Reversal of Klein reflection by magnetic barriers in bilayer graphene

Massless Dirac fermions in monolayer graphene exhibit total transmission when normally incident on a scalar potential barrier, a consequence of the Klein paradox originally predicted by O Klein for relativistic electrons obeying the 3 + 1 dimensional Dirac equation. For bilayer graphene, charge carriers are massive Dirac fermions and, due to different chiralities, electron and hole states are not coupled to each other. Therefore, the wavefunction of an incident particle decays inside a barrier as for the non-relativistic Schr?dinger equation. This leads to exponentially small transmission upon normal incidence. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission even at normal incidence. The general consequences of this behavior for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.     

Superconductivity at the Normal Metal/Dirac Semimetal Cd_3As_2 Interface

We investigate the interface between a three-dimensional Dirac semimetal Cd₃As₂ and a normal metal via softpoint contact spectroscopy measurement.The superconducting gap features were detected below 3.8 K and 7.1 K in the case of Cd₃As₂ single crystals sputter-coated with the Pt and Au films,respectively,in the differential conductance dI/dV-V plots of the point contacts.As the applied magnetic field increased,the drop in the zerobias contact resistanc...     

Dirac semimetal in three dimensions

We show that the pseudorelativistic physics of graphene near the Fermi level can be extended to three dimensional (3D) materials. Unlike in phase transitions from inversion symmetric topological to normal insulators, we show that particular space groups also allow 3D Dirac points as symmetry protected degeneracies. We provide criteria necessary to identify these groups and, as an example, present ab initio calculations of β-cristobalite BiO(2) which exhibits three Dirac points at the Fermi level. We find that β-cristobalite BiO(2) is metastable, so it can be physically realized as a 3D analog to graphene.     

Theory of magnetic oscillations in Weyl semimetals

Weyl semimetals are a new class of Dirac material that possesses bulk energy nodes in three dimensions, in contrast to two dimensional graphene. In this paper, we study a Weyl semimetal subject to an applied magnetic field. We find distinct behavior that can be used to identify materials containing three dimensional Dirac fermions. We derive expressions for the density of states, electronic specific heat, and the magnetization. We focus our attention on the quantum oscillations in the magnetization. We find phase shifts in the quantum oscillations that distinguish the Weyl semimetal from conventional three dimensional Schrödinger fermions, as well as from two dimensional Dirac fermions. The density of states as a function of energy displays a sawtooth pattern which has its origin in the dispersion of the three dimensional Landau levels. At the same time, the spacing in energy of the sawtooth spike goes like the square root of the applied magnetic field which reflects the Dirac nature of the fermions. These features are reflected in the specific heat and magnetization. Finally, we apply a simple model for disorder and show that this tends to damp out the magnetic oscillations in the magnetization at small fields.     

Thermal boundary conductance across metal-nonmetal interfaces: effects of electron-phonon coupling both in metal and at interface

We theoretically investigate the thermal boundary conductance across metal-nonmetalinterfaces in the presence of the electron-phonon coupling not only in metal but also atinterface. The thermal energy can be transferred from metal to nonmetal via threechannels: (1) the phonon-phonon coupling at interface; (2) the electron-phonon coupling atinterface; and (3) the electron-phonon coupling within metal and then subsequently thephonon-phonon coupling at interface. We find that these three channels can be described byan equivalent series-parallel thermal resistor network, based on which we derive out theanalytic expression of the thermal boundary conductance. We then exemplify differentcontributions from each channel to the thermal boundary conductance in three typicalinterfaces: Pb-diamond, Ti-diamond, and TiN-MgO. Our results reveal that the competitionamong above channels determines the thermal boundary conductance.     

Spin accumulation in the semi classical and quantum regimes

We consider spin accumulation at a ferromagnet-normal metal interface in the presence of magnetic scattering in the normal metal. In the classical regime, we discuss the inverse Drude scaling of the conductance as a function of the interface transparencies. We present a treatment based on an exact solution of the Boltzmann equation. In the quantum regime, we solve a single impurity “spin-flip Fabry Perot interferometer” for quantum coherent multiple scatterings, in which we find a resonance in the spin flip channels. This resonance appears to be the quantum analog of the semi classical inverse Drude scaling of the conductance.     

