Fractal Landau-Level Spectra in Twisted Bilayer Graphene

The Hofstadter butterfly spectrum for Landau levels in a two-dimensional periodic lattice is a rare example exhibiting fractal properties in a truly quantum system. However, the observation of this physical phenomenon in a conventional material will require a magnetic field strength several orders of magnitude larger than what can be produced in a modern laboratory. It turns out that for a specific range of rotational angles twisted bilayer graphene serves as a special system with a fractal energy spectrum under laboratory accessible magnetic field strengths. This unique feature arises from an intriguing electronic structure induced by the interlayer coupling. Using a recursive tight-binding method, we systematically map out the spectra of these Landau levels as a function of the rotational angle. Our results give a complete description of LLs in twisted bilayer graphene for both commensurate and incommensurate rotational angles and provide quantitative predictions of magnetic field strengths for observing the fractal spectra in these graphene systems

Charge Transport through Graphene Junctions with Wetting Metal Leads

Graphene is believed to be an excellent candidate material for next-generation electronic devices. However, one needs to take into account the nontrivial effect of metal contacts in order to precisely control the charge injection and extraction processes. We have performed transport calculations for graphene junctions with wetting metal leads (metal leads that bind covalently to graphene) using nonequilibrium Green’s functions and density functional theory. Quantitative information is provided on the increased resistance with respect to ideal contacts and on the statistics of current fluctuations. We find that charge transport through the studied two-terminal graphene junction with Ti contacts is pseudo-diffusive up to surprisingly high energies

Fractal Landau-Level Spectra in Twisted Bilayer Graphene

The Hofstadter butterfly spectrum for Landau levels in a two-dimensional periodic lattice is a rare example exhibiting fractal properties in a truly quantum system. However, the observation of this physical phenomenon in a conventional material will require a magnetic field strength several orders of magnitude larger than what can be produced in a modern laboratory. It turns out that for a specific range of rotational angles twisted bilayer graphene serves as a special system with a fractal energy spectrum under laboratory accessible magnetic field strengths. This unique feature arises from an intriguing electronic structure induced by the interlayer coupling. Using a recursive tight-binding method, we systematically map out the spectra of these Landau levels as a function of the rotational angle. Our results give a complete description of LLs in twisted bilayer graphene for both commensurate and incommensurate rotational angles and provide quantitative predictions of magnetic field strengths for observing the fractal spectra in these graphene systems

Coupled Dirac Fermions and Neutrino-like Oscillations in Twisted Bilayer Graphene

The low-energy quasiparticles in graphene can be described by a Dirac–Weyl Hamiltonian for massless fermions, hence graphene has been proposed to be an effective medium to study exotic phenomena originally predicted for relativistic particle physics, such as Klein tunneling and Zitterbewegung. In this work, we show that another important particle-physics phenomenon, the neutrino oscillation, can be studied and observed in a particular graphene system, namely, twisted bilayer graphene. It has been found that graphene layers grown epitaxially on SiC or by the chemical vapor deposition method on metal substrates display a stacking pattern with adjacent layers rotated by an angle with respect to each other. The quasiparticle states in two distinct graphene layers act as neutrinos with two flavors, and the interlayer interaction between them induces an appreciable coupling between these two “flavors” of massless fermions, leading to neutrino-like oscillations. In addition, our calculation shows that anisotropic transport properties manifest in a specific energy window, which is accessible experimentally in twisted bilayer graphene. Combining two graphene layers enables us to probe the rich physics involving multiple interacting Dirac fermions

Dimensional Effects on the Charge Density Waves in Ultrathin Films of TiSe₂

Charge density wave (CDW) formation in solids is a critical phenomenon involving the collective reorganization of the electrons and atoms in the system into a wave structure, and it is expected to be sensitive to the geometric constraint of the system at the nanoscale. Here, we study the CDW transition in TiSe₂, a quasi-two-dimensional layered material, to determine the effects of quantum confinement and changing dimensions in films ranging from a single layer to multilayers. Of key interest is the characteristic length scale for the transformation from a two-dimensional case to the three-dimensional limit. Angle-resolved photoemission spectroscopy (ARPES) measurements of films with thicknesses up to six layers reveal substantial variations in the energy structure of discrete quantum well states; however, the temperature-dependent band gap renormalization converges at just three layers. The results indicate a layer-dependent mixture of two transition temperatures and a very-short-range CDW interaction within a three-dimensional framework