Coherent quantum transport in normal-metal/<Emphasis Type="Italic">d</Emphasis>-wave superconductor/normal-metal double tunnel junctions

Taking into account the effects of quantum interference and interface scattering, combining the electron current with hole current contribution to tunnel current, we study the coherent quantum transport in normal-metal/d-wave superconductor/ normal-metal (NM/d-wave SC/NM) double tunnel junctions by using extended Blonder-Tinkham-Klapwijk (BTK) approach. It is shown that all quasiparticle transport coefficients and conductance spectrum exhibit oscillating behavior with the energy, in which periodic vanishing of Andreev reflection (AR) above superconducting gap is found. In tunnel limit for the interface scattering strength taken very large, there are a series of bound states of quasiparticles formed in SC.     

Zeeman effects on d-wave superconductor and tunneling spectrum in normal-metal/d-wave superconductor tunnel junction

We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman energy difference between the two splitting peaks in the conductance spectrum is equal to2h0 (h0 is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks,however, neither of them can influence the Zeeman effect.     

塞曼效应对正常金属/超导/正常金属双隧道结中的相干隧穿电导的影响

在超导中通过外加塞曼磁场,研究正常金属/超导/正常金属双隧道结中的量子相干输运。同时考虑从一个正常金属电极注入一电子,从另一个正常金属电极注入一空穴,推导出系统的微分电导的一般公式。研究表明,电导谱随偏压展示振荡行为,随着温度和磁场的增大,其振荡振幅被降低,且塞曼能可导致电导峰的塞曼劈裂。在隧道极限下,超导体中会形成一系列束缚态。     

Coherent quantum transport in two-dimensional electron gas/superconductor double junctions with Rashba spin-orbit coupling

Based on the extended Blonder-Tinkham-Klapwijk (BTK) approach, we have investigated the coherent quantum transport in two-dimensional electron gas/superconductor (2DEG/SC) double tunneling junctions in the presence of the Rashba spin-orbit coupling (RSOC). It is found that all the reflection coefficients in BTK theory as well as conductance spectra oscillate with the external voltage and energy. The oscillation feature of conductance can be tuned largely by the RSOC for low insulating barriers, while for high insulating barriers it is almost independent of the RSOC. These phenomena are essentially different from those found in ferromagnet/superconductor double tunneling junctions.     

磁性隧道结中的量子相干输运研究

采用散射矩阵的方法研究了铁磁/绝缘层/半导体/绝缘层/铁磁(FM/I/SM/I/FM)磁性双隧道结的量子相干输运特性.研究发现当隧穿电子平均自由程(l_p)和中间层半导体厚度(L)可比拟时双结隧道磁阻(TMR)将随L的变化产生量子振荡,当l_p远大于L时振荡拐点处出现cut-off波矢,分析表明cut-off波矢主要是来自于隧道结两边的铁磁和半导体层隧穿电子动量波矢的高度不匹配性,随着L关键词： cut-off 波矢 量子相干 振荡 隧道磁阻     

塞曼效应对正常金属/d波超导结中微分电导的影响

通过外加塞曼磁场在d波超导中,研究磁场对d波超导及其正常金属/d波超导结中隧道谱的影响。研究表明(1)塞曼磁场能使能隙变小,且随着磁场变大,超导态会变为正常态,产生一级相变;(2)塞曼磁场可导致零偏压电导峰劈裂,劈裂宽度为2h0(h0为塞曼能)。     

Zeeman effects on d-wave superconductor and tunneling spectrum in normal-metal/d-wave superconductor tunnel junction

We study the Zeeman effect on the d-wave superconductor and tunneling spectrum in normal-metal(N)/d-wave superconductor(S) junction by applying a Zeeman magnetic field to the S. It is shown that: (1) the Zeeman magnetic field can lead to the S gap decreasing, and with the increase in Zeeman energy, the superconducting state is changed to the normal state, exhibiting a first-order phase transition; (2) the Zeeman magnetic field may make the zero-bias conductance peak split into two peaks, and the energy difference between the two splitting peaks in the conductance spectrum is equal to 2h ₀ (h ₀ is the Zeeman energy); (3) both the barrier strength of interface scattering and the temperature can lower the magnitudes of splitting peaks, of which the barrier strength can lead to the splitting peaks becoming sharp and the temperature can smear out the peaks, however, neither of them can influence the Zeeman effect.     

