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.     

The enigma of the quantum Hall effect in graphene

We apply Laughlin’s gauge argument to analyze the ν=0 quantum Hall effect observed in graphene when the Fermi energy lies near the Dirac point, and conclude that this necessarily leads to divergent bulk longitudinal resistivity in the zero temperature thermodynamic limit. We further predict that in a Corbino geometry measurement, where edge transport and other mesoscopic effects are unimportant, one should find the longitudinal conductivity vanishing in all graphene samples which have an underlying ν=0 quantized Hall effect. We argue that this ν=0 graphene quantum Hall state is qualitatively similar to the high field insulating phase (also known as the Hall insulator) in the lowest Landau level of ordinary semiconductor two-dimensional electron systems. We establish the necessity of having a high magnetic field and high mobility samples for the observation of the divergent resistivity as arising from the existence of disorder-induced density inhomogeneity at the graphene Dirac point.     

Magnetotransport properties of graphene layers decorated with colloid quantum dots

The hybrid graphene-quantum dot devices can potentially be used to tailor the electronic, optical, and chemical properties of graphene. Here, the low temperature electronic transport properties of bilayer graphene decorated with PbS colloid quantum dots(CQDs) have been investigated in the weak or strong magnetic fields. The presence of the CQDs introduces additional scattering potentials that alter the magnetotransport properties of the graphene layers, leading to the observation of a new set of magnetoconductance oscillations near zero magnetic field as well as the high-field quantum Hall regime.The results bring about a new strategy for exploring the quantum interference effects in two-dimensional materials which are sensitive to the surrounding electrostatic environment, and open up a new gateway for exploring the graphene sensing with quantum interference effects.     

Z2 topological order and the quantum spin Hall effect

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z2 order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multiband and interacting systems.     

Dissipative quantum hall effect in graphene near the Dirac point

We report on the unusual nature of the nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counterpropagating edge states. Such states, intrinsic to massless Dirac quasiparticles, manifest themselves in a large longitudinal resistivity rho(xx) > or approximately h/e(2), in striking contrast to rho(xx) behavior in the standard QHE. The nu=0 state in graphene is also predicted to exhibit pronounced fluctuations in rho(xy) and rho(xx) and a smeared zero Hall plateau in sigma(xy), in agreement with experiment. The existence of gapless edge states puts stringent constraints on possible theoretical models of the nu=0 state.     

Quenching of the quantum Hall effect in graphene with scrolled edges

Edge nanoscrolls are shown to strongly influence transport properties of suspended graphene in the quantum Hall regime. The relatively long arclength of the scrolls in combination with their compact transverse size results in formation of many nonchiral transport channels in the scrolls. They short circuit the bulk current paths and inhibit the observation of the quantized two-terminal resistance. Unlike competing theoretical proposals, this mechanism of disrupting the Hall quantization in suspended graphene is not caused by ill-chosen placement of the contacts, singular elastic strains, or a small sample size.     

Edge physics of graphene in the quantum Hall regime

We study the electronic edge states of graphene in the quantum Hall regime. For non-interacting electrons, graphene supports both electron-like and hole-like edge states. We find there are half as many edge states of each type in the lowest Landau level compared to higher Landau levels, leading to a quantization of the Hall conductance that is shifted relative to standard two dimensional electron gases. We also consider the effect of quantum Hall ferromagnetism on this edge structure, and find an unusual Luttinger liquid at the edge in undoped graphene. This arises due to a domain wall that forms near the edge between partially spin-polarized and valley-polarized regions. The domain wall has a U(1) degree of freedom which generates both collective and charged gapless excitations, whose consequences for tunneling experiments are discussed.     

Unconventional integer quantum Hall effect in graphene

Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity sigma(xy) = -(2e2/h)(2n+1) with n = 0, 1, ..., which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the n=0 Landau level and was discovered in recent experiments on ultrathin graphite films.     

Detection of hidden localized states by the quantum Hall effect in graphene

We fabricated a monolayer graphene transistor device in the shape of the Hall-bar structure, which produced an exactly symmetric signal following the sample geometry. During electrical characterization, the device showed the standard integer quantum Hall effect of monolayer graphene except for a broader range of several quantum Hall plateaus corresponding to small filling factors in the electron region. We investigated this anomaly on the basis of localized states owing to the presence of possible electron traps, whose energy levels were estimated to be near the Dirac point. In particular, the inequality between the filling of electrons and holes was ascribed to the requirement of excess electrons to fill the trap levels. The relations between the quantum Hall plateau, Landau level, and filling factor were carefully analyzed to reveal the details of the localized states in this graphene device.     

On the quantum phase transition of a quantum Hall liquid

It is shown that, in the absence of disorder, a quantum Hall liquid undergoes a second-order quantum phase transition as function of the applied magnetic field. The analysis is carried out in the framework of the Chem-Simons-Ginzburg-Landau theory which is shown to exhibit a nontrivial infrared stable fixed point. The corresponding critical exponents are found to be gaussian, and thus universal and independent of the filling fraction.     

Localization in a quantum spin Hall system

The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.     

Electronic transport and quantum hall effect in bipolar graphene p-n-p junctions

We have developed a device fabrication process to pattern graphene into nanostructures of arbitrary shape and control their electronic properties using local electrostatic gates. Electronic transport measurements have been used to characterize locally gated bipolar graphene p-n-p junctions. We observe a series of fractional quantum Hall conductance plateaus at high magnetic fields as the local charge density is varied in the p and n regions. These fractional plateaus, originating from chiral edge states equilibration at the p-n interfaces, exhibit sensitivity to interedge backscattering which is found to be strong for some of the plateaus and much weaker for other plateaus. We use this effect to explore the role of backscattering and estimate disorder strength in our graphene devices.     

