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The structural and electronic properties of germanene coated Ge$_2$Pt clusters have been determined by scanning tunneling microscopy and spectroscopy at room temperature. The interior of the germanene sheet exhibits a buckled honeycomb structure with a lattice constant of 4.3 AA and a buckling of 0.2 AA. The zigzag edges of germanene are reconstructed and display a 4$times$ periodicity. The differential conductivity of the interior of the germanene sheet has a V-shape, which is reminiscent of the density of states of a two-dimensional Dirac system. The minimum of the differential conductivity is located close to the Fermi level and has a non-zero value, which we ascribe to the metallic character of the underlying Ge$_2$Pt substrate. Near the reconstructed germanene zigzag edges the shape of the differential conductivity changes from a V-shape to a more parabolic-like shape, revealing that the reconstructed germanene zigzag edges do not exhibit a pronounced metallic edge state.
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Using a gold (111) surface as a substrate we have grown in situ by molecular beam epitaxy an atom-thin, ordered, two-dimensional multi-phase film. Its growth bears strong similarity with the formation of silicene layers on silver (111) templates. One of the phases, forming large domains, as observed in Scanning Tunneling Microscopy, shows a clear, nearly flat, honeycomb structure. Thanks to thorough synchrotron radiation core-level spectroscopy measurements and advanced Density Functional Theory calculations we can identify it to a $sqrt{3}$x$sqrt{3}$R(30{deg}) germanene layer in coincidence with a $sqrt{7}$x$sqrt{7}$R(19.1{deg}) Au(111) supercell, thence, presenting the first compelling evidence of the birth of a novel synthetic germanium-based cousin of graphene.
We present a framework to elucidate the existence of accidental contacts of energy bands, particularly those called Dirac points which are the point contacts with linear energy dispersions in their vicinity. A generalized von-Neumann-Wigner theorem we propose here gives the number of constraints on the lattice necessary to have contacts without fine tuning of lattice parameters. By counting this number, one could quest for the candidate of Dirac systems without solving the secular equation. The constraints can be provided by any kinds of symmetry present in the system. The theory also enables the analytical determination of k-point having accidental contact by selectively picking up only the degenerate solution of the secular equation. By using these frameworks, we demonstrate that the Dirac points are feasible in various two-dimensional lattices, e.g. the anisotropic Kagome lattice under inversion symmetry is found to have contacts over the whole lattice parameter space. Spin-dependent cases, such as the spin-density-wave state in LaOFeAs with reflection symmetry, are also dealt with in the present scheme.
Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB$_2$ is presented. Two-dimensional ZrB$_2$ is a mechanically stable d- and p-orbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of SOC, is able to remove selectively the Dirac cones. A rational explanation in terms of d- and p-orbital mixing is provided to elucidate the origin of the infrequent amount of Dirac cones in a flat structure. The versatility of transition metal d-orbitals combined with the honeycomb lattice provided by the B atoms yields novel features never observed in a two-dimensional material.
We propose a new concept of two-dimensional (2D) Dirac semiconductor which is characterized by the emergence of fourfold degenerate band crossings near the band edge and provide a generic approach to realize this novel semiconductor in the community of material science. Based on the first-principle calculations and symmetry analysis, we discover recently synthesised triple-layer (TL)-BiOS2 is such Dirac semiconductor that features Dirac cone at X/Y point, protected by nonsymmorphic symmetry. Due to sandwich-like structure, each Dirac fermion in TL-BiOS2 can be regarded as a combination of two Weyl fermions with opposite chiralities, degenerate in momentum-energy space but separated in real space. Such Dirac semiconductor carries layer-dependent helical spin textures that never been reported before. Moreover, novel topological phase transitions are flexibly achieved in TL-BiOS2: (i) an vertical electric field can drive it into Weyl semiconductor with switchable spin polarization direction, (ii) an extensive strain is able to generate ferroelectric polarization and actuate it into Weyl nodal ring around X point and into another type of four-fold degenerate point at Y point. Our work extends the Dirac fermion into semiconductor systems and provides a promising avenue to integrate spintronics and optoelectronics in topological materials.
Knowing the band structure of materials is one of the prerequisites to understand their properties. Therefore, especially in the last decades, angle-resolved photoemission spectroscopy (ARPES) has become a highly demanded experimental tool to investigate the band structure. However, especially in thin film materials with a layered structure and several capping layers, access to the electronic structure by ARPES is limited. Therefore, several alternative methods to obtain the required information have been suggested. Here, we directly invert the results by cyclotron resonance experiments to obtain the band structure of a two-dimensional (2D) material. This procedure is applied to the mercury telluride quantum well with critical thickness which is characterized by a 2D electron gas with linear dispersion relations. The Dirac-like band structure in this material could be mapped both on the electron and on the hole side of the band diagram. In this material, purely linear dispersion of the hole-like carriers is in contrast to detectable quadratic corrections for the electrons.
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