Measurement of the nonlinear Meissner effect in superconducting Nb films using a resonant microwave cavity: A probe of unconventional pairing symmetries
N. Groll, A. Gurevich, I. Chiorescu
备注:
published version
发表信息:
published 11 January 2010 in Physical Review B Rapid Comm. 81, 020504(R) (2010)
We report observation of the nonlinear Meissner effect (NLME) in Nb films by measuring the resonance frequency of a planar superconducting cavity as a function of the magnitude and the orientation of a parallel magnetic field. Use of low power rf probing in films thinner than the London penetration depth, significantly increases the field for the vortex penetration onset and enables NLME detection under true equilibrium conditions. The data agree very well with calculations based on the Usadel equations. We propose to use NLME angular spectroscopy to probe unconventional pairing symmetries in superconductors.
Superconducting correlations which are long-ranged in magnetic systems have attracted much attention due to their spin-polarization properties and potential use in spintronic devices. Whereas experiments have demonstrated the slow decay of such correlations, it has proven more difficult to obtain a smoking gun signature of their odd-frequency character which is responsible, e.g. for their gapless behavior. We here demonstrate that the magnetic susceptibility response of a normal metal in contact with a superconducting spin-valve provides precisely this signature, namely in form of an anomalous…
The Meissner effect is one of the defining properties of superconductivity, with a conventional superconductor completely repelling an external magnetic field. In contrast to this diamagnetic behavior, odd-frequency superconducting pairing has often been seen to produce a paramagnetic Meissner effect, which instead makes the superconductor unstable due to the attraction of magnetic field. In this work we study how both even- and odd-frequency superconducting pairing contributes to the Meissner effect in a generic two-orbital superconductor with a tunable odd-frequency pairing component. By div…
It is generally believed that superconducting materials are divided into two classes: `conventional' and `unconventional'. Conventional superconductors (the elements and thousands of compounds including $MgB_2$) are described by conventional London-BCS-Eliashberg electron-phonon theory. There is no general agreement as to what mechanism or mechanisms describe `unconventional' superconductors such as the heavy fermions, organics, cuprate and pnictide families. However all superconductors, whether `conventional' or `unconventional', exhibit the Meissner effect. I argue that there is a single mec…
The coupling of a superconductor to a different material often results in a system with unconventional superconducting properties. A conventional superconductor is a perfect diamagnet expelling magnetic fields out of its volume, a phenomenon known as Meissner effect. Here, we show that the simple adsorption of a monolayer of chiral molecules, which are non-magnetic in solution, onto the surface of a conventional superconductor can markedly change its diamagnetic Meissner response. By measuring the internal magnetic field profile in superconducting Nb thin films under an applied transverse fiel…
Doped Bi$_2$Se$_3$ is proposed to be a nematic superconductor originating from unusual inter-orbital pairing. We classify all induced superconducting pair correlations in Bi$_2$Se$_3$ and discover that intra-orbital odd-frequency pairing dominates over a significant range of frequencies. Moreover, we explore the contributions of even- and odd-frequency pairing to the Meissner effect, including separating intra- and inter-band processes in the response function. Contrary to expectations, and due to inter-band contributions, we find a diamagnetic odd-frequency Meissner effect.
We investigate the influence of critical spin fluctuations on electromagnetic responses in the odd-frequency superconductivity. It is shown that the Meissner kernel of the odd-frequency superconductivity is strongly reduced by the critical spin fluctuation or the massless spin wave mode in the antiferromagnetic phase. These results imply that the superfluid density is reduced, and the London penetration depth is lengthened for the odd-frequency pairing. It is also shown that the zero field Flude-Ferrell-Larkin-Ovchinnikov pairing is spontaneously realized both for even- and odd-frequency in th…
Superconductors with unconventional pairings have been a fascinating subject of research, for which a central issue is to explore effects that can be used to characterize the pairing. The process of Andreev reflection--the reflection of an electron as a hole at a normal-mental-superconductor interface by transferring a Cooper pair into the superconductor--offers a basic mechanism to probe the pairing through transport. Here we predict that in Andreev reflection from unconventional superconductors, the reflected hole acquires an anomalous spatial shift normal to the plane of incidence, arising …
In the frame of a four fermion interaction theory, we investigated the collective excitation in light-heavy fermion pairing systems. When the two species of fermions posses different masses and chemical potentials but keep the same Fermi surface, we found that the sound velocity in superfluids and the Meissner mass or inverse penetration depth in superconductors have the same mass ratio dependence as the ratio of the transition temperature to the zero temperature gap.
