superconductivity and the quantum Hall effect are distinct states of matter occurring in apparently incompatible physical conditions. Recent theoretical developments suggest that the coupling of the quantum Hall effect with a superconductor can provide fertile ground for realizing exotic topological excitations such as non-Abelian Majorana fermions or Fibonacci particles. As a step toward that goal, we report observation of Andreev reflection at the junction of a quantum Hall edge state in a single layer graphene and a quasi-two-dimensional niobium diselenide (NbSe_{2}) superconductor. Our principal finding is the observation of an anomalous finite-temperature conductance peak located precisely at the Dirac point, providing a definitive evidence for inter-Landau-level Andreev reflection in a quantum Hall system. Our observations are well supported by detailed numerical simulations, which offer additional insight into the role of the edge states in Andreev physics. This study paves the way for investigating analogous Andreev reflection in a fractional quantum Hall system coupled to a superconductor to realize exotic quasiparticles.

Interfacial engineering in graphene bandgap

Graphene exhibits superior mechanical strength, high thermal conductivity, strong light-matter interactions, and, in particular, exceptional electronic properties. These merits make graphene an outstanding material for numerous potential applications. However, a graphene-based high-performance transistor, which is the most appealing application, has not yet been produced, which is mainly due to the absence of an intrinsic electronic bandgap in this material. Therefore, bandgap opening in graphene is urgently needed, and great efforts have been made regarding this topic over the past decade. In this review article, we summarise recent theoretical and experimental advances in interfacial engineering to achieve bandgap opening. These developments are divided into two categories: chemical engineering and physical engineering. Chemical engineering is usually destructive to the pristine graphene lattice via chemical functionalization, the introduction of defects, doping, chemical bonds with substrates, and quantum confinement; the latter largely maintains the atomic structure of graphene intact and includes the application of an external field, interactions with substrates, physical adsorption, strain, electron many-body effects and spin-orbit coupling. Although these pioneering works have not met all the requirements for electronic applications of graphene at once, they hold great promise in this direction and may eventually lead to future applications of graphene in semiconductor electronics and beyond.

Geometric and electronic structures of monolayer hexagonal boron nitride with multi-vacancy

Hexagonal boron nitride (h-BN) is an electrical insulator with a large band gap of 5 eV and a good thermal conductor of which melting point reaches about 3000 °C. Due to these properties, much attention was given to the thermal stability rather than the electrical properties of h-BN experimentally and theoretically. In this study, we report calculations that the electronic structure of monolayer h-BN can be influenced by the presence of a vacancy defect which leads to a geometric deformation in the hexagonal lattice structure. The vacancy was varied from mono- to tri-vacancy in a supercell, and different defective structures under the same vacancy density were considered in the case of an odd number of vacancies. Consequently, all cases of vacancy defects resulted in a geometric distortion in monolayer h-BN, and new energy states were created between valence and conduction band with the Fermi level shift. Notably, B atoms around vacancies attracted one another while repulsion happened between N atoms around vacancies, irrespective of vacancy density. The calculation of formation energy revealed that multi-vacancy including more B-vacancies has much lower formation energy than vacancies with more N-vacancies. This work suggests that multi-vacancy created in monolayer h-BN will have more B-vacancies and that the presence of multi-vacancy can make monolayer h-BN electrically conductive by the new energy states and the Fermi level shift.

Magnetic Catalysis in Graphene Effective Field Theory

We report on the first calculation of magnetic catalysis at zero temperature in a fully nonperturbative simulation of the graphene effective field theory. Using lattice gauge theory, a nonperturbative analysis of the theory of strongly interacting, massless, (2+1)-dimensional Dirac fermions in the presence of an external magnetic field is performed. We show that in the zero-temperature limit, a nonzero value for the chiral condensate is obtained which signals the spontaneous breaking of chiral symmetry. This result implies a nonzero value for the dynamical mass of the Dirac quasiparticle.

Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene

Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.

Topological spin and valley pumping in silicene

We propose to realize adiabatic topological spin and valley pumping by using silicene, subject to the modulation of an in-plane ac electric field with amplitude Ey and a vertical electric field consisting of an electrostatic component and an ac component with amplitudes and . By tuning and , topological valley pumping or spin-valley pumping can be achieved. The low-noise valley and spin currents generated can be useful in valleytronic and spintronic applications. Our work also demonstrates that bulk topological spin or valley pumping is a general characteristic effect of two-dimensional topological insulators, irrelevant to the edge state physics.

