Macroscopic concentration of massless charge carriers with linear conic spectrum - Dirac Fermions (DF) - was shown in 2004 to exist in highly oriented pyrolytic graphite (HOPG) and governs its electronic properties. These carriers can have the same nature as DF observed in graphite monolayer(graphene) and let to view HOPG as superposition of 2D carbon layers, almost independent electronically. We overview here the recent experimental evidences of 2D DF in graphite and their similarity with carriers in graphene.
Dirac and Normal Fermions in Graphite and Graphene: Implications to the Quantum Hall Effect
在准2D高取向热解石墨（HOPG）中测量的磁阻和量子霍尔效应（QHE）的Shubnikov de Haas（SdH）振荡的光谱分析[Phys.Rev.Lett. 90，156402（2003）]揭示了两种类型的载流子：具有Berry相位0的正常（有质量）电子和具有Berry相位π的Dirac类（无质量）空穴。我们证明，最近报道的整数和半整数QHE的双层和单层石墨烯同时发生在HOPG样品。
The band structure of ABC-stacked N-layer graphene comprises topologically corresponding flat surface and gapped bulk subbands, as a consequence of the unique stacking configuration. In this paper, the bulk subbands are for the first times ever obtained for arbitrary N. A non-perturbative effective Hamiltonian closed in the bulk subspace is derived and used. The gapped bulk subbands are shown to evolve towards the zero energy with increasing N and in the infinite limit, they touch linearly along a circle. This outcome is a manifestation of the dimensional crossover to a three-dimensional Dirac…
Three dimensional (3D) topological insulators (TIs) are an important class of materials with applications in electronics, spintronics and quantum computing. With the recent development of truly bulk insulating 3D TIs, it has become possible to realize surface dominated phenomena in electrical transport measurements e.g. the quantum Hall (QH) effect of massless Dirac fermions in topological surface states (TSS). However, to realize more advanced devices and phenomena, there is a need for a platform to tune the TSS or modify them e.g. gap them by proximity with magnetic insulators, in a clean ma…
Comment on "Consistent Interpretation of the Low-Temperature Magnetotransport in Graphite Using the Slonczewski-Weiss-McClure 3D Band-Structure Calculations" (arXiv:0902.1925)
在2004年，我们已经表明，石墨中的导电性的很大一部分是由无质量的线性光谱的空穴-狄拉克费米子，与大量的正常载流子-电子共存。在最近的一封信[物理。102，166403（2009），arXiv：0902.1925] Schneider等人修改了我们的结论，指出两种类型的载体都是巨大的。由于这两个群体使用相同的方法来确定Shubnikov de Haas振荡的相位，我们在这里评论说，争议源于Schneider 2009等人对实验结果的不当处理。
We calculate the electronic structure of AA'AA'...-stacked alternating twist N-layer (tNG) graphene for N = 3, 4, 5, 6, 8, 10, 20 layers and bulk alternating twist (AT) graphite systems where the lattice relaxations are modeled by means of molecular dynamics simulations. We show that the symmetric AA'AA'... stacking is energetically preferred among all interlayer sliding geometries for progressively added layers up to N=6. Lattice relaxations enhance electron-hole asymmetry, and reduce the magic angles with respect to calculations with fixed tunneling strengths that we quantify from few layers…
We review the recently proposed Dirac composite fermion theory of the half-filled Landau level. This paper is based on a talk given at the Nambu Symposium at University of Chicago, March 11-13, 2016.
We report two-dimensional quantum transport and Dirac fermions in BaMnBi2 single crystals. BaMnBi2 is a layered bad metal with highly anisotropic conductivity and magnetic order below 290 K. Magnetotransport properties, nonzero Berry phase, small cyclotronmass, and the first-principles band structure calculations indicate the presence of Dirac fermions in Bi square nets. Quantum oscillations in the Hall channel suggest the presence of both electron and hole pockets, whereas Dirac and parabolic states coexist at the Fermi level.
We report two-dimensional quantum transport and Dirac fermions in YbMnBi2 single crystals. YbMnBi2 is a layered material with anisotropic conductivity and magnetic order below 290 K. Magnetotransport properties, nonzero Berry phase and small cyclotron mass indicate the presence of quasi two dimensional Dirac fermions. Quantum oscillations in Hall resistivity suggest the presence of both electron and hole parts of the Fermi surface whereas the Berry phase suggests spin-orbit coupling.
