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.
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.
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.
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.
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.
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.
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.
- Reports on progress in physics. Physical Society (Great Britain)
- Published over 4 years ago
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.
Perpendicularly magnetized materials have attracted significant interest owing to their high anisotropy, which gives rise to extremely narrow, nanosized domain walls. As a result, the recently studied current-induced domain wall motion (CIDWM) in these materials promises to enable a new class of data, memory and logic devices. Here we propose the spin Hall effect as an alternative mechanism for CIDWM. We are able to carefully tune the net spin Hall current in depinning experiments on Pt/Co/Pt nanowires, offering unique control over CIDWM. Furthermore, we determine that the depinning efficiency is intimately related to the internal structure of the domain wall, which we control by the application of small fields along the nanowire. This manifestation of CIDWM offers an attractive degree of freedom for manipulating domain wall motion by charge currents, and sheds light on the existence of contradicting reports on CIDWM in perpendicularly magnetized materials.
We reveal an intriguing manifestation of topology, which appears in the depletion rate of topological states of matter in response to an external drive. This phenomenon is presented by analyzing the response of a generic two-dimensional (2D) Chern insulator subjected to a circular time-periodic perturbation. Because of the system’s chiral nature, the depletion rate is shown to depend on the orientation of the circular shake; taking the difference between the rates obtained from two opposite orientations of the drive, and integrating over a proper drive-frequency range, provides a direct measure of the topological Chern number (ν) of the populated band: This “differential integrated rate” is directly related to the strength of the driving field through the quantized coefficient η0 = ν/ℏ(2), where h = 2π ℏ is Planck’s constant. Contrary to the integer quantum Hall effect, this quantized response is found to be nonlinear with respect to the strength of the driving field, and it explicitly involves interband transitions. We investigate the possibility of probing this phenomenon in ultracold gases and highlight the crucial role played by edge states in this effect. We extend our results to 3D lattices, establishing a link between depletion rates and the nonlinear photogalvanic effect predicted for Weyl semimetals. The quantized circular dichroism revealed in this work designates depletion rate measurements as a universal probe for topological order in quantum matter.