Fingerprints of unconventional pairing in superconductor-hole-gas heterostructures
Institute of Science and Technology Austria (ISTA)(奥地利科学技术研究所);Niels Bohr Institute, University of Copenhagen(哥本哈根大学尼尔斯·玻尔研究所);Department of Physics, Norwegian University of Science and Technology(挪威科技大学物理系)
We present the theoretical approach to study the unconventional Josephson junction (uJJ) made by putting the non-superconduncting strip on the top of superconducting strip. We work in the framework of the Ginzburg-Landau, Bogoliubov de Gennes and Usadel formalisms. We solve the non-linear parital differential equations numerically for few simple cases. We obtaine the eigenenergies of the uJJ by means of combined GL and BdGe method. cases. We predict the occurence of the physical effect, which we call the topological Meissner effect. Basing on the obtained results and current knowledge on Josep…
A general analysis of Meissner effect and spin susceptibility of a uniform superconductor in an asymmetric two-component fermion system is presented in nonrelativistic field theory approach. We found that, the pairing mechanism dominates the magnetization property of superconductivity, and the asymmetry enhances the paramagnetism of the system. At the turning point from BCS to breached pairing superconductivity, the Meissner mass squared and spin susceptibility are divergent at zero temperature. In the breached pairing state induced by chemical potential difference and mass difference between …
We study and classify the proximity-induced superconducting pairing in a topological insulator (TI)-superconductor (SC) hybrid structure for SCs with different symmetries. The Dirac surface state gives a coupling between spin-singlet and spin-triplet pairing amplitudes as well as pairing that is odd in frequency for p-wave SCs. We also find that all SCs induce pairing that is odd in both frequency and orbital (band) index, with oddness in frequency and orbital index being completely interchangeable. The different induced pairing amplitudes significantly modifies the density of states in the TI…
Revealing Hidden Unconventional Pairing through Nonreciprocal Transport
International Center for Quantum Materials, School of Physics, Peking University(北京大学物理学院量子材料科学中心);Beijing Academy of Quantum Information Sciences(北京量子信息科学研究院);Department of Physics, Hong Kong University of Science and Technology(香港科技大学物理系);Department of Physics, The University of Tokyo(东京大学物理学系);CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences(中国科学院理论物理研究所理论物理国家重点实验室);School of Physical Science and Technology, Soochow University(苏州大学物理科学与技术学院);Institute for Advanced Study, Soochow University(苏州大学未来技术学院);Interdisciplinary Center for Theoretical Physics and Information Sciences, Fudan University(复旦大学理论物理与信息科学交叉研究中心);Hefei National Laboratory(合肥国家实验室)
Recent results about the coexistence of ferromagnetism and unconventional superconductivity with spin-triplet Cooper pairing are reviewed on the basis of the quasi-phenomenological Ginzburg-Landau theory. The superconductivity in the mixed phase of coexistence of ferromagnetism and unconventional superconductivity is triggered by the spontaneous magnetization. The mixed phase is stable whereas the other superconducting phases that usually exist in unconventional superconductors are either unstable or metastable at relatively low temperatures in a quite narrow domain of the phase diagram and th…
We develop a theory for interlayer pairing of chiral electrons in graphene materials which results in an unconventional superconducting (S) state with s-wave spin-triplet order parameter. In a pure bilayer graphene, this superconductivity exhibits a gapless property with an exotic effect of temperature-induced condensation causing an increase of the pairing amplitude (PA) with increasing temperature. We find that a finite doping opens a gap in the excitation spectrum and weakens this anomalous temperature-dependence. We further explore the possibility of realizing variety of pairing patterns w…
The formation of electron pairs is a prerequisite of superconductivity. The fermionic nature of electrons yields four classes of superconducting correlations with definite symmetry in spin, space and time. Here, we suggest double quantum dots coupled to conventional s-wave superconductors in the presence of inhomogeneous magnetic fields as a model system exhibiting unconventional pairing. Due to their small number of degrees of freedom, tunable by gate voltages, quantum-dot systems provide an ideal tool to gain fundamental insight in unconventional pairing. We propose two detection schemes for…
