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Concept: Hall effect


Quasi-particle excitations in graphene exhibit a unique behavior concerning two key phenomena of mesoscopic physics: electron localization and the quantum Hall effect. A direct transition between these two states has been found in disordered two-dimensional electron gases at low magnetic field. It has been suggested that it is a quantum phase transition, but the nature of the transition is still debated. Despite the large number of works studying either the localization or the quantum Hall regime in graphene, such a transition has not been investigated for Dirac fermions. Here we discuss measurements on low-mobility graphene where the localized state at low magnetic fields and a quantum Hall state at higher fields are observed. We find that the system undergoes a direct transition from the insulating to the Hall conductor regime. Remarkably, the transverse magneto-conductance shows a temperature independent crossing point, pointing to the existence of a genuine quantum phase transition.

Concepts: Electron, Magnetic field, Fundamental physics concepts, Spin, Condensed matter physics, Electric current, Hall effect, Quantum Hall effect


Insulating states can be topologically nontrivial, a well-established notion that is exemplified by the quantum Hall effect and topological insulators. By contrast, topological metals have not been experimentally evidenced until recently. In systems with strong correlations, they have yet to be identified. Heavy-fermion semimetals are a prototype of strongly correlated systems and, given their strong spin-orbit coupling, present a natural setting to make progress. Here, we advance a Weyl-Kondo semimetal phase in a periodic Anderson model on a noncentrosymmetric lattice. The quasiparticles near the Weyl nodes develop out of the Kondo effect, as do the surface states that feature Fermi arcs. We determine the key signatures of this phase, which are realized in the heavy-fermion semimetal Ce3Bi4Pd3 Our findings provide the much-needed theoretical foundation for the experimental search of topological metals with strong correlations and open up an avenue for systematic studies of such quantum phases that naturally entangle multiple degrees of freedom.

Concepts: Quantum mechanics, Fundamental physics concepts, Condensed matter physics, Hall effect, Electrical resistance, Quantum spin Hall effect, Quantum Hall effect, Elementary charge


Incorporating ferromagnetic dopants into three-dimensional topological insulator thin films has recently led to the realisation of the quantum anomalous Hall effect. These materials are of great interest since they may support electrical currents that flow without resistance, even at zero magnetic field. To date, the quantum anomalous Hall effect has been investigated using low-frequency transport measurements. However, transport results can be difficult to interpret due to the presence of parallel conductive paths, or because additional non-chiral edge channels may exist. Here we move beyond transport measurements by probing the microwave response of a magnetised disk of Cr-(Bi,Sb)2Te3. We identify features associated with chiral edge plasmons, a signature that robust edge channels are intrinsic to this material system. Our results provide a measure of the velocity of edge excitations without contacting the sample, and pave the way for an on-chip circuit element of practical importance: the zero-field microwave circulator.

Concepts: Electron, Electromagnetism, Magnetic field, Condensed matter physics, Electric current, Semiconductor, Hall effect


Spin-based computing schemes could enable new functionalities beyond those of charge-based approaches. Examples include nanomagnetic logic, where information can be processed using dipole coupled nanomagnets, as demonstrated by multi-bit computing gates. One fundamental benefit of using magnets is the possibility of a significant reduction in the energy per bit compared with conventional transistors. However, so far, practical implementations of nanomagnetic logic have been limited by the necessity to apply a magnetic field for clocking. Although the energy associated with magnetic switching itself could be very small, the energy necessary to generate the magnetic field renders the overall logic scheme uncompetitive when compared with complementary metal-oxide-semiconductor (CMOS) counterparts. Here, we demonstrate a nanomagnetic logic scheme at room temperature where the necessity for using a magnetic field clock can be completely removed by using spin-orbit torques. We construct a chain of three perpendicularly polarized CoFeB nanomagnets on top of a tantalum wire and show that an unpolarized current flowing through the wire can ‘clock’ the perpendicular magnetization to a metastable state. An input magnet can then drive the nanomagnetic chain deterministically to one of two dipole-coupled states, ‘2 up 1 down’ or ‘2 down 1 up’, depending on its own polarization. Thus, information can flow along the chain, dictated by the input magnet and clocked solely by a charge current in tantalum, without any magnetic field. A three to four order of magnitude reduction in energy dissipation is expected for our scheme when compared with state-of-the-art nanomagnetic logic.

