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In d$_{x^2-y^2}$-wave superconductors, the effect of s-wave point disorder has been extensively studied in the literature. In this work, we study the anisotropic disorder with a the form of $V_{kk'}^{\rm imp}=V_if_kf_{k'}$ with $f_k=\cos(2\theta)$ (with $\theta$ the azimuthal angle of $k$), as proposed to be caused by apical oxygen vacancies in overdoped La-based cuprate films, under the Born approximation. The disorder self-energy and d-wave pairing affect each other and have to be solved simultaneously self-consistently. We find the self-energy is reduced at low frequencies and thus weakens the pair-breaking effect. This frequency-dependence vanishes in the dirty limit for which the disorder is well described by a scattering rate $\Gamma_k=\Gamma_if_k^2$. One consequence of the disorder effect is the gap-to-$T_c$ ratio $2\Delta(0)/T_c$ is greatly enhanced by the d-wave disorder, much larger than the s-wave disorder and the clean BCS value $4.28$. At last, we generalize the d-wave scattering rate to a general form $\Gamma_\theta=\Gamma_\alpha|\theta-\theta_0|^\alpha$ around each nodal direction $\theta_0$. We find the density of states $\rho(\omega)-\rho(0)\propto|\omega|$ ($\omega^2$) for all $\alpha\ge1$ ($\alpha, Comment: 5 pages, 6 figures

We revisit the Hall effect and magnetoresistivity by incorporating the anisotropic scattering caused by apical oxygen vacancies in overdoped La-based cuprates. The theoretical calculations within the Fermi liquid picture agree well with a handful of anomalous magneto-transport data, better than the results using an isotropic scattering rate alone. In particular, we obtain the upturn of Hall coefficient $R_H$ with decreasing temperature $T$, the initial drop of $R_H$ in magnetic field $B$ in all overdoped regimes, the linear resistivity $\rho$ versus $B$ near the van Hove doping level, the temperature dependence of the magnetoresistivity ratio, and the violation of Kohler's law. These results suggest that many of the anomalous transport behaviors in overdoped La$_{2-x}$Sr$_x$CuO$_4$ could actually be understood within the Fermi liquid picture., Comment: 6 pages, 5 figures

In our recent work [Phys. Rev. Lett. 128, 137001 (2002)], we proposed that the apical oxygen vacancies act as anisotropic scattering impurities. Within the Born approximation, this leads to a quasi-particle scattering rate that is maximal (zero) in the antinodal (nodal) direction. This unique angular dependence provides a straightforward mechanism for some puzzling experimental results in overdoped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) films regarding the superfluid density $\rho_s$ and optical conductivity $\sigma_1$. In a recent comment by H. U. Ozdemir et al. [arXiv:2206.01301], the importance of the nature of the impurity scattering is re-emphasized, but some challenges to our picture are raised: that we did not consider the change of the electrostatic potential for in-plane electrons once the apical oxygen is missing, the change of Fermi surface topology as the van Hove point is passed, self-energy corrections caused by d-wave pairing, and vertex corrections caused by forward scattering. These concerns are interesting but are either irrelevant or further enhances our conclusions. We discuss these points one by one in this reply.

Recently, several experiments on La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) challenged the Fermi liquid picture for overdoped cuprates, and stimulated intensive debates [1]. In this work, we study the magnetotransport phenomena in such systems based on the Fermi liquid assumption. The Hall coefficient $R_H$ and magnetoresistivity $\rho_{xx}$ are investigated near the van Hove singularity $x_{\tiny\text{VHS}}\approx0.2$ across which the Fermi surface topology changes from hole- to electron-like. Our main findings are: (1) $R_H$ depends on the magnetic field $B$ and drops from positive to negative values with increasing $B$ in the doping regime $x_{\tiny\text{VHS}}, Comment: 6 pages, 4 figures

The electronic structure and possible electronic orders in monolayer NbF$_4$ are investigated by density functional theory and functional renormalization group. Because of the niobium-centered octahedra, the energy band near the Fermi level is found to derive from the $4d_{xy}$ orbital, well separated from the other bands. Local Coulomb interaction drives the undoped system into an antiferromagnetic insulator. Upon suitable electron/hole doping, the system is found to develop $d_{x^2-y^2}$-wave superconductivity with sizable transition temperature. Therefore, the monolayer NbF$_4$ may be an exciting $4d^1$ analogue of cuprates, providing a new two-dimensional platform for high-$T_c$ superconductivity., Comment: 5 pages, 6 color figures

