We investigate the impurity scattering rates for quasi-particles in vortex cores of sign-reversing s-wave superconductors as a probe to detect the internal phase difference of the order parameters among different Fermi surfaces. The impurity scattering rates and coherence factors are related to quasiparticle interference effect by the scanning tunneling microscopy and spectroscopy technique. With use of the Born and Kramer-Pesch approximations for the Andreev bound states, we show that the sign-reversed forward scatterings are dominant in vortex cores. Owing to the coherence factor in vortex cores of \pm s-wave superconductors, the impurity scattering rate of the Andreev bound states has a characteristic distribution on the Fermi surfaces. For comparison, the impurity scattering rates in vortex cores of s-wave and d-wave superconductors are also discussed.
We study the impurity effects on the transition temperature Tc with use of the T-matrix approximation. We propose a way to visualize the multi-orbital effect by introducing the hybridization function characterizing the multi-orbital effect for the impurity scattering. Characterizing function does not depend on the superconducting pairing symmetry, since this function is defined by the eigenvectors in normal states. The result indicates that an impurity-robust superconductivity does not necessarily imply a sign- preserving pairing. Visualizing the hybridization effect in the effective five-band…
What is the fundamental reason for Hall Anomaly in Type II Superconductors: Independent Vortex Dynamics Effect or a Manifestation of Vortex Many-Body Effect? For a long time researchers in this field had not realized the importance of vortex many-body effects in the understanding of the so-called anomalous Hall effect. In this note I give a brief account of the situation in the light of a recent Phys Rev Lett.
To understand the impurity effect on Tc in FeAs superconductors, we analyze a simple two-band BCS model with repulsive interband interaction. The realized fully-gapped superconducting state with sign reversal, which is predicted by spin fluctuation theories in this compound, is suppressed by impurities due to the interband hopping of Cooper pairs, if the interband impurity scattering $I'$ is equal to the intraband one $I$. When $|I'/I| < 1$, in highly contrast, Tc is almost unchanged by strong impurity scattering since the interband scattering is almost prohibited by the multiple scattering ef…
The sign-reversing fully gapped superconducting state, which is expected to be realized in oxypnictide superconductors, can be prominently affected by nonmagnetic impurities due to the interband scattering of Cooper pairs. We study this problem based on the isotropic two-band BCS model: In oxypnictide superconductors, the interband impurity scattering $I'$ is not equal to the intraband one $I$. In the Born scattering regime, the reduction in Tc is sizable and the impurity-induced density of states (DOS) is prominent if $I\sim I'$, due to the interband scattering. Although impurity-induced DOS …
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…
We explain that the study of impurity effect in iron pnictides are correctly calculated based on the T-matrix approximation, contrary to the Comment by Bang. The replacement T with T-I proposed by Bang breaks the perturbation theory and is therefore erroneous.
We theoretically study a non-magnetic impurity effect on the vortex bound states of a multi-quantum vortex. The zero-energy peak of the local density of states is investigated for vortex cores with the winding numbers 2 and 4 within the framework of the quasiclassical theory of superconductivity. We find that the zero-energy peaks, which appear away from the vortex center in the clean limit, move towards the vortex center with increasing the impurity scattering rate, resolving a contradiction between an experimental result and previous theoretical predictions.
We numerically study the effect of non-magnetic impurities on the vortex bound states in noncentrosymmetric systems. The local density of states (LDOS) around a vortex is calculated by means of the quasiclassical Green's function method. We find that the zero energy peak of the LDOS splits off with increasing the impurity scattering rate.
We pointed out that the main claim of Ref.[1] that the presence of the orbital degree of freedom is essential to describe the correct impurity effects for Iron-based superconductors is incorrect and demonstrated the equivalent results of Tc suppression due to impurities by both the band basis model and the orbital basis model.
