title: Evolution of interlayer coupling in twisted molybdenum disulfide bilayers.
abstract: Van der Waals coupling is emerging as a powerful method to engineer physical properties of atomically thin two-dimensional materials. In coupled graphene-graphene and graphene-boron nitride layers, interesting physical phenomena ranging from Fermi velocity renormalization to Hofstadter's butterfly pattern have been demonstrated. Atomically thin transition metal dichalcogenides, another family of two-dimensional-layered semiconductors, can show distinct coupling phenomena. Here we demonstrate the evolution of interlayer coupling with twist angles in as-grown molybdenum disulfide bilayers. We find that the indirect bandgap size varies appreciably with the stacking configuration: it shows the largest redshift for AA- and AB-stacked bilayers, and a significantly smaller but constant redshift for all other twist angles. Our observations, together with ab initio calculations, reveal that this evolution of interlayer coupling originates from the repulsive steric effects that leads to different interlayer separations between the two molybdenum disulfide layers in different stacking configurations.
authors.affiliation: 1] Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA [2] State Key Laboratory for Mesoscopic Physics, School of Physics and Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China.
authors.forename: Kaihui
authors.initials: K
authors.lastname: Liu
authors.affiliation: Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, USA.
authors.forename: Liming
authors.initials: L
authors.lastname: Zhang
authors.affiliation: 1] Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA [2] Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Ting
authors.initials: T
authors.lastname: Cao
authors.affiliation: Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA.
authors.forename: Chenhao
authors.initials: C
authors.lastname: Jin
authors.affiliation: 1] Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA [2] Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Diana
authors.initials: D
authors.lastname: Qiu
authors.affiliation: Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Qin
authors.initials: Q
authors.lastname: Zhou
authors.affiliation: 1] Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA [2] Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA [3] Kavli Energy NanoSciences Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Alex
authors.initials: A
authors.lastname: Zettl
authors.affiliation: 1] Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, USA [2] Kavli Energy NanoSciences Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA [3] Department of Materials Science and Engineering, University of California at Berkeley, Berkeley, California 94720, USA.
authors.forename: Peidong
authors.initials: P
authors.lastname: Yang
authors.affiliation: 1] Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA [2] Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Steve G
authors.initials: SG
authors.lastname: Louie
authors.affiliation: 1] Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA [2] Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA [3] Kavli Energy NanoSciences Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Feng
authors.initials: F
authors.lastname: Wang