We use functional renormalization group method to study a three-orbital model for superconducting Sr$_2$RuO$_4$. Although the pairing symmetry is found to be chiral $p$-wave, the atomic spin-orbit coupling induces near-nodes for quasiparticle excitations. Our theory explains a major experimental puzzle between $d$-wave-like feature observed in thermal experiments and the chiral $p$-wave triplet pairing revealed in nuclear-magnetic-resonance and Kerr effect., Comment: 6 pages, 5 figures

The superconducting state is achieved by the condensation of Cooper pairs and is protected by the superconducting gap. The pairing interaction between the two electrons of a Cooper pair determines the superconducting gap function. Thus, it is very pivotal to detect the gap structure for understanding the mechanism of superconductivity. In cuprate superconductors, it has been well established that the superconducting gap may have a d-wave function �� = ��_0cos2��. This gap function has an alternative sign change by every pi/2 in the momentum space when the in-plane azimuthal angle theta is scanned. It is very hard to visualize this sign change. Early experiments for recommending or proving this d-wave gap function were accomplished by the specially designed phase sensitive measurements based on the Josephson effect. Here we report the measurements of scanning tunneling spectroscopy in one of the model cuprate system Bi2Sr2CaCu2O8+�� and conduct the analysis of phase-referenced quasiparticle interference (QPI). Due to the unique quasiparticle excitations in the superconducting state of cuprate, we have seen the seven basic scattering vectors that connect each pair of the terminals of the banana-shaped contour of constant quasiparticle energy (CCE). The phase-referenced QPI clearly visualizes the sign change of the d-wave gap. Our results illustrate a very effective way for determining the sign change of unconventional superconductors., 36 pages, 10 figures

Motivated by the success of experimental manipulation of the band structure through biaxial strain in Sr$_2$RuO$_4$ thin film grown on a mismatched substrate, we investigate theoretically the effects of biaxial strain on the electronic instabilities, such as superconductivity (SC) and spin density wave (SDW), by functional renormalization group. According to the experiment, the positive strain (from lattice expansion) causes charge transfer to the $\gamma$-band and consequently Lifshitz reconstruction of the Fermi surface. Our theoretical calculations show that within a limited range of positive strain a p-wave superconducting order is realized. However, as the strain is increased further the system develops into the SDW state well before the Lifshitz transition is reached. We also consider the effect of negative strains (from lattice constriction). As the strain increases, there is a transition from p-wave SC state to nodal s-wave SC state. The theoretical results are discussed in comparison to experiment and can be checked by further experiments., Comment: 9 pages, 5 color figures

We propose to utilize the sub-system fidelity (SSF), defined by comparing a pair of reduced density matrices derived from the degenerate ground states, to identify and/or characterize symmetry protected topological (SPT) states in one-dimensional interacting many-body systems. The SSF tells whether two states are locally indistinguishable (LI) by measurements within a given sub-system. Starting from two polar states (states that could be distinguished on either edge), the other combinations of these states can be mapped onto a Bloch sphere. We prove that a pair of orthogonal states on the equator of the Bloch sphere are LI, independently of whether they are SPT states or cat states (symmetry-preserving states by linear combinations of states that break discrete symmetries). Armed with this theorem, we provide a scheme to construct zero-energy exitations that swap the LI states. We show that the zero mode can be located anywhere for cat states, but is localized near the edge for SPT states. We also show that the SPT states are LI in a finite fraction of the bulk (excluding the two edges), whereas the symmetry-breaking states are distinguishable. This can be used to pinpoint the transition from SPT states to the symmetry-breaking states., Comment: 7 pages, 4+1 figures

Linear dispersion near the Dirac points in the band structure of graphenes can give rise to novel physical properties. We calculate the electronic contribution to the Raman spectra in graphenes, which also shows novel features. In the clean limit, the Raman spectrum in the undoped graphene is linear (with a universal slope against impurity scattering) at low energy due to the linear dispersion near the Dirac points, and it peaks at a position corresponding to the van Hove singularity in the band structure. In a doped graphene, the electronic Raman absorption is forbidden up to a vertical inter-band particle-hole gap. Beyond the gap the spectrum follows the undoped case. In the presence of impurities, absorption within the gap (in the otherwise clean case) is induced, which is identified as the intra-band contribution. The Drude-like intra-band contribution is seen to be comparable to the higher energy inter-band Raman peak. The results are discussed in connection to experiments.

