Electronic structures of vacancies in Co_(3)Sn_(2)S_(2)

Co_(3)Sn_(2)S_(2)has attracted a lot of attention for its multiple novel physical properties,including topological nontrivial surface states,anomalous Hall effect,and anomalous Nernst effect.Vacancies,which play important roles in functional materials,have attracted increasing research attention.In this paper,by using density functional theory calculations,we first obtain band structures and magnetic moments of Co_(3)Sn_(2)S_(2)with exchange–correlation functionals at different levels.It is found that the generalized gradient approximation gives the positions of Weyl points consistent with experiments in bulk Co_(3)Sn_(2)S_(2).We then investigate the electronic structures of defects on surfaces with S and Sn terminations which have been observed in experiments.The results show that the single sulfur vacancy on the S-terminated surface introduces localized bond states inside the bandgap near the Fermi level.For di-and tri-sulfur vacancies,the localized defect states hybridize with neighboring ones,forming bonding states as well as anti-bonding states.The Sn vacancy on the Sn-terminated surface also introduces localized bond states,which are merged with the valence bands.These results provide a reference for future experimental investigations of vacancies in Co_(3)Sn_(2)S_(2).

Educational divergence among urban residents and migrant workers: Evidence from China

While the Harris-Todaro model is a traditional approach used in researching the urban-rural dichotomy,it fails to explain families’goals to maximize their current utility in terms of intertemporal decision-making con‐ditions.To fill this gap,in this paper,an urban-rural dichotomy model involving labor migration and educa‐tion is established,in which it is assumed that family utility derives from consumption and children’s educa‐tional achievement.The steady-state path derived through the Bellman equation suggests that increasing edu‐cational investment and family education intensity leads to a significant urban-rural difference in children’s educational achievement.Compared with the traditional Harris-Todaro model,the transversality condition is loosened in this model,while the unavailability of loans constrains migrant families.Four hypotheses are made and tested using an empirical study.An ordinary least squares regression was used in the analysis,but due to the endogeneity caused by missing variables,the instrumental variable method and two-stage least squares regression were used.The results demonstrate that the household registration system can explain 44.5%of the educational achievement difference,and the initial difference is inflated 4.73 times after nine years of compulsory education.This divergence could increase the differences caused by household registra‐tion status,resulting in larger income gaps and intergenerational heredity of identities.