Chirality sensitive effect on surface states in chiral p-wave superconductors

We study the local density of states at the surface of a chiral p-wave superconductor in the presence of a weak magnetic field. As a result, the formation of low-energy Andreev bound states is either suppressed or enhanced by an applied magnetic field, depending on its orientation with respect to the chirality of the p-wave superconductor. Similarly, an Abrikosov vortex, which is situated not too far from the surface, leads to a zero-energy peak of the density of states, if its chirality is the same as that of the superconductor, and to a gap structure for the opposite case. We explain the underlying principle of this effect and propose a chirality sensitive test on unconventional superconductors.     

Quasi-particle structure around a single vortex in high-Tc superconductors

For analyzing the checker-board like modulation of the local density of states (LDOS) around a vortex observed in the slightly overdoped Bi₂Sr₂CaCu₂O_x, we examined the effect of pseudogap state of high-T_c superconductors to the LDOS around the vortex. We first derived the Bogoliubov-de Gennes equation for d-wave superconductivity (d-SC) in the presence of d-spin density wave (d-SDW). Using the Fourier–Bessel expansion, we solved this equation for a single vortex state, numerically. We found that the peak of the bound states around E = 0 becomes small and modulation of the LDOS is observed for larger d-SDW order parameter.     

Direct observation of geometrical phase transitions in mesoscopic superconductors by scanning tunneling microscopy

Using scanning tunneling microscopy, we mapped the distribution of the local density of states in a single crystal superconductor heterostructure with an array of submicron normal metal islands. We observe the coexistence of strongly interacting multiquanta vortex lattice with interstitial Abrikosov vortices. The newly formed composite magnetic flux structure undergoes a series of phase transitions between different topological configuration states. The vortex configuration states are strongly dependent on the number of flux quanta and the nanoscale confinement architecture of the mesoscopic superconductor. Here, we present images of vortex phase transitions due to confinement effects when the number of magnetic flux quanta in the system changes. The vortex dynamics in these systems could serve as a model for behavior of confined many-body systems when the number of particles changes.     

The vortex physics which comes from the vortex core

A theoretical view of vortex core states and of their effects on physics of vortices in clean s- and d-wave-type II superconductors is presented based on a semi-classical picture of a vortex core as an Andreev potential well containing many quasiparticle states. We discuss the density of states, the vortex dissipation, Hall effect, and the vortex mass. The dynamic characteristics are determined by relaxation of core excitations driven by a moving vortex. In a d-wave superconductor, gap nodes make the core states more extended and introduce novel features into thermodynamics and kinetics of vortices.     

Effect of surface Andreev bound states on the Bean-Livingston barrier in d-wave superconductors

We study the influence of surface Andreev bound states in d-wave superconductors on the Bean-Livingston surface barrier for entry of a vortex line into a strongly type-II superconductor. Starting from Eilenberger theory, we derive a generalization of London theory to incorporate the anomalous surface currents arising from the Andreev bound states. This allows us to find an analytical expression for the modification of the Bean-Livingston barrier in terms of a single parameter describing the influence of the Andreev bound states. We find that the field of first vortex entry is significantly enhanced. Also, the depinning field for vortices near the surface is renormalized. Both effects are temperature dependent and depend on the orientation of the surface relative to the d-wave gap.     

Circuit theory of unconventional superconductor junctions

We extend the circuit theory of superconductivity to cover transport and proximity effect in mesoscopic systems that contain unconventional superconductor junctions. The approach fully accounts for zero-energy Andreev bound states forming at the surface of unconventional superconductors. As a simple application, we investigate the transport properties of a diffusive normal metal in series with a d-wave superconductor junction. We reveal the competition between the formation of Andreev bound states and proximity effect that depends on the crystal orientation of the junction interface.     

