Fermi Wave Vector Mismatch Research Articles

Determination of spin polarization of metals and gap of superconductors by spin-polarized Andreev reflection spectroscopy

Andreev reflection spectroscopy (ARS) is a unique technique that can determine the spin polarization of a metal as well as the gap of a superconductor but d-wave superconductors are seldomly used in ARS due to the lack of quantitative model to extract parameters from experiments. Here we calculate spin-polarized ARS based on the modified Blonder-Tinkham-Klapwijk model for both s- and d-wave superconductors of a three-dimensional (3D) interface with a point angle. We show that the 3D interface and the point angle can drastically affect the spectra for both s- and d-wave ARS. For s-wave, the 3D effect is similar to that of an interfacial barrier but it can generate a variety of rich features in d-wave ARS and induce Andreev bound states (ABS). The spin polarization can linearly suppress both s- and d-wave spectra including ABS. We show that the ABS states can be controlled by the spin polarization, the point angle and the interfacial barrier but very high polarization is required to completely suppress the ABS. Furthermore, the Fermi wavevector mismatch as well as the carrier effective mass mismatch can cause effects very similar to that of an interfacial barrier for both s- and d-wave ARS.

Identifying the graphene d-wave superconducting symmetry by an anomalous splitting zero-bias conductance peak

Not until recently, was a gate-tunable, high-temperature superconducting proximity effect in graphene demonstrated experimentally. And usually in d-wave superconductor (SC) hybrid structure, ferromagnetism and spin-triplet states could result in a splitting zero-bias conductance peak (ZBCP). Herein, we theoretically present an anomalous splitting ZBCP in a graphene-based ferromagnet/Rashba spin–orbit coupling (RSOC)/insulator/d-wave SC hybrid structure. With increasing the exchange field from h/EF = 0, the ZBCP starts to turn into a splitting one with a zero-bias conductance dip (ZBCD) sandwiched in between two subpeaks, while from h/EF = 1, the two subpeaks and ZBCD begin to gradually shrink till the ZBCP reappears. The anomalous splitting ZBCP can be modulated by the RSOC strength, magnitude of Fermi wave vector mismatch as well as insulator barrier strength. These peculiar features are ascribed to the novel spin-triplet Andreev reflection in the context of the RSOC, characteristic by the anisotropic d-wave pair symmetry combined with the relativistic nodal fermions, which in turn can be experimentally used to directly identify not only the proximity-induced ferromagnetism and RSOC but d-wave pair symmetry in graphene. These results pave the way to a new class of tunable, high-temperature superconducting spintronic devices based on large-scale graphene.

Spin transport and Spin Tunnelling Magneto-Resistance (STMR) of F[formula omitted]NCSC[formula omitted]F spin valve

In this work, we study the spin transport at the Ferromagnet|Noncentrosymmetric Superconductor (F|NCSC) junction of a Ferromagnet|Noncentrosymmetric Superconductor|Ferromagnet (F|NCSC|F) spin valve. We investigate the Tunnelling Spin-Conductance (TSC), spin current and Spin Tunnelling Magneto-Resistance (STMR), and their dependence on various important parameters like Rashba Spin-Orbit Coupling (RSOC), strength and orientation of magnetization, an external in-plane magnetic field, barrier strength and a significant Fermi Wavevector Mismatch (FWM) at the ferromagnetic and superconducting regions. The study has been carried out for different singlet-triplet mixing of the NCSC gap parameter. We develop Bogoliubov-de Gennes (BdG) Hamiltonian and use the extended Blonder–Tinkham–Klapwijk (BTK) approach along with the scattering matrix formalism to calculate the scattering coefficients. Our results strongly suggest that the TSC is highly dependent on RSOC, magnetization strength and its orientation, and singlet-triplet mixing of the gap parameter. It is observed that NCSC with moderate RSOC shows maximum conductance for a partially opaque barrier in presence of low external magnetic field. For a strongly opaque barrier and a nearly transparent barrier a moderate value and a low value of field respectively are found to be suitable. Moreover, NCSC with large singlet component is appeared to be useful. In addition, for NCSC with large RSOC and low magnetization strength, a giant STMR (%) is observed. We have also seen that the spin current is strongly magnetization orientation dependent. With the increase in bias voltage spin current increases in transverse direction, but the component along the direction of flow is almost independent.

