arXiv subjects

Zhi-Qiang Gao

Publications and source records attributed to Zhi-Qiang Gao.

20 records · Page 2Linked to original sources

arXiv2020

Effects of Defects in Superconducting Phase of Twisted Bilayer Graphene

In this work the effects of defects in the superconducting phases of the twisted bilayer graphene (TBG) are investigated. A will-accepted low energy effective model and a non-magnetic impurity potential to mimic defects are employed. Different superconducting pairing symmetries, including $s$-wave, $(d+id)$-wave and $(p+ip)$-wave pairing, are considered. In single impurity case, the local density of states (DOS) are calculated for the pairing symmetries above. For different pairing symmetries the number and property of bound states induced by defects are different. In multi-impurity case, the phase diagrams are calculated in terms of effective gap and the strength and density of impurities. In unconventional superconducting phases, namely $(p+ip)$-wave and $(d+id)$-wave phases, superconductivity will be destroyed by impurities with strong strength or concentration. These results can in principle be detected in scanning tunnelling microscopy (STM) experiments, and therefore the pairing symmetry, at least whether the superconductivity is conventional or unconventional, may be determined.

cond-mat.supr-con↗

arXiv2016

Second and third orders asymptotic expansions for the distribution of particles in a branching random walk with a random environment in time

Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the time.For the normalised counting measure of the number of particles of generation $n$ in a given region, we give the second and third orders asymptotic expansions of the central limit theorem under rather weak assumptions on the moments of the underlying branching and moving laws. The obtained results and the developed approaches shed light on higher order expansions. In the proofs, the Edgeworth expansion of central limit theorems for sums of independent random variables, truncating arguments and martingale approximation play key roles. In particular, we introduce a new martingale, show its rate of convergence, as well as the rates of convergence of some known martingales, which are of independent interest.

math.PR↗