The odd-frequency superconducting state appears generally in hybrid structures consisting of conventional superconductors and other materials, and features electrons that form temporally non-local Cooper pairs. The quasiclassical theory of superconductivity has been extensively used to model such systems, finding in many cases excellent agreement with experimental measurements. Therefore, it is of interest to study effective models of odd-frequency superconductivity to predict new phenomena associated with this form of unconventional pairing. We establish necessary criteria that the quasiclass…
It was recently pointed out that so-called "superhydrides", hydrogen-rich materials that appear to become superconducting at high temperatures and pressures, exhibit physical properties that are different from both conventional and unconventional standard type I and type II superconductors [1,2]. Here we consider magnetic field expulsion in the first material in this class discovered in 2015, sulfur hydride [3]. A nuclear resonant scattering experiment has been interpreted as demonstration that the Meissner effect takes place in this material [4,5]. Here we point out that the observed effect, …
Microscopic details such as interactions and Fermiology determine the structure of superconducting pairing beyond the spatial symmetry classification along irreducible point group representations. From the effective pairing vertex, the pairing wave function related to superconducting order unfolds in its orbital-resolved Fourier profile which we call the harmonic fingerprint (HFP). The HFP allows to formulate a concise connection between microsopic parameter changes and their impact on superconductivity. From a random phase approximation analysis of twisted bilayer graphene (TBG) involving $d+…
On the assumption that two electrons with the same group velocity effectively attract each other a simple model Hamiltonian is proposed to question the existence of unconventional electron pairs formed by electrons in a strong periodic potential.
We investigate Meissner effect in normal metal/superconductor junctions where the interface is spin-active. We find that orbital magnetic susceptibility of the normal metal shows highly nontrivial behaviors. In particular, the magnetic susceptibility depends on the temperature in an oscillatory fashion, accompanied by its sign change. Correspondingly, magnetic field and current density can spatially oscillate in the normal metal. The possible spontaneous formation of the current pattern is also discussed. These results are attributed to the generation of odd-frequency pairing due to the spin-a…
The Fermi-liquid theory of superconductivity is applicable to a broad range of systems that are candidates for unconventional pairing. Fundamental differences between unconventional and conventional anisotropic superconductors are illustrated by the unique effects that impurities have on the low-temperature transport properties of unconventional superconductors. For special classes of unconventional superconductors the low-temperature transport coefficients are {\it universal}, i.e. independent of the impurity concentration and scattering phase shift. The existence of a universal limit depends…
Unconventional superconductivity is usually associated with symmetry breaking in the system. Here we consider a simple setup consisting of a solid state material with conduction electrons and an applied surface acoustic wave (SAW), that can break time and spatial translation symmetries. We study the symmetries of the possible SAW-induced order parameters, showing that even-frequency spin-triplet odd-parity order parameter can occur. We suggest different methods of how to engineer the symmetries of the order parameters using SAWs and the applications of such setups.
We study the proximity-induced superconducting state in a general bilayer -- conventional $s$-wave superconductor hybrid structure. For the bilayer we include a general parabolic dispersion, Rashba spin-orbit coupling, and finite layer tunneling as well as the possibility to apply a bias potential and a magnetic Zeeman field, in order to address experimentally relevant bilayer systems, ranging from topological insulator thin films to generic double quantum well systems. By extracting the proximity-induced anomalous Green's function in the bilayer we show on a very rich structure for the superc…
Non-magnetic impurities can lift the accidental degeneracy of unconventional pairing states, such as the $(d + i g)$-wave state recently proposed for Sr$_2$RuO$_4$. This type of effect would lead to a superconducting double transition upon impurity doping. In a model calculation it is shown how this behavior depends on material parameters and how it could be detected.