Revealing the ultrafast dynamics of three-dimensional (3D) Dirac fermions upon photoexcitation is critical for both fundamental science and device applications. So far, how the cooling of 3D Dirac fermions differs from that of two-dimensional (2D) Dirac fermions and whether there is population inversion are fundamental questions that remain to be answered. Here we reveal the ultrafast dynamics of Dirac fermions in a model 3D Dirac semimetal Cd$_3$As$_2$ by ultrafast time- and angle-resolved photoemission spectroscopy (TrARPES) with a tunable probe photon energy from 5.3 - 6.9 eV. The energy- a…
The low energy physics of both graphene and surface states of three-dimensional topological insulators is described by gapless Dirac fermions with linear dispersion. In this work, we predict the emergence of a "heavy" Dirac fermion in a graphene/topological insulator hetero-junction, where the linear term almost vanishes and the corresponding energy dispersion becomes highly non-linear. By combining {\it ab initio} calculations and an effective low-energy model, we show explicitly how strong hybridization between Dirac fermions in graphene and the surface states of topological insulators can r…
The symmetries that protect massless Dirac fermions from a gap opening may become ineffective if the Dirac equation is discretized in space and time, either because of scattering between multiple Dirac cones in the Brillouin zone (fermion doubling) or because of singularities at zone boundaries. Here we introduce an implementation of Dirac fermions on a space-time lattice that removes both obstructions. The quasi-energy band structure has a tangent dispersion with a single Dirac cone that cannot be gapped without breaking both time-reversal and chiral symmetries. We show that this topological …
The type-II Weyl/Dirac fermions are a generalization of conventional or type-I Weyl/Dirac fermions, whose conic spectrum is tilted such that the Fermi surface becomes lines in two dimensions, and surface in three dimensions rather than discrete points of the conventional Weyl/Dirac fermions. The mass-independent renormalization group calculations show that the tilting parameter decreases monotonically with respect to the length scale, which leads to a transition from two dimensional type-II Weyl/Dirac fermions to the type-I ones. Because of the non-trivial Fermi surface, a photon gains a finit…
Zone-resolved photoelectronic scoping of the local bonding and electronic dynamics at the graphite skin with and without atomic vacancy and the associated graphene edge states
The magnetotransport properties of massless Dirac fermions in a gapless HgTe quantum well are investigated. In samples with narrow channels, a large negative magnetoresistance with a Lorentzian profile is observed, which is interpreted as a manifestation of electron viscosity due to electron-electron interaction. Comparison of experiment with theory yields the shear stress relaxation time of the Dirac fermions caused by electron-electron scattering.
We study the quantum Hall effect of Dirac fermions on the surface of a Wilson-Dirac type topological insulator thin film in the strong topological insulating phase. Although a magnetic field breaks time reversal symmetry of the bulk, the surface states can survive even in a strong field regime. We examine how the Landau levels of the surface states are affected by symmetry breaking perturbations.
The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form ${\mathcal H}ψ=E {\mathcal P}ψ$, with Hermitian tight-binding operators ${\mathcal H}$, ${\mathcal P}$, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fe…
Composite fermions in fractional quantum Hall (FQH) systems are believed to form a Fermi sea of weakly interacting particles at half filling $ν=1/2$. Recently, it was proposed (D. T. Son, Phys. Rev. X 5, 031027 (2015)) that these composite fermions are Dirac particles. In our work, we demonstrate experimentally that composite fermions found in monolayer graphene are Dirac particles at half filling. Our experiments have addressed FQH states in high-mobility, suspended graphene Corbino disks in the vicinity of $ν=1/2$. We find strong temperature dependence of conductivity $σ$ away from half fill…
The Datta-Das-type spin field-effect transistor, using a two-dimensional electron gas in a semiconductor heterostructure as a channel, plays a key role in spintronics. Here, we theoretically present a type of spin field-effect transistor based on massless birefringent Dirac fermions in polar Dirac semimetals. The manipulation of spin arises from the existence of the strong spin-orbit coupling, polar space groups, and Dirac cones in a single phase. The oscillatory channel conductance can be controlled by the sign of gate voltage in addition to its magnitude due to the gapless band structures of…
A brief survey is given of theoretical works on surface states (SSs) in Dirac materials. Within the formalism of envelope wave functions and boundary conditions for these functions, a minimal model is formulated that analytically describes surface and edge states of various (topological and non-topological) types in several systems with Dirac fermions (DFs). The applicability conditions of this model are discussed.