Manipulating interface states in monolayer-bilayer graphene planar junctions

We report on transport properties of monolayer-bilayer graphene planar junctions in a magnetic field. Due to its unique geometry, the edge and interface states can be independently manipulated by either interlayer potential or Zeeman field, and the conductance exhibits interesting quantized behaviors. In the hybrid graphene junction, the quantum Hall (QH) conductance is no longer antisymmetric with respect to the charge neutrality point. When the Zeeman field is considered, a quantum spin Hall (QSH) phase is found in the monolayer region while the weak-QSH phase stays in the bilayer region. In the presence of both interlayer potential and Zeeman field, the bilayer region hosts a QSH phase, whereas the monolayer region is still in a QH phase, leading to a spin-polarized current in the interface. In particular, the QSH phase remains robust against the disorder.

Energy Gaps and Layer Polarization of Integer and Fractional Quantum Hall States in Bilayer Graphene

Owing to the spin, valley, and orbital symmetries, the lowest Landau level in bilayer graphene exhibits multicomponent quantum Hall ferromagnetism. Using transport spectroscopy, we investigate the energy gaps of integer and fractional quantum Hall (QH) states in bilayer graphene with controlled layer polarization. The state at filling factor ν=1 has two distinct phases: a layer polarized state that has a larger energy gap and is stabilized by high electric field, and a hitherto unobserved interlayer coherent state with a smaller gap that is stabilized by large magnetic field. In contrast, the ν=2/3 quantum Hall state and a feature at ν=1/2 are only resolved at finite electric field and large magnetic field. These results underscore the importance of controlling layer polarization in understanding the competing symmetries in the unusual QH system of BLG.

Efficient solution-processed small-molecule solar cells by insertion of graphene quantum dots

In this work, we have demonstrated the results of several positive effects that arise from the addition of graphene quantum dots (GQDs) to solution-processed small molecule bulk-heterojunction (SM-BHJ) solar cells fabricated from a p-DTS(FBTTh(2))(2)/[6,6]-phenyl C(71) butyric acid methyl-ester (PC(71)BM). The device with an optimized ratio of GQDs exhibits increased current density and fill factor owing to 10% improved external quantum efficiency (EQE) and induction of a favorable SM-BHJ morphology. Additionally, the multiple scattering of the GQDs in the SM-BHJ leads to longer optical pathlengths according to the analysis of diffuse reflectance spectra and UV/Vis absorption spectra. The GQD inserted SM-BHJ film at the optimized concentration exhibits decreased charge transport resistance significantly by impedance measurements with effective charge extraction in the device which contributes to 15% enhancement of power conversion efficiency (PCE).

Reduced graphene oxide for fiber-optic humidity sensing

Graphene-based electrical chemical vapor sensors can achieve extremely high sensitivity, whereas the comparatively slow sensing response and recovery, the research focused on only low concentration detection, have been known as drawbacks for many applications requiring rapid and high concentration detection. Here we report a novel graphene-based fiber-optic relative humidity (RH) sensor relying on fundamentally different sensing mechanism. The sensor can achieve power variation of up to 6.9 dB in high relative humidity range (70-95%), and display linear response with correlation coefficient of 98.2%, sensitivity of 0.31 dB/%RH, response speed of faster than 0.13%RH/s, and good repeatability in 75-95%RH. Theoretical analysis of sensing mechanism can explain the experimental result, and reveal the broad applying prospect of the sensor for other kinds of chemical vapor detection. This novel graphene-based optical sensor provides a beneficial complement to the existing electrical ones, and will promote the employment of graphene in chemical sensing techniques.

Ternary CuIn7Se11 : towards ultra-thin layered photodetectors and photovoltaic devices

A few-layered ternary Cu-In-Se compound is synthesized, the photoconductivity is measured, and 2D photovoltaic devices are fabricated. Few-layered CuIn7 Se11 has a strong photoresponse and the potential to serve as the active medium in ultra-thin photovoltaic devices.

