Altermagnetic superconductors offer the possibility of exploring unconventional superconductivity, including topological states and finite-momentum superconductivity, with promising applications in spintronics and quantum information. However, a direct experimental confirmation of their existence remains elusive. In this work, we propose non-magnetic impurities as probes of the interplay between altermagnetism and superconductivity. These impurities induce spin-polarized subgap states whose spatial extension reflects the magnetic order of the substrate material. Depending on whether or not the impurity respects the bulk symmetries, these states form spin-degenerate or spin-split doublets. An external magnetic field aligned with the Néel vector can further control the doublet splitting. We further demonstrate that coupling between impurity states leads to a position-dependent, spin-sensitive hybridization, enabling another approach for \textit{in situ} control of atomic-size quantum devices. These findings provide unambiguous experimental signatures of altermagnetic superconductivity accessible via local measurements such as scanning tunneling microscopy and open unexplored pathways for designing tunable quantum devices.
Altermagnetic spin textures coupled to superconductors: Domain wall spin-triplet superconductivity and supercurrent-induced torques
Hearne Institute of Theoretical Physics, Department of Physics & Astronomy, Louisiana State University（路易斯安那州立大学物理与天文学系赫恩理论物理研究所）；Institute for Theoretical Physics III, University of Stuttgart（斯图加特大学理论物理第三研究所）
研究与传统 s 波超导体耦合的交变磁体中库珀对形式，考虑交变磁序参量空间不均匀性，发现超导性受交变磁畴影响，有三重态热点等，还存在超电流与交变磁序的相互作用，为相关研究提供独特机会。
Inherent momentum-dependent gap structure of altermagnetic superconductors
Niels Bohr Institute, University of Copenhagen（尼尔斯·玻尔研究所，哥本哈根大学）；Department of Physics, University of Wisconsin–Milwaukee（威斯康星大学密尔沃基分校物理系）；Department of Physics and Astronomy, Uppsala University（乌普萨拉大学物理与天文学系）
Abrikosov vortices in altermagnetic superconductors
Centro de Física de Materiales (CFM-MPC) Centro Mixto CSIC-UPV/EHU（材料物理中心（CFM-MPC）CSIC-巴斯克国立大学混合中心）；Donostia International Physics Center (DIPC)（圣塞巴斯蒂安国际物理中心）
Altermagnetic superconducting diode effect from non-collinear compensated magnetism in Mn$_3$Pt
Hearne Institute of Theoretical Physics, Department of Physics & Astronomy, Louisiana State University（路易斯安那州立大学）；Department of Physics, Indian Institute of Technology Delhi（印度理工学院德里分校）；Institute for Theoretical Physics III, University of Stuttgart（斯图加特大学）
Highly anisotropic collective modes of altermagnetic superconductors with Bogoliubov Fermi surfaces
Centre for Theoretical and Computational Physics, College of Physics, Qingdao University（青岛大学物理学院理论计算物理中心）；Centre for Quantum Technology Theory, Swinburne University of Technology（斯威本科技大学量子技术理论中心）
Recently topological superconducting states has attracted a lot of interest. In this work, we consider a topo- logical superconductor with $Z_2$ topological mirror order [1] and s$\pm$-wave superconducting pairing symmetry, within a two-orbital model originally designed for iron-based superconductivity [2]. We predict the existence of gapless edge states. We also study the local electronic structure around an adsorbed interstitial magnetic impurity in the system, and find the existence of low-energy in-gap bound states even with a weak spin polar- ization on the impurity. We also discuss the r…
We study a chain of magnetic impurities on a conventional superconductor with spin-orbit coupling, treating the superconducting order fully self-consistently. We find and quantify strong hybridization between the topological edge Majorana bound states (MBSs) and in-gap Yu-Shiba-Rusinov (YSR) states, which causes increasing energy oscillations as a function of magnetic impurity strength, even when the direct MBS overlap is negligible. By treating the MBS as a topological boundary state, dependent only on the effective mass gap, we arrive at a fully parameter-free functional form of the its loca…
Spin transport in a normal meta-altermagnetic superconducting nanowire junction
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Hefei National Laboratory（合肥国家实验室）；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）
We address the question of whether individual nonmagnetic impurities can induce zero-energy states in time-reversal-invariant topological superconductors, and define a class of symmetries which guarantee the existence of such states for a specific value of the impurity strength. These symmetries allow the definition of a position-space topological Z_2 invariant, which is related to the standard bulk topological Z_2 invariant. Our general results are applied to the time-reversal-invariant p-wave phase of the doped Kitaev-Heisenberg model, where we demonstrate how a lattice of impurities can dri…
