Dirac Electron System Research Articles

Spectral function of the two-dimensional system of massless Dirac electrons

We determine the one-particle spectral function for the two-dimensional system of massless Dirac electrons interacting via the long-range Coulomb interaction. The electron self-energy is calculated within the G0W0 approximation, paying particular attention to the contribution coming from the collective plasmon mode. We find that, due to the acoustic plasmon dispersion, the spectral function has a renormalized quasi-particle δ-peak at the chemical potential along with a side band for the Fermi wave vector together with a wide structure with a pronounced spectral weight near the Dirac point. The present approach is appropriate for the wide range of energy scales given by the plasmon energy which may be probed in angle-resolved photoemission spectroscopy (ARPES) experiments.

Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones

We theoretically study the effect of the motion and the merging of Dirac cones on the interlayer magnetoresistance in multilayer graphene-like systems. This merging, which can be induced by a uniaxial strain, gives rise in a monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase whereby Dirac points disappear. Based on a universal Hamiltonian, proposed to describe the motion and the merging of Dirac points in two-dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene-like layers using the Kubo formula in the quantum limit where only the contribution of the n = 0 Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance can also result from a coupling between the Dirac valleys, which is enhanced as the magnetic field amplitude increases. Our results describe the behavior of the magnetotransport in the organic conductor α-(BEDT)2I3 and in a stack of deformed graphene-like systems. The latter can be simulated by optical lattices or microwave experiments in which the merging of Dirac cones can be observed.

Ultraviolet divergence and Ward-Takahashi identity in a two-dimensional Dirac electron system with short-range impurities

Dirac electrons in two-dimensional continuum space subject to $\ensuremath{\delta}$-function impurities, which have inherent ultraviolet divergence, fail to be gauge-invariant if regularized by the standard momentum (Brillouin-zone) cutoff. A regularization scheme which respects gauge invariance is proposed here based on the cutoff in the impurity-potential range. The relation to a lattice model, which has no ultraviolet divergence, is also discussed.

Renormalized transport properties of randomly gapped two-dimensional Dirac fermions

We investigate the scaling properties of the recently acquired fermionic non--linear $\sigma$--model which controls gapless diffusive modes in a two--dimensional disordered system of Dirac electrons beyond charge neutrality. The transport on large scales is governed by a novel renormalizable nonlocal field theory. For zero mean random gap, it is characterized by the absence of a dynamic gap generation and a scale invariant diffusion coefficient. The $\beta$ function of the DC conductivity, computed for this model, is in perfect agreement with numerical results obtained previously.

Spin polarization dependence of quasiparticle properties in graphene

We address spin polarization dependence of graphene's Fermi liquid properties quantitatively using a microscopic Random Phase Approximation theory in an interacting spin-polarized Dirac electron system. We show an enhancement of the minority-spin many-body velocity renormalization at fully spin polarization due to reduction in the electron density and consequently increase in the interaction between electrons near the Fermi surface. We also show that the spin dependence of the Fermi velocity in the chiral Fermi systems is different than that in a conventional two-dimensional electron liquid. In addition, we show that the ratio of the majority- to minority-spin lifetime is smaller than unity and related directly to the polarization and electron energy. The spin-polarization dependence of the carrier Fermi velocity is of significance in various spintronic applications.

Superconducting and excitonic quantum phase transitions in doped Dirac electronic systems

We investigate the effect of superconducting and excitonic interactions, as well as their competition, on Dirac electrons on a bipartite planar lattice. It is shown that, at half-filling, Cooper pairs and excitons coexist if the superconducting and excitonic coupling parameters are equal and above a threshold corresponding to a quantum critical point. In the case where only the excitonic interaction is present, we obtain a critical chemical potential, as a function of the interaction strength. Conversely, if only the superconducting interaction is considered, we show that the superconducting gap displays a characteristic dome as charge carriers are doped into the system. We also show that, as the chemical potential increases, superconductivity tends to suppress the excitonic order parameter.

Thermodynamic properties of the superconductivity in quasi-two-dimensional Dirac electronic systems

The thermodynamic properties of superconducting Dirac electronic systems is analyzed in the vicinity of quantum critical point. The system is characterized by a quantum critical point at zero doping, such that the critical temperature vanishes below some finite value of interaction strength. It is found that the specific heat jump of the system largely deviates from the conventional BCS theory value in the vicinity of quantum critical point. We investigated the region of applicability of the mean-field theory using the Ginzburg-Landau functional.