Motivated by the recent discovery of high temperature antiferromagnet SrRu$_2$O$_6$ and its potential to be the parent of a new superconductor, we construct a minimal $t_{2g}$-orbital model on a honeycomb lattice to simulate its low energy band structure. Local Coulomb interaction is taken into account through both random phase approximation and mean field theory. Experimentally observed Antiferromagnetic order is obtained in both approximations. In addition, our theory predicts that the magnetic moments on three $t_{2g}$-orbitals are non-collinear as a result of the strong spin-orbit coupling of Ru atoms., Comment: 5 pages, 5 figures

Using functional renormalization group we investigated possible superconductivity in doped Sr$_2$IrO$_4$. In the electron doped case, a $d^*_{x^2-y^2}$-wave superconducting phase is found in a narrow doping region. The pairing is driven by spin fluctuations within the single conduction band. In contrast, for hole doping an $s^*_{\pm}$-wave phase is established, triggered by spin fluctuations within and across the two conduction bands. In all cases there are comparable singlet and triplet components in the pairing function. The Hund's rule coupling reduces (enhances) superconductivity for electron (hole) doping. Our results imply that hole doping is more promising to achieve a higher transition temperature. Experimental perspectives are discussed., Comment: 6 pages, 6 color figures

Majorana fermions have been intensively studied in recent years for their importance to both fundamental science and potential applications in topological quantum computing1,2. Majorana fermions are predicted to exist in a vortex core of superconducting topological insulators3. However, they are extremely difficult to be distinguished experimentally from other quasiparticle states for the tiny energy difference between Majorana fermions and these states, which is beyond the energy resolution of most available techniques. Here, we overcome the problem by systematically investigating the spatial profile of the Majorana mode and the bound quasiparticle states within a vortex in Bi2Te3/NbSe2. While the zero bias peak in local conductance splits right off the vortex center in conventional superconductors, it splits off at a finite distance ~20nm away from the vortex center in Bi2Te3/NbSe2, primarily due to the Majorana fermion zero mode. While the Majorana mode is destroyed by reducing the distance between vortices, the zero bias peak splits as a conventional superconductor again. This work provides strong evidences of Majorana fermions and also suggests a possible route to manipulating them., Comment: 16 pages, 4 figures

We constructed tight-binding models for the new superconductor SrPtAs according to first principle calculations, and by functional renormalization group we investigated the effect of electron correlations and spin-orbital coupling (SOC) in Cooper pairing. We found that out of the five $d$-orbitals, the $(xz,yz)$-orbitals are the active ones responsible for superconductivity, and ferromagnetic fluctuations enhanced by the proximity to the van Hove singularity triggers $f$-wave triplet pairing. The superconducting transition temperature increases as the Fermi level is closer to the van Hove singularity until ferromagnetism sets in. The $d$-vector of the triplet pairing component is pinned by SOC along the out-of-plane direction. Experimental perspectives are discussed., Comment: enlarged version, 10 pages, 9 color figures

By an exact formulation of tunnelling into a multi-band superconductor in terms of Green's functions, we demonstrate that the multi-band feature of the iron-based superconductors can lead to novel interference between Andreev reflections and decoherence effect of quasi-particles to Andreev reflections in a tunnelling junction. These effects depend on the relative sign of the gaps for s-wave pairing, and the sign of the Fermi velocities also matters for tunnelling along the nodal direction of d-wave gaps. Experimental probe of such effects could determine both the pairing symmetry and the relative sign of the gaps on different bands., Comment: 4 pages 3 figs, polished version, typo removed, citation fixed

Motivated by recent scanning tunneling microscopy experiments on surfaces of Bi$_{1-x}$Sb$_{x'}$\cite{yazdanistm,gomesstm} and Bi$_2$Te$_3$,\cite{kaptunikstm,xuestm} we theoretically study the electronic structure of a 3-dimensional (3D) topological insulator in the presence of a local impurity or a domain wall on its surface using a 3D lattice model. While the local density of states (LDOS) oscillates significantly in space at energies above the bulk gap, the oscillation due to the in-gap surface Dirac fermions are very weak. The extracted modulation wave number as a function of energy satisfies the Dirac dispersion for in-gap energies and follows the border of the bulk continuum above the bulk gap. We have also examined analytically the effects of the defects by using a pure Dirac fermion model for the surface states and found that the LDOS decays asymptotically faster at least by a factor of 1/r than that in normal metals, consistent with the results obtained from our lattice model., Comment: 7 pages, 5 figures