We study the subgap spectrum of a 2D Abrikosov vortex in an s-wave superconductor in the absence and presence of a point impurity. By solving the Eilenberger equations without impurity for two models of the vortex (including a self-consistent one), we find multiple subgap spectral branches. The number of these branches may be arbitrary large provided that the magnetic field screening length is large enough. The quasiclassical spectrum of the vortex has a local gap with a width of the order of the bulk gap and a spatial extent of several coherence lengths. The existence of such gap is the prere…
The low-temperature shrinking of the vortex core (Kramer-Pesch effect) is studied for an isolated single vortex for chiral p-wave and s-wave superconducting phases. The effect of nonmagnetic impurities on the vortex core radius is numerically investigated in the Born limit by means of a quasiclassical approach. It is shown that in the chiral p-wave phase the Kramer-Pesch effect displays a certain robustness against impurities owing to a specific quantum effect, while the s-wave phase reacts more sensitively to impurity scattering. This suggests chiral p-wave superconductors as promising candid…
We study the effects of non-magnetic impurity scattering on the Andreev bound states (ABS) in an isolated vortex in a two-dimensional chiral p-wave superconductor numerically. We incorporate the impurity scattering effects into the quasiclassical Eilenberger formulation through the self-consistent $t$-matrix approximation. Within this scheme, we calculate the local density of states (LDOS) around two types of vortices: "parallel" ("anti-parallel") vortex where the phase winding of the pair-potential coming from vorticity and that coming from chirality have the same (opposite) sign. When the sc…
We theoretically investigate a non-magnetic impurity effect on the temperature dependence of the vortex core shrinkage (Kramer-Pesch effect) in a single-band s-wave superconductor. The Born limit and the unitary limit scattering are compared within the framework of the quasiclassical theory of superconductivity. We find that the impurity effect inside a vortex core in the unitary limit is weaker than in the Born one when a system is in the moderately clean regime, which results in a stronger core shrinkage in the unitary limit than in the Born one.
We perform large-scale numerical calculations self-consistently solving the Bogoliubov-de Gennes (BdG) equations in the magnetic field together with random impurities to directly demonstrate the typical quasi-particle interference (QPI) in the presence of vortices as observed by scanning tunneling microscopy/spectroscopy experiments in unconventional superconductors. The calculations reveal that vortex itself never works as a scatter causing the QPI pattern but vortex core containing impurity brings about the enhancement of the sign-preserving QPI peaks. Its origin is Andreev bound-states dist…
Based on the five-orbital model, we study the effect of local impurity in iron pnictides, and find that the interband impurity scattering is promoted by the d-orbital degree of freedom. This fact means that the fully-gapped sign-reversing s-wave state, which is predicted by spin fluctuation theories, is very fragile against impurities. In the BCS theory, only 1% impurities with intermediate strength induce huge pair-breaking, resulting in the large in-gap state and prominent reduction in Tc, contrary to the prediction based on simple orbital-less models. The present study provides a stringent …
The vortex state thermal and transport properties of the high T_c copper oxides can be understood in a d-wave gap model and are dominated by the extended quasiparticle states that exist along the nodal directions in momentum space. The Doppler shift on these states due to the circulating supercurrents around the vortex core, introduces new van Hove ridges into the energy dependent local density of states (LDOS) as a function of distance in the region between cores. We emphasize the topology of these ridges and the effect on them of local impurity scattering in Born and unitary limit. We treat …
We report a nontrivial transition in the core structure of vortices in two-band superconductors as a function of interband impurity scattering. We demonstrate that, in addition to singular zeros of the order parameter, the vortices there can acquire a circular nodal line around the singular point in one of the superconducting components. It results in the formation of the peculiar "moat"-like profile in one of the superconducting gaps. The moat-core vortices occur generically in the vicinity of the impurity-induced crossover between $s_{\pm}$ and $s_{++}$ states.
Thermal transport measurements have been performed on single-crystalline Co-doped BaFe2As2 down to 0.1 K and under magnetic fields up to 7 T. Significant peak anomalies are observed in both thermal conductivity and thermal Hall conductivity below Tc as an indication of the enhancement of the quasiparticle mean-free path. Moreover, we find a sizable residual T-linear term in thermal conductivity, possibly due to a finite quasiparticle density of states in the superconducting gap induced by impurity pair breaking. Our findings support a pairing symmetry compatible with the theoretically predicte…
Based on a two-orbital model and taking into account the presence of the impurity, we studied theoretically the electronic structure in the vortex core of the iron-Pnictide superconducting materials. The vortex is pinned when the impurity is close to the vortex core. The bound states shows up for the unpinned vortex and are wiped out by a impurity. Our results are in good agreement with recent experiments and present a consistent explanation for the different electronic structure of vortex core revealed by experiments on different materials.
