Early theory has predicted the existence of atomically thin boron layers—borophenes.However,boron is electron deficient,making its atomic layers polymorphic and their synthesis challenging.Towards the synthesis of borophenes,metal substrate is crucial as it not only serves a physical support for stabilizing the atomically thin materials but also acts as a catalytic surface to facilitate the 2D material growth.In particular,the metal substrates can lead to smaller nucleation barrier for the growth of borophenes than that for growing 3D structures.1 Using cluster expansion method combined with first-principles calculations,we show that the structure of 2D boron sensitively depends on metal substrate.The preferred 2D boron on weakly interacting Au exhibits a nonplanar structure with significant buckling and remains polymorphic as in vacuum,whereas on more reactive Cu and Ni,the degeneracy lifts off and a planar structure is identified to be uniquely stable.2 Our theoretical finding appears to be confirmed by a couple of subsequent experiments,which reported the synthesis of 2D boron on Ag using molecule beam epitaxy method.3,4 We further show that nanoscale undulations can be preferred in borophene on Ag(111).This “wavy” configuration is unusually more stable than its planar form on flat Ag(111)and excellently agrees with our atomic-scale characterizations of borophenes grown on Ag(111)in terms of topography,wave length,Moire pattern and prevalence of vacancy defects.5