Interfacial charge and spin transport inZ2topological insulators

The Kane-Mele model realizes a two-dimensional version of a ${\mathbb{Z}}_{2}$ topological insulator as an idealized model of graphene with intrinsic and extrinsic (Rashba) spin-orbit couplings. We study the transport of charge and spin in such a Dirac electron system in the presence of a sharp potential step, that is, a $\mathit{pn}$ junction. An electron incident normal to the junction is completely reflected when Rashba coupling is dominant, whereas it is perfectly transmitted when the two types of couplings are balanced. The latter manifests in charge transport as a peak of conductance and a dip in Fano factor. Charge transport occurs in the direction normal to the barrier, whereas a spin current is induced along the barrier that is also localized in its vicinity. It is demonstrated that contributions from interband matrix elements and evanescent modes are responsible for such an interfacial spin Hall current. Our analysis of spin transport is based on the observation that in the case of vanishing Rashba coupling, each channel carries a conserved spin current, whereas only the integrated spin current is a conserved quantity in the general case. The perfect transmission/reflection of charge and conserved spin current is a consequence of reflection symmetry. Finally, we provide a quasiclassical picture of charge and spin transport by imaging flow lines over the entire sample and Veselago lensing (negative refraction).

Negative c-axis magnetoresistance in graphite

We have studied the c-axis interlayer magnetoresistance (ILMR), R c ( B ) in graphite. The measurements have been performed on strongly anisotropic highly oriented pyrolytic graphite (HOPG) and single crystalline Kish graphite samples in magnetic field up to B = 9 T , and the temperature interval 2 K ⩽ T ⩽ 300 K . We have observed negative magnetoresistance, d R c / d B < 0 , for B ‖ c -axis for both samples above a certain field B m ( T ) > 5.4 T and 0.2 T for HOPG and Kish graphite, respectively. The results can be understood consistently by assuming that ILMR is related to a tunneling between zero-energy Landau levels of quasi-two-dimensional Dirac fermions, in a close analogy with the behavior reported for α-(BEDT-TTF) 2I 3 [N. Tajima, et al., Phys. Rev. Lett. 102 (2009) 176403], another multilayer Dirac electron system.

Anomalous orbital magnetism in Dirac-electron systems: Role of pseudospin paramagnetism

The orbital diamagnetic susceptibility is calculated in monolayer and bilayer graphenes with band gap as well as in three-dimensional Dirac systems. It is demonstrated that the pseudo-spin degree of freedom such as valleys produces paramagnetic susceptibility in an equal manner as the real spin dominating over the Landau diamagnetism. The pseudo-spin paramagnetism explains the origin of a singular diamagnetism which is present only in the band-gap region and disappears rapidly inside the conduction and valence bands.

Velocity-modulation control of electron-wave propagation in graphene

Wave propagation control by spatial modulation of velocity has a long history in optics and acoustics. We address velocity-modulation control of electron wave propagation in graphene and other two-dimensional Dirac-electron systems, pointing out a key distinction of the Dirac-wave case. We also propose a strategy for pattern transfer from a remote metallic layer that is based on many-body velocity renormalization.

Negative Interlayer Magnetoresistance and Zero-Mode Landau Level in Multilayer Dirac Electron Systems

The interlayer magnetotransport has been considered in multilayer Dirac electron systems, in which two-dimensional electron layers with Dirac-cone dispersion stack with weak interlayer coupling. Under magnetic fields, one Landau level (zero-mode) always appears at the contact point of Dirac cones, and tunneling between the zero-modes on neighboring layers dominates interlayer transport in multilayer systems. The increase of zero-mode degeneracy causes strong negative magnetoresistance. Spin splitting of the zero-mode could change the negative magnetoresistance to the positive one in high magnetic fields and low temperatures. The magnetotransport features observed in an organic conductor α-(BEDT-TTF) 2 I 3 are discussed based on the present model.

Effects of a magnetic field on superconductivity and quantum criticality in quasi-two-dimensional systems with Dirac electrons

We study the effects of an external magnetic field on the superconducting phase diagram of a quasi-two-dimensional system of Dirac electrons at an arbitrary temperature. At zero temperature, there is a quantum phase transition connecting a normal and a superconducting phase, occurring at a critical line that corresponds to a magnetic field dependent critical coupling parameter, which should be observed in planar materials containing Dirac electrons, such as Cu x TiSe 2 . Moreover, the superconducting gap is obtained as a function of temperature, magnetic field and coupling parameter ( λ R ) . From this, we extract the critical magnetic field B c as a function of the temperature. For small values of B c , we obtain a linear decay of the critical field, which is similar to the behavior observed experimentally in the copper doped dichalcogenide Cu x TiSe 2 and also in intercalated graphite.