We respond to P. Ao's comment in arXiv:1907.09263, which suggests that vortex many-body effects are the origin of Hall sign reversal in few-unit-cell thick Bi-2212 cuprate crystals (Phys. Rev. Lett. 122, 247001 (2019)). Our experimental results are incompatible with the theoretical predictions detailed in Ao's comment.
We develop a scheme of Gor'kov Green's functions to treat impurity effects on Caroli-de Gennes-Matricon (CdGM) mode in superconductors (SCs) by improving the Kopnin-Kravtsov scheme with respect to the coherence factors and applicability to various SCs. We can study the impurity effects keeping the discreteness of the energy spectrum in contrast to the quasiclassical theory. We can thus apply this scheme to the SCs with the small quasiclassical parameter $k_{\mathrm{F}}ξ_{0}$ (which is the product of the Fermi wavenumber $k_{\mathrm{F}}$ and the coherence length $ξ_{0}$ in pure SC at zero tempe…
We study impurity effects in vortex core of two-dimensional moderately clean su perconductors within the quasiclassical theory. The impurity scattering rate $\G amma(E)$ of the Andreev bound states in vortex core with +1 vorticity of p-wav e superconductors with ${\mib d}=\hat{\mib z}(p_x+\iu p_y)$ is suppre ssed, compared to the normal state scattering rate $Γ_{\rm n}$ in the energ y region $Γ_{\rm n}^3/E_δ^2\ll E\ll E_δ\equiv |δ_0|Δ_ınfty$ with scattering phase shift $δ_0$ $(|δ_0|\ll 1)$ and the pair-po tential in bulk $Δ_\infty$. Further we find that $Γ(E)/Γ_{\rm n}$ for p-wave superconduct…
The impurity problems within vortex cores of two-dimensional s-wave and chiral p-wave superconductors are studied numerically in the framework of the quasiclassical theory of superconductivity and self-consistent Born approximation under a trial form of the pair potential. The dispersion and impurity scattering rate (the inverse of the relaxation time) of the Andreev bound state localized in vortex cores are deduced from the angular-resoloved local density of states. The energy dependence of the impurity scattering rates depends on the pairing symmetry; particularly, in the chiral p-wave vorte…
We study the impurity effects on the Caroli-de Gennes-Matricon (CdGM) states, particularly on the level spacings in a vortex core in topological s-wave superconductor (SC) by two means, numerically and analytically. The topological s-wave SC belongs to the same class as a chiral p-wave SC and thus there are two inequivalent vortices in terms of any symmetry operation. We take into account this inequivalence and numerically calculate the scattering rates based on an improved version of Kopnin-Kravtsov (iKK) scheme, which enables us to treat the discrete levels in the presence of white-noise dis…
We investigate charge densities around the vortex cores of an s-wave and a chiral p-wave superconductor (SC) in two dimension within quasiclassical theory. We consider contributions of particle-hole asymmetry through gradient expansions in first order of a quasiclassical parameter using augmented quasiclassical theory. The chiral p-wave SC has two inequivalent vortices: one is charged and the other is uncharged on the basis of Bogoliubov--de Gennes (BdG) equation. We explain this qualitatively distinct charges also by the augmented quasiclassical theory. In addition, we find that much larger c…
The low temperature thermal conductivity of a d-wave superconductor is considered for arbitrary strength of the impurity potential. A random distribution of vortices is included within the usual semiclassical approach. The vortex-quasiparticle scattering is accounted for phenomenologically, in addition to impurity scattering. Application of the theory to recent data on high purity YBa$_{2}$Cu$_{3}$O$_{6.99}$ shows excellent agreement with experiment, both in zero field and in the presence of an applied magnetic field. We find that the strength of the impurity potential required to describe the…
The vortices of two-dimensional chiral $p$-wave superconductors are predicted to exhibit some exotic behaviors; one of their curious features is the existence of two types of vortices (each vortex has vorticity either parallel or antiparallel to the Cooper pair's chirality) and the robustness of the antiparallel vortices against nonmagnetic Born-like impurities. In this work, we study the impurity effect on the vortex of the chiral $p$-wave superconductors through the quasiclassical Green's function formalism. We take account of impurities via the self-consistent $t$-matrix approximation so th…
We study the vortex lattice in a two-dimensional s-wave topological superconductor with Rashba spin-orbit coupling and Zeeman field by solving the Bogoliubov-de Gennes equations self-consistently for the superconducting order parameter. We find that when spin-orbit coupling is relatively weak, one of the two underlying chiralities in the topological superconducting state can be strongly manifest in the vortex core structure and govern the response of the system to vorticity and a nonmagnetic impurity where the vortex is pinned. The Majorana zero mode in the vortex core is found to be robust ag…