Intersubband pairing induced Fulde-Ferrell phase in metallic nanofilms

We consider a free-standing metallic nanofilm with a predominant intersubband paring which emerges as a result of the confinement in the growth direction. We show that the Fermi wave vector mismatch between the subbands, detrimental to the intersubband pairing, can be compensated by the non-zero center of mass momentum of the Cooper pairs. This leads to the spontaneous appearance of the intersubband Fulde-Ferrell (IFF) state, even in the absence of an external magnetic field. Our study of the intrasubband pairing channel on the stability of the IFF phase shows that the former strongly competes with the intersubband pairing, which prohibits the coexistence of the two superconducting phases. Interestingly, upon application of the magnetic field we find a transition to an exotic mixed spin-singlet subband-triplet and spin-triplet subband-singlet paired state. Finally, we discuss the possibility of existence of the IFF pairing in novel superconducting materials.

Effect of Rashba spin–orbit coupling, magnetization, and mixing of gap parameter on tunneling conductance in F∣NCSC junction of an F∣NCSC∣F spin valve

In this paper, we study the quantum transport at the Ferromagnet∣Noncentrosymmetric Superconductor (F∣NCSC) interface of an F∣NCSC∣F spin valve. In this context, we investigate the tunneling conductance and its dependence on Rashba spin–orbit coupling (RSOC) considering different barrier strength and a significant Fermi wavevector mismatch (FWM) at the ferromagnetic and superconducting regions. The study is carried out for different magnetization orientations and strengths. We develop a Bogoliubov–de Gennes (BdG) Hamiltonian, introducing RSOC and exchange interaction for such a hybrid structure. To study charge conductance, we use an extended Blonder–Tinkham–Klapwijk approach along with scattering matrix formalism to calculate the scattering coefficients. Our results strongly suggest that the tunneling conductance is strongly dependent on RSOC, magnetization strength, its orientation, and the FWM. This work has also been done for different singlet–triplet mixings of the gap parameter. We have observed that with the rise of singlet–triplet mixing ratio, the conductance decreases. It is also observed that a transparent barrier with moderate RSOC and magnetization strength with arbitrary orientation is highly suitable for maximum conductance.

Electric Field and Light Field Modulated Josephson Effect in Silicene-Based SNS Josephson Junction: Andreev Reflection and Free Energy

We investigate the Josephson effect in superconductor-normal-superconductor junction (SNS) base on an unbiased silicene under the perpendicular electric field and off-resonance circularly polarized light both analytically and numerically. The Andreev reflection (during the subgap transport), free energy, Josephson current, and the reversal of the Josephson effect are explored. The Andreev reflection is complete (for tunnel limit) in the NS interface even for the clean sample and without the Fermi wave vector mismatch, which is opposite to the case of ferromagnet-superconductor interface. The dynamical polarization of the related degrees of freedom is also related to the 0 − π transition and the generation of ϕ0-junction. In the short junction limit, the approximated results about the Andreev level and free energy are also discussed. Beside the low-energy limit of the tight-binding model, the finite-size effect is needed to be taken into account. The effect of the time-dependent drive and the Green’s function method also represented in the end of this paper.

Fulde–Ferrell state in superconducting core/shell nanowires: role of the orbital effect

The orbital effect on the Fulde–Ferrell (FF) phase is investigated in superconducting core/shell nanowires subjected to the axial magnetic field. Confinement in the radial direction results in quantization of the electron motion with energies determined by the radial j and orbital m quantum numbers. In the external magnetic field, the twofold degeneracy with respect to the orbital magnetic quantum number m is lifted which leads to the Fermi wave vector mismatch between the paired electrons, . This mismatch is transferred to the nonzero total momentum of the Cooper pairs, which results in a formation of the FF phase occurring sequentially with increasing magnetic field. By changing the nanowire radius R and the superconducting shell thickness d, we discuss the role of the orbital effect in the FF phase formation in both the nanowire-like () and nanofilm-like () regime. We have found that the irregular pattern of the FF phase which appears for the case of the nanowire-like regime, for the nanofilm-like geometry evolves towards the regular distribution in which the FF phase stability regions emerge periodically between the BCS states. The transition between these two different phase diagrams is explained as resulting from the orbital effect and the multigap character of superconductivity in the core/shell nanowires.