The Andreev reflection amplitude at a clean interface between a half-metallic ferromagnet (H) and a superconductor (S) for which the half metal's magnetization has a gradient perpendicular to the interface is proportional to the excitation energy $\varepsilon$ and vanishes at $\varepsilon=0$ [Béri {\em et al.}, Phys.\ Rev.\ B {\bf 79}, 024517 (2009)]. Here we show that the presence of impurities at or in the immediate vicinity of the HS interface leads to a finite Andreev reflection amplitude at $\varepsilon=0$. This impurity-assisted Andreev reflection dominates the low-bias conductance of a …
Heterostructures allow the realization of electronic states that are difficult to obtain in isolated systems. Exemplary is the case of quasi-one-dimensional heterostructures formed by a superconductor and a semiconductor with spin-orbit coupling in which Majorana zero-energy modes can be realized. We study the effect of a single impurity on the spectrum of superconducting heterostructures. We find that the coupling between the superconductor and the semiconductor can strongly affect the impurity-induced states and may induce additional subgap bound states that are not present in isolated unifo…
The order parameter of bulk two-dimensional superconductors is classified as nodal, if it vanishes for a direction in momentum space, or gapful if it does not. Each class can be topologically nontrivial if Andreev bound states are formed at the edges of the superconductor. Non-magnetic impurities in the superconductor affect the formation of Andreev bound states and can drastically change the tunneling spectra for small voltages. Here, we investigate the mean current and its fluctuations for two-dimensional tunnel junctions between a normal-metal and unconventional superconductors by solving t…
We study an Anderson impurity embedded in a d-wave superconductor carrying a supercurrent. The low-energy impurity behavior is investigated by using the numerical renormalization group method developed for arbitrary electronic bath spectra. The results explicitly show that the local impurity state is completely screened upon the non-zero current intensity. The impurity quantum criticality is in accordance with the well-known Kosterlitz-Thouless transition.
We discuss the effect of an anisotropic impurity potential on the critical temperature, local density of states in the vicinity of a single impurity, and the quasiparticle density of states for a finite impurity concentration in a d-wave superconductor. Different scattering regimes are concerned.
We study subgap states induced by a single impurity in an s-wave superconductor with suppressed pairing. For concreteness, we consider a bulk superconductor containing a normal spherical region. We find that a point impurity in this system induces two Yu-Shiba-Rusinov states inside the minigap instead of one, which one would have in a homogeneous superconductor. Moreover, the subgap states appear even if the impurity is nonmagnetic. We prove that this result actually holds almost for any superconductor with a real and spatially inhomogeneous order parameter, if the quasiparticle spectrum is ga…
We study a single impurity effect on the local density of states in a d-wave superconductor accounting for the momentum-dependent impurity potential. We show that the anisotropy of the scattering potential can alter significantly the spatial dependence of the quasiparticle density of states in the vicinity of the impurity.
We present some of the recent theoretical studies on the impurity effects in conventional superconductors, such as magnetic and ordinary impurity effects in dirty and weak localization limits, and describe successfully unexplained experimental results. We find that the critical sheet resistance for the suppression of superconductivity in thin films depends on superconductor, and point out that impurity dopings in high T_c superconductors cause a metal-insulator transition and thereby suppress T_c.
We study theoretically the effect of impurity scattering in f-wave (or E_{2u}) superconductors. The quasi-particle density of states of f-wave superconductor is very similar to the one for d-wave superconductor as in hole-doped high T_c cuprates. Also in spite of anisotropy in Delta(k), both the normalized superfluid density and the thermal conductivity is completely isotropic.