Magnetic field effects on the superconducting and quantum critical properties of layered systems with Dirac electrons

We study the effects of an external magnetic field on the superconducting properties of a quasi-two-dimensional system of Dirac electrons at an arbitrary temperature. An explicit expression for the superconducting gap is obtained as a function of temperature, magnetic field and coupling parameter ( λ R ) . From this, we extract the B × λ R , T × λ R and B × T phase diagrams. The last one shows a linear decay of the critical field for small values thereof, which is similar to the behavior observed experimentally in the copper doped dichalcogenide Cu x TiSe 2 and also in intercalated graphite. The second one, presents a coupling dependent critical temperature T c that resembles the one observed in high- T c cuprates in the underdoped region and also in Cu x TiSe 2. The first one, exhibits a quantum phase transition connecting a normal and a superconducting phase, occurring at a critical line that corresponds to a magnetic field dependent critical coupling parameter. This should be observed in planar materials containing Dirac electrons, such as Cu x TiSe 2.

Quantum criticality and superconductivity in quasi-two-dimensional Dirac electronic systems

We present a theory describing the superconducting (SC) interaction of Dirac electrons in a quasi-two-dimensional system consisting of a stack of N planes. The occurrence of a SC phase is investigated both at T = 0 and T ≠ 0 , in the case of a local interaction, when the theory must be renormalized and also in the situation where a natural physical cutoff is present in the system. In both cases, at T = 0 , we find a quantum phase transition connecting the normal and SC phases at a certain critical coupling. The phase structure is shown to be robust against quantum fluctuations. The SC gap is determined for T = 0 and T ≠ 0 , both with and without a physical cutoff and the interplay between the gap and the SC order parameter is discussed. Our theory qualitatively reproduces the SC phase transition occurring in the underdoped regime of the high- T c cuprates. This fact points to the possible relevance of Dirac electrons in the mechanism of high- T c superconductivity.

Relativistic Effect and Nonconservative Spin–Orbital Forces in the Radiative Transition of Molecules

A treatment is given of a one-electron orbital model for a many-electron molecule, in which each electron is allowed to interact with the over-all orbital and spin magnetic fields, as well as the (Coulomb) electric field of the rest of the electrons and nuclei. It is shown that when redundancy is properly taken care of, by introducing a factor of 12 for the mutual-magnetic vector potential Aij between the electrons, the subsequent reduction of Dirac's equation reproduces all of Darwin's orbit–orbit, spin–own-orbit, spin–other-orbit, and spin–spin interactions, etc., given by the Breit–Pauli approximation. The above treatment is extended to a system of Dirac electrons interacting with the (time-dependent) electromagnetic field of radiation, in which field–field interaction in the form of Aij·Aj (radiation), is also included. After integration over the photon space, effective transition operators for the large-component spinors are obtained. When the non-Hermitian part of the “Dirac Hamiltonian” for the large-component spinors is not neglected as was customarily done, it is shown that the effective transition operators are already complete, in the sense that they already contain the relativistic-correction-of-mass terms, nonconservative force terms, and corrections due to operation on small-component spinors. This is shown from the Hermiticity of the operators as well as from explicit derivations. In explicit derivations, the origin of each of the effective transition operators is traced and tabulated. It is shown that for a spinless electron, or a Dirac electron described by an equation linear in time, and by a four-component spinor, the use of the transition dipole-length operator is justified. However, the straightforward use of the transition dipole-length operator on the large-component spinors, approximated by Breit–Pauli eigenstates, would neglect not only corrections due to small-component spinors but also the “ordinary” spin radiation term due to the direct spin interaction with the magnetic field of radiation. This interaction is shown to come from a nonconservative force acting on the electron, which is not derivable from a vector potential. All other external electromagnetic forces derivable from a vector potential are shown to contribute to radiation in a similar manner, and such contributions are obtainable by analogy to the classical Lagrangian–Hamiltonian formalism for conservative forces. The internal orbital and spin magnetic forces, such as spin–own-orbit interaction, are shown to contribute to radiation through the non-Hermitian part of the “Dirac Hamiltonian.” Although these forces can be represented by “effective” vector potentials, it is emphasized that the latter are not usable as (the external) vector potentials in the relativistic Lagrangian, and in the Dirac equation. The magnitudes of the effective transition operators obtained in our treatment are estimated (Table I, see also Table II) for a constant vector potential of radiation over the molecule, and for a (linearly) position-dependent vector potential. For application to single–triplet transitions, the relative importance of the spin-dependent transition operators, coming from nonconservative forces, non-Hermitian terms, and from corrections for small-component spinors is examined. Explicit expressions of these operators for different propagation and polarization directions are also given (Table III). For example, spin–other-orbit interaction is shown to contribute to Δ S = ± 1 radiative transitions between states of the same parity. The two-electron radiative transition operators, due to the inclusion of the mutual electromagnetic interaction of the electrons, may be of interest in cooperative optical phenomena, double excitations, and in the radiative contribution to van der Waals forces. The inclusion of the radiative transition operators from the non-Hermitian term also offers several alternative two-photon transition possibilities.