In a p-wave Fermi superfluid suffering from the nonmagnetic impurity scatterings, a coefficient of a gradient term becomes divergent upon cooling. Consequences of this divergent rigidity in the stable vortices in the B phase in globally isotropic aerogel are considered where the "impurity scattering" events are brought by the aerogel structure. For a moderately strong "impurity scatterings", the superfluid transition line T_c(P) has a quantum critical point at a low but finite pressure. We find that, with decreasing T_c via the lowering of the pressure, the distance between the half cores comp…
The interplay of magnetic impurity and vortex in a topological superconductor is of fundamental interest with major implications for implementing quantum computation. There are multiple degrees of freedom interacting with the impurity in the system, including the Majorana zero mode (MZM), the Caroli de Gennes Matricon (CdGM) states, and the electron bulk states that form Cooper pairs, which makes the impurity pinned vortex state elusive to date in topological superconductors. Here, we present an accurate solution of the problem, based on a generalized mapping scheme and the density-matrix reno…
We show that the Wiedemann-Franz law is violated at zero temperature in the vortex state of a d-wave BCS superconductor with isotropic impurity scattering. We use a semiclassical approach to include the Doppler shift experienced by the quasiparticles due to the circulating supercurrents and consider as well the Andreev scattering from an array of vortices assumed to be randomly distributed. We also show that the vertex corrections to the electric conductivity, which can be large when there is significant anisotropy in the impurity scattering, become unimportant as the magnetic field is increas…
The thermal conductivity $κ$ is calculated for the Abrikosov vortex lattice with d-wave pairing. The Andreev scattering rate arises from the self energy term in Gorkov's integral equation for the corresponding Green's function. The impurity scattering rate is calculated self-consistently from this Green's function in the t-matrix approximation. Neither point-like impurity scattering with a phase shift in the almost unitary limit nor in the Born limit can consistently explain recent zero-field and finite-field measurements of $κ/T$ at low $T$ in ultraclean YBCO. Our theory also applies to the s…
Motivated by the recent experiments that reported the discovery of vortex Majorana bound states (vMBSs) in iron-based superconductors, we establish a portable scheme to unveil the non-Abelian statistics of vMBSs using normal fermionic modes. The unique non-Abelian statistics of vMBSs is characterized by the charge flip signal of the fermions that can be easily read out through the charge sensing measurement. In particular, the charge flip signal will be significantly suppressed for strong hybridized vMBSs or trivial vortex modes, which efficiently identifies genuine vMBSs. To eliminate the err…
The specific heat coefficient gamma_s(H) and the electronic thermal conductivity kappa_{es}(H) are calculated for Abrikosov's vortex lattice by taking into account the effects of supercurrent flow and Andreev scattering. First we solve the gap equation for the entire range of magnetic fields. We take into account vertex corrections due to impurity scattering calculated in the Born approximation. The function gamma_s(H)/gamma_n increases from zero and becomes approximately linear above H/H_{c2} \sim 0.1. The dependence on impurity scattering is substantially reduced by the vertex corrections. T…
Using the semiclassical approach to the energy levels of the fermions bound to the vortex core, we found the difference between the states in nonchiral and chiral superconductors, determined by the Berry phase. The bound states of fermions in the singly quantized vortex in the layered superconductor with the symmetry of superfluid 3He-A is E=nω_0 (as distinct from E=(n+1/2)ω_0 in s-wave superconductor) and thus contains the state with exactly zero energy. This is in accordance with the result obtained in microscopic theory by Kopnin and Salomaa. Using this approach for calculations of the effe…
We develop an alternative method to solve the Eilenberger equations numerically for the vortex-lattice states of type-II superconductors. Using it, we clarify the magnetic-field and impurity-concentration dependences of the magnetization, the entropy, the Pauli paramagnetism, and the mixing of higher Landau levels in the pair potential for two-dimensional $s$- and $d_{x^2-y^2}$-wave superconductors with the cylindrical Fermi surface.