We investigate the single normal impurity effect in a superconductor by the holographic method. When the size of impurity is much smaller than the host superconductor, we can reproduce the Anderson theorem, which states that a conventional s-wave superconductor is robust to a normal (non-magnetic) impurity with small impurity strength. However, by increasing the size of the impurity in a fixed-size host superconductor, we find a decreasing critical temperature $T_c$ of the host superconductor, which agrees with the results in condensed matter literatures. More importantly, the phase transition…
Tunneling conductance spectra between a normal metal / d-wave superconductor junction under the presence of bulk impurities in the superconductor are studied. The quasiclassical theory has been applied to calculate the spatial variation of the pair potential and the effect of impurity scattering has been introduced by t-matrix approximation. The magnitude of a subdominant s-wave component at the interface is shown to robust against the impurity scattering while that for a subdominant $d_{xy}$-wave component is largely suppressed with the increase of the impurity scattering rate. The zero-bias …
We investigate the role of a finite potential range of a nonmagnetic impurity for the local density of states in a d_{x^2-y^2} superconductor. Impurity induced subgap resonances are modified by the appearance of further scattering channels beyond the $s$--wave scattering limit. The structure of the local density of states (DOS) in the vicinity of the impurity is significantly enhanced and therefore improves the possibility for observing the characteristic anisotropic spatial modulation of the local DOS in a d_{x^2-y^2} superconductor by scanning tunneling microscopy.
Scanning tunneling microscopy can provide a probe for the detailed study of quasiparticle states in high-Tc superconductors. We propose that it can also be used to acquire specific information about impurity-induced quasiparticle states and the superconducting order-parameter structure. In particular, the local density of states is found to be sensitive to impurity-induced resonances and to the symmetry of the order parameter.
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 examine the effect of a single, non-magnetic impurity in a multiband, extended s-wave superconductor allowing for anisotropy of the gaps on the Fermi surfaces. We derive analytic expressions for the Green's functions in the continuum and analyse the conditions for the existence of sharp impurity-induced resonant states. Underlying band structure is more relevant for the multiband than for single band case, and mismatch between the bands generically makes the formation of the impurity states less likely in the physical regime of parameters. We confirm these conclusions by numerically solving…
We study the impurity effect in the time reversal symmetry (${\cal T}$) breaking superconductor based on the Bogoliubov-de Gennes (BdG) equations. In ${\cal T}$-violating superconductors, spontaneous currents are induced around the impurity. The current patterns around the impurity reflect the structures of the Cooper pairs. We investigate impurity problem numerically for two kinds of ${\cal T}$ violating superconductors $(p_{x}\pm {\rm i}p_{y}$ and $d+{\rm i}s)$ and investigate the currents around the impurity. We also study the effects of the magnetic impurity in p-wave ($p_{x}\pm {\rm i}p_{…
Impurity nuclear spin relaxation is studied theoretically. A single impurity generates a bound state localized around the impurity atom in unconventional superconductors. With increasing impurity potential, the relaxation rate $T_1^{-1}$ is reduced by the impurity potential. However, it has a peak at low temperatures due to the impurity bound state. The peak disappears at non-impurity sites. The impurity site NMR measurement detecting a local electronic structure just on the impurity atom is very useful for identifying the unconventional pairing states.
We study the influence of anisotropy of the impurity potential on isotope coefficient of an impure superconductor in Born limit. From the isotope coefficient of non-magnetic and magnetic impurities including an angle-resolved Fermi surface density of state, anisotropy order parameter and impure potential, we make the assumption that the form of them are in the harmonic form and are investigated. Our numerical calculation of isotope coefficient can fit well with experimental data of high-Tc superconductors.
We discuss a case of a strong anisotropic impurity scattering within the model introduced in our previous paper [Phys. Rev. B54, 15463 (1996)] and clarify our former statement about a possible enhancement of the critical temperature in this scattering regime. We show that for the anisotropy of the impurity potential determined by the functions from the non-identity irreducible representations of the crystal point group, the critical temperature decreases with the impurity scattering rate which is consistent with a generally understood role of disorder in superconductors.
