Massless Dirac Fermion System Research Articles

Symmetry-protected quantization and bulk-edge correspondence of massless Dirac fermions: Application to the fermionic Shastry-Sutherland model

The fermionic Shastry-Sutherland model has a rich phase diagram, including phases with massless Dirac fermions, a quadratic band crossing point, and a pseudospin-1 Weyl fermion. Berry phases defined by the one-dimensional momentum as a parameter are quantized into 0 or pi due to the inversion symmetry combined with the time reversal, or existence of the glide plane, which also protects the massless Dirac cones with continuous parameters. This is the symmetry protected Z2 quantization. We have further demonstrated the Z2 Berry phases generically determine the existence of edge states in various phases and with different types of the boundaries as the bulk-edge correspondence of the massless Dirac fermion systems.

Quantum Hall effect in multilayered massless Dirac fermion systems with tilted cones

We report the first observation of Shubnikov-de Haas (SdH) oscillations and quantized Hall resistance in the multilayered massless Dirac fermion system $\alpha$-(BEDT-TTF)$_2$I$_3$ with tilted cones. Holes were injected into the thin crystal fixed on a polyethylene naphthalate (PEN) substrate by contact electrification. The detection of SdH oscillations whose phase was modified by Berry's phase $\pi$ strongly suggested that the carrier doping was successful in this system. We succeeded in detecting the quantum Hall effect (QHE) with the steps which is the essence of two dimensional Dirac fermion systems. The number of effectively doped layers was examined to be two in this device. We reveal that the correlation between effective layers plays an important role in QHE.

Anomalous Thermoelectric Transport and Giant Nernst Effect in Multilayered Massless Dirac Fermion System

We have measured the thermopower and Nernst effect of the multilayered massless Dirac fermion system α-(BEDT-TTF)2I3 under pressure. In the quantum limit region, the extremely large Nernst effect rather than the Seebeck effect was observed. This unusual behavior results from the intrinsic nature of the zero-mode Landau level characteristic of the Dirac fermion system. The possible origin of the giant Nernst signal compared with that of graphene is the sharp width of the Landau level and the Zeeman gap in high-purity α-(BEDT-TTF)2I3 crystal.

Plasma oscillations of edge Dirac fermions

The dispersion law of one-dimensional plasmons in a quasi-one-dimensional system of massless Dirac fermions has been calculated. Two model two-dimensional systems where bands of edge states filled with such Dirac fermions appear at the edge have been considered. Edge states in the first system, topological insulator, are due to topological reasons. Edge states in the second system, system of massive Dirac fermions, have Tamm origin. It has been shown that the dispersion laws of plasmons in both systems in the long-wavelength limit differ only in the definition of the parameters (velocity and localization depth of Dirac fermions). The frequency of plasmons is formally quantum (ω ∝ ħ−1/2) and, in the case of the Coulomb interaction between electrons, depends slightly on the Fermi level EF. The dependence on EF is stronger in the case of short-range interaction. The quantum features of oscillations of massless one-dimensional Dirac fermions are removed by introducing the mass of Dirac fermions at the Fermi level and their density. Correspondence to the dispersion law of classical one-dimensional plasma oscillations in a narrow stripe of “Schrodinger” electrons has been revealed.

Chiral Scars in Chaotic Dirac Fermion Systems

Do relativistic quantum scars in classically chaotic systems possess unique features that are not shared by nonrelativistic quantum scars? We report a class of relativistic quantum scars in massless Dirac fermion systems whose phases return to the original values or acquire a 2π change only after circulating twice about some classical unstable periodic orbits. We name such scars chiral scars, the successful identification of which has been facilitated tremendously by our development of an analytic, conformal-mapping-based method to calculate an unprecedentedly large number of eigenstates with high accuracy. Our semiclassical theory indicates that the physical origin of chiral scars can be attributed to a combined effect of chirality intrinsic to massless Dirac fermions and the geometry of the underlying classical orbit.

Transport Phenomena in Multilayered Massless Dirac Fermion System α-(BEDT-TTF)2I3

A zero-gap state with a Dirac cone type energy dispersion was discovered in an organic conductor α-(BEDT-TTF)2I3 under high hydrostatic pressures. This is the first two-dimensional (2D) zero-gap state discovered in bulk crystals with a layered structure. In contrast to the case of graphene, the Dirac cone in this system is highly anisotropic. The present system, therefore, provides a new type of massless Dirac fermion system with anisotropic Fermi velocity. This system exhibits remarkable transport phenomena characteristic to electrons on the Dirac cone type energy structure.

Specific Heat of the Multilayered Massless Dirac Fermion System

We have measured the specific heat of the multilayered massless Dirac fermion system α-(BEDT-TTF) 2 I 3 under pressure. The temperature dependence of the specific heat is almost quadratic at low temperature, suggesting massless Dirac dispersion in this system. In a magnetic field, the specific heat shows anomalous behavior, which can be understood by assuming the zero-mode Landau level characteristic of the Dirac fermion system and its spin splitting. These results are in good agreement with the reported magnetoresistance.