Tunneling conductance study of a metal-superconductor junction in the presence of Rashba spin orbit coupling

The tunneling conductance for a junction device consisting of a normal metal and a singlet superconductor is studied with Rashba spin orbit coupling (RSOC) being present in the metallic lead and the interface separating the two regions via an extended Blonder-Tinkham-Klapwijk (BTK) formalism. Interesting interplay between the RSOC and a number of parameters that have experimental significance, and characterize either the junction or the superconducting leads, such as the barrier transparency, quasiparticle lifetime, Fermi wavevector mismatch, an in-plane magnetic field and their effects on the tunneling conductance are investigated in details for both a s-wave and a d-wave superconductor. In an opaque barrier, in presence of a quasiparticle lifetime, a Fermi wavevector mismatch or an external in-plane magnetic field, RSOC enhances the conductance corresponding to low biasing energies, that is, at energies lesser than the superconducting gap, while the reverse is noted for energies exceeding the magnitude of the gap. Further, there are exciting anomalies noted in the conductance spectrum for the d-wave gap which can be understood by incorporating the interplay between the superconducting gap and the angle of incident of the charge carriers.

Fulde-Ferrell state induced by the orbital effect in a superconducting nanowire

We show that the Fulde-Ferrell (FF) phase may appear as a sole result of the orbital effect in a cylindrical metallic nanowire. Namely, in the external magnetic field the twofold degeneracy with respect to the orbital magnetic quantum number $m$ is lifted, which leads to a Fermi wave vector mismatch between the subbands with opposite orbital momenta in the paired state. This mismatch can be compensated by the nonzero total momentum of the Cooper pairs created by electrons from the split subbands which results in the formation of the FF phase. In this manner, a transformation of the orbital motion into a linear supercurrent parallel to the applied field is taking place. With the increasing magnetic field a series of FF stability regions appear, in between which the standard BCS superconducting phase is stable. For the sake of completeness, we show, that the inclusion of the Zeeman term in the model does not change the picture qualitatively, particularly if larger $m$ states contribute essentially to the Fermi-surface splitting. A brief but important note concerning the possibility of steering the supercurrent by an applied magnetic field parallel to it, is also provided.

Strained graphene Josephson junction with anisotropic d-wave superconductivity

Effect of proximity-induced superconductivity in the new two-dimensional structures, as graphene and topological insulator on the Andreev bound states (ABSs) and Josephson supercurrent has attracted much efforts. Motivated by this subject, we study, in particular, the influence of anisotropic Fermi velocity and unconventional d-wave pairing in a strained graphene-based superconductor/normal/ superconductor junction. Strain is applied in the zigzag direction of graphene sheet. In this process, effect of zero energy states and Fermi wavevector mismatch are investigated. It is shown, that strain up to 22% in graphene lattice differently affects Josephson currents in parallel and perpendicular directions of strain. Strain causes to exponentially decrease the supercurrent in the strain direction, whereas increase for other direction. We find that, in one hand, the ABSs strongly depend on strain and, on the other hand, a gap opens in the states with respect to non-zero incidence angle of quasiparticles, where a period of 2π is obtained for Andreev states. Moreover, we observe no gap for θs≠0, when the zero energy states (ZESs) occur in α=π/4 due to anisotropic superconducting gap. In this case, ABSs have a period of 4π.S

Spontaneous appearance of nonzero-momentum Cooper pairing: Possible application to the iron-pnictides

We suggest that an inhomogeneous (non-zero momentum) paired phase can appear in the absence of an external magnetic field in the system with a predominant interband pairing and with separate Fermi-surface sheets. The Fermi wave vector mismatch which appears in such situation can be compensated by nonzero center-of-mass momentum of the Cooper pairs, what can lead to a spontaneous appearance of the Fulde-Ferrell type of superconducting state. The idea is examined using a tight-binding model which emulates the hole-like and the electron-like bands of iron based superconductor. The state can appear for the case of both spin-singlet and -triplet pairing channels.

