Nodeless State Research Articles

Photonic bandgap engineering using second-order supersymmetry

First-order supersymmetry (SUSY) adapted from quantum physics to optics manipulates the transverse refractive index of guided-wave structures using a nodeless ground state to obtain intended modal content. Second-order SUSY can be implemented using excited states as a seed function, even with the presence of nodes. We apply second-order SUSY to the coupled-mode equations by recasting them as the Dirac equation. This enables the engineering of non-uniform surface corrugation of waveguide gratings and coupling potential, which encapsulates the Bragg interaction between counterpropagating modes. We show that the added bound states appear as transmission resonances inside the bandgap of the finite grating. The probability density of each state provides the longitudinal modal energy distribution in the waveguide grating. The smooth modal energy distribution of the states obtained by SUSY can mitigate longitudinal spatial hole burning in high power laser operation. We demonstrate that degenerate second-order SUSY allows the insertion of two states, which can coalesce into Friedrich-Wintgen type bound states in the continuum (BIC) for one-dimensional grating. We show that the eigenfunctions of BIC states are doubly degenerate with opposite parity, and the corresponding transmission resonances have phase changes of 2π across these states. One-dimensional BIC states can find application as robust high-speed all-optical temporal integrators by lifting restrictions on the length of various sections in the phase-shifted grating.

Band-selective clean-limit and dirty-limit superconductivity with nodeless gaps in the bilayer iron-based superconductor CsCa2Fe4As4F2

The optical properties of the new iron-based superconductor CsCa$_2$Fe$_4$As$_4$F$_2$ with $T_c \sim 29$~K have been determined. In the normal state a good description of the low-frequency response is obtained with a superposition of two Drude components of which one has a very low scattering rate (narrow Drude-peak) and the other a rather large one (broad Drude-peak). Well below $T_c \sim 29$~K, a pronounced gap feature is observed which involves a complete suppression of the optical conductivity below $\sim$ 110~cm$^{-1}$ and thus is characteristic of a nodeless superconducting state. The optical response of the broad Drude-component can be described with a dirty-limit Mattis-Bardeen-type response with a single isotropic gap of $2\Delta \simeq 14$~meV. To the contrary, the response of the narrow Drude-component is in the ultra-clean-limit and its entire spectral weight is transferred to the zero-frequency $\delta(\omega)$ function that accounts for the loss-free response of the condensate. These observations provide clear evidence for a band-selective coexistence of clean- and dirty-limit superconductivity with nodeless gaps in CsCa$_2$Fe$_4$As$_4$F$_2$.

Nodal topology in d -wave superconducting monolayer FeSe

A nodeless $d$-wave state is likely in superconducting monolayer FeSe on SrTiO$_3$. The lack of nodes is surprising but has been shown to be a natural consequence of the observed small interband spin-orbit coupling. Here we examine the evolution from a nodeless state to the nodal state as this spin-orbit coupling is increased from a topological perspective. We show that this evolution depends strongly on the orbital content of the superconducting degrees of freedom. In particular, there are two $d$-wave solutions, which we call orbitally trivial and orbitally nontrivial. In both cases, the nodes carry a $\pm 2$ topological winding number that originates from a chiral symmetry. However, the momentum space distribution of the positive and negative charges is different for the two cases, resulting in a different evolution of these nodes as they annihilate to form a nodeless superconductor. We further show that the orbitally trivial and orbitally nontrivial nodal states exhibit different Andreev flat band spectra at the edge.

Information-entropic measures for non-zero l states of confined hydrogen-like ions

Relative Fisher information (IR), which is a measure of correlative fluctuation between two probability densities, has been pursued for a number of quantum systems, such as, 1D quantum harmonic oscillator (QHO) and a few central potentials namely, 3D isotropic QHO, hydrogen atom and pseudoharmonic potential (PHP) in both position ($r$) and momentum ($p$) spaces. In the 1D case, the $n=0$ state is chosen as reference, whereas for a central potential, the respective circular or node-less (corresponding to lowest radial quantum number $n_{r}$) state of a given $l$ quantum number, is selected. Starting from their exact wave functions, expressions of IR in both $r$ and $p