Specific heat study of massless Dirac fermion system α‐(BEDT‐TTF)2I3 under pressure

AbstractThe specific heat of massless Dirac fermion system α‐(BEDT‐TTF)2I3 was measured under pressure. In low temperature, the temperature dependence of the specific heat is almost quadratic reflecting the massless Dirac dispersion. In magnetic field, the specific heat shows anomalous behavior which can be understood by assuming the existence of the zero‐mode Landau level characteristic of the Dirac fermions system and its spin splitting. These results are consistent with the reported magnetoresistance. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Magnetotransport in organic Dirac fermion system at the quantum limit: Interlayer Hall effect and surface transport via helical edge states

AbstractWe discuss two anomalous features of interlayer magnetotransport observed in α‐(BEDT‐TTF)2I3 in terms of massless Dirac fermions: the interlayer Hall effect and high‐field interlayer magnetoresistance (MR). The former is the anomalous Hall effect, which does not depend on magnetic field strength. It depends only on field orientation showing cotθ‐type angle dependence. We have derived the lowest order contribution of interlayer coupling to conductivity and successfully reproduced the interlayer Hall effect as a transport phenomenon in the massless Dirac fermion system at the quantum limit. The latter is an exponential increase of interlayer MR and its follow‐on saturation in higher magnetic fields. The exponential increase is evidence of the existence of a mobility gap at the Fermi level. It strongly suggests that the ν = 0 quantum Hall state is realized by spin splitting. In this case, two edge states with opposite spin and chirality are formed on the edge surface. The surface transport via edge states becomes dominant in interlayer transport in high enough fields, where bulk transport becomes exponentially small. The observed saturation of interlayer MR is well explained with this scenario.

Landau Quantization and the Thickness Limit of Topological Insulator Thin Films ofSb2Te3

We report the experimental observation of Landau quantization of molecular beam epitaxy grown Sb{2}Te{3} thin films by a low-temperature scanning tunneling microscope. Different from all the reported systems, the Landau quantization in a Sb{2}Te{3} topological insulator is not sensitive to the intrinsic substitutional defects in the films. As a result, a nearly perfect linear energy dispersion of surface states as a 2D massless Dirac fermion system is achieved. We demonstrate that four quintuple layers are the thickness limit for a Sb{2}Te{3} thin film being a 3D topological insulator. The mechanism of the Landau-level broadening is discussed in terms of enhanced quasiparticle lifetime.

Magnetotransport of Massless Dirac Fermions in Multilayer Organic Conductors

Magnetotransport has been considered in multilayer massless Dirac fermion systems, in which two-dimensional (2D) layers with a pair of Dirac-cone dispersion stack with weak interlayer coupling. The Fermi level is assumed to be fixed at the Dirac point resulting in the zero-gap conductor. At the high-field quantum limit, where only the n = 0 Landau level at the Dirac point is partially occupied, all elements of conductivity tensor have been evaluated by the lowest order contribution of interlayer coupling. We have deduced saturation of in-plane resistance, local maxima of in-plane Hall resistance, negative interlayer magnetoresistance, and cotθ-type unusual angle-dependence of interlayer Hall resistance. These results propose good explanations for mysterious transport features observed in organic zero-gap conductors, α-(BEDT-TTF)2I3 and its related compounds.

Anomalous Interlayer Hall Effect in Multilayer Massless Dirac Fermion System at the Quantum Limit

Magnetotransport features, particularly interlayer Hall effect, have been discussed in multilayer massless Dirac fermion systems, in which two-dimensional layers having Dirac-cone dispersion are stacked with weak interlayer coupling. At the quantum limit, where only the n =0 Landau level is partially occupied, the conductivity tensor has been evaluated by the lowest order contribution of interlayer coupling. In addition to in-plane transport behaviors, we have obtained the remarkable interlayer Hall effect which exhibits no dependence on field strength but anomalous dependence on field orientation. These results have successfully explained mysterious transport features observed in a zerogap organic conductor, α-(BEDT-TTF) 2 I 3 .

Graphene: The Magic of Flat Carbon

Graphene is the first example of a truly two-dimensional crystal. This opens many interesting directions of research concerning the thermodynamics, lattice dynamics, and structural properties of such systems. Being a gapless semiconductor with a linear energy spectrum, single-layer graphene realizes a two-dimensional, massless Dirac fermion system that is of crucial importance for understanding unusual electronic properties, such as an anomalous QHE, absence of the Anderson localization, etc. These peculiarities are important for developing new electronic devices such as carbon transistors. Recent developments in production of large quantities of graphene, as well as the possibility of its chemical modification make such developments very feasible.