Spin-polarized quasiparticle transport in ferromagnet/d-wave superconductor junctions

Within a scattering framework, a theoretical study is presented for the spin-polarized quasiparticle transport in ferromagnet/d-wave superconductor junctions. We find that the subgap conductance behavior is qualitatively different from a nonmagnetic junction, and can also be significantly different from those of a ferromagnet/s-wave junction. For a ballistic ferromagnet/d-wave superconductor junction, under appropriate conditions, a zero-bias conductance minimum could be achieved. In addition, a conductance maximum at finite bias could be evolved by interfacial scattering. For a normal-metal/ferromagnet/d-wave superconductor junction, conductance resonances are predicted.     

双势垒磁性隧道结中量子阱共振隧穿效应的第一性原理理论

磁性隧道结材料中自旋相关的量子阱态所导致的共振隧穿现象具有很重要的研究和应用价值.文章介绍了最近在Fe(001)/MgO/Fe/MgO/Fe双势垒磁性隧道结中存在的量子阱共振隧穿效应的理论研究工作.通过量子阱态的第一性原理的计算以及结合对中间Fe薄膜孤岛结构所导致Coulomb阻塞效应的分析,证实了最近Nozaki等人(Nozaki T et al. Phys. Rev. Lett., 2006,96:027208 )实验中得到的振荡效应确实来源于中间Fe层多数自旋电子在Γ点处形成的Δ1对称性的量子阱态.     

量子线/铁基超导隧道结中隧道谱的研究

考虑铁基超导中能带间的相互作用和界面对每一个能带的散射作用, 利用推广的Blonder-Tinkham-Klapwijk模型, 并通过求解Bogoliubov-de Gennes 方程研究了具有不同类型双能隙系统的量子线/铁基超导隧道结中准粒子的输运系数和隧道谱. 研究表明: 1)在弹道极限时, 随着带间相互作用的增大, s_± 波隧道谱中零偏压附近的平台演变成电导峰; s₊₊ 波的平台演变成凹陷; p波的零偏压电导峰被压低. 2)界面对两个能带的散射作用不为零时, 随着带间相互作用的增大, s_± 波和s₊₊ 波两能隙处的峰值将降低, 而两峰间的凹陷值将变大; p波的零偏压电导峰被压低, 非零偏压电导增大. 3)界面对每个能带的散射, 可使其产生的电导峰变得更加尖锐, 但可压低和抹平另一个带产生的电导峰值. 这些结果对于澄清铁基超导体的能隙结构和区别不同类型铁基超导体有所帮助.     

Recent progresses of quantum confinement in graphene quantum dots

Graphene quantum dots (GQDs) not only have potential applications on spin qubit, but also serve as essential platforms to study the fundamental properties of Dirac fermions, such as Klein tunneling and Berry phase. By now, the study of quantum confinement in GQDs still attract much attention in condensed matter physics. In this article, we review the experimental progresses on quantum confinement in GQDs mainly by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Here, the GQDs are divided into Klein GQDs, bound-state GQDs and edge-terminated GQDs according to their different confinement strength. Based on the realization of quasi-bound states in Klein GQDs, external perpendicular magnetic field is utilized as a manipulation approach to trigger and control the novel properties by tuning Berry phase and electron–electron (e–e) interaction. The tip-induced edge-free GQDs can serve as an intuitive mean to explore the broken symmetry states at nanoscale and single-electron accuracy, which are expected to be used in studying physical properties of different two-dimensional materials. Moreover, high-spin magnetic ground states are successfully introduced in edge-terminated GQDs by designing and synthesizing triangulene zigzag nanographenes.     