High-Tc superconductivity in layered cuprates is described in a BCS-BEC formalism with linearly-dispersive s- and d-wave Cooper pairs moving in quasi-2D finite-width layers about the CuO_2 planes. This yields a closed formula for Tc determined by the layer width, the Debye frequency, the pairing energy, and the in-plane penetration depth. The new formula reasonably reproduces empirical values of superconducting Tc's for seven different compounds among the LSCO, YBCO, BSCCO and TBCCO layered cuprates.
The present review is given on the paramagnetic Meissner effect observed in conventional and ceramic high-Tc superconductors. We discuss two mechanisms leading to this phenomenon: the d-wave and the flux compensation. It is shown that the chiral glass phase may occur in granular superconductors possessing d-wave pairing symmetry. Dynamical phenomena such as AC susceptibility, compensation effect, anomalous microwave absorption, aging effect, AC resistivity and enhancement of critical current due to the external electric field are considered.
As shown in former papers, the nonadiabatic Heisenberg model presents a novel mechanism of Cooper pair formation which is not the result of an attractive electron-electron interaction but can be described in terms of quantum mechanical constraining forces. This mechanism operates in narrow, roughly half-filled superconducting bands of special symmetry and is evidently responsible for the formation of Cooper pairs in all superconductors. Here we consider this new mechanism within an outer magnetic field. We show that in the magnetic field the constraining forces produce Cooper pairs of non-vani…
We study the pairing symmetry of a doped Kane-Mele model on a honeycomb lattice with on-site Coulomb interaction. The pairing instability of Cooper pair is calculated based on the linearized Eliashberg equation within the random phase approximation (RPA). When the magnitude of the spin-orbit coupling is weak, even-frequency spin-singlet even-parity (ESE) pairing is dominant. On the other hand, with the increase of the spin-orbit coupling, we show that the even-frequency spin-triplet odd-parity (ETO) f-wave pairing exceeds ESE one. ETO f-wave pairing is supported by the longitudinal spin fluctu…
Signatures of nodal line/point superconductivity have been observed in half-Heusler compounds, such as LnPtBi (Ln = Y, Lu). Topologically non-trivial band structures, as well as topological surface states, has also been confirmed by angular-resolved photoemission spectroscopy in these compounds. In this work, we present a systematical classification of possible gap functions of bulk states and surface states in half-Heusler compounds and the corresponding topological properties based on the representations of crystalline symmetry group. Different from all the previous studies based on four ban…
The pairing mechanism in iron-based superconductors is believed to be unconventional, i.e. not phonon-mediated. The achieved transition temperatures Tc in these superconductors are still significantly below those of some of the cuprates, with the exception of single layer FeSe films on SrTiO3 showing a Tc between 60 and 100 K, i.e. an order of magnitude larger than in bulk FeSe. This enormous increase of Tc demonstrates the potential of interface engineering for superconductivity, yet the underlying mechanism of Cooper pairing is not understood. Both conventional and unconventional mechanisms …
Understanding the nature of Cooper pairs is essential to describe the properties of superconductors. The original proposal of Bardeen, Cooper, and Schrieffer (BCS) was based on electrons pairing with same energy and zero center-of-mass momentum. With the advent of new superconductors, different forms of pairing have been discussed. In particular, Cooper pairs with finite center-of-mass momentum have received large interest. Along with such finite-momentum pairs, pairing of electrons at different energies is also central to understanding some superconductors. Here, we investigate the interplay …
Giant and nil proximity effects and unconventional symmetry of cuprate superconductors are explained as a result of the strong Froehlich interaction of holes with c-axis polarised optical phonons acting together with an anisotropic nonlocal deformation potential.
We rigorously prove that an extended Hubbard model with attraction in two dimensions has an unconventional pairing ground state for any electron filling. The anisotropic spin-0 or anisotropic spin-1 pairing symmetry is realized, depending on a phase parameter characterizing the type of local attractive interactions. In both cases the ground state is unique. It is also shown that in a special case, where there are no electron hopping terms, the ground state has Ising-type Néel order at half-filling, when on-site repulsion is furthermore added. Physical applications are mentioned.
For the iron-based high $T_c$ superconductor LaFeAsO$_{1-x}$F$_x$, we construct a minimal model, where all of the five Fe $d$ bands turn out to be involved. We then investigate the origin of superconductivity with a five-band random-phase approximation by solving the Eliashberg equation. We conclude that the spin fluctuation modes arising from the nesting between the disconnected Fermi pockets realise, basically, an extended s-wave pairing, where the gap changes sign across the nesting vector.
