Impurity state in the vortex core of d-wave superconductors: Anderson impurity model versus unitary impurity model

Using an extended Anderson/Kondo impurity model to describe the magnetic moments around an impurity doped in high-$T_{\text{c}}$ d-wave cuprates and in the framework of the slave-boson meanfield approach, we study numerically the impurity state in the vortex core by exact diagonalization of the well-established Bogoliubov-de Gennes equations. The low-energy impurity state is found to be good agreement with scanning tunnelingmicroscopy observation. After pinning a vortex on the impurity site, we compare the unitary impurity model with the extended Anderson impurity model by examining the effect of the magnetic field on the impurity state. We find that the impurity resonance in the unitary impurity model is strongly suppressed by the vortex; while it is insensitive to the field in the extended Anderson impurity model.Comment: 8 pages, 3 figure

Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model, we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat, $C_{\rm imp}$, to be calculated accurately from local static correlation functions; specifically via $C_{\rm imp}=\frac{\partial E_{\rm ionic}}{\partial T} + 1/2\frac{\partial E_{\rm hyb}}{\partial T}$, where $E_{\rm ionic}$ and $E_{\rm hyb}$ are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to $C_{\rm imp}$. For the non-degenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The new approach could also be of interest within other impurity solvers, e.g., within quantum Monte Carlo techniques.Comment: 16 pages, 15 figures, published versio

Motion of an impurity particle in an ultracold quasi-one-dimensional gas of hard-core bosons

The low-lying eigenstates of a one-dimensional (1D) system of many impenetrable point bosons and one moving impurity particle with repulsive zero-range impurity-boson interaction are found for all values of the impurity-boson mass ratio and coupling constant. The moving entity is a polaron-like composite object consisting of the impurity clothed by a co-moving gray soliton. The special case with impurity-boson interaction of point hard-core form and impurity-boson mass ratio $m_i/m$ unity is first solved exactly as a special case of a previous Fermi-Bose (FB) mapping treatment of soluble 1D Bose-Fermi mixture problems. Then a more general treatment is given using second quantization for the bosons and the second-quantized form of the FB mapping, eliminating the impurity degrees of freedom by a Lee-Low-Pines canonical transformation. This yields the exact solution for arbitrary $m_i/m$ and impurity-boson interaction strength.Comment: 4 pp., 2 figures, revtex4; error in Eq.(6) corrected and derivation simplifie

Impurity-induced resonant states in topological nodal-line semimetals

Nodal-line semimetals are characterized by a kind of topologically nontrivial bulk-band crossing, giving rise to almost flat surface states. Yet, a direct evidence of the surface states is still lacking. Here we study theoretically impurity effects in topological nodal-line semimetals based on the T-matrix method. It is found that for a bulk impurity, some in-gap states may be induced near the impurity site, while the visible resonant impurity state can only exist for certain strength of the impurity potentials. For a surface impurity, robust resonant impurity states exist in a wide range of impurity potentials. Such robust resonant states stem from the topological protected weak dispersive surface states, which can be probed by scanning tunneling microscopy, providing a strong signature of the topological surface states in the nodal-line semimetals.Comment: 7 pages, 5 figure

Single Impurity Effects in Multiband Superconductors with Different Sign Order Parameters

A single impurity problem is investigated for multiband s-wave superconductors with different sign order parameters (+-s-wave superconductors) suggested in Fe-pnictide superconductors. Not only intraband but also interband scattering is considered at the impurity. The latter gives rise to impurity-induced local boundstates close to the impurity. We present an exact form of the energy of the local boundstates as a function of strength of the two types of impurity scattering. The essential role of the impurity is unchanged in finite number of impurities. The main conclusions for a single impurity problem help us understand effects of dense impurities in the +-s-wave superconductors. Local density of states around the single impurity is also investigated. We suggest impurity site nuclear magnetic resonance as a suitable experiment to probe the local boundstates that is peculiar to the +-s-wave state. We find that the +-s-wave model is mapped to a chiral dx2-y2+-idxy-wave, reflecting the unconventional nature of the sign reversing order parameter. For a quantum magnetic impurity, interband scattering destabilizes the Kondo singlet.Comment: 23 pages, 7 figures, to be published in J. Phys. Soc. Jpn. (2009) No.

Two regimes for effects of surface disorder on the zero-bias conductance peak of tunnel junctions involving d-wave superconductors

Impurity-induced quasiparticle bound states on a pair-breaking surface of a d-wave superconductor are theoretically described, taking into account hybridization of impurity- and surface-induced Andreev states. Further a theory for effects of surface disorder (of thin impurity surface layer) on the low-bias conductance of tunnel junctions is developed. We find a threshold $n_c$ for surface impurity concentration $n_S$, which separates the two regimes for surface impurity effects on the zero-bias conductance peak (ZBCP). Below the threshold, surface impurities do not broaden the ZBCP, but effectively reduce its weight and generate impurity bands. For low $n_S$ impurity bands can be, in principle, resolved experimentally, being centered at energies of bound states induced by an isolated impurity on the surface. For larger $n_S$ impurity bands are distorted, move to lower energies and, beginning with the threshold concentration $n_S=n_c$, become centered at zero energy. With increasing $n_S$ above the threshold, the ZBCP is quickly destroyed in the case of strong scatterers, while it is gradually suppressed and broaden in the presence of weak impurity potentials. More realistic cases, taking into account additional broadening, not related to the surface disorder, are also considered.Comment: 9 pages, 7 figure