Emergent topological ordered phase for the Ising-XY model revealed by cluster-updating Monte Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy.At low temperatures,theoretical predictions[Phys.Rev.A 72053604(2005)]and[arXiv:0706.1609]indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering.However,due to ergodic difficulties faced by Monte Carlo methods at low temperatures,this topological phase has not been numerically explored.We propose a linear cluster updating Monte Carlo method,which flips spins without rejection in the anisotropy limit but does not change the energy.Using this scheme and conventional Monte Carlo methods,we succeed in revealing the nature of topological phases with half-vortices and domain walls.In the constructed global phase diagram,Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier.We also propose and explore a wide range of quantities,including magnetism,superfluidity,specific heat,susceptibility,and even percolation susceptibility,and obtain consistent and reliable results.Furthermore,we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes,as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections.The critical exponents of different types of phase transitions are reasonably fitted.The results are useful to help cold atom experiments explore the half-vortex topological phase.

Chlorine-Substituent Regulation in Dopant-Free Small-Molecule Hole-Transport Materials Improves the Effi ciency and Stability of Inverted Perovskite Solar Cells

Although doped hole-transport materials(HTMs)off er an effi ciency benefi t for perovskite solar cells(PSCs),they inevi-tably diminish the stability.Here,we describe the use of various chlorinated small molecules,specifi cally fl uorenone-triphenylamine(FO-TPA)-x-Cl[x=para,meta,and ortho(p,m,and o)],with diff erent chlorine-substituent positions,as dopant-free HTMs for PSCs.These chlorinated molecules feature a symmetrical donor-acceptor-donor structure and ideal intramolecular charge transfer properties,allowing for self-doping and the establishment of built-in potentials for improving charge extraction.Highly effi cient hole-transfer interfaces are constructed between perovskites and these HTMs by strategi-cally modifying the chlorine substitution.Thus,the chlorinated HTM-derived inverted PSCs exhibited superior effi ciencies and air stabilities.Importantly,the dopant-free HTM FO-TPA-o-Cl not only attains a power conversion effi ciency of 20.82% but also demonstrates exceptional stability,retaining 93.8%of its initial effi ciency even after a 30-day aging test conducted under ambient air conditions in PSCs without encapsulation.These fi ndings underscore the critical role of chlorine-substituent regulation in HTMs in ensuring the formation and maintenance of effi cient and stable PSCs.