We present a general and exact formalism for finding the evolution of a quantum system subject to external telegraph noise. The various qubit decoherence rates are determined by the eigenvalues of a transfer matrix. The formalism can be applied to a qubit subject to an arbitrary combination of dephasing and relaxational telegraph noise, in contrast to existing non-perturbative methods that treat only one or the other of these limits. We present 3 applications: 1) We obtain the full qubit dynamics on time scales short compared with the enviromental correlation times. In the strong coupling cases this reveals unexpected oscillations and induced magnetization components; 2) We find in strong coupling case strong violations of the widely used relation 1/T$_2$ = 1/2T$_1$ + 1/T$_{\phi}$, which is a result of perturbation theory; 3) We discuss the effects of bang-bang and spin-echo controls of the qubit dynamics in general settings of the telegraph noises. %The result shows that these methods are not very effective in %reducing decoherence arising from a single telegraph noise. Finally, we discuss the extension of the method to the cases of many telegraph noise sources and multiple qubits. The method still works when white noise is also present., Comment: 7 pages, 6 figures, revised and extended

The recent angle-resolved photoemission measurements performed up to binding energies of the order of 1eV reveals a very robust feature: the nodal quasi-particle dispersion breaks up around 0.3-0.4eV and reappears around 0.6-0.8eV. The intensity map in the energy-momentum space shows a waterfall like feature between these two energy scales. We argue and numerically demonstrate that these experimental features follow naturally from the strong correlation effects built in the familiar t-J model, and reflect the connection between the fermi level and the lower Hubbard band. The results were obtained by a mean field theory that effectively projects electrons by quantum interference between two bands of fermions instead of binding slave particles., Comment: 5 pages 2 figs

In the under- to optimal-doping regimes of electron-doped cuprates, it was theoretically suspected that there is a coexistence of superconducting (SC) and antiferromagnetic (AFM) orders. The quasi-particle excitations could be gapped by both orders, and the effective gap is non-monotonic d-wave-like in the momentum space. Alternatively the gap was also speculated as a pure pairing gap. Using an effective microscopic model, we consider the manifestation of the quasi-particle gap in the electronic Raman spectra in a range of doping levels, where the relative strength of the SC and AFM order parameters varies. We demonstrate that from the electronic Raman spectra the effective single-particle gap can be disentangled into contributions from the two distinctive orders. This would help to tell whether the non-monotonic gap is due to the coexistence of SC and AFM orders., Comment: 5 pages, 3 figures

We report the finding of time-reversal-symmetry-breaking $d_{x^2-y^2}+ id_{xy}$ superconducting ground state in the slave-boson mean-field theory for the t-J model on triangular lattice. For $t/J=-5$ ($t/J=-9$) pairing exists for $x < 13%$ ($x, 3 figures, text polished, to appear in Phys. Rev. B

We improve a previous theory of doped Mott insulators with duality between pairing and magnetism by a further duality transform. As the result we obtained a quantum Ginzburg-Landau theory describing the Cooper pair condensate and the dual of spin condensate. We address the superconductivity by doping a Mott insulator, which we call Mott superconductivity. Some fingerprints of such novelty in cuprates are the scaling between neutron resonance energy and superfluid density, and the induced {\it quantized} spin moment by vortices or Zn impurity (together with circulating charge supper-current to be checked by experiments)., Comment: 4 pages, no figures, sequential to cond-mat/0306395

Motivated by recent discoveries of novel superconductors such as Na$_x$CoO$_2\cdot y$H$_2$O and Sr$_2$RuO$_4$, we analysize features of quasi-particle scattering due to impurities and interfaces for possible gapful $d_{x^2-y^2}+id_{xy}$ and $p_x+ip_y$ Cooper pairing. A bound state appears near a local impurity, and a band of bound states form near an interface. We obtained analytically the bound state energy, and calculated the space and energy dependent local density of states resolvable by high-resolution scanning tunnelling microscopy. For comparison we also sketch results of impurity and surface states if the pairing is nodal p- or d-wave., Comment: 4 pages, 4 figures

The nanometer-scale gap inhomogeneity revealed by recent STM images of BSCCO surface suggests that the ``gap coherence length'' is of that order. Thus a robust pairing gap can develop despite the poorly screened Coulomb interaction. This can be taken as an evidence that the pairing in high $T_c$ materials occurs primarily in the neutral (spin) sector. We provide theoretical support for this point of view., Comment: 4 pages, 5 figures