Specular Andreev reflection in graphene

By combining the Dirac equation of relativistic quantum mechanics with the Bogoliubov-de Gennes equation of superconductivity we investigate the electron-hole conversion at a normal-metal-superconductor interface in graphene. We find that the Andreev reflection of Dirac fermions has several unusual features: (1) the electron and hole occupy different valleys of the band structure; (2) at normal incidence the electron-hole conversion happens with unit efficiency in spite of the large mismatch in Fermi wavelengths at the two sides of the interface; and, most fundamentally: (3) away from normal incidence the reflection angle may be the same as the angle of incidence (retroreflection) or it may be inverted (specular reflection). Specular Andreev reflection dominates in weakly doped graphene, when the Fermi wavelength in the normal region is large compared to the superconducting coherence length.     

Analysis of the anomalous Hall effect in a double layer of a ferromagnetic and a normal metal

A new method is suggested to investigate the mechanism of the anomalous Hall effect (AHE) in ferromagnetic metals. Using a double layer of a ferromagnet and a normal metal of increasing thickness one can manipulate the AHE in the ferromagnet without changing the ferromagnet's structure and electronic properties. The conduction electrons from the normal metal carry their drift velocity across the interface into the ferromagnetic film and induce an additional AHE conductance ΔG_xy. Its dependence on the mean free path in the normal metal distinguishes between the side jump and the skew scattering mechanisms for the AHE in the ferromagnet.     

Demonstration of a new transport regime of photon in two-dimensional photonic crystal

A new transport regime of photon in two-dimensional photonic crystal near the Dirac point has been demonstrated by exact numerical simulation. In this regime, the conductance of photon is inversely proportional to the thickness of sample, which can be described by Dirac equation very well. Both of bulk and surface disorders always reduce the transmission, which is in contrast to the previous theoretical prediction that they increase the conductance of electron at the Dirac point of graphene. However, regular tuning of interface structures can cause the improvement of photon conductance. Furthermore, large conductance fluctuations of photon have also been observed, which is similar to the case of electron in graphene.     

Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

In graphene,conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature.For this reason,the bounding of electrons in graphene in the form of geometries of quantum dots is impossible.In gapless graphene,due to its unique electronic band structure,there is a minimal conductivity at Dirac points,that is,in the limit of zero doping.This creates a problem for using such a highly motivated new material in electronic devices.One of the ways to overcome this problem is the creation of a band gap in the graphene band structure,which is made by inversion symmetry breaking(symmetry of sublattices).We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for "local chemical potential" and "local gap".The calculated energy spectrum exhibits quite different features with and without the perturbations.A characteristic equation for bound states(BSs) has been obtained.It is surprisingly found that the relation between the radial functions of sublattices wave functions,i.e.,f_m~+(r),g_m~+(r),and f_m~-(r),g_m~-(r),can be established by SO(2) group.     

Coherent transmission of nodal Dirac fermions through a graphene-based superconducting double barrier junction

Transport characteristics of relativistic electrons through graphene-based d-wave superconducting double barrier junction and ferromagnet/d-wave superconductor/normal metal double junction have been investigated based on the Dirac–Bogoliubov–de Gennes equation. We have first presented the results of superconducting double barrier junction. In the subgap regime, both the crossed Andreev and nonlocal tunneling conductance all oscillate with the bias voltage due to the formation of Andreev bound states in the normal metal region. Moreover, the critical voltage beyond which the crossed Andreev conductance becomes to zero decreases with increasing value of superconducting pair potential α. In the presence of the ferromagnetism, the MR through graphene-based ferromagnet/ d-wave superconductor/normal metal double junction has been investigated. It is shown that the MR increases from exchange splitting h ₀=0 to h ₀=E _F (Fermi energy), and then it goes down. At h ₀=E _F, MR reaches its maximum 100. In contrast to the case of a single superconducting barrier, Andreev bound states also manifest itself in the zero bias MR, which result in a series of peaks except the maximum one at h ₀=E _F. Besides, the resonance peak of the MR can appear at certain bias voltage and structure parameter. Those phenomena mean that the coherent transmission can be tuned by superconducting pair potential, structure parameter, and external bias voltage, which benefits the spin-polarized electron device based on the graphene materials.     