We present the results of a microscopic calculation of the longitudinal thermal conductivity of quasiparticles, $κ_{xx}$, in a 2D d-wave superconductor in the vortex state. Our approach takes into account both impurity scattering and a contribution to the thermal transport lifetime due to the scattering of quasiparticles off of vortices. We compare the results with the experimental measurements on high-T$_c$ cuprates and organic superconductors.
Both impurity- and magnetic-field-induced quasiparticle states in chiral $p$-wave superconductors are investigated theoretically by solving the Bogoliubov--de Gennes equations self-consistently. At the strong scattering limit, we find that a universal state bound to the impurity can be induced for both a single nonmagnetic impurity and a single magnetic impurity. Furthermore, we find that different chiral order parameters and the corresponding supercurrents have uniform distributions around linear impurities. Calculations of the local density of states in the presence of an external magnetic f…
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 impurit…
We numerically show that the zero-energy Majorana surface states are suppressed around a vortex in the three-dimensional topological superconductors such as Cu$_{x}$Bi$_{2}$Se$_{3}$ and Sn$_{1-x}$In$_{x}$Te. On the other hand, the zero-energy Majorana bound states along the vortex line are robust against cut by the surface. The suppression of the surface bound states is similar to that with a magnetic impurity on the surface of the topological insulator. The suppression of the surface-bound states around a vortex can be observed as the unconventional energy dependence of imaging of the scannin…
We show that the Wiedemann-Franz law is violated in the vortex state of a d-wave superconductor at zero temperature. We use a semiclassical approach, which includes the Doppler shift on the quasiparticles as well as the Andreev scattering from a random distribution of vortices. We also show that the vertex corrections to the electrical conductivity due to the anisotropy of impurity scattering become unimportant in the presence of a sufficiently large magnetic field.
We show that standard impurities, magnetic or nonmagnetic, weak or strong, can cause topological phase transitions inside the vortex cores of a conventional s-wave superconductor. Because of the nonzero angular momentum of Cooper pairs in the vortex cores, the vortex bound states in a two dimensional superconductor are sensitive to impurities in a way similar to the Yu-Shiba-Rusinov bound states induced by magnetic impurities. In three dimensional cases, the vortex bound states can be driven into topologically nontrivial phases by an impurity chain inside the vortex core. The system can host M…
We investigate two-dimensional Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to an additional depletion of the superfluid density. We demonstrate the existence of the intermediate superfluid state where the condensate and localized bosons present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto the three dimensiona…
Impurity injection into superfluid helium is a simple yet unique method with diverse applications, including high-precision spectroscopy, quantum computing, nano/micro materialsynthesis, and flow visualisation. Quantised vortices are believed to play a major role in the interaction between superfluid helium and light impurities. However, the basic principle governing the interaction is still controversial for dense materials such as semiconductor and metal impurities. Herein, we provide experimental evidence of the attraction of the dense silicon nanoparticles to the quantised vortex cores. We…
We investigate the dynamics of a quantized vortex and a nuclear impurity immersed in a neutron superfluid within a fully microscopic time-dependent three-dimensional approach. The magnitude and even the sign of the force between the quantized vortex and the nuclear impurity have been a matter of debate for over four decades. We determine that the vortex and the impurity repel at neutron densities, 0.014 fm$^{-3}$ and 0.031 fm$^{-3}$, which are relevant to the neutron star crust and the origin of glitches, while previous calculations have concluded that the force changes its sign between these …
The magneto-thermal conductivity kappa is calculated for the vortex state of UPd_2Al_3 by assuming horizontal gap nodes. The Green's function method we employed takes into account the effects of supercurrent flow and Andreev scattering on the quasiparticles due to Abrikosov's vortex lattice order parameter. The calculated angular dependence of kappa_{yy} for field rotation theta_0 in the ac-plane depends strongly on field strength H, impurity scattering, anisotropy of the Fermi velocity, and temperature. For finite temperatures and the clean unitary scattering limit we get qualitative agreemen…
The local quasiparticle spectra around the vortex core of a d-wave superconductor in the mixed state is studied by solving the lattice Bogoliubov-de Gennes equations self-consistently. It is shown that in addition to the zero-energy states, there also exist core states of high angular momentum. A nonmagnetic unitary impurity sitting at the core center is nondestructive to these core states and the zero-energy resonant state induced by itself is still visible in the local quasiparticle spectrum. The calculated imaging shows a fourfold ``star'' shape of the local density of states whose orientat…