Concepts: Electromagnetism, Magnetic field, Fundamental physics concepts, Magnet, Electric current, Magnetism, Magnetic moment, Hall effect


We report local and non-local measurements in pin-hole dominated mesoscopic multigraphene spin-valves. Local spin-valve measurements show spurious switching behavior in resistance during magnetic field sweeping similar to the signal observed due to spin injection into multigraphene. The switching behavior has been explained in terms of a local Hall effect due to a thickness irregularity of the tunnel barrier. The local Hall effect appears due to a large local magnetostatic field produced near the roughness in the AlO(x) tunnel barrier. In our samples the resistance change due to the local Hall effect remains negligibly small above 75 K. A strong local Hall effect might hinder spin injection into multigraphene, resulting in no spin signal in non-local measurements.

Concepts: Magnetic field, Spin, Electric current, Magnetism, Semiconductor, Hall effect, Magnetostatics, Current density


Investigating the structure of quantized plateaus in the Hall conductance of graphene is a powerful way of probing its crystalline and electronic structure and will also help to establish whether graphene can be used as a robust standard of resistance for quantum metrology. We use low-temperature scanning gate microscopy to image the interplateau breakdown of the quantum Hall effect in an exfoliated bilayer graphene flake. Scanning gate images captured during breakdown exhibit intricate patterns where the conductance is strongly affected by the presence of the scanning probe tip. The maximum density and intensity of the tip-induced conductance perturbations occur at half-integer filling factors, midway between consecutive quantum Hall plateau, while the intensity of individual sites shows a strong dependence on tip-voltage. Our results are well-described by a model based on quantum percolation which relates the points of high responsivity to tip-induced scattering in a network of saddle points separating localized states.

Concepts: Condensed matter physics, Graphene, Scanning probe microscopy, Hall effect, Electrical resistance, Quantum Hall effect, Quantum electronics, Quantization


The growth of large-domain single crystalline graphene with the controllable number of layers is of central importance for large-scale integration of graphene devices. Here we report a new pathway to greatly reduce the graphene nucleation density from ~10(6) to 4 nuclei cm(-2), enabling the growth of giant single crystals of monolayer graphene with a lateral size up to 5 mm and Bernal-stacked bilayer graphene with the lateral size up to 300 μm, both the largest reported to date. The formation of the giant graphene single crystals eliminates the grain boundary scattering to ensure excellent device-to-device uniformity and remarkable electronic properties with the expected quantum Hall effect and the highest carrier mobility up to 16,000 cm(2) V(-1) s(-1). The availability of the ultra large graphene single crystals can allow for high-yield fabrication of integrated graphene devices, paving a pathway to scalable electronic and photonic devices based on graphene materials.

Concepts: Condensed matter physics, Chemistry, Carbon, Graphene, Materials science, Hall effect, Quantum Hall effect, Crystallite


Graphene, a monolayer sheet of carbon atoms, exhibits intriguing electronic properties that arise from its massless Dirac dispersion of electrons. A striking example is the half-integer quantum Hall effect, which endorses the presence of Dirac cones or, equivalently, a non-zero (π) Berry’s (topological) phase. It is curious how these anomalous features of Dirac electrons would affect optical properties. Here we observe the quantum magneto-optical Faraday and Kerr effects in graphene in the terahertz frequency range. Our results detect the quantum plateaus in the Faraday and Kerr rotations at precisely the quantum Hall steps that hallmark the Dirac electrons, with the rotation angle defined by the fine-structure constant. The robust quantum Hall plateaus in the optical regime, besides being conceptually interesting, may open avenues for new graphene-based optoelectronic applications.

Concepts: Electron, Quantum mechanics, Fundamental physics concepts, Condensed matter physics, Graphene, Frequency, Hall effect, Quantum Hall effect


Two-dimensional electron systems in the presence of a magnetic field support topologically ordered states, in which the coexistence of an insulating bulk with conducting one-dimensional chiral edge states gives rise to the quantum Hall effect. For systems confined by sharp boundaries, theory predicts a unique edge-bulk correspondence, which is central to proposals of quantum Hall-based topological qubits. However, in conventional semiconductor-based two-dimensional electron systems, these elegant concepts are difficult to realize, because edge-state reconstruction due to soft boundaries destroys the edge-bulk correspondence. Here we use scanning tunnelling microscopy and spectroscopy to follow the spatial evolution of electronic (Landau) levels towards an edge of graphene supported above a graphite substrate. We observe no edge-state reconstruction, in agreement with calculations based on an atomically sharp boundary. Our results single out graphene as a system where the edge structure can be controlled and the edge-bulk correspondence is preserved.

Concepts: Electron, Magnetic field, Quantum mechanics, Graphene, Manifold, Hall effect, Quantum Hall effect, Landau quantization


We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.

Concepts: Photon, Energy, Quantum mechanics, Condensed matter physics, Graphene, Hall effect, Quantum Hall effect