Fractional Fowler-Nordheim Law for Field Emission from Rough Surface with Nonparabolic Energy Dispersion

The theories of field electron emission from perfectly planar and smooth canonical surfaces are well understood, but they are not suitable for describing emission from rough, irregular surfaces arising in modern nanoscale electron sources. Moreover, the existing models rely on Sommerfeld's free-electron theory for the description of electronic distribution which is not a valid assumption for modern materials with nonparabolic energy dispersion. In this paper, we derive analytically a generalized Fowler-Nordheim (FN) type equation that takes into account the reduced space-dimensionality seen by the quantum mechanically tunneling electron at a rough, irregular emission surface. We also consider the effects of non-parabolic energy dispersion on field-emission from narrow-gap semiconductors and few-layer graphene using Kane's band model. The traditional FN equation is shown to be a limiting case of our model in the limit of a perfectly flat surface of a material with parabolic dispersion. The fractional-dimension parameter used in this model can be experimentally calculated from appropriate current-voltage data plot. By applying this model to experimental data, the standard field-emission parameters can be deduced with better accuracy than by using the conventional FN equation.Comment: 8 pages, 4 figure

Transition from ultrafast laser photo-electron emission to space charge limited current in a 1D gap

A one-dimensional (1D) model has been constructed to study the transition of the time-dependent ultrafast laser photo-electron emission from a flat metallic surface to the space charge limited (SCL) current, including the effect of non-equilibrium laser heating on metals at the ultrafast time scale. At a high laser field, it is found that the space charge effect cannot be ignored and the SCL current emission is reached at a lower value predicted by a short pulse SCL current model that assumed a time-independent emission process. The threshold of the laser field to reach the SCL regime is determined over a wide range of operating parameters. The calculated results agree well with particle-in-cell (PIC) simulation. It is found that the space charge effect is more important for materials with lower work function like tungsten (4.4 eV) as compared to gold (5.4 eV). However for a flat surface, both materials will reach the space charge limited regime at the sufficiently high laser field such as $>$ 5 GV/m with a laser pulse length of tens to one hundred femtoseconds.Comment: 12 pages, 3 figures, printed in {\itshape J. Phys. D: Appl. Phys.

Nonlocal transistor based on pure crossed Andreev reflection in a EuO-graphene/superconductor hybrid structure

We study the interband transport in a superconducting device composed of graphene with EuO-induced exchange interaction. We show that pure crossed Andreev reflection can be generated exclusively without the parasitic local Andreev reflection and elastic cotunnelling over a wide range of bias and Fermi levels in an EuO-graphene/superconductor/EuO-graphene device. The pure non-local conductance exhibits rapid on/off switching and oscillatory behavior when the Fermi levels in the normal and the superconducting leads are varied. The oscillation reflects the quasiparticle propagation in the superconducting lead and can be used as a tool to probe the subgap quasiparticle mode in superconducting graphene, which is inaccessible from the current-voltage characteristics. Our results suggest that the device can be used as a highly tunable transistor that operates purely in the non-local and spin-polarized transport regime.Comment: 5 pages, 4 figures; To appear in Phys. Rev.

Motion-induced radiation from electrons moving in Maxwell's fish-eye

In \u{C}erenkov radiation and transition radiation, evanescent wave from motion of charged particles transfers into radiation coherently. However, such dissipative motion-induced radiations require particles to move faster than light in medium or to encounter velocity transition to pump energy. Inspired by a method to detect cloak by observing radiation of a fast-moving electron bunch going through it by Zhang {\itshape et al.}, we study the generation of electron-induced radiation from electrons' interaction with Maxwell's fish-eye sphere. Our calculation shows that the radiation is due to a combination of \u{C}erenkov radiation and transition radiation, which may pave the way to investigate new schemes of transferring evanescent wave to radiation.Comment: 17 pages, 8 figures, including the Supplementary Information appended in publication. Scientific Reports 201

Preschool or prep school? Rethinking the role of early years education

Governments around the world continue to grapple with issues relating to how preschool services should be delivered, what type of provision is most appropriate, and for what purpose. These issues are particularly pertinent in a fast evolving early years sector such as the United Kingdom and many parts of the world where early years education has become a highly political topic. This article argues that given current emphasis on 'school readiness' and the formalisation of children's learning in England and internationally, tensions remain about the role of early years education and what it entails - as a nexus for enriching children's lives and learning experiences, or simply preparing children for schooling. Building on Genishi's work on rethinking dominant values of early years education and respecting the importance of inclusion and diversity, the discussion explores debates around assessment, pedagogy and the curriculum in supporting children's learning and how these are deeply embedded in wider societal values. The article calls for a rethinking of the role of early years education - the values, choices, and judgements that societies make which inform children's learning and the contexts in which they learn

Massive MIMO 1-Bit DAC Transmission: A Low-Complexity Symbol Scaling Approach

We study multi-user massive multiple-input single-output (MISO) systems and focus on downlink transmission, where the base station (BS) employs a large antenna array with low-cost 1-bit digital-to-analog converters (DACs). The direct combination of existing beamforming schemes with 1-bit DACs is shown to lead to an error floor at medium-to-high SNR regime, due to the coarse quantization of the DACs with limited precision. In this paper, based on the constructive interference we consider both a quantized linear beamforming scheme where we analytically obtain the optimal beamforming matrix, and a non-linear mapping scheme where we directly design the transmit signal vector. Due to the 1-bit quantization, the formulated optimization for the non-linear mapping scheme is shown to be non-convex. To solve this problem, the non-convex constraints of the 1-bit DACs are firstly relaxed, followed by an element-wise normalization to satisfy the 1-bit DAC transmission. We further propose a low-complexity symbol scaling scheme that consists of three stages, in which the quantized transmit signal on each antenna element is selected sequentially. Numerical results show that the proposed symbol scaling scheme achieves a comparable performance to the optimization-based non-linear mapping approach, while its corresponding complexity is negligible compared to that of the non-linear scheme.Comment: 15 page