In the superclean case the spectrum of vortex core excitations in the presence of disorder is not random but consists of two series of equally-spaced levels. The I-V characteristics of such superconductors displays many interesting phenomena. A series of resonances is predicted at frequencies commensurate with the spacing of the vortex excitations. These resonances reveal an even-odd anomaly. In the presence of one weak impurity the excitation levels can approach each other and almost cross. Absorption at very low frequencies is identified with the resonances arising in this case. The results …
From the spatial structure of vortex lattice state calculated by Eilenberger theory, we study the resonance line shape of Knight shift of the paramagnetic moments in the s-wave and the d-wave superconductors, comparing with the Redfield pattern of the internal field distribution. We discuss the deviation from the temperature dependence of the Yosida function, and the magnetic field dependence of the paramagnetic susceptibility. In addition to the calculation in the clean limit, influences of the impurity scattering are estimated in the Born limit and in the unitary limit. These results are hel…
We calculate the dependence of the interlayer quasiparticle conductivity, $σ_q$, in a Josephson coupled d-wave superconductor on the magnetic field B||c and the temperature T. We consider a clean superconductor with resonant impurity scattering and a dominant coherent interlayer tunneling. When pancake vortices in adjacent layers are weakly correlated at low T the conductivity increases sharply with B before reaching an extended region of slow linear growth, while at high T it initially decreases and then reaches the same linear regime. For correlated pancakes $σ_q$ increases much more strongl…
In an accompanying paper [arXiv:0903.0011v1] we have studied the equilibrium properties of vortices in a chiral quasi-twodimensional triplet superfluid/superconductor. Here we extend our studies to include the dynamical response of a vortex core in a chiral triplet superconductor to an external a.c. electromagnetic field. We consider in particular the response of a doubly quantized vortex with a homogeneous core in the time-reversed phase. The external frequencies are assumed to be comparable in magnitude to the superconducting gap frequency, such that the vortex motion is non-stationary but c…
We derive the generalized Ginzburg-Landau free energy functional for conventional and unconventional singlet superconductors in the presence of paramagnetic, orbital and impurity effects. Within the mean field theory, we determine the criterion for appearence of the non uniform (Fulde-Ferrell-Larkin-Ovchinnikov) superconducting state, with vortex lattice structure and additional modulation along the magnetic field. We also discuss the possible change of the order of transition from normal to superconducting state. We find that the superconducting phase diagram is very sensitive to geometrical …
We fabricate van der Waals heterostructure devices using few unit cell thick Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ for magnetotransport measurements. The superconducting transition temperature and carrier density in atomically thin samples can be maintained to close to that of the bulk samples. As in the bulk sample, the sign of the Hall conductivity is found to be opposite to the normal state near the transition temperature but with a drastic enlargement of the region of Hall sign reversal in the temperature-magnetic field phase diagram as the thickness of samples decreases. Quantitative analysis of …
In light of recent proposals to realize a topological superconductor on the surface of strong topological insulators, we study impurity and vortex scattering in two dimensional topological superconductivity. We develop a theory of quasiparticle interference in a model of the surface of a three dimensional strong topological insulator with a pairing term added. We consider a variety of different scatterers, including magnetic and nonmagnetic impurity as well as a local pairing order parameter suppression associated with the presence of a vortex core. Similar to the case of a surface of a three …
We investigate the multiquantum vortex states in type-II superconductor both in "clean" and "dirty" regimes defined by impurity scattering rate. Within quasiclassical approach we calculate self-consistently the order parameter distributions and electronic local density of states (LDOS) profiles. In the clean case we find the low temperature vortex core anomaly predicted analytically in G.E. Volovik, JETP Lett. {\bf 58}, 455 (1993) and obtain the interference patterns in LDOS distributions analogous to found previously in the framework of Bogolubov-de Gennes theory. In dirty regime the multiqua…
The pair-potential and current density around a single vortex of the two-dimensional chiral p-wave superconductor with ${\mib d}={\mib z}(p_x \pm \iu p_y)$ are determined self-consistently within the quasiclassical theory of superconductivity. Shrinking of the vortex core at low temperatures are considered numerically and analytically. Temperature-dependences of the spatial variation of pair-potential and circular current around the core and density of states at zero energy are the same as those in the isotropic s-wave case. When the senses of vorticity and chirality are opposite, however, we …
