Andreev levels in a graphene–superconductor surface

In order to consider the Dirac-like spectrum of graphene we employ the Bogoliubov de Gennes–Dirac formalism to determine the quasiparticle Andreev levels in an NS surface (normal–superconductor). The normal region is characterized by a width L while the superconducting region is semi-infinite and both regions are made of doped graphene. The quasiparticle energy spectrum is originated by the Andreev reflections that occur in the NS interface. It is shown that this spectrum depends on the width of the normal region and the Fermi energy in each region. When the Fermi energy in the normal metal is lower than the gap of the superconductor region, the spectrum is affected by specular Andreev reflections. The equation that is obtained to find the spectrum is very general and we solve it for some particular cases. We find that the energy spectrum oscillates when the Fermi energy in graphene is changed. Finally we obtain under some approximations an equation for the energy spectrum which is similar in structure as those obtained for an INS conventional junction.     

Tunneling conductance through the half-metal/conical magnet/superconductor junctions in the adiabatic and non-adiabatic regimes: Self-consistent calculations

The tunneling conductance through the half-metal/conical magnet/superconductor (HM/CM/SC) junctions is investigated with the use of the Bogoliubov–de Gennes equations in the framework of Blonder–Tinkham–Klapwijk formalism. Due to the spin band separation in the HM, the conductance in the subgap region is mainly determined by the anomalous Andreev reflection, the probability of which strongly depends on the spin transmission in the CM layer. We show that the spins of electrons injected from the HM can be transmitted through the CM to the SC either adiabatically or non-adiabatically depending on the period of the spatial modulation of the exchange field. We find that the conductance in the subgap region oscillates as a function of the CM layer thickness wherein the oscillations transform from the irregular pattern in the non-adiabatic regime to the regular one in the adiabatic regime. For both adiabatic and non-adiabatic transport regimes the conductance is studied over a broad range of parameters determining the spiral magnetization in the CM. We find that in the non-adiabatic regime, the decrease of the exchange field amplitude in the CM leads to the emergence of the conductance peak for the particular CM thickness in agreement with recent experiments.     

Anisotropic pairing symmetry effect on crossed Andreev reflection in a graphene-based transistor

Crossed Andreev reflection (CAR) under the influence of anisotropic pairing symmetry is considered. It is shown that CAR is sensitive to the Fermi energy and the orientation of the gap. In addition, the oscillatory period of CAR can be not only tunable by the potential energy in the superconductor region, it also can be modulated by the length of the superconductor region. The physical origination for those phenomena has also been analyzed.     

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.     

Klein Paradox of Two-Dimensional Dirac Electrons in Circular Well Potential

We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation:For large enough potential depth, the bound states disappear from the spectra. Applications to graphene systems are discussed.     

Strain-modulated anisotropic Andreev reflection in a graphene-based superconducting junction

We investigate the Andreev reflection across a uniaxial strained graphene-based superconducting junction. Compared with pristine graphene-based superconducting junction, three opposite properties are found. Firstly, in the regime of the interband conversion of electron-hole, the Andreev retro-reflection happens. Secondly, in the regime of the intraband conversion of electron-hole, the specular Andreev reflection happens. Thirdly, the perfect Andreev reflection, electron-hole conversion with unit efficiency, happens at a nonzero incident angle of electron. These three exotic properties arise from the strain-induced anisotropic band structure of graphene, which breaks up the original relation between the direction of velocity of particle and the direction of the corresponding wavevector. Our finding gives an insight into the understanding of Andreev reflection and provides an alternative method to modulate the Andreev reflection.     

Andreev reflection in a patterned graphene nanoribbon superconducting heterojunction

In the study, an improved superconducting heterojunction is made up of a zigzag graphene nanoribbon, which is patterned by a triangle and supports localized edge mode. Since all the localized edge modes stem from a pattern operation, the structure features of the pattern exert an enormous function on the coherent quantum transport. Especially, the patterned modes can enhance the Andreev reflection largely both in the ferromagnetic nanoribbon edge and the antiferromagnetic nanoribbon edge. The spin resolved zero bias conductances, in sharp contrast to its counterpart in the infinite width superconducting heterojunction, exhibit the different dependence on the patterned ferromagnetic interaction.     

Tunneling conductance of graphene NIS junctions

We show that, in contrast with conventional normal metal-insulator-superconductor (NIS) junctions, the tunneling conductance of a NIS junction in graphene is an oscillatory function of the effective barrier strength of the insulating region, in the limit of a thin barrier. The amplitude of these oscillations is maximum for aligned Fermi surfaces of the normal and superconducting regions and vanishes for a large Fermi surface mismatch. The zero-bias tunneling conductance, in sharp contrast to its counterpart in conventional NIS junctions, becomes maximum for a finite barrier strength. We also suggest experiments to test these predictions.     

拓扑绝缘体基铁磁/f-波超导隧道结Andreev反射研究

基于Bogoliubov-de Gennes方程和Blonder-Tinkham-Klapwijk理论研究了三维拓扑绝缘体基铁磁/各向异性f-波超导隧道结的Andreev反射,其中f-波超导体选取f₁和f₂-波两种配对势.研究发现,对于f₁和f₂波,铁磁体中的磁能隙可以增强传统的Andreev逆向反射,但对Andreev镜面反射有抑制作用;但随着施加在超导体顶部电极上的栅极电位的增加,两种类型的反射都会增强.通过改变磁能隙,可以调节两种反射在准粒子输运过程中占有优势的程度.这些结果提供了一种实验检测拓扑绝缘体薄膜中镜面Andreev反射的方法.此外,隧穿电导和散粒噪声谱的差异可用于区分f₁和f₂波配对势.     