Spontaneous Appearance of the Spin-Triplet Fulde-Ferrell-Larkin-Ovchinnikov Phase in a Two-Band Model: Possible Application to LaFeAsO 1−x F x

The possibility of a spontaneous spin-triplet paired phase of the Fulde-Ferrell-Larkin-Ovchinnikov type is studied. As it is shown in a system with the dominant interband pairing and two distinct Fermi surface sheets, the Fermi wave-vector mismatch can be compensated by a nonzero center-of-mass momentum of the Cooper pairs. This idea is examined with the use of a model which describes the two hole-like bands in the iron-based superconductor. It is shown that for the proper range of model parameters, the minima of the free energy appear which correspond to a nonzero Cooper pair momentum. Different superconducting gap symmetries are analyzed, and the corresponding phase diagrams are shown.

Spin-triplet paired state induced by Hund’s rule coupling and correlations: a fully statistically consistent Gutzwiller approach

The intrasite and intersite spin-triplet pairing gaps induced by interband Hund’s rule coupling and their correlations are analyzed in the doubly degenerate Hubbard Hamiltonian. To include the effect of correlations, the statistically consistent Gutzwiller approximation is used. In this approach the consistency means that the averages calculated from the self-consistent equations and those determined variationally coincide with each other. Emphasis is put on the solution for which the average particle number is conserved when carrying out the Gutzwiller projection. This method leads to a stable equal-spin paired state in the so-called repulsive interactions limit (U > 3J) in the regime of moderate correlations. The interband hybridization introduces an inequivalence of the bands which, above a critical magnitude, suppresses the paired state due to both the Fermi-wavevector mismatch for the Cooper pair and the interband hopping allowed by the Pauli principle.

Equal-spin Andreev reflection in ferromagnet/superconductor junctions with the interfacial Rashba spin-orbit coupling

We study the conductance spectra of ferromagnet/superconductor (F/S) junctions in the presence of the interfacial Rashba spin-orbit coupling (IRSOC). IRSOC provides the spin-flip mechanism with which the equal-spin Andreev reflection occurs. We first investigate the effect of the F spin polarization P on the conductance G and find that a zero-bias G peak forms for the highly polarized F in F/s-wave and F/dx2−y2-wave S junctions, while in F/dxy-wave S junctions with increasing P, G exhibits a conversion from a zero-bias peak to a zero-bias dip. For half-metal F (HMF)/S junctions with s-wave and dx2−y2-wave pairing by varying the magnetization direction α, G first increases and then decreases, exhibiting a maximal zero-bias peak at α = π/2, and in F/dxy-wave S junctions, G at nonzero bias exhibits a nonmonotonic behavior with α. The effect of the Fermi wave vector mismatch on G is also discussed.

Superconducting proximity effects in metals with a repulsive pairing interaction

Studies of the superconducting proximity effect in normal conductor/superconductor $(N/S)$ junctions almost universally assume no effective electron-electron coupling in the $N$ region. While such an approximation leads to a simple description of the proximity effect, it is unclear how it could be rigorously justified. We reveal a much more complex picture of the proximity effect in $N/S$ bilayers, where $S$ is a clean s-wave BCS superconductor and $N$ is a simple metal with a repulsive effective electron coupling. We elucidate the proximity effect behavior using a highly accurate method to self-consistently solve the Bogoliubov-deGennes equations. We present our results for a wide range of values of the interface scattering, the Fermi wave vector mismatch, the temperature, and the ratio $g$ of the effective interaction strengths in the $N$ and $S$ region. We find that the repulsive interaction, represented by a negative $g$, strongly alters the signatures of the proximity effect as can be seen in the spatial dependence of the Cooper pair amplitude and the pair potential, as well as in the local density of states near the interface.

Effects of interface spin-orbit coupling on tunneling between normal metal and chiralp-wave superconductor

We study the tunneling conductance of a clean normal metal/chiral p-wave superconductor junction using the extended Blonder-Tinkham-Klapwijk formalism. It is shown that the spin-orbit coupling of the Rashba type that is present near the interface causes the subgap conductance peaks associated with the Andreev surface bound states to shift to a nonzero bias. We also investigate the effect of the Fermi wavevector mismatch between the normal metal and the superconductor.

