The model dependence in the study of the magic-angle twisted bilayer-graphene(MA-TBG)is an important issue in the research area.It has been argued previously that the two-band tight-binding(TB)model(per spin and valle...The model dependence in the study of the magic-angle twisted bilayer-graphene(MA-TBG)is an important issue in the research area.It has been argued previously that the two-band tight-binding(TB)model(per spin and valley)cannot serve as a start point for succeeding studies as it cannot correctly describe the topological aspect of the continuumtheory model near the Dirac nodes in the mini Brillouin zone(MBZ).For this purpose,we adopt the faithful TB model[Phys.Rev.B 99195455(2019)]with five bands(per spin and valley)as our start point,which is further equipped with extended Hubbard interactions.Then after systematic random-phase-approximation(RPA)based calculations,we study the electron instabilities of this model,including the density wave(DW)and superconductivity(SC),near the van Hove singularity(VHS).Our results are as follows.In the case neglecting the tiny inter-valley exchange interaction,the exact SU(2)K×SU(2)K symmetry leads to the degeneracy between the inter-valley charge DW(CDW)and the spin DW(SDW)(which would be mixed then),and that between the singlet d+id-wave and triplet p+ip-wave topological SCs.When a realistic tiny inter-valley exchange interaction is turned on with nonzero coefficient(J_H=0),the SDW or CDW is favored respectively at the critical point,determined by JH→0-or JH→0+.In the mean time,the degeneracy between the singlet d+id-wave and triplet p+ip-wave topological SCs is also lifted up by the tiny JH.These results are highly similar to the results of our previous study[arXiv:2003.09513]adopting the two-band TB model,with the reason lying in that both models share the same symmetry and Fermi-surface(FS)nesting character near the VHS.Such a similarity suggests that the low-energy physics of the doped MA-TBG is mainly determined by the symmetry and the shape of the FS of the doped system,and is insensitive to other details of the band structure,including the topological aspects near the Dirac nodes in the MBZ.展开更多
The rheological properties of two specific waterborne polyurethane （PU） paints were studied by both macrorheological and microrheological methods. During the macrorheological measurement on a rotary rheometer, evapo...The rheological properties of two specific waterborne polyurethane （PU） paints were studied by both macrorheological and microrheological methods. During the macrorheological measurement on a rotary rheometer, evaporation of solvent cannot be totally excluded, which has an influence on the reliability of rheological results. So, the linear oscillatory frequency sweep results （storage and loss modulus versus frequency） and steady shear results （viscosity versus shear rate） got from the rotary rheometer measurement are only used for qualitative analysis. As the evaporation of solvent can be neglected during microrheological measurements on a diffusing wave spectroscope （DWS）, the results of storage modulus （G3 and loss modulus （G＇~） versus frequency are more credible than the results obtained from the rotary rheometer measurement. Thus, the results of G＇ and G＂ versus frequency from DWS measurements are used for quantitative analysis in this work. The G＇ for both of the waterborne PU paints are larger than G＂ at low frequency and that is opposite at high frequency in the experimental angular frequency range. The values of modulus at same frequency and viscosity at low shear rate for the two PU paints have apparent difference, which determines the difference of their application.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674025,12074031,and 11674151)the National Key Research and Development Program of China(Grant No.2016YFA0300300)。
文摘The model dependence in the study of the magic-angle twisted bilayer-graphene(MA-TBG)is an important issue in the research area.It has been argued previously that the two-band tight-binding(TB)model(per spin and valley)cannot serve as a start point for succeeding studies as it cannot correctly describe the topological aspect of the continuumtheory model near the Dirac nodes in the mini Brillouin zone(MBZ).For this purpose,we adopt the faithful TB model[Phys.Rev.B 99195455(2019)]with five bands(per spin and valley)as our start point,which is further equipped with extended Hubbard interactions.Then after systematic random-phase-approximation(RPA)based calculations,we study the electron instabilities of this model,including the density wave(DW)and superconductivity(SC),near the van Hove singularity(VHS).Our results are as follows.In the case neglecting the tiny inter-valley exchange interaction,the exact SU(2)K×SU(2)K symmetry leads to the degeneracy between the inter-valley charge DW(CDW)and the spin DW(SDW)(which would be mixed then),and that between the singlet d+id-wave and triplet p+ip-wave topological SCs.When a realistic tiny inter-valley exchange interaction is turned on with nonzero coefficient(J_H=0),the SDW or CDW is favored respectively at the critical point,determined by JH→0-or JH→0+.In the mean time,the degeneracy between the singlet d+id-wave and triplet p+ip-wave topological SCs is also lifted up by the tiny JH.These results are highly similar to the results of our previous study[arXiv:2003.09513]adopting the two-band TB model,with the reason lying in that both models share the same symmetry and Fermi-surface(FS)nesting character near the VHS.Such a similarity suggests that the low-energy physics of the doped MA-TBG is mainly determined by the symmetry and the shape of the FS of the doped system,and is insensitive to other details of the band structure,including the topological aspects near the Dirac nodes in the MBZ.
基金financially supported by the National Natural Science Foundation of China(Nos.2127415251473168 an21234007)
文摘The rheological properties of two specific waterborne polyurethane （PU） paints were studied by both macrorheological and microrheological methods. During the macrorheological measurement on a rotary rheometer, evaporation of solvent cannot be totally excluded, which has an influence on the reliability of rheological results. So, the linear oscillatory frequency sweep results （storage and loss modulus versus frequency） and steady shear results （viscosity versus shear rate） got from the rotary rheometer measurement are only used for qualitative analysis. As the evaporation of solvent can be neglected during microrheological measurements on a diffusing wave spectroscope （DWS）, the results of storage modulus （G3 and loss modulus （G＇~） versus frequency are more credible than the results obtained from the rotary rheometer measurement. Thus, the results of G＇ and G＂ versus frequency from DWS measurements are used for quantitative analysis in this work. The G＇ for both of the waterborne PU paints are larger than G＂ at low frequency and that is opposite at high frequency in the experimental angular frequency range. The values of modulus at same frequency and viscosity at low shear rate for the two PU paints have apparent difference, which determines the difference of their application.