Crossed Andreev reflection in graphene normal-superconductor-normal structures with pseudo-diffusive interfaces

In this Letter graphene normal-superconductor-normal heterostructures are modeled for studying the crossed Andreev reflection. A thin layer of undoped graphene with Fermi energy at the Dirac point at is assumed the interface between superconductor layer and each normal lead. The resulting contribution of the crossed Andreev reflection to the nonlocal conductance equals that of the electron elastic cotunneling. We explain this as another figure of merit for pseudodiffusive conduction at the Dirac point of the undoped layers. Also structures with only one undoped layer at the interface between the superconductor and one of the normal leads, as well as structures in which one of the leads is ferromagnetic, show pseudodiffusive conduction at the Dirac points.     

铁磁绝缘层对正常金属/铁磁绝缘层/正常金属/p波超导结隧道谱的影响

在正常金属/铁磁绝缘层/正常金属/自旋三重态p波超导隧道结中,考虑到铁磁绝缘层的磁散射和粗糙界面散射,运用Bogoliubov-de Gennes(BdG)方程和Blonder-Tinkham-Klapwijk(BTK)理论模型,研究了铁磁绝缘层对隧道结微分电导的影响.研究表明:(1)对于px波,粗糙界面散射和磁散射都能使零偏压电导峰变低,能隙处凹陷升高;随着磁散射的增强,谱线的尖锐峰消失,宽峰逐渐变为凹陷;(2)对于py波,粗糙界面散射和磁散射都能使零能凹陷上移,能隙峰变低,随着粗糙界面散射的增强,两能隙峰间距减小;随着中间正常金属层厚度的增加,能隙内电导随外加偏压呈现振荡行为,能隙外电导仅与普通势垒有关;(3)对于px+ipy波,随着粗糙界面散射的增强,零偏压电导峰被压低,双凹陷处的值逐渐增大为小的能隙峰,而磁散射并不改变谱线中各凹陷处的电导值.     

Spin-polarized conductance in graphene-based FSF junctions

In this paper, conductance of spin and electron in graphene-based ferromagnet—superconductor (FS) and parallel and antiparallel ferromagnet–superconductor–ferromagnet (FSF) junctions are studied. Using the Dirac–Bogoliubov–de Gennes equations, Andreev and normal reflections are obtained and then using these coefficients, conductance of spin and electrons are calculated at the FS interface(s) analytically. As a result, both the energy dependence of spin and charge differential conductances are investigated and a comparison between electron and spin transport is done in this paper. Effect of exchange energy of ferromagnet h on conductances is studied too.     

Dirac electrons in solids

Electronic band structures in solids sometimes have features similar to Dirac electrons in vacuum. Well-known examples are bismuth and graphite; 4×4 original Dirac matrix in three dimension (3d) in the former with strong spin–orbit interaction, while 2×2 massless Dirac in two dimension (2d) with weak inter-layer coupling described essentially by Weyl equation in the latter. Recently one layer of graphite, graphene, is realized and studied both extensively and intensively. Other recent examples include a molecular solid, α-(BEDT-TTF)₂I₃$\mathrm{\alpha }\mathrm{-}(\mathrm{BEDT}\mathrm{-}\mathrm{TTF}{)}_2{\mathrm{I}}_3$, which has a layered structure with electronic states described by tilted-Weyl equation, and Fe-pnictides. There is also a theoretical proposal that one of inverse perovskites, Ca₃PbO, can be a candidate in 3d with strong spin–orbit interaction similar to bismuth. The particular feature of Dirac electrons in solids is a small, or even vanishing, band gap and then thermodynamic or transport properties are affected by inter-band coupling of electronic states. Typical ones are responses to external magnetic field. Actually, it has long been known that orbital susceptibility of these Dirac electrons has very particular features resulting from inter-band effects of magnetic field. It is of interest to see such inter-band effects on Hall effects to be compared with orbital susceptibility, which will be introduced in this paper, together with possible consequences of mutual interaction between valleys triggered by tilting in molecular solids.     

