Symmetry And Moiré Superlattice Effects On Electronic Band Structures Of Low-dimensional Dirac Materials

Tuning electronic band structures of materials can modify the electrical,optical and magnetic properties,which is one of the most important topics in condensed matter physics.Modifying symmetry and constructing moirésuperlattice are two effective methods to control band structure.For condensed matter,symmetries include time-reversal symmetry,symmorphic and non-symmorphic crystal symmetries.Modifying symmetries can directly change the electronic and topological properties.Moiréeffect appears in superlattices by stacking two or more layers of two-dimensional materials.The moiréeffect modifies electronic structure in the momentum space and induces small moiréBrillouin zone.Angle-resolved photoelectron spectroscopy（ARPES）can directly probe electronic band structure of condensed matter,with energy-,momentum-and spin-resolutions.Dirac materials host linearly-dispersive Dirac cones in the electronic structures.In this thesis,we systematically investigate the evolutions of one-dimensional（1D）massless Dirac fermions with different crystal symmetry.We also detect the high-order moiréeffect on two-dimensional（2D）massless Dirac fermions in graphene/silicon carbide hetero Gstructure.The following research work has been carried out:（1）In contrast to Dirac material NbSi_0.45Te₂ with 1D long-range order,3D translational symmetry recovers in Nb X_1/3Te₂（X=Si,Ge）.We experimentally observed a weak topological insulator state in Nb X_1/3Te₂.Using bulk-sensitive soft x-ray ARPES,we experimentally determine the bulk band structure and observe hourglass-type nodes protected by non-symmorphic symmetries.Spin-orbit coupling gaps the nodes,and the system turns into a weak topological insulator state.Combining vacuum ultraviolet spin-resolved ARPES with surface sensitivity and first-principles calculations,we directly resolve the topological surface states with the spin-momentum locking,which serves as direct evidence for weak topological insulator phase.In contrast to ordinary topological insulator which induced by band inversion without symmetry protection,the weak topological insulator are stable and guaranteed by non-symmorphic symmetries.（2）We observed higher-order moiréeffects in graphene/silicon carbide heterostructure（graphene/Si C）.Both the lattice constants difference and twist angle between graphene and Si C are large,and the first-order moiréeffect is weak in graphene/Si C.On the other hand,we can construct two supercells of graphene and Si C,which have the same twist angle and small lattice mismatches,leading to promising higher-order moiréeffect.We observed higher-order moiréeffects in real space by scanning tunneling microscopy and low-energy electron diffractometer.Using ARPES,we directly observe multiple Dirac cone replicas with first-,second-,and third-orders momentum transfer,induced by higher-order moiréeffects in momentum space directly.（3）We provide a way to design the high-order moiréeffect in heterostructures with large lattice mismatches and rotation angles.A twist angle can be designed so that two high-orderΓpoints of two constituent materials are very close to each other.It corresponds to two supercells with similar lattice constants and small angle in real space.Higher-order moiréeffect is expected to be promising.It provides an efficient way to design the moiréeffect using materials hosting exotic properties such as magnetism or superconductivity without the limitation of good lattice constant match.