The wave nature of electrons in low-dimensional structures manifests itself in conventional electrical measurements as a quantum correction to the classical conductance. This correction comes from the interference of scattered electrons which results in electron localisation and therefore a decrease of the conductance. In graphene, where the charge carriers are chiral and have an additional (Berry) phase of π, the quantum interference is expected to lead to anti-localisation: an increase of the conductance accompanied by negative magnetoconductance (a decrease of conductance in magnetic field). Here we observe such negative magnetoconductance which is a direct consequence of the chirality of electrons in graphene. We show that graphene is a unique two-dimensional material in that, depending on experimental conditions, it can demonstrate both localisation and anti-localisation effects. We also show that quantum interference in graphene can survive at unusually high temperatures, up to T~200 K.
Due to the chiral nature of electrons in a monolayer of graphite (graphene) one can expect weak antilocalisation and a positive weak-field magnetoresistance in it. However, trigonal warping (which breaks p/-p symmetry of the Fermi line in each valley) suppresses antilocalisation, while inter-valley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore conventional negative magnetoresistance. We show this by evaluating the dependence of the magnetoresistance of graphene on relaxation rates associated with various possible ways …
We look at the magnetic field induced weak localisation peak of graphene samples with different mobilities. At very low temperatures, low mobility samples exhibit a very broad peak as a function of the magnetic field, in contrast to higher mobility samples, where the weak localisation peak is very sharp. We analyze the experimental data in the context of the localisation length, which allows us to extract, both the localisation length and the phase coherence length of the samples, regardless of their mobilities. This analysis is made possible by the observation that the localisation length und…
We have performed the first experimental investigation of quantum interference corrections to the conductivity of a bilayer graphene structure. A negative magnetoresistance - a signature of weak localisation - is observed at different carrier densities, including the electro-neutrality region. It is very different, however, from the weak localisation in conventional two-dimensional systems. We show that it is controlled not only by the dephasing time, but also by different elastic processes that break the effective time-reversal symmetry and provide invervalley scattering.
We show that the manifestation of quantum interference in graphene is very different from that in conventional two-dimensional systems. Due to the chiral nature of charge carriers, it is sensitive not only to inelastic, phase-breaking scattering, but also to a number of elastic scattering processes. We study weak localization in different samples and at different carrier densities, including the Dirac region, and find the characteristic rates that determine it. We show how the shape and quality of graphene flakes affect the values of the elastic and inelastic rates and discuss their physical o…
Quantum transport and spintronics regimes are studied in p- and n-doped atomic layers of hexagonal transition metal dichalcogenides (TMDCs), subject to the interplay between the valley structure and spin-orbit coupling. We find how spin relaxation of carriers depends on their areal density and show that it vanishes for holes near the band edge, leading to the density-independent spin diffusion length, and we develop a theory of weak localisation/antilocalisation, describing the crossovers between the orthogonal, double-unitary and symplectic regimes of quantum transport in TMDCs.
We show that electron states in disordered graphene, with an onsite potential that induces inter-valley scattering, are localised for all energies at disorder as small as 1/6 of the band width of clean graphene. We clarify that, in order for this Anderson-type localisation to be manifested, graphene flakes of size of approximately 200 x 200 nm^2 or larger are needed. For smaller samples, due to the surprisingly large extent of the electronic wave functions, a regime of apparently extended (or even critical) states is identified. Our results complement earlier studies of macroscopically large s…
We report the first experimental study of the quantum interference correction to the conductivity of bilayer graphene. Low-field, positive magnetoconductivity due to the weak localisation effect is investigated at different carrier densities, including those around the electroneutrality region. Unlike conventional 2D systems, weak localisation in bilayer graphene is affected by elastic scattering processes such as intervalley scattering. Analysis of the dephasing determined from the magnetoconductivity is complemented by a study of the field- and density-dependent fluctuations of the conductan…
Experimental evidence from both spin-valve and quantum transport measurements points towards unexpectedly fast spin relaxation in graphene. We report magnetotransport studies of epitaxial graphene on SiC in a vector magnetic field showing that spin relaxation, detected using weak-localisation analysis, is suppressed by an in-plane magnetic field, $B_{\parallel}$, and thereby proving that it is caused at least in part by spinful scatterers. A non-monotonic dependence of effective decoherence rate on $B_{\parallel}$ reveals the intricate role of scatterers' spin dynamics in forming the interfere…
Bilayer graphene (two coupled graphitic monolayers arranged according to Bernal stacking) is a two-dimensional gapless semiconductor with a peculiar electronic spectrum different from the Dirac spectrum in the monolayer material. In particular, the electronic Fermi line in each of its valleys has a strong p -> -p asymmetry due to a trigonal warping, which suppresses the weak localization effect. We show that weak localisation in bilayer graphene may be present only in devices with pronounced intervalley scattering, and we evaluate the corresponding magnetoresistance.