双势垒磁性隧道结中量子阱共振隧穿效应的第一性原理理论

磁性隧道结材料中自旋相关的量子阱态所导致的共振隧穿现象具有很重要的研究和应用价值，文章介绍了最近在Fe（001）／MgO／Fe／MgO／Fe双势垒磁性隧道结中存在的量子阱共振隧穿效应的理论研究工作，通过量子阱态的第一性原理的计算以及结合对中间Fe薄膜孤岛结构所导致Coulomb阻塞效应的分析，证实了最近Nozaki等人（Nozaki T et al．Phys．Rev．Lett．，2006，96：027208）实验中得到的振荡效应确实来源于中间Fe层多数自旋电子在Г点处形成的△1对称性的量子阱态．Coulomb阻塞效应的存在正是导致实验中低温下量子阱共振隧穿效应不够明显的主要原因．     

磁性d波超导/铁磁/磁性d波超导结中的约瑟夫森效应

通过求解磁性d波超导中的能隙和磁交换能的自洽方程, 研究磁性d波超导/铁磁/磁性d波超导结中的约瑟夫森电流. 计算结果表明: 1)临界电流随中间的铁磁层厚度呈现出两种不同周期的振荡混合, 通过增强铁磁层中的磁交换能q₀和铁磁/磁性d波超导界面处的势垒强度z₀, 短周期分量可从长周期中分离出来, 反之, 通过降低q₀和z₀, 长周期分量可从短周期中分离出来; 2)在两边磁性d波超导的磁化方向取平行时, 在取一些特定的铁磁层厚度下, 磁性d波超导中的磁交换能可增强系统的临界电流. 关键词： 磁性d波超导体 铁磁体 约瑟夫森电流     

Zeeman effects on Josephson current in d-wave superconductor/d-wave superconductor junctions

This paper solves a self-consistent equation for the d-wave superconducting gap and the effective exchange field in the mean-field approximation, and studies the Zeeman effects on the d-wave superconducting gap and thermodynamic potential. The Josephson currents in the d-wave superconductor(S)/insulating layer(I)/d-wave S junctions are calculated as a function of the temperature, exchange field, and insulating barrier strength under a Zeeman magnetic field on the two d-wave Ss. It is found that the Josephson critical currents in d-wave S/d-wave S junction to a great extent depend on the relative orientation of the effective exchange field of the two S electrodes, and the crystal orientation of the d-wave S. The exchange field under certain conditions can enhance the Josephson critical current in a d-wave S/I/d-wave S junction.     

Zeeman effects on d-wave superconductor and the coherent tunneling spectrum in normal-metal/d-wave superconductor/normal-metal tunnel junctions

We solve a self-consistent equation for the d-wave superconducting gap and the magnetization in the mean-field approximation, study the Zeeman effects on the thermodynamic potential of d-wave superconductor (S) and coherent quantum transport in normal-metal (N)/d-wave S/N double tunnel junctions. Taking simultaneously into account the electron-injected current from one N electrode and the hole-injected current from the other N electrode, we derive a general formula for the differential conductance in a N/d-wave S/N system under a Zeeman magnetic field on the d-wave S. It is found that oscillations of all quasiparticle transport coefficients and differential conductance with the bias voltage and the thickness of the d-wave S depend to a great extent on the crystal orientation of the d-wave S. In the N/d-wave S/N junctions, the Zeeman magnetic field can lead to the Zeeman splitting of conductance peaks, and the temperature can reduce the coherent effect.     