Selective Andreev reflection tuned by magnetic barriers in graphene-superconductor hybrid junctions

We investigate the direction-dependent Andreev reflection of normal state-superconductor junctions both in monolayer and bilayer graphene with a single magnetic barrier by means of the Green?s function formalism. Such a barrier is capable of tuning the preferred angles of incidence for the Andreev retro-reflection. It enhances the specular reflection probability for certain angles of incidence in bilayer-based hybrid structures. We further study the impacts of magnetic barriers on the monolayer and bilayer hybrid structures by calculating the differential conductances within the Blonder–Tinkham–Klapwijk formula for experimental comparisons.     

Andreev reflection and tunneling spectrum in a superlattice of metal-superconductor junctions

The tunneling spectrum of an electron and a hole in a superlattice of NS junctions is computed using the BTK approach and the transfer matrix method. It shows sharp resonances at some energies above the superconducting gap. The sharper the resonance is the more layers the superlattice has. We find for the first time a mechanism to balance the incident and outgoing currents on the superlattice by averaging over the phase between the incident electron and the incident hole. This mechanism is more natural and physical than those in literatures.     

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.     

Spin transport properties in ferromagnet/superconductor junctions on topological insulator

The spin-dependent Andreev reflection is investigated theoretically by analyzing the electronic transport in a thin-film topological insulator (TI) ferromagnet/superconductor (FM/SC) junction. The tunneling conductance and shot noise are calculated based on the Dirac-Bogoliubov-de Gennes equation and Blonder-Tinkham-Klapwijk theory. It is found that the magnetic gap in ferromagnet can enhance the Andreev retro-reflection but suppress the specular Andreev reflection. The gate potential applied to the electrode on top of superconductor can enhance the two types of reflections. There is a transition between the two types of reflections at which both the tunneling conductance and differential shot noise become zero. These results provide a method to realize and detect experimentally the intra-band specular Andreev reflection in thin film TI-based FM/SC structures.     

Study of transport properties in superconducting junctions of double insulating barrier

In this work we analyze the Tomasch effect in double barrier insulating superconducting N₁ISIN₂ (N: normal metal, I: insulator and S: superconductor) junctions. From the solution of the Bogoliubov–de Gennes equations we find that the differential conductance presents resonances when the applied voltage changes. These resonances are originated by the formation of quasibound states in the superconducting region and depend on the symmetry of the pair potential. We develop an analytical model in order to find the quasibound states energies and its lifetimes. This model allows us to calculate the voltage at which each resonance appears and the resonance widths. We calculate and analyze the dependence of the transmission coefficients with the thickness of the superconducting layer.     

Zero bias conductance peak in InAs nanowire coupled to superconducting electrodes

We report the occurrence of the zero-bias conductance peak (ZBCP) in an InAs nanowire coupled to PbIn superconductors with varying temperature, bias voltage, and magnetic field. The ZBCP is suppressed with increasing temperature and bias voltage above the Thouless energy of the nanowire. Applying a magnetic field also diminishes the ZBCP when the resultant magnetic flux reaches the magnetic flux quantum h/2e. Our observations are consistent with theoretical expectations of reflectionless tunneling, in which the phase coherence between an electron and its Andreev-reflected hole induces the ZBCP as long as time-reversal symmetry is preserved.     

Tunneling conductance in topological insulator ferromagnet/p-wave superconductor junctions

The tunneling conductance in topological insulator (TI) ferromagnet/p-wave superconductor (FM/pS) junction is studied based on the Blonder–Tinkham–Klapwijk (BTK) theory. The Fermi energy mismatch between FM and pS as well as the finite quasiparticle lifetime are considered. Three kinds of pairings p_x, p_y, and p_x+ip_y-waves for pS are chosen. It is found that the spectrum strongly depend on the magnetic gap, the gate potential, the quasiparticle lifetime as well as the type of the pair potential symmetry. The pair potential symmetry drastically affects the formation of the zero-energy bound states dependent on the magneto effect or the Fermi energy mismatch effect. The finite quasiparticle lifetime effect can suppress the Andreev resonant scattering process at eV=Δ₀ and smear the dips in the conductance.     

石墨烯铁磁-绝缘层-超导结的输运

本文运用平均场模型的Dirac-Bogoliubov-de-Gennes方程和Bolonder-Tinkham-Klapwijk理论研究石墨烯铁磁-绝缘层-超导结的输运性质.研究表明:考虑有限宽度的绝缘层,隧穿电导-电压曲线呈现无衰减的振荡行为;同时隧穿电导随铁磁层中的交换能呈现非单调变化.对上述现象从石墨烯中类Dirac准粒子色散关系密切相关的电子散射过程予以解释.     

Anomalous density of states in hybrid normal metal-superconductor bilayers

In contact with a superconductor, the Andreev reflection of the electrons locally modifies the N metal electronic properties, including the local density of states (LDOS). We investigated the LDOS in superconductor-normal metal (Nb-Au) bilayers using a very low temperature (60 mK) STM on the normal metal side. High resolution tunneling spectra measured on the Au surface show a clear proximity effect with an energy gap of reduced amplitude compared to the bulk Nb gap. The dependence of this mini-gap width with the normal metal thickness is discussed in terms of the Thouless energy. Within the mini-gap, the density of states does not reach zero and shows clear sub-gap features. We compare the experimental spectra with the well-established quasi-classical theory.