Within the framework of the Ginzburg-Landau theory for $d_{x^2-y^2}+id_{xy}$-wave superconductors, we discuss the pairing state phase transition in the absence of the Zeeman coupling between the Cooper pair orbital angular momentum and the magnetic field. We find that above a temperature $T_{\ast}$, the pairing state in a magnetic field is pure $d_{x^{2}-y^{2}}$-wave. However, below $T_{\ast}$, the pairing state is $d_{x^{2}-y^{2}}+id_{xy}$-wave at low fields, and it becomes pure $d_{x^{2}-y^{2}}$-wave at higher fields. Between these pairing states there exists a field driven phase transition . The transition field increases with decreasing temperature. In the field-temperature phase diagram, the phase transition line is obtained theoretically by a combined use of a variational method and the Virial theorem. The analytical result is found to be in good agreement with numerical simulation results of the Gingzburg-Landau equations. The validity of the variational method is discussed. The difference to the case with the Zeeman coupling is discussed, which may be utilized to the detection of the Zeeman coupling., Comment: 5 pages, 2 figures, submitted to PRB Brief Report

The problem of fluxon generation in Josephson junctions by a current pulse is addressed, with the help of the inverse scattering transform theory. The threshold conditions for soliton (breather or fluxon) generation are obtained analytically, with respect to relevant studies in the same direction. The reliability of the theory is examined by direct numerical experiments. Fairly good agreements exist between the theory and the numerical results, particularly in the case of semi-infinitely long junctions. Practically long (L～10λ) Josephson junctions are also explored, namely, overlap, in-line and circularly-symmetric annular junctions. Explained are those factors that complicate the generation processes suck as boundary effects, stability of soliton states against the driving current, soliton return effect and the applied magnetic field (in annular junctions only). The current pulse method is shown to be effective and practical for fluxon generation in Josephson junctions.

The effects of ＣＣｌ 4 ，ＣＨ 2 Ｃｌ 2 and ＣＨＣｌ 3 on the phosphatidycholine (PC) have been studied by means of ultraviolet spectroscopy. The spectra show one maximum of PC in ＣＣｌ 4 and two maxima of PC in ＣＨ 2 Ｃｌ 2 and in ＣＨＣｌ 3 . The properties of the maxima of the spectra can be explained. The collective state of PC molecule in membrane can also be examined.

The dynamics of rotationally symmetric sine Gordon solitons of large radius under poten-tial and dissipative perturbations is considered, with the help of a collective-coordinate desc-ription of the soliton and the Lagrangian variation method. The particle-like character of the soliton is emphasized The equation of motlon and in particular, the general momentum of the soliton are obtained in a canonical manner. It is possible to discuss the dynamics of the soliton even without applying the explicit form of the perturbating potential All dyna-mical regimes in the phase space are explored. Such phenomena as the soliron return effect, soliton escaping and saddle point are addressed In the presence of dissipation, the corrected equation of soliton motion is obtained from the generalized variational equation. Finally, the application of the theoretical treatment is considered for the fluxon dynamics in a circularly symmetric Josephson junction. The analytical results are examined by direct numerical simu-lations, fairly good agreements being achieved. it turns out that the presented ueaMnem provides a reliable description of the dynamics of the sol tons considered.

Thermal fluctuations in a Josephson-fluxon oscillator are considered with emphasises on the stochastic dynamics of fluxon and the non-trivial continuum-mode excitations. Analytical expressions for the radiation line-width of the oscillator are derived from perturbation theory and standard stochastic process theory. The averaged kinetic energy of a low-velocity fluxon is shown to be kBT/2. The continuum excitations are explored in the framework of the inverse scattering transform approach. The averaged energy per wave mode turns out to be kBT,and this justifies the adiabatic approximation applied in the fluxon stochastic dynamics.

We have analysed the circularly symmetric sine-Gordon equation with bias and dissipation by means of a simplified perturbation theory. Analytic solutions that describe the dynamical behaviour of a quasisoliton trapped within the annular junction have been obtained. Between the results of our theory and numerical simulation, there exists a good agreement for the first zero field step (ZFS) in the l-V characteristic. A brief discussion of our results is also presented.

In this paper, we present a model of 2-D RICKY spin glass with nm1/21m beins the magnetic impurity concertration and 1 the mean free path (this corresponds to a large concertration of nonmagnetic defects). The specific heat and the magnetic susceptibility at low and high temperatures are calculated. The percolation theory is applied to the transition region. The broad maximum of the specific heat and the "cusp" of the magnetic susceptibility are explained.