Physics at Lancaster University

Electronic properties of graphene films and carbon nanotubes

Landau level degeneracy and quantum Hall effect in a graphite bilayer

Electronic transport properties of a graphite monolayer [graphene] have for many decades attracted theoretical interest due to a Dirac-like spectrum of charge carriers in this gapless semiconductor. Recently it has proved possible to fabricate ultra-thin graphitic devices only a few-layers thick including mono- and bilayer structures, resulting in studies of the quantum Hall effect in monolayer graphene. My contribution [Ref.3 below] was to show that quasiparticles in bilayer graphene are chiral quasiparticles exhibiting Berry phase 2pi, with a dominantly parabolic dispersion and a peculiar Landau level spectrum, including a double-degenerate zero-energy Landau level incorporating two different orbital states with the same energy. Taking into account spin and valley degeneracies, the zero-energy Landau level in a bilayer is 8-fold degenerate, as compared to the 4-fold degeneracy of other bilayer states and the 4-fold degeneracy of all Landau levels in a monolayer. This led to a joint publication [Ref.2] with the Manchester experimental mesoscopic physics group, demonstrating that the structure and degeneracies of the Landau level spectrum in a bilayer determine a specific sequencing of plateaus in the density dependence of the QHE conductivity sigma_xy which is distinguishably different from that of Dirac-type quasiparticles in a graphite monolayer and of non-chiral carriers in conventional semiconductor structures.

Weak localisation magnetoresistance in graphene

The chiral nature of electrons in graphene suppresses backscattering and, thus, can be expected to cause weak antilocalisation and a positive weak-field magnetoresistance. However, this can be true only for purely potential scattering, while any violation of the hexagonal symmetry by static disorder in a realistic graphene sheet or by edges in a narrow wire tends to restore conventional negative magnetoresistance. We show this [Ref.1] by evaluating the dependence of the magnetoresistance of graphene on relaxation rates associated with various possible ways of breaking the high original symmetry of the system.

Some graphene/nanotube links:

• Manchester experimental mesoscopic physics group
• Marcus Lab mesoscopic physics (Harvard)
• The Nanotube Site (Michigan State)
• Molecular biophysics group (TU Delft)

Spin polarized transport

Research into spin polarized transport is motivated by the desire to develop a form of electronics which utilizes the spin polarization of carriers. Ferromagnetic (F) metals have more carriers of one spin polarization (known as majority carriers) present at the Fermi energy than of the inverse polarization (minority carriers) and, in a ferromagnet-ferromagnet (FF) junction, the resistance depends on the relative orientation of the magnetization in the ferromagnets. With parallel magnetizations, carriers flow from majority to majority bands (and minority to minority) whereas in a junction with antiparallel magnetizations, carriers flow from majority to minority bands (and vice versa). The resulting spin current mismatch produces a larger contact resistance in the antiparallel orientation, an effect known as tunneling magnetoresistance in FF junctions and giant magnetoresistance in multilayer structures.

Recently we have considered the theory of spin-polarized transport at low temperatures in hybrid nanostructures combining ferromagnetic (F) and superconducting (S) materials. A resistance increase has been predicted in a circuit consisting of a monodomain F wire connected to an S electrode instead of a normal (N) electrode. It arises from the need to match the spin-polarized current in the ferromagnet to the spin-less current in the superconductor. My contribution to this field began with an analysis of the weak localization correction to the F/S interface resistance. Weak localization is caused by the quantum interference of pairs of coherent quasi-particles in the ferromagnet and it is affected by boundary conditions. Particles that escape into a normal electrode at an F/N junction suffer dephasing whereas Andreev reflection from a superconducting electrode at an F/S junction may enable a particle to return coherently thus increasing the weak localization correction.

Spin relaxation processes, such as spin-orbit scattering at impurities or magnon emission, can reduce spin current mismatch. We considered the role of magnon emission in the formation of the subgap I(V) characteristics of an F/S junction. We predict a new process, magnon-assisted Andreev reflection, that involves the transfer of a singlet pair of electrons from the superconductor to the ferromagnet where one of the electrons emits a magnon that carries away excess spin. A striking feature of the I(V) characteristics is that the current in the limit of zero temperature is asymmetric with respect to bias voltage because, while magnon emission is allowed, there are no thermally excited magnons available to absorb.

More recently we have developed a model of the magnetothermopower of a mesoscopic tunnel junction between two ferromagnetic metals that arises from magnon-assisted tunnelling processes. In our model, the thermopower is generated in the course of thermal equilibration between two baths of magnons, mediated by electrons. For a junction between two half-metallic ferromagnets with antiparallel polarizations, we predict a particularly large thermopower effect, S_AP ~ - k_B/e, in contrast to S_P ~ 0 for a parallel configuration.

Correlation function spectroscopy in semiconducting heterostructures

A project a few years ago involved a collaboration with the experimental group of Prof. R. J. Haug at the University of Hannover. Their experiment probed the local density of states (LDOS) of a heavily doped GaAs emitter via resonant tunnelling through a localized impurity state and measurements showed that the amplitude of mesoscopic fluctuations of the LDOS decreases as a function of bias voltage. We interpreted this as being due to an increase in the relaxation rate of quasi-particles in the emitter as a function of excitation energy. Since the fluctuations arise from the quantum interference of elastically scattered quasi-particles, the effective dimensionality is determined by the relation between the typical size of the emitter and the typical length-scale over which coherence is maintained. Therefore the effective dimensionality is expected to depend on the bias voltage because of the energy dependence of the relaxation rate. We calculated the variance and correlation functions of the LDOS fluctuations with respect to voltage and magnetic field for different effective dimensionalities. A numerical calculation was performed to describe the crossovers between dimensionalities where the correlation functions are sensitive to the shape of the emitter and the position of the resonant impurity. By comparing these theoretical results with correlation functions obtained experimentally, the energy dependence of the inelastic lifetime was extracted.