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.     

Exploring Majorana zero modes in iron-based superconductors

Majorana zero modes (MZMs) are Majorana-fermion-like quasiparticles existing in crystals or hybrid platforms with topologically non-trivial electronic structures. They obey non-Abelian braiding statistics and are considered promising to realize topological quantum computing. Discovery of MZM in the vortices of the iron-based superconductors (IBSs) has recently fueled the Majorana research in a way which not only removes the material barrier requiring construction of complicated hybrid artificial structures, but also enables observation of pure MZMs under higher temperatures. So far, MZMs have been observed in iron-based superconductors including FeTe_0.55Se_0.45, (Li_0.84Fe_0.16)OHFeSe, CaKFe₄As₄, and LiFeAs. In this topical review, we present an overview of the recent STM studies on the MZMs in IBSs. We start with the observation of MZMs in the vortices in FeTe_0.55Se_0.45 and discuss the pros and cons of FeTe_0.55Se_0.45 compared with other platforms. We then review the following up discovery of MZMs in vortices of CaKFe₄As₄, impurity-assisted vortices of LiFeAs, and quantum anomalous vortices in FeTe_0.55Se_0.45, illustrating the pathway of the developments of MZM research in IBSs. Finally, we give perspective on future experimental works in this field.     

Tunneling into multiwalled carbon nanotubes: coulomb blockade and the Fano resonance

Tunneling spectroscopy measurements of single tunnel junctions formed between multiwalled carbon nanotubes (MWNTs) and a normal metal are reported. Intrinsic Coulomb interactions in the MWNTs give rise to a strong zero-bias suppression of a tunneling density of states that can be fitted numerically to the environmental quantum-fluctuation theory. An asymmetric conductance anomaly near zero bias is found at low temperatures and interpreted as Fano resonance in the strong tunneling regime.     

正常金属-d波超导隧道结中杂质和界面散射对微分电导的影响

考虑到正常金属区域的杂质散射和界面粗糙的散射,运用Bogoliubov-de Gennes (BdG)方程和Bolonder-Tinkham-Klapwijk(BTK)理论模型,计算正常金属-d波超导隧道结的微分电导.计算发现：隧道谱强烈地依赖电子的入射角和超导体晶轴方位,并能展示零偏压电导峰的存在;此外,杂质散射能使隧道谱的凹陷分裂出两个小凹陷,而界面粗糙能抹平和压低零偏压电导峰和能隙电导峰.这些结果都将很好地解释高T_c超导隧道谱的实验现象. 关键词：     

Majorana零模式的电导与低压振荡散粒噪声

Majorana零能量模式是自身的反粒子,在拓扑量子计算中有重要应用.本文研究量子点与拓扑超导纳米线混合结构,通过量子点的输运电荷检测Majorana零模式.利用量子主方程方法,发现有无Majorana零模式的电流与散粒噪声存在明显差别.零模式导致稳态电流差呈反对称,在零偏压处显示反常电导峰.电流差随零模式分裂能的增大而减小,随量子点与零模式耦合的增强而增大.另一方面,零模式导致低压散粒噪声相干振荡,零频噪声显著增强.分裂能导致相干振荡愈加明显且零频噪声减小,而量子点与零模式的耦合使零频噪声增强.当量子点与电极非对称耦合时,零模式使电子由反聚束到聚束输运,亚泊松噪声增强为超泊松噪声.稳态电流差结合低压振荡的散粒噪声能够揭示Majorana零模式是否存在.     

Reflectionless tunneling at the interface between nanoparticles and superconductors

Interfaces between disordered normal (DN) materials and superconductors (S) are known to generate conductance peaks at zero-bias voltage (V) and magnetic field (B). Using molecularly linked Au nanoparticle films as the DN component, we find that superimposed on conductance peaks are oscillations that depend simultaneously on both V and B. Such correlated conductance oscillations are predicted by a "reflectionless tunneling" phenomenon but have not been observed in other DN-S systems. Length scales extracted from periods of conductance oscillation correlate well with film nanostructure.     

N/I/d波超导体c轴隧道结的微分电导

以方势垒描述绝缘层,对N/I/d波超导体c轴隧道结的微分电导进行了研究.结果表明:在N/I/d波超导体c轴隧道结的隧道谱中存在V型结构、能隙外的凹陷和小的零偏压电导峰.这一结果能很好的解释相关的实验现象.     