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number C_s for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, C_s is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states,consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit(RSO) interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling.Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.     

Electrically tunable quantum anomalous Hall effect in graphene decorated by 5d transition-metal adatoms

Based on first-principles calculations, we predict that 5d transition metals on graphene present a unique class of hybrid systems exhibiting topological transport effects that can be manipulated effectively by external electric fields. The origin of this phenomenon lies in the exceptional magnetic properties and the large spin-orbit interaction of the 5d metals leading to significant magnetic moments accompanied with colossal magnetocrystalline anisotropy energies. A strong magnetoelectric response is predicted that offers the possibility to switch the spontaneous magnetization direction by moderate electric fields, enabling an electrically tunable quantum anomalous Hall effect.     

Integer quantum Hall effect in trilayer graphene

By using high-magnetic fields (up to 60 T), we observe compelling evidence of the integer quantum Hall effect in trilayer graphene. The magnetotransport fingerprints are similar to those of the graphene monolayer, except for the absence of a plateau at a filling factor of ν=2. At a very low filling factor, the Hall resistance vanishes due to the presence of mixed electron and hole carriers induced by disorder. The measured Hall resistivity plateaus are well reproduced theoretically, using a self-consistent Hartree calculations of the Landau levels and assuming an ABC stacking order of the three layers.     

铁磁石墨烯体系的CT不变量子自旋霍尔效应

文章作者在垂直磁场作用下的铁磁石墨烯体系里预言了一种新类型的量子自旋霍尔效应.这量子自旋霍尔效应与自旋轨道耦合无关,体系也不具有时间反演不变性;但是有CT不变（C为电子-空穴变换、T为时间反演变换）.由于量子自旋霍尔效应,体系的纵向电阻和自旋霍尔阻出现量子化平台.特别是,自旋霍尔阻的量子化平台有很强的抗杂质干扰能力.     

Interlayer transport in bilayer quantum Hall systems

Bilayer quantum Hall systems have a broken symmetry ground state at a filling factor which can be viewed either as an excitonic superfluid or as a pseudospin ferromagnet. We present a theory of interlayer transport in quantum Hall bilayers that highlights remarkable similarities and critical differences between transport in Josephson junction and ferromagnetic metal spin-transfer devices. Our theory is able to explain the size of the large but finite low-bias interlayer conductance and the voltage width of this collective transport anomaly.     

Transverse electric field-induced quantum valley Hall effects in zigzag-edge graphene nanoribbons

We have investigated gapless edge states in zigzag-edge graphene nanoribbons under a transverse electric field across the opposite edges by using a tight-binding model and the density functional theory calculations. The tight-binding model predicted that a quantum valley Hall effect occurs at the vacuum-nanoribbon interface under a transverse electric field and, in the presence of edge potentials with opposite signs on opposite edges, an additional quantum valley Hall effect occurs under a much lower field. Dangling bonds inevitable at the edges of real nanoribbons, functional groups terminating the edge dangling bonds, and spin polarizations at the edges result in the edge potentials. The density functional theory calculations confirmed that asymmetric edge terminations, such as one having hydrogen at an edge and fluorine at the other edge, lead to the quantum valley Hall effect even in the absence of a transverse electric field. The electric field-induced half-metallicity in the antiferromagnetic phase, which has been intensively investigated in the last decade, was revealed to originate from a half-metallic quantum valley Hall effect.     

Assessment of bilayer silicene to probe as quantum spin and valley Hall effect

Silicene takes precedence over graphene due to its buckling type structure and strong spin orbit coupling. Motivated by these properties, we study the silicene bilayer in the presence of applied perpendicular electric field and intrinsic spin orbit coupling to probe as quantum spin/valley Hall effect. Using analytical approach, we calculate the spin Chern-number of bilayer silicene and then compare it with monolayer silicene. We reveal that bilayer silicene hosts double spin Chern-number as compared to single layer silicene and therefore accordingly has twice as many edge states in contrast to single layer silicene. In addition, we investigate the combined effect of intrinsic spin orbit coupling and the external electric field, we find that bilayer silicene, likewise single layer silicene, goes through a phase transitions from a quantum spin Hall state to a quantum valley Hall state when the strength of the applied electric field exceeds the intrinsic spin orbit coupling strength. We believe that the results and outcomes obtained for bilayer silicene are experimentally more accessible as compared to bilayer graphene, because of strong SO coupling in bilayer silicene.     

The stability of the fractional quantum Hall effect in topological insulators

With the recent observation of graphene-like Landau levels at the surface of topological insulators, the possibility of fractional quantum Hall effect, which is a fundamental signature of strong correlations, has become of interest. Some experiments have reported intra-Landau level structure that is suggestive of fractional quantum Hall effect. This paper discusses the feasibility of fractional quantum Hall effect from a theoretical perspective, and argues that while this effect should occur, ideally, in the n=0 and |n|=1 Landau levels, it is ruled out in higher |n| Landau levels. Unlike graphene, the fractional quantum Hall effect in topological insulators is predicted to show an interesting asymmetry between n=1 and n=−1 Landau levels due to spin-orbit coupling.