磁性半导体/磁性d波超导结中的自旋极化输运

通过求解磁性d波超导中的能隙与磁交换能的自恰方程,利用推广的Blonder-Tinkham-Klapwijk 理论研究磁性半导体/磁性d波超导结中自旋极化准粒子输运系数与微分电导. 计算表明： 1) 磁性d波超导结中的磁交换能h₀可导致零偏压电导峰与能隙电导峰劈裂,劈裂的宽度为2h₀;2) 磁性半导体中的磁交换能h_FS可使零偏压电导峰劈裂的峰值变低. 而由能隙电导峰劈裂的两个子峰,当两种磁性材料的磁 关键词： 磁性半导体 磁性d波超导体 自旋极化输运     

Tunneling transport in topological insulator normal metal/insulator/d-wave superconductor junctions

We investigate the tunneling conductance in a normal metal/insulator/d-wave superconductor (NM/I/d-wave SC) junction with a barrier of thickness d and with an arbitrary gate voltage V(0) applied across the barrier region, formed on the surface of a topological insulator, using the Dirac-Bogoliubov-de Gennes equation and Blonder-Tinkham-Klapwijk?(BTK) formalism. We find that the tunneling conductance as a function of both d and V(0) displays an oscillatory behavior whose amplitude decreases with increase of V(0). We also find that when the Andreev resonant condition is met, the tunneling conductance approaches a maximum value of 2G(0), independent of the gate voltage V(0).     

Charge transport through ferromagnet/two-dimensional electron gas/d-wave superconductor junctions with Rashba spin-orbit coupling

Along the lines of Blonder, Tinkham and Klapwijk, we investigate the charge transport through ferromagnet/two-dimensional electronic gas/d-wave superconductor (F/2DEG/S) junctions in the presence of Rashba spin-orbit (SO) coupling and focus our attention on the interplay between spin polarization and spin precession. At zero spin polarization, the spin-mixing scattering resulted from Rashba SO coupling decreases the zero-bias conductance peak. Under spin polarization, spin precession introduces novel Andreev reflection, which competes with the effect of spin-mixing scattering. If the F layer is a half metal, the later effect is overwhelmed by that of novel Andreev reflection. As a result, the zero-bias conductance dip caused by spin polarization is enhanced, and at strong Rashba SO coupling, a split zero-bias peak is found in the gap. In an intermediate region where the two effects are comparable with each other, the zero-bias conductance shows a reentrant behavior as a function of Rashba SO coupling.     

Resonant Andreev reflection in a normal-metal/quantum-dot/superconductor system with coupled Majorana bound states

Andreev reflection(AR) in a normal-metal/quantum-dot/superconductor(N–QD–S) system with coupled Majorana bound states(MBSs) is investigated theoretically. We find that in the N–QD–S system, the AR can be enhanced when coupling to the MBSs is incorporated. Fano line-shapes can be observed in the AR conductance spectrum when there is an appropriate QD–MBS coupling or MBS–MBS coupling. The AR conductance is always e~2/2h at the zero Fermi energy point when only QD–MBSs coupling is considered. In addition, the resonant AR occurs when the MBS–MBS coupling roughly equals to the QD energy level. We also find that an AR antiresonance appears when the QD energy level approximately equals to the sum of the QD–MBS coupling and the MBS–MBS coupling. These features may serve as characteristic signatures for the probe of MBSs.     

Differential conductance in normal-metal/insulator/metal/d-wave superconductor junction carrying a supercurrent

This paper applies the Bogoliubov--de Gennes equation and the Blonder--Tinkham--Klapwijk approach to study the oscillatory behaviour of differential conductance in a normal metal/insulator/metal/d-wave superconductor junction carrying a supercurrent I_s. We find that (i) a three-humped structure appears at a nearly critical supercurrent I_s and z ≈ 0.5 for the normal metal/insulator/metal/d_x² + y²-wave superconductor junction; (ii) the zero-bias conductance peak splits into two peaks with sufficiently large applied current for the normal metal/insulator/metal/d_xy-wave superconductor junction; (iii) the conductance spectrum exhibits oscillating behaviour with the bias voltage and the peaks of the resonances are suppressed by increasing supercurrent I_s.