Unlike anomalous quantum Hall insulators, clean single-band chiral superconductors do not exhibit intrinsic Hall effect at the one-loop approximation. Finite ac Hall conductance was found to emerge beyond one-loop, such as with vertex corrections associated with extrinsic random impurity scatterings. In this paper, we investigate the effect of impurities embedded in single-band chiral superconductors in a superlattice pattern, instead of in random distributions. The impurity-induced Bogoliubov quasiparticle bound states hybridize to form subgap bands, constituting an emergent low-energy effect…
Effects of impurity scattering on tunneling conductance in dirty normal-metal/insulator/superconductor junctions are studied based on the Kubo formula and the recursive Green function method. The zero-bias conductance peak (ZBCP) is a consequence of the unconventional pairing symmetry in superconductors. The impurity scattering in normal metals suppresses the amplitude of the ZBCP. The degree of the suppression agrees well with results of the quasiclassical Green function theory. When superconductors have $d$+is-wave pairing symmetry, the time-reversal symmetry is broken in superconductors and…
The effects of impurity and spin-orbit scattering potentials can strongly affect the Zeeman response of a d-wave superconductor. Here, both the phase diagram and the quasiparticle density of states are calculated within the Born approximation and it is found that the spin-orbit interaction influences in a qualitatively different way the Zeeman response of d-wave and s-wave superconductors.
We investigate the mutual influence of impurities in two-dimensional d-wave superconductors involving self-consistent solutions of the Bogoliubov-de Gennes equations. The local order parameter suppression, the local density of states (LDOS) as well as the interference of impurity-induced structures are analyzed. We employ an impurity position averaging scheme for the DOS that does not neglect these interference effects, as the commonly used $T$-matrix approaches do.
The emergence of a topological superconducting state in van der Waals heterostructures provides a new platform for exploring novel strategies to control topological superconductors. In particular, impurities in van der Waals heterostructures, generically featuring a moire pattern, can potentially lead to the unique interplay between atomic and moire length scales, a feature absent in generic topological superconductors. Here we address the impact of non-magnetic impurities on a topological moire superconductor, both in the weak and strong regime, considering both periodic arrays and single imp…
Effects of impurities and disorder on quasiparticle spectrum in superconducting iron pnictides are considered. Possibility for occurrence of localized energy levels due to impurities within the superconducting gap and the related modification of band structure and of superconducting order parameter are discussed. The evolution of superconducting state with impurity doping is traced.
We study the presence of impurity bound states within a five-band Hubbard model relevant to iron-based superconductors. In agreement with earlier studies, we find that in the absence of Coulomb correlations there exists a range of repulsive impurity potentials where in-gap states are generated. In the presence of weak correlations, these states are generally pushed to the edges of the gap, whereas for larger correlations the onsite impurity potential induces a local magnetic region which reintroduces the low-energy bound states into the gap.
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 c…
The pointlike impurity scattering is studied for a superconductor with different pairing symmetries based on a minimal two band model proposed by S. Raghu $et$ $al.$ [Phys. Rev. B {\bf 77}, R220503 (2008)], and the self-consistent Bogoliubov-de Gennes equations. Two intra-gap resonance peaks are found at or near the nonmagnetic impurity site for a typical $s_{x^2y^2}$ symmetry and strong scattering potentials. Such intra-gap resonance peaks are absent for the sign unchanged s-wave and $d_{x^2-y^2}$-wave order parameter. Thus we propose that a non-magnetic impurity with strong scattering potent…
Imaging the effects of an impurity like Zn in high-Tc superconductors [Nature 61 (2000) 746] has rekindled interest in defect problems in the superconducting phase. This has prompted us here to re-examine the early work of March and Murray [Phys. Rev. 120 (1960) 830] on the linear response function in an initially translationally invariant Fermi gas. In particular, we present corresponding results for a superconductor at zero temperature, both in the s- and in the d-wave case, and mention their direct physical relevance in the case when the impurity potential is highly localized.
