Electronic structure near an impurity and terrace on the surface of a 3-dimensional topological insulator

Motivated by recent scanning tunneling microscopy experiments on surfaces of Bi$_{1-x}$Sb$_{x'}$\cite{yazdanistm,gomesstm} and Bi$_2$Te$_3$,\cite{kaptunikstm,xuestm} we theoretically study the electronic structure of a 3-dimensional (3D) topological insulator in the presence of a local impurity or a domain wall on its surface using a 3D lattice model. While the local density of states (LDOS) oscillates significantly in space at energies above the bulk gap, the oscillation due to the in-gap surface Dirac fermions are very weak. The extracted modulation wave number as a function of energy satisfies the Dirac dispersion for in-gap energies and follows the border of the bulk continuum above the bulk gap. We have also examined analytically the effects of the defects by using a pure Dirac fermion model for the surface states and found that the LDOS decays asymptotically faster at least by a factor of 1/r than that in normal metals, consistent with the results obtained from our lattice model.Comment: 7 pages, 5 figure

The semi-discrete AKNS system: Conservation laws, reductions and continuum limits

In this paper, the semi-discrete Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy is shown in spirit composed by the Ablowitz-Ladik flows under certain combinations. Furthermore, we derive its explicit Lax pairs and infinitely many conservation laws, which are non-trivial in light of continuum limit. Reductions of the semi-discrete AKNS hierarchy are investigated to include the semi-discrete Korteweg-de Vries (KdV), the semi-discrete modified KdV, and the semi-discrete nonlinear Schr\"odinger hierarchies as its special cases. Finally, under the uniform continuum limit we introduce in the paper, the above results of the semi-discrete AKNS hierarchy, including Lax pairs, infinitely many conservation laws and reductions, recover their counterparts of the continuous AKNS hierarchy

Exploring and Assessing Effectiveness of English Medium Instruction Courses: The Students’ Perspectives

AbstractThis paper investigates students’ perceptions of the English medium instruction courses at Southern Taiwan University of Science & Technology (STUST) in terms of their learning motivation, learning anxiety, and learning achievement. 157 students, including 93 local and 64 foreign students, participated in the study by completing a self-assessment questionnaire on EMI course taking experiences. A quantitative method was employed to analyze data, performing statistical procedures of descriptive statistics, independent-samples t-tests, and Pearson correlation using SPSS 17.0. The major findings of the study are as follows: (1) most participants were motivated to take EMI courses to strengthen English ability and professional knowledge, (2) most participants agreed with the helpfulness of EMI courses, (3) interactions with students of other nationalities motivated learning, (4) major anxiety experienced by local students stemmed from self-perceived low English proficiency, (5) there exists significant reverse association between learning anxiety and achievement or motivation, and (6) there exists significant differences between local and international students in measures of motivation, anxiety, and achievement