Andreev Bound States at the Onset of Phase Coherence in Bi(2)Sr(2)CaCu(2)O(8)

A new technique of planar tunneling spectroscopy has been developed to access the in-plane density of states of optimally doped Bi(2)Sr(2)CaCu(2)O(8) single crystals. The low energy spectrum is observed to depend on crystallographic orientation. When tunnel current is injected nominally along the Cu-Cu bond direction, a zero-bias conductance peak is observed to appear simultaneously with the onset of bulk superconductivity. These data demonstrate the existence of surface-induced states in this system and confirm the d-wave symmetry of the superconducting order parameter.     

Differential conductance of normal metal-insulator-d-wave superconductor junctions with interface roughness

Within the framework of Blonder-Tinkham-Klapwijk (BTK) model and taking into account the interface roughness, we calculate the differential conductance of normal metal-insulator-d-wave superconductor junctions. We find that the tunneling spectrum depends strongly on both the incident angle of electrons and the crystalline axis orientation of the superconductor, and exhibits the zero-bias anomaly under suitable arrangements. Interestingly, even in the absence of the insulating layer, the tunneling spectrum of normal metal-d-wave superconductor junctions differs significantly from that for normal metal-s-wave superconductor due to the interface roughness. Moreover, both the tunnel conductance peak at the energy gap and the zero-bias conductance peak are suppressed by the interface roughness. Our results can explain many experimental measurements on the tunneling spectra of high-T_c superconductors.     

Surface states and tunneling spectroscopy of high-Tcsuperconductors

Recent studies of high- T_csuperconductors have clarified new aspects of tunneling spectroscopy. The unconventional pairing states, i.e. d-wave symmetry in these materials have been established through various measurements. Differently from isotropic s-wave superconductors, d-wave pairing states have an internal phase of the pair potential. The internal phase modifies the surface states due to the interference effect of the quasiparticles. Along these lines, a novel formula of tunneling spectroscopy has been presented that fully takes into account of the anisotropy of the pair potential. The most essential difference of this formula from conventional ones is that it suggests the phase-sensitive capability of tunneling spectroscopy. The formula suggests that the symmetry of the pair potential is determined by the orientational dependence measurements of tunneling spectroscopy. Along these lines, several experiments have been performed on high-T_c superconductors. The observation of the zero-bias conductance peaks (ZBCP) on Y Ba₂Cu₃O_7 − δstrongly suggests the d_{x² − y²}-wave pairing states of hole-doped high-T_c superconductors. On the other hand, the absence of ZBCP on (electron-doped)Nd_1.85Ce_0.15CuO_4 − δindicates that the pair potential of this material is a nodeless state. In this paper, recent developments of tunneling spectroscopy for anisotropic superconductors are reviewed both on theoretical and experimental aspects.     

铁基超导体FeSe0.5Te0.5表面隧道谱的研究

用扫描隧道显微镜/谱仪仔细研究了铁基超导单晶FeSe_0.5Te_0.5样品的表面形貌和隧道谱, 测量到了清晰的表面原子形貌和在空间比较稳定的隧道谱结构．在样品中测量的隧道谱零能态密度比较高, 说明样品里面有比较强的非弹性准粒子散射. 在正能5 mV附近有个较大的背景鼓包, 这一背景在很高温度也未消失. 空间中Se和Te集中的位置会带来高能背景的变化, 超导能隙附近谱的形状大致相同. 较强的非弹性准粒子散射破坏了超导的准粒子散射, 因此没有在二维微分电导图中发现超导准粒子相干散射的特征亮斑.     

量子线/绝缘层/p波超导体结的隧道谱

用Bogoliubov-de Gennes方程来研究量子线/绝缘层/p波超导体结(q/I/p)中的准粒子输运过程，利用推广的Blonder，Tinkham和Klapwijk模型计算绝对零度和有限温度下q/I/p的一级谐波隧道谱.和量子线/绝缘层/d波超导体结的一级谐波隧道谱不同的是q/I/p的一级谐波隧道谱中存在零偏压电导峰.随着q/I/p中绝缘层的势垒散射增强，q/I/p的一级谐波隧道谱中零偏压电导峰变高.     

Observation of broken time-reversal symmetry with Andreev bound state tunneling spectroscopy

Quasiparticle (QP) planar tunneling spectroscopy is used to investigate the density of states (DoS) of YBa₂Cu₃O₇ (YBCO). Temperature, crystallographic orientation, doping, damage and magnetic field dependencies confirm that the observed zero-bias conductance peak (ZBCP) is an Andreev bound state (ABS), an intrinsic property of a d-wave superconducting order parameter (OP) at an interface. In zero applied field, the splitting of the ZBCP below 8 K confirms a near-surface phase transition into a superconducting state with spontaneously broken time-reversal symmetry (BTRS). Tunneling into the ABS provides a phase-sensitive spectroscopy that can be used to measure a variety of DoS properties in an unconventional superconductor.     