Theory of pairing symmetry in the vortex states

We investigate pairing symmetry in an Abrikosov vortex and vortex lattice. It is shown that the Cooper pair wave function at the center of an Abrikosov vortex with vorticity m has a different parity with respect to frequency from that in the bulk if m is an odd number, while it has the same parity if m is an even number. As a result, in a conventional vortex with m = 1, the local density of states at the Fermi energy has a maximum (minimum) at the center of the vortex core in an even (odd)-frequency superconductor. In the vortex lattice of s-wave superconductor, we find that only odd-frequency pairing is present at the core centers, while at the midpoint of the vortex lines, only even-frequency pairing exists. Thus, the odd and even-frequency pairings also form the lattice in the vortex lattice state. We also propose a scanning tunneling microscope experiment using a superconducting tip to explore odd-frequency superconductivity.     

On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations

We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations of superconductivity, with multiple magnetic flux quanta per fundamental cell. We also revisit the existence proof for the Abrikosov vortex lattices, streamlining some arguments and providing some essential details missing in earlier proofs for a single magnetic flux quantum per a fundamental cell.     

Topological origin of zero-energy edge states in particle-hole symmetric systems

A criterion to determine the existence of zero-energy edge states is discussed for a class of particle-hole symmetric Hamiltonians. A "loop" in a parameter space is assigned for each one-dimensional bulk Hamiltonian, and its topological properties, combined with the chiral symmetry, play an essential role. It provides a unified framework to discuss zero-energy edge modes for several systems such as fully gapped superconductors, two-dimensional d-wave superconductors, and graphite ribbons. A variance of the Peierls instability caused by the presence of edges is also discussed.     

Ordered states and structural transitions in a system of Abrikosov vortices with periodic pinning

A system of Abrikosov vortices in a quasi-two-dimensional HTSC plate is considered for various periodic lattices of pinning centers. The magnetization and equilibrium configurations of the vortex density for various values of external magnetic field and temperature are calculated using the Monte Carlo method. It is found that the interaction of the vortex system with the periodic lattice of pinning centers leads to the formation of various ordered vortex states through which the vortex system passes upon an increase or a decrease in the magnetic field. It is shown that ordered vortex states, as well as magnetic field screening processes, are responsible for the emergence of clearly manifested peaks on the magnetization curves. Extended pinning centers and the effect of multiple trapping of vortices on the behavior of magnetization are considered. Melting and crystallization of the vortex system under the periodic pinning conditions are investigated. It is found that the vortex system can crystallize upon heating in the case of periodic pinning.     

Low-energy subgap states and the magnetic flux periodicity in d-wave superconducting rings

Wave functions of low-energy quasiparticle subgap states in d-wave superconducting rings, threaded by an Aharonov-Bohm magnetic flux, are found analytically. The respective energies are closest to the midgap position at small magnetic fluxes and deviate from the Fermi surface due to the Doppler shift, produced by the supercurrent. The Doppler-shifted zero-energy states result in a paramagnetic response of the ring at small fluxes. The states exist only for even angular momenta of the center of mass of Cooper pairs, in agreement with recent numerical studies of the problem. This macroscopic quantum effect in d-wave rings results in broken h/2e periodicity, retaining only the h/e periodic behavior of the supercurrent with varying magnetic flux.     

高温超导体的核磁共振研究

文章回顾了用核磁共振技术研究高温超导体的进展,着重介绍了局域电荷分布、d波超导能隙以及赝能隙的性质.除了CuO2面上空穴密度总数,Cu和O轨道上面空穴数的分布是决定Tc的重要参数.转变温度Tc取决于自旋晶格弛豫率,奈特位移可以显示出d波配对,而d波配对使得准粒子可以从涡线中心 “漏”到外面.超导能隙函数里存在节点,这也是非磁性杂质以及晶体无序会导致Tc明显降低的原因.高温超导体零温正常态在45T的强磁场下变成“费米弧”金属态,这说明赝能隙态和超导态共存于高温超导物质中.     