Tunable band gaps in graphene/GaN van der Waals heterostructures

Van der Waals (vdW) heterostructures consisting of graphene and other two-dimensional materials provide good opportunities for achieving desired electronic and optoelectronic properties. Here, we focus on vdW heterostructures composed of graphene and gallium nitride (GaN). Using density functional theory, we perform a systematic study on the structural and electronic properties of heterostructures consisting of graphene and GaN. Small band gaps are opened up at or near the Γ point of the Brillouin zone for all of the heterostructures. We also investigate the effect of the stacking sequence and electric fields on their electronic properties. Our results show that the tunability of the band gap is sensitive to the stacking sequence in bilayer-graphene-based heterostructures. In particular, in the case of graphene/graphene/GaN, a band gap of up to 334 meV is obtained under a perpendicular electric field. The band gap of bilayer graphene between GaN sheets (GaN/graphene/graphene/GaN) shows similar tunability, and increases to 217 meV with the perpendicular electric field reaching 0.8 V Å(-1).

Selective equilibration of spin-polarized quantum Hall edge states in graphene

We report on transport measurements of dual-gated, single-layer graphene devices in the quantum Hall regime, allowing for independent control of the filling factors in adjoining regions. Progress in device quality allows us to study scattering between edge states when the fourfold degeneracy of the Landau level is lifted by electron correlations, causing edge states to be spin and/or valley polarized. In this new regime, we observe a dramatic departure from the equilibration seen in more disordered devices: edge states with opposite spins propagate without mixing. As a result, the degree of equilibration inferred from transport can reveal the spin polarization of the ground state at each filling factor. In particular, the first Landau level is shown to be spin polarized at half filling, providing an independent confirmation of a conclusion of Young et al. [Nat. Phys. 8, 550 (2012). The conductance in the bipolar regime is strongly suppressed, indicating that copropagating edge states, even with the same spin, do not equilibrate along PN interfaces. We attribute this behavior to the formation of an insulating ν = 0 stripe at the PN interface.

Dynamical mass generation of composite Dirac fermions and fractional quantum Hall effects near charge neutrality in graphene

We develop a composite Dirac fermion theory for the fractional quantum Hall effects (QHE) near charge neutrality in graphene. We show that the interactions between the composite Dirac fermions lead to a dynamical mass generation through exciton condensation. The four-fold spin-valley degeneracy is fully lifted due to the mass generation and exchange effects such that the odd-denominator fractional QHE observed in the vicinity of charge neutrality can be understood in terms of the integer QHE of composite Dirac fermions. At a filling factor ν = 1/2, we show that the massive composite Dirac fermion liquid is unstable against chiral p-wave pairing for weak Coulomb interactions and the ground state is a paired non-Abelian quantum Hall state described by the Moore-Read Pfaffian in the long wavelength limit.

Splitting of the zero-energy Landau level and universal dissipative conductivity at critical points in disordered graphene

We report on robust features of the longitudinal conductivity (σ(xx)) of the graphene zero-energy Landau level in the presence of disorder and varying magnetic fields. By mixing an Anderson disorder potential with a low density of sublattice impurities, the transition from metallic to insulating states is theoretically explored as a function of Landau-level splitting, using highly efficient real-space methods to compute the Kubo conductivities (both σ(xx) and Hall σ(xy)). As long as valley degeneracy is maintained, the obtained critical conductivity σ(xx) =/~ 1.4e(2)/h is robust upon an increase in disorder (by almost 1 order of magnitude) and magnetic fields ranging from about 2 to 200 T. When the sublattice symmetry is broken, σ(xx) eventually vanishes at the Dirac point owing to localization effects, whereas the critical conductivities of pseudospin-split states (dictating the width of a σ(xy) = 0 plateau) change to σ(xx) =/~ e(2)/h, regardless of the splitting strength, superimposed disorder, or magnetic strength. These findings point towards the nondissipative nature of the quantum Hall effect in disordered graphene in the presence of Landau level splitting.

Magneto-transport of graphene and quantum phase transitions in the quantum Hall regime

In this paper we show the electronic transport and the quantum phase transitions that characterize the quantum Hall regime in graphene placed on SiO(2) substrates at magnetic fields up to 28 T and temperatures down to 4 K. The analysis of the temperature dependence of the Hall and longitudinal resistivity reveals intriguing non-universalities of the critical exponents of the plateau-insulator transition. These exponents depend on the type of disorder that governs the electrical transport and its characterization is important for the design and fabrication of novel graphene nano-devices.