We study the effect of a single non-magnetic impurity in A$_{y}$Fe$_{2-x}$Se$_{2}$ (A=K, Rb, or Cs) superconductors by considering various pairing states based on a three-orbital model consistent with the photoemission experiments. The local density of states on and near the impurity site has been calculated by solving the Bogoliubov-de Gennes equations self-consistently. The impurity-induced in-gap bound states are found only for attractive impurity scattering potential, as in the cases of doping of Co or Ni, which is characterized by the strong particle-hole asymmetry, in the nodeless $d_{x^…
We discuss the weak-coupling BCS theory of a superconductor with the impurities, accounting for their anisotropic momentum-dependent potential. The impurity scattering process is considered in the t-matrix approximation and its influence on the superconducting critical temperature is studied in the Born and unitary limit for a d- and (d+s)-wave superconductors. We observe a significant dependence of the pair-breaking strength on the symmetry of the scattering potential and classify the impurity potentials according to their ability to alter T_c. A good agreement with the experimental data for …
The effect of weak anisotropic (momentum-dependent) impurity scattering in unconventional superconductors has been investigated. It is shown that the anisotropic scattering can lead either to a small reduction or a small enhancement of the isotropic pair-breaking effect. The influence of the anisotropy of the scattering potential becomes significant for the order parameters with large Fermi surface average values. In that case an unexpected enhancement (up to 10%) of the critical temperature over the critical temperature in the absence of impurities is predicted for a small impurity concentrat…
We study the influence of non-magnetic impurity scatterings on the tunneling conductance of a junction consisting of a normal metal and a disordered unconventional superconductor by solving the quasiclassical Eilenberger equation self-consistently. We find that the impurity scatterings in both the Born and unitary limits affect the formation of the Andreev bound states and modify strongly the tunneling spectra around zero bias. Our results are interpreted well by the appearance of odd-frequency Cooper pairs near the interface and by the divergent behavior of the impurity self-energy. The prese…
We discuss the polar Kerr effect (PKE) in a chiral p-wave (p_x+i p_y-wave) superconductor. It is found that the off-diagonal component of a current-current correlation function is induced by impurity scattering in the chiral p-wave condensate, and a nonzero Hall conductivity is obtained using the Kubo formula. We estimate the Kerr rotation angle by using this impurity-induced Hall conductivity and compare it with experimental results [Jing Xia et al., Phys. Rev. Lett. 97, 167002 (2006)].
We consider the influence of a magnetic field H on the quasiparticle bound states near scalar impurities in d-wave superconductors. A ``Doppler shift'' in the excitation energies induced by the supercurrent leads to several important effects. At large but finite impurity strength, there are corrections to the energy and width of the impurity-induced resonance, proportional to H^2. On the other hand, in the limit of very strong impurity potential (unitary limit), the bound state is destroyed and acquires a finite width proportional to H/ln H. There are also considerable changes in the asymptoti…
We study the unconventional superconducting correlations caused by a single isolated magnetic impurity in a conventional s-wave superconductor. Due to the local breaking of time-reversal symmetry, the impurity induces unconventional superconductivity which is even in both space and spin variables but odd under time inversion. We derive an exact proportionality relation between the even-frequency component of the local electron density of states and the imaginary part of the odd-frequency local pairing function. By applying this relation to scanning tunneling microscopy spectra taken on top of …
The specific heat jump at a normal-superconducting phase transition in an anisotropic superconductor with nonmagnetic impurities is calculated within a weak-coupling mean field approximation. It is shown that its dependence on the impurity concentration is remarkably different for d-wave and (d+s)-wave states. This effect may be used as a test for the presence of an s-wave admixture in the cuprates.
The influence of (non-magnetic and magnetic) impurities on the transition temperature of a d-wave superconductor is studied anew within the framework of BCS theory. Pairing interaction decreases linearly with the impurity concentration. Accordingly $T_{c}$ suppression is proportional to the (potential or exchange) scattering rate, $1/τ$, due to impurities. The initial slope versus $1/τ$ is found to depend on the superconductor contrary to Abrikosov-Gor'kov type theory. Near the critical impurity concentration $T_{c}$ drops abruptly to zero. Because the potential scattering rate is generally mu…
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…
Qualitative differences in the spectrum of a superconductor near magnetic impurity pairs with moments aligned parallel and antiparallel are derived. A proposal is made for a new, nonmagnetic scanning tunneling spectroscopy of magnetic impurity interactions based on these differences. Near parallel impurity pairs the mid-gap localized spin-polarized states associated with each impurity hybridize and form bonding and anti-bonding molecular states with different energies. For antiparallel impurity moments the states do not hybridize; they are degenerate.