Topological Superconductivity in Cu(x)Bi(2)Se(3)

A topological superconductor (TSC) is characterized by the topologically protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator Cu(x)Bi(2)Se(3), which superconducts below ～3 K, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting Cu(x)Bi(2)Se(3) present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topological superconductivity in Cu(x)Bi(2)Se(3). In addition, we found an unusual pseudogap that develops below ～20 K and coexists with the topological superconducting state.     

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.     

Surface states and tunneling spectroscopy of high-Tcsuperconductors

Recent studies of high- T_csuperconductors have clarified new aspects of tunneling spectroscopy. The unconventional pairing states, i.e. d-wave symmetry in these materials have been established through various measurements. Differently from isotropic s-wave superconductors, d-wave pairing states have an internal phase of the pair potential. The internal phase modifies the surface states due to the interference effect of the quasiparticles. Along these lines, a novel formula of tunneling spectroscopy has been presented that fully takes into account of the anisotropy of the pair potential. The most essential difference of this formula from conventional ones is that it suggests the phase-sensitive capability of tunneling spectroscopy. The formula suggests that the symmetry of the pair potential is determined by the orientational dependence measurements of tunneling spectroscopy. Along these lines, several experiments have been performed on high-T_c superconductors. The observation of the zero-bias conductance peaks (ZBCP) on Y Ba₂Cu₃O_{7 − δ}strongly suggests the d_{x² − y²}-wave pairing states of hole-doped high-T_c superconductors. On the other hand, the absence of ZBCP on (electron-doped)Nd_1.85Ce_0.15CuO_{4 − δ}indicates that the pair potential of this material is a nodeless state. In this paper, recent developments of tunneling spectroscopy for anisotropic superconductors are reviewed both on theoretical and experimental aspects.     

Topological Majorana and Dirac zero modes in superconducting vortex cores

We provide an argument based on flux insertion to show that certain superconductors with a nontrivial topological invariant have protected zero modes in their vortex cores. This argument has the flavor of a two-dimensional index theorem and applies to disordered systems as well. It also provides a new way of understanding the zero modes in the vortex cores of a spinless px+ipy superconductor. Applying this approach to superconductors with and without time-reversal and spin-rotational symmetry, we predict the necessary and sufficient conditions for protected zero modes to exist in their vortices.     

Charge Transport Properties of the Majorana Zero Mode Induced Noncollinear Spin Selective Andreev Reflection

We study the charge transport properties of the spin-selective Andreev reflection(SSAR)effect between a spin polarized scanning tunneling microscope(STM)tip and a Majorana zero mode(MZM).Considering both the MZM and the excited states,we calculate the conductance and the shot noise power of the noncollinear SSAR using scattering theory.We find that the excited states give rise to inside peaks.Moreover,we numerically calculate the shot noise power and the Fano factor of the SSAR effect.Our calculation shows that the shot noise power and the Fano factor are related to the angle between the spin polarization direction of the STM tip and that of the MZM,which provide additional characteristics to detect the MZM via SSAR.     

Resonant transport through midgap states in voltage-biased Josephson junctions of d-wave superconductors

We study theoretically the ac Josephson effect in voltage-biased planar junctions of d-wave superconductors. For some orientations of the superconductors a current peak is found at finite voltage in the current–voltage characteristics. We pick out the relevant physical processes and write down an analytical formula for the current which clearly shows how the midgap state acts as a resonance and produces the peak. We present a possible explanation for the zero-bias conductance peak, recently found in experiments on grain boundary junctions of high-temperature superconductors, in terms of resonant transmission through midgap state of quasiparticles undergoing multiple Andreev reflections. We note that within our framework the zero-bias conductance peak appears in rather transparent Josephson junctions of d-wave superconductors.     

正常金属/自旋三重态p波超导体结隧道谱的奇异性

利用Blonder，Tinkham和Klapwijk理论计算了正常金属/绝缘层/正常金属/自旋三重态的p波超导体结的隧道谱和平均电流.计算结果表明：在自旋三重态p波超导结的隧道谱中存在零偏压电导峰、零偏压电导凹陷和双凹陷结构，并有微分电导随偏压震荡的现象出现，在I-V曲线上出现电流台阶.这些结果在理论上支持Sr₂RuO₄的超导态是自旋三重态p波超导态. 关键词： 自旋三重态超导体 p波超导体 隧道谱