The effects of the magnetopolaron on the energy gap opening in graphene

The magnetopolaron is formed via electron-acoustic deformation phonon coupling in the presence of a magnetic field in monolayer graphene. We find that an energy gap (EG) is opened due to the electron-phonon coupling. Both linear and square-root forms for the dependence of the EG on the magnetic field are obtained, which are in agreement with experimental measurements. Furthermore, we suggest that the EG can be estimated through observing the variation of Fermi velocity in cyclotron resonance experiments. The relation of the EG with the Debye cut-off wavenumber is also discussed.

Gap opening in the zeroth Landau level in gapped graphene: pseudo-Zeeman splitting in an angular magnetic field

We present a theoretical study of gap opening in the zeroth Landau level in gapped graphene as a result of pseudo-Zeeman interaction. The applied magnetic field couples with the valley pseudospin degree of freedom of the charge carriers leading to the pseudo-Zeeman interaction. To investigate its role in transport at the charge neutrality point (CNP), we study the integer quantum Hall effect in gapped graphene in an angular magnetic field in the presence of pseudo-Zeeman interaction. Analytical expressions are derived for the Hall conductivity using the Kubo-Greenwood formula. We also determine the longitudinal conductivity for elastic impurity scattering in the first Born approximation. We show that pseudo-Zeeman splitting leads to a minimum in the collisional conductivity at high magnetic fields and a zero plateau in the Hall conductivity. Evidence for activated transport at CNP is found from the temperature dependence of the collisional conductivity.

Magnetoresistance measurements of graphene at the charge neutrality point

We report on transport measurements of the insulating state that forms at the charge neutrality point of graphene in a magnetic field. Using both conventional two-terminal measurements, sensitive to bulk and edge conductance, and Corbino measurements, sensitive only to the bulk conductance, we observed a vanishing conductance with increasing magnetic fields. By examining the resistance changes of this insulating state with varying perpendicular and in-plane fields, we probe the spin-active components of the excitations in total fields of up to 45 T. Our results indicate that the ν=0 quantum Hall state in single layer graphene is not spin-polarized.

Quantum Hall effects in graphene-based two-dimensional electron systems

In this article we review the quantum Hall physics of graphene-based two-dimensional electron systems, with a special focus on recent experimental and theoretical developments. We explain why graphene and bilayer graphene can be viewed respectively as J D 1 and 2 chiral two-dimensional electron gases (C2DEGs), and why this property frames their quantum Hall physics. The current status of experimental and theoretical work on the role of electron-electron interactions is reviewed at length with an emphasis on unresolved issues in the field, including the role of disorder in current experiments. Special attention is given to the interesting low magnetic field limit, and to the relationship between quantum Hall effects and the spontaneous anomalous Hall effects that might occur in bilayer graphene systems in the absence of a magnetic field.

Transport through graphene on SrTiO3

We report transport measurements through graphene on SrTiO(3) substrates as a function of magnetic field B, carrier density n, and temperature T. The large dielectric constant of SrTiO(3) very effectively screens long-range electron-electron interactions and potential fluctuations, making Dirac electrons in graphene virtually noninteracting. The absence of interactions results in an unexpected behavior of the longitudinal resistance in the N=0 Landau level and in a large suppression of the transport gap in nanoribbons. The "bulk" transport properties of graphene at B=0 T, on the contrary, are completely unaffected by the substrate dielectric constant.

Gate-defined graphene quantum point contact in the quantum Hall regime

We investigate transport in a gate-defined graphene quantum point contact in the quantum Hall regime. Edge states confined to the interface of p and n regions in the graphene sheet are controllably brought together from opposite sides of the sample and allowed to mix in this split-gate geometry. Among the expected quantum Hall features, an unexpected additional plateau at 0.5h/e2 is observed. We propose that chaotic mixing of edge channels gives rise to the extra plateau.