Theory of in-plane magnetoresistance in two-dimensional massless Dirac fermion system

We present the theory of the inplane magnetoresistance in two-dimensional massless Dirac fermion systems including the Zeeman splitting and the electron-electron interaction effect on the Landau level broadening within a random phase approximation. With the decrease in temperature, we find a characteristic temperature dependence of the inplane magnetoresistance showing a minimum followed by an enhancement with a plateau. The theory is in good agreement with the experiment of the layered organic conductor \alpha-(BEDT-TTF)_2I_3 under pressure. In-plane magnetoresistsnce of graphene is also discussed based on this theory.

Spin and valley splittings in multilayered massless Dirac fermion system

The interlayer magnetoresistance in a multilayered massless Dirac fermion system, $\ensuremath{\alpha}\text{\ensuremath{-}}{(\text{BEDT-TTF})}_{2}{\text{I}}_{3}$, under hydrostatic pressure was investigated. We succeeded in detecting the zero-mode $(n=0)$ Landau level and its spin splitting in the magnetic field normal to the two-dimensional plane. We demonstrated that the effective Coulomb interaction in the magnetic field intensifies the spin splitting of zero-mode Landau carriers. At temperatures below 2 K, magnetic fields above several Tesla break the twofold valley degeneracy.

Crossover from Positive to Negative Interlayer Magnetoresistance in Multilayer Massless Dirac Fermion System with Non-Vertical Interlayer Tunneling

We present a theoretical description of the interlayer magnetoresistance in the layered Dirac fermion system with the application to the organic conductor α-(BEDT-TTF) 2 I 3 under pressure. Assuming a non-vertical interlayer tunneling and including higher Landau level effects we calculate the interlayer conductivity using the Kubo formula. We propose a physical picture of the experimentally observed crossover from the negative interlayer magnetoresistance, where the Dirac fermion zero energy Landau level plays a central role, to the positive interlayer magnetoresistance that is the consequence of the Landau level mixing effect upon non-vertical interlayer hopping. The crossover magnetic field depends on the Landau level broadening factor and can be used to determine the Dirac fermion Landau level energy spectrum.

Interaction-driven instabilities of a Dirac semimetal

We explore the possible particle-hole instabilities that can arise in a system of massless Dirac fermions on both the honeycomb and pi-flux square lattices with short range interactions. Through analytical and numerical studies we show that these instabilities can result in a number of interesting phases. In addition to the previously identified charge and spin density wave phases and the exotic `quantum anomalous Hall' (Haldane) phase, we establish the existence of the dimerized Kekule phase over a significant portion of the phase diagram and discuss the possibility of its spinful counterpart, the `spin Kekule' phase. On the pi-flux square lattice we also find various stripe phases, which do not occur on the honeycomb lattice. The Kekule phase is described by a Z3 order parameter whose singly quantized vortices carry fractional charge +/- e/2. On the pi-flux lattice the analogous dimerized phase is described by a Z4 order parameter. We perform a fully self-consistent calculation of the vortex structure inside the dimerized phase and find that close to the core the vortex resembles a familiar superconducting U(1) vortex, but at longer length scales a clear Z4 structure emerges with domain walls along the lattice diagonals.

Spin Hall effect in a system of Dirac fermions in the honeycomb lattice with intrinsic and Rashba spin-orbit interaction

We consider spin Hall effect in a system of massless Dirac fermions in a graphene lattice. Two types of spin-orbit interaction, pertinent to the graphene lattice, are taken into account---the intrinsic and Rashba terms. Assuming perfect crystal lattice, we calculate the topological contribution to spin Hall conductivity. When both interactions are present, their interplay is shown to lead to some peculiarities in the dependence of spin Hall conductivity on the Fermi level.

Graphene: The Magic of Flat Carbon

Graphene is the first example of a truly two-dimensional crystal. This opens many interesting directions of research concerning the thermodynamics, lattice dynamics, and structural properties of such systems. Being a gapless semiconductor with a linear energy spectrum, single-layer graphene realizes a two-dimensional, massless Dirac fermion system that is of crucial importance for understanding unusual electronic properties, such as an anomalous QHE, absence of the Anderson localization, etc. These peculiarities are important for developing new electronic devices such as carbon transistors. Recent developments in production of large quantities of graphene, as well as the possibility of its chemical modification make such developments very feasible.

Effect of the Zero-Mode Landau Level on Interlayer Magnetoresistance in Multilayer Massless Dirac Fermion Systems

We report on the experimental results of interlayer magnetoresistance in the multilayer massless Dirac fermion system alpha-(BEDT-TTF)2I3 under hydrostatic pressure and its interpretation. We succeeded in detecting the zero-mode Landau level (n=0 Landau level) that is expected to appear at the contact points of Dirac cones in the magnetic field normal to the two-dimensional plane. The characteristic feature of zero-mode Landau carriers including the Zeeman effect is clearly seen in the interlayer magnetoresistance.