A strong-coupling expansion for the Hubbard model

We reconsider the strong-coupling expansion for the Hubbard model recently introduced by Sarker and Pairault {\it et al.} By introducing slave particles that act as projection operators onto the empty, singly occupied and doubly occupied atomic states, the perturbation theory around the atomic limit distinguishes between processes that do conserve or do not conserve the total number of doubly occupied sites. This allows for a systematic $t/U$ expansion that does not break down at low temperature ($t$ being the intersite hopping amplitude and $U$ the local Coulomb repulsion). The fermionic field becomes a two-component field, which reflects the presence of the two Hubbard bands. The single-particle propagator is naturally expressed as a function of a $2 \times 2$ matrix self-energy. Furthermore, by introducing a time- and space-fluctuating spin-quantization axis in the functional integral, we can expand around a ``non-degenerate'' ground-state where each singly occupied site has a well defined spin direction (which may fluctuate in time). This formalism is used to derive the effective action of charge carriers in the lower Hubbard band to first order in $t/U$. We recover the action of the t-J model in the spin-hole coherent-state path integral. We also compare our results with those previously obtained by studying fluctuations around the large-$U$ Hartree-Fock saddle point.Comment: 20 pages RevTex, 3 figure

Mandarin Chinese Teacher Education Issues and solutions

Mandarin Chinese is the most widely spoken language in the world, and in a rapidly globalizing environment, speaking it is an increasingly important skill for young people in the UK. 'Mandarin Chinese Teacher Education' stems from the work of the UCL Institute of Education Confucius Institute, which supports the development of Mandarin Chinese as a language on offer in schools as part of the mainstream curriculum. This edited collection brings together researchers, teachers involved in action research and student-teachers, in an effort to address the current lack of literature specifically aimed at supporting Chinese language teachers. It features: • practical ideas for teachers of Chinese to implement in their own classrooms • evaluation of differing strategies and approaches unique to teaching Chinese • examples of using action research to help teachers reflect on their own practice while informing practice across the discipline. The book will be useful for PGCE Mandarin students, teacher trainers and those involved in the development of Mandarin Chinese in schools across the UK and further afield

Impact of disorder on the 5/2 fractional quantum Hall state

We compare the energy gap of the \nu=5/2 fractional quantum Hall effect state obtained in conventional high mobility modulation doped quantum well samples with those obtained in high quality GaAs transistors (heterojunction insulated gate field-effect transistors). We are able to identify the different roles that long range and short range disorders play in the 5/2 state and observe that the long range potential fluctuations are more detrimental to the strength of the 5/2 state than short-range potential disorder.Comment: PRL 106, 206806 (2011

Fluctuation Dominated Josephson Tunneling with a Scanning Tunneling Microscope

We demonstrate Josephson tunneling in vacuum tunnel junctions formed between a superconducting scanning tunneling microscope tip and a Pb film, for junction resistances in the range 50-300 k$\Omega$. We show that the superconducting phase dynamics is dominated by thermal fluctuations, and that the Josephson current appears as a peak centered at small finite voltages. In the presence of microwave fields (f=15.0 GHz) the peak decreases in magnitude and shifts to higher voltages with increasing rf power, in agreement with theory.Comment: 4 pages, REVTeX, submitted to PR