Measurement of the ν=1/3 fractional quantum hall energy gap in suspended graphene

We report on magnetotransport measurements of multiterminal suspended graphene devices. Fully developed integer quantum Hall states appear in magnetic fields as low as 2 T. At higher fields the formation of longitudinal resistance minima and transverse resistance plateaus are seen corresponding to fractional quantum Hall states, most strongly for ν=1/3. By measuring the temperature dependence of these resistance minima, the energy gap for the 1/3 fractional state in graphene is determined to be at ∼20  K at 14 T.

Magnetoconductance oscillations and evidence for fractional quantum Hall states in suspended bilayer and trilayer graphene

We report pronounced magnetoconductance oscillations observed on suspended bilayer and trilayer graphene devices with mobilities up to 270,000 cm²/V s. For bilayer devices, we observe conductance minima at all integer filling factors ν between 0 and -8, as well as a small plateau at ν=1/3. For trilayer devices, we observe features at ν=-1, -2, -3, and -4, and at ν∼0.5 that persist to 4.5 K at B=8 T. All of these features persist for all accessible values of Vg and B, and could suggest the onset of symmetry breaking of the first few Landau levels and fractional quantum Hall states.

Density of states and zero Landau Level probed through capacitance of graphene

We report capacitors in which a finite electronic compressibility of graphene dominates the electrostatics, resulting in pronounced changes in capacitance as a function of magnetic field and carrier concentration. The capacitance measurements have allowed us to accurately map the density of states D, and compare it against theoretical predictions. Landau oscillations in D are robust and zero Landau level (LL) can easily be seen at room temperature in moderate fields. The broadening of LLs is strongly affected by charge inhomogeneity that leads to zero LL being broader than other levels.

Metal to insulator transition on the N=0 Landau level in graphene

The magnetotransport in single layer graphene has been experimentally investigated in magnetic fields up to 18 T as a function of temperature. A pronounced T dependence is observed for T≲50  K, which is either metallic, or insulating, depending on the filling factor ν. The metal-insulator transition (MIT) occurs at |ν{c}|∼0.65 and in the regime of the dissipative transport, where the longitudinal resistance Rxx>1/2R{K}. The critical resistivity (Rxx per square) is ρ{xx}(ν{c})≈1/2R{K} and is correlated with the appearance of zero plateau in Hall conductivity σ{xy}(ν) and peaks in σ{xx}(ν). This leads us to construct a universal low-T (n, B) phase diagram of this quantum phase transition.

Electronic properties of a biased graphene bilayer

We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system-a biased bilayer. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its four-band and two-band continuum approximations, and the four-band model is shown to always be a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, made out of either SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point for understanding the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, such as the second-nearest-neighbour hopping energies t' (in-plane) and γ(4) (inter-layer), and the on-site energy Δ.

Quantum Hall effect near the charge neutrality point in a two-dimensional electron-hole system

We study the transport properties of HgTe-based quantum wells containing simultaneously electrons and holes in a magnetic field B. At the charge neutrality point (CNP) with nearly equal electron and hole densities, the resistance is found to increase very strongly with B while the Hall resistivity turns to zero. This behavior results in a wide plateau in the Hall conductivity sigma(xy) approximately = 0 and in a minimum of diagonal conductivity sigma(xx) at nu = nu(p) - nu(n) = 0, where nu(n) and nu(p) are the electron and hole Landau level filling factors. We suggest that the transport at the CNP point is determined by electron-hole "snake states" propagating along the nu = 0 lines. Our observations are qualitatively similar to the quantum Hall effect in graphene as well as to the transport in a random magnetic field with a zero mean value.

Interaction-induced shift of the cyclotron resonance of graphene using infrared spectroscopy

We report a study of the cyclotron resonance (CR) transitions to and from the unusual n=0 Landau level (LL) in monolayer graphene. Unexpectedly, we find the CR transition energy exhibits large (up to 10%) and nonmonotonic shifts as a function of the LL filling factor, with the energy being largest at half filling of the n=0 level. The magnitude of these shifts, and their magnetic field dependence, suggests that an interaction-enhanced energy gap opens in the n=0 level at high magnetic fields. Such interaction effects normally have a limited impact on the CR due to Kohn's theorem [W. Kohn, Phys. Rev. 123, 1242 (1961)], which does not apply in graphene as a consequence of the underlying linear band structure.