In a recent work by Schrodi $\textit{et al}$. [Phys. Rev. B. $\textbf{104}$, L140506 (2021)], the authors find an unconventional superconducting state with a sign-changing order parameter using the Migdal-Eliashberg theory, including the first vertex correction. This unconventional solution arises despite using an isotropic bare electron-phonon coupling in the Hamiltonian. We examine this claim using hybrid quantum Monte Carlo for a single-band Holstein model with a cuprate-like noninteracting band structure and identical parameters to Schrodi $\textit{et al}$.. Our Monte Carlo results for the…
The pairing mechanism in A$_3$C$_{60}$ is investigated by studying the properties of a three-orbital Hubbard model with antiferromagnetic Hund coupling in the normal and superconducting phase. Local orbital fluctuations are shown to be substantially enhanced in the superconducting state, with a fluctuation energy scale that matches the low-energy peak in the spectral weight of the order parameter. Our results demonstrate that local orbital fluctuations provide the pairing glue in strongly correlated fulleride superconductors and support the spin/orbital freezing theory of unconventional superc…
Cooper pairs in two-dimensional unconventional superconductors with broken inversion symmetry are in a mixture of an even-parity spin-singlet pairing state with an odd-parity spin-triplet pairing state. We study the magnetic properties of the impurity bound states in such superconductors and find striking signatures in their spin polarization which allow to unambiguously discriminate a non-topological superconducting phase from a topological one. Moreover, we show how these properties, which could be measured using spin-polarized scanning tunneling microscopy (STM), also enable to determine th…
The common wisdom that the phonon mechanism of electron pairing in the weak-coupling Bardeen-Cooper-Schrieffer (BCS) superconductors leads to conventional s-wave Cooper pairs is revised. An inevitable anisotropy of sound velocity in crystals makes the phonon-mediated attraction of electrons non-local in space providing unconventional Cooper pairs with a nonzero orbital momentum in a wide range of electron densities. As a result of this anisotropy quasi-two dimensional charge carriers undergo a quantum phase transition from an unconventional d-wave superconducting state to a conventional s-wave…
The structures, the phase diagrams, and the appearance of a neutron resonance signaling an unconventional superconducting state provide phenomenological evidence relating the cuprates, the Fe-pnictides/chalcogenides as well as some heavy fermion and actinide materials. Single- and multi-band Hubbard models have been found to describe a number of the observed properties of these materials so that it is reasonable to examine the origin of the pairing interaction in these models. In this review, based on the experimental phenomenology and studies of the pairing interaction for Hubbard-like models…
Based on an effective two-band model and using the fluctuation-exchange (FLEX) approach, we explore spin fluctuations and unconventional superconducting pairing in Fe-based layer superconductors. It is elaborated that one type of interband antiferromagnetic (AF) spin fluctuation stems from the interband Coulomb repulsion, while the other type of intraband AF spin fluctuation originates from the intraband Coulomb repulsion. Due to the Fermi-surface topology, a spin-singlet extended s-wave superconducting state is more favorable than the nodal $d_{XY}$-wave state if the interband AF spin fluctua…
A low-energy fixed-point Hamiltonian is constructed for the s-wave odd-frequency pairing state with staggered ordering vector in the two-channel Kondo lattice. The effective model is justified because it reproduces low-energy behaviors of self energy obtained by the dynamical mean-field theory. The retardation effect is essential for the odd-frequency pairing, which comes from the hybridization process between conduction electrons and pseudofermions originating from localized spins at low energies. Using the effective Hamiltonian, the electromagnetic response functions are microscopically calc…
The fermion Cooper pairing with unequal masses is investigated in a standard field theory approach. We derived the superfluid density and Meissner mass squared of the U(1) gauge field in a general two species model and found that the often used proportional relation between the two quantities is broken down when the fermion masses are unequal. In weak coupling region, the superfluid density is always negative but the Meissner mass squared becomes mostly positive when the mass ratio between the pairing fermions is large enough. We established a proper momentum configuration of the LOFF pairing …