Tunneling conductance of ferromagnet/noncentrosymmetric superconductor junctions

Based on the extended Blonder-Tinkham-Klapwijk formalism, the tunneling conductance characteristics of a planar junction between a ferromagnet and a noncentrosymmetric superconductor are studied. The effects of the Rashba spin-orbit coupling (RSOC), the exchange energy, and the Fermi wave-vector mismatch (FWM) on the conductance are all taken into account. In the absence of the FWM, it is found that far away from the gap edge the conductance is suppressed by the RSOC, while around the gap edge it is almost independent of RSOC. The interplay of the RSOC and the exchange energy causes an enhancement of the subgap conductance, which is more pronounced when the RSOC is small. When the FWM is introduced, it is shown that the conductance is monotonically enhanced as the FWM parameter decreases.

Interplay between antiferromagnetic order and spin polarization in ferromagnetic metal/electron-doped cuprate superconductor junctions

Recently we proposed a theory of point-contact spectroscopy and argued that the splitting of zero-bias conductance peak in electron-doped cuprate superconductor point-contact spectroscopy is due to the coexistence of antiferromagnetic (AF) and $d$-wave superconducting orders [Phys. Rev. B 76, 220504(R) (2007)]. Here we extend the theory to study the tunneling in the ferromagnetic metal/electron-doped cuprate superconductor (FM/EDSC) junctions. In addition to the AF order, the effects of spin polarization, Fermi-wave vector mismatch between the FM and EDSC regions, and effective barrier are investigated. It is shown that there exists midgap surface-state contribution to the conductance to which Andreev reflections are largely modified due to the interplay between the exchange field of ferromagnetic metal and the AF order in EDSC. Low-energy anomalous conductance enhancement can occur which could further test the existence of AF order in EDSC. Finally, we propose a more accurate formula in determining the spin-polarization value in combination with the point-contact conductance data.

Tunneling conductance in superconductor/ferromagnet junctions: Self-consistent approach

We evaluate the tunneling conductance of clean ferromagnet/superconductor junctions via a fully self-consistent numerical solution of the microscopic Bogoliubov-de Gennes equations. We present results for a relevant range of values of the Fermi wave-vector mismatch (FWM), the spin polarization, and the interfacial scattering strength. For nonzero spin polarization, the conductance curves vary nonmonotonically with FWM. The FWM dependence of our results is stronger than that previously found in non-self-consistent calculations since, in the self-consistent case, the effective scattering potential near the interface depends on the FWM. The dependence on interfacial scattering is monotonic. These results confirm that it is impossible to characterize both the FWM and the interfacial scattering by a single effective parameter and that analysis of experimental data via the use of such one-parameter models is unreliable.

Thermodynamics and phase diagrams of layered superconductor/ferromagnet nanostructures

We study the thermodynamics of clean, layered superconductor/ferromagnet nanostructures using fully self-consistent methods to solve the microscopic Bogoliubov-deGennes equations. From these self-consistent solutions the condensation free energies are obtained. The trilayer superconductor/ferromagnet/superconductor junction is studied in particular detail: first-order transitions between 0 and $\ensuremath{\pi}$ states as a function of the temperature $T$ are located by finding where the free energies of the two phases cross. The occurrence of these transitions is mapped as a function of the thickness ${d}_{F}$ of the $F$ layer and of the Fermi wave-vector mismatch parameter $\ensuremath{\Lambda}$. Similar first-order transitions are found for systems with a larger number of layers: examples are given in the seven-layer (three-junction) case. The latent heats associated with these phase transitions are evaluated and found to be experimentally accessible. The transition temperature to the normal state is calculated from the linearized Bogoliubov-deGennes equations and found to be in good agreement with experiment. Thus, the whole three-dimensional phase diagram in $T$, ${d}_{F}$, and $\ensuremath{\Lambda}$ space can be found. The first-order transitions are associated with dips in the transition temperature ${T}_{c}$ to the nonsuperconducting state, which should facilitate locating them. Results are also given for the magnetic moment and the local density of states at the first-order transition.