Enhancement of subgap conductance in a graphene superconductor junction by valley polarization

We theoretically study the differential conductance of a graphene/graphene superconductor junction, where the valley polarization of Dirac electrons is considered in the nonsuperconducting region. It is shown that the subgap conductance will increase monotonically with the valley-polarization strength when the chemical potential μ is near the Dirac point μ≤ 3?(? is the superconducting gap), whereas it will decrease monotonically when μ is far away from the Dirac point, μ≥ 5?.The former case is induced by the specular Andreev reflection while the retro-reflection accounts for the later result. Our findings may shed light on the control of conductance of a graphene superconductor junction by valley polarization.     

Long-range coherence and mesoscopic transport in N–S metallic structures

We review the mesoscopic transport in a diffusive proximity superconductor made of a normal metal (N) in metallic contact with a superconductor (S). The Andreev reflection of electrons on the N–S interface is responsible for the diffusion of electron pairs in N. Superconducting-like properties are induced in the normal metal. In particular, the conductivity of the N metal is locally enhanced by the proximity effect. A re-entrance of the metallic conductance occurs when all the energies involved (e.g. temperature and voltage) are small. The relevant characteristic energy is the Thouless energy which is divided by the diffusion time for an electron travelling throughout the sample. In loop-shaped devices, a 1 / T temperature-dependent oscillation of the magnetoresistance arises with a large amplitude from the long-range coherence of low-energy pairs.     

Existence of Global-In-Time Solutions to a Generalized Dirac-Fock Type Evolution Equation

We consider a generalized DiracFock type evolution equation deduced from nophoton Quantum Electrodynamics, which describes the selfconsistent timeevolution of relativistic electrons, the observable ones as well as those filling up the Dirac sea. This equation has been originally introduced by Dirac in 1934 in a simplified form. Since we work in a Hartree-Fock type approximation, the elements describing the physical state of the electrons are infinite rank projectors. Using the Bogoliubov-Dirac-Fock formalism, introduced by ChaixIracane (J. Phys. B., 22, 37913814, 1989), and recently established by Hainzl-Lewin-Séré, we prove the existence of globalintime solutions of the considered evolution equation.     

苯基分子器件 量子相干输运第一性原理研究

摘要：分子器件在纳米尺度下,电子的相干性将对体系的电导产生重大影响。本文基于第一性原理计算研究了苯分子连接于一维金属电极下的电荷输运性质。发现一维金电极连接下,不同的连接方式（para与meta）体系下的电导将会有显著差别,而一维铂电极连接下,体系的电导差别不大。我们通过计算电极的能带,发现金电极与铂电极在费米面处的散射态数目有差别。 当量子相干效应导致散射态局域化发生改变时,由于铂电极的通道数较多,电子依然可以通过扩展的通道输运,因此不同连接方式下的电导变化不明显。     

Characteristics of transmission of electrons in a quantum wire tangentially attached to a superconductor ring threaded by magnetic flux

We present numerical investigations of the transmission properties of electrons in a normal quantum wire tangentially attached to a superconductor ring threaded by magnetic flux. A point scatterer with a δ -function potential is placed at node to model scattering effect. We find that the transmission characteristics of electrons in this structure strongly depend on the normal or superconducting state of the ring. The transmission probability as a function of the energy of incident electrons, in the case of a superconductor ring threaded by one quantum magnetic flux, emerges one deep dip, imposed upon the first broad bump in spectrum. This intrinsic conductance dip originates from the superconductor state of the ring. When increasing the magnetic flux from one quantum magnetic flux to two, the spectrum shifts toward higher energy region in the whole. This conductance dip accordingly shifts and appears in the second bump. In the presence of a point-scatterer at the node, the spectrum is substantially modified. Based on the condition of the formation of the standing wave functions in the ring and the broken of the time-reserve symmetry of Schr?dinger equation after switching magnetic flux, the characteristics of transmission of electrons in this structure can be well understood. Received 6 November 2001