Understanding the wave transport and localisation is a major goal in the study of lattices of different nature. In general, inhibiting the energy transport on a perfectly periodic and disorder-free system is challenging, however, some specific lattice geometries allow localisation due to the presence of dispersionless (flat) bands in the energy spectrum. Here, we report on the experimental realisation of a quasi-one-dimensional photonic graphene ribbon supporting four flat-bands. We study the dynamics of fundamental and dipolar modes, which are analogous to the s and p orbitals, respectively. …
In this review article we describe spin-dependent transport in materials with spin-orbit interaction of Rashba type. We mainly focus on semiconductor heterostructures, topological insulators, graphene and hybrid structures involving superconductors as well. We start from basic properties of Rashba Hamiltonian in a two dimensional electron gas and then describe transport properties in two- and quasi-one-dimensional systems. The problem of spin current generation and interference effects in mesoscopic devices is described in detail. We address also the role of Rashba interaction on localisation …
Staking layered materials revealed to be a very powerful method to tailor their electronic properties. It has indeed been theoretically and experimentally shown that twisted bilayers of graphene (tBLG) with a rotation angle $θ$, forming Moiré pattern, confine electrons in a tunable way as a function of $θ$. Here, we study electronic structure and transport in tBLG using tight-binding numerical calculations in commensurate twisted bilayer structures and a pertubative continuous theory, which is valid for not too small angles ($θ> \sim 2^\circ $). This two approaches allow to understand the effe…
We characterise the dynamics of electrons in twisted bilayer graphene by analysing the time-evolution of electron waves in the atomic lattice. We perform simulations based on a kernel polynomial technique using Chebyshev polynomial; this method does not requires any diagonalisation of the system Hamiltonian. Our simulations reveal that the inter-layer electronic coupling induces the exchange of waves between the two graphene layers. This wave transfer manifests as oscillations of the layer-integrated probability densities as a function of time. For the bilayer case, it also causes a difference…
The thesis examines the topics of disorder and electron-electron interactions in three distinct quantum systems. Firstly, the Anderson transition is studied for the BCC and FCC lattices. We obtain high precision results for the critical disorder at the band centre and the critical exponent. Comparing the critical disorder between the SC, BCC and FCC lattices, an increase is observed as a function of the coordination number of the lattice. The critical exponent is found to be approximately 1.5 in agreement with the value for the SC lattice. Energy-disorder phase diagrams are plotted for both la…
Electron binding by charge disorder surrounding gapped bilayer graphene
National Graphene Institute, University of Manchester（国家石墨烯研究所，曼彻斯特大学）；Department of Physics & Astronomy, University of Manchester（曼彻斯特大学物理与天文系）；Institut für Theoretische Physik, Universität Regensburg（雷根斯堡大学理论物理研究所）；Research Institute of Electrical Communication, Tohoku University（东北大学电气通信研究所）
Nodal semimetals (e.g. Dirac, Weyl and nodal-line semimetals, graphene, etc.) and systems of pinned particles with power-law interactions (trapped ultracold ions, nitrogen defects in diamonds, spins in solids, etc.) are presently at the centre of attention of large communities of researchers working in condensed-matter and atomic, molecular and optical physics. Although seemingly unrelated, both classes of systems are abundant with novel fundamental thermodynamic and transport phenomena. In this paper, we demonstrate that low-energy field theories of quasiparticles in semimetals may be mapped …