The origin of Cooper pairing in high-temperature superconductors, such as the copper-oxide and iron-based system, is still under debate. High transition temperatures together with unconventional pairing states support the picture of an electronic pairing glue in the cuprates, where superconductivity is mediated by collective bosonic excitations of the electron fluid. In other materials, most importantly iron based systems with only hole or only electron pockets, the microscopic origin is hotly debated. Scanning tunneling microscopy (STM) has been shown to be a powerful experimental probe to de…
We have directly imaged the anisotropic nonlinear Meissner effect in an unconventional superconductor through the nonlinear electrodynamic response of both (bulk) gap nodes and (surface) Andreev bound states. A superconducting thin film is patterned into a compact self-resonant spiral structure, excited near resonance in the radio-frequency range, and scanned with a focused laser beam perturbation. At low temperatures, direction-dependent nonlinearities in the reactive and resistive properties of the resonator create photoresponse that maps out the directions of nodes, or of bound states assoc…
We show that a chain of nonmagnetic impurities deposited on a fully gapped two- or three-dimensional superconductor can become a topological one-dimensional superconductor with protected Majorana bound states at its end. A prerequisite is that the pairing potential of the underlying superconductor breaks the spin-rotation symmetry, as it is generically the case in systems with strong spin-orbit coupling. We illustrate this mechanism for a spinless triplet-superconductor p+ip and a time-reversal symmetric Rashba superconductor with a mixture of singlet and triplet pairing. For the latter, we sh…
We investigate the possibility of realizing unconventional superconductivity in doped band insulators on the square lattice and the honeycomb lattice, where the latter is found to be a good candidate due to the disconnectivity of the Fermi surface. We propose applying the theory to the superconductivity in doped layered nitride $β$-$M$NCl ($M=$Hf, Zr). Finally, we compare two groups of superconductors with disconnected Fermi surface, $β$-$M$NCl and the iron pnictides, which have high $T_c$ despite some faults against superconductivity are present.
We use magnetic long range order as a tool to probe the Cooper pair wave function in the iron arsenide superconductors. We show theoretically that antiferromagnetism and superconductivity can coexist in these materials only if Cooper pairs form an unconventional, sign-changing state. The observation of coexistence in Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ then demonstrates unconventional pairing in this material. The detailed agreement between theory and neutron diffraction experiments, in particular for the unusual behavior of the magnetic order below $T_{c}$, demonstrates the robustness of our…
Probing Sign-Changing Order Parameters via Impurity States in unconventional superconductors: Implications for La$_3$Ni$_2$O$_7$ Superconductors with interlayer pairing
For a newly discovered iron-based high $T_c$ superconductor LaFeAsO$_{1-x}$F$_x$, we have constructed a minimal model, where inclusion of all the five Fe $d$ bands is found to be necessary. Random-phase approximation is applied to the model to investigate the origin of superconductivity. We conclude that the multiple spin fluctuation modes arising from the nesting across the disconnected Fermi surfaces realize an extended s-wave pairing, while d-wave pairing can also be another candidate.
We show that finite angular momentum pairing chiral superconductors on the triangular lattice have point zeroes in the complex gap function. A topological quantum phase transition takes place through a nodal superconducting state at a specific carrier density $x_c$ where the normal state Fermi surface crosses the isolated zeros. For spin singlet pairing, we show that the second nearest neighbor $d+id$-wave pairing can be the dominant pairing channel. The gapless critical state at $x_c\simeq0.25$ has six Dirac points and is topologically nontrivial with a $T^3$ spin relaxation rate below $T_c$.…
We study superfluid properties of fermions on a 2D lattice using a finite-range pairing interaction derivable from an extended Hubbard model. We obtain signatures of unconventional pair-symmetry states, $d_{x^2-y^2}$ and extended-s ($s^*$), in the BCS-BEC crossover region. The fermion momentum distribution function, $v_k^2$, the ratio of the Bogoliubov coefficients, $v_k/u_k$, and the Fourier transform of $v_k^2$ are among the properties that are strikingly different for d- and $s^*$ symmetries in the crossover region. Fermionic atoms in 2D optical lattices may provide a way to observe these s…