Index theoretic characterization of d-wave superconductors in the vortex state

We study analytically the low energy spectrum of a lattice d-wave superconductor in the vortex lattice state. For an inversion symmetric hc/2e vortex lattice and in the presence of particle-hole symmetry we prove an index theorem that imposes a lower bound on the number of zero-energy modes. Generic cases are constructed in which this bound exceeds the number of zero modes of an equivalent lattice of hc/e vortices, despite the identical point group symmetries. The quasiparticle spectrum around the zero modes is doubly degenerate and exhibits a Dirac-like dispersion, with velocities that become universal functions of Delta(0)/t in the limit of low magnetic field. For weak particle-hole symmetry breaking, the gapped state can be characterized by a topological quantum number, related to spin-Hall conductivity, which generally differs in the cases of the hc/2e and hc/e vortex lattices.     

STM studies of the electronic structure of vortex cores in Bi(2)Sr(2)CaCu(2)O(8+delta)

We report on low temperature scanning tunneling microscopy (STM) studies of the electronic structure of vortex cores in Bi 2Sr 2CaCu 2O (8+delta). At the vortex core center, an enhanced density of states is observed at energies near Omega = +/-7 meV. Spectroscopic imaging at these energies reveals an exponential decay of these "core states" with a decay length of 22+/-3 A. The fourfold symmetry sometimes predicted for d-wave vortices is not seen in spectroscopic vortex images. A locally nodeless order parameter induced by the magnetic field may be consistent with these measurements.     

双能隙介观超导体的涡旋结构模拟

本文运用了含时Ginzburg-Landau理论研究了双能带结构的介观超导体在外磁场作用下涡旋随时间的演化. 给出了实际温度在s波和d波的临界温度之间s波、d波以及磁场的分布, 从 理论上模拟得到涡旋进入和退出样品的磁场"过热"与"过冷"现象, 以及介观超导样品边界对涡旋结构分布的影响. 关键词： 涡旋结构 双能带 含时Ginzburg-Landau理论 超导     

Extinction of quasiparticle scattering interference in cuprate superconductors

The quasiparticle scattering interference phenomenon characterized by the peaks in the local density of states is studied within the kinetic energy driven superconducting mechanism in the presence of a single impurity. By calculation of the Fourier transformed ratio of the local density of states at opposite energy, it is shown that the quasiparticle scattering interference phenomenon can be described qualitatively by a single impurity in the kinetic energy driven homogeneous d-wave superconducting state. The amplitude of the peak increases with increasing energy at the low energy, and reaches a maximum at the intermediate energy, then diminishes to zero at the high energy. The theory also predicts that with increasing doping, the position of the peak along the nodal direction moves towards to the center of the Brillouin zone, while the position of the peak along the antinodal direction is shifted to large momentum region.     

Instabilities in the vortex matter and the peak effect phenomenon

In single crystals of 2H-NbSe2, we identify for the first time a crossover from a weak collective to a strong pinning regime in the vortex state which is not associated with the peak effect phenomenon. Instead, we find the crossover is associated with an anomalous history dependent magnetization response. In the dc magnetic field (Bdc)-temperature (T) vortex matter phase diagram we demarcate this pinning crossover boundary. We also delineate another boundary which separates the strong pinning region from a thermal fluctuation dominated regime, and find that a peak effect appears on this boundary.     

Anomalous scaling and gapless fermions of d-wave superconductors in a magnetic field

The problem of dx2-y2-wave quasiparticles in a weakly disordered Abrikosov vortex lattice is studied. Starting with a periodic lattice, the topological structure of the magnetic crystal momenta of gapless fermions is found for the particle-hole symmetric case. If in addition the site centered inversion symmetry is present, both the location and the number of the gapless fermions can be determined using an index theorem. In the case of spatially aperiodic vortex array, Simon and Lee scaling is found to be violated due to a quantum anomaly. The electronic density of states is found to scale with the root-mean-square vortex displacement as sqrt[H]f(u2rms/xi2), while thermal conductivity is H independent, but different from the H=0 case.     

Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions

An important characteristic of topological band insulators is the necessary presence of in-gap edge states on the sample boundary. We utilize this fact to show that when the boundary is reconnected with a twist, there are always zero-energy defect states. This provides a natural connection among novel defects in the two-dimensional p{x}+ip{y} superconductor, the Kitaev model, the fractional quantum Hall effect, and the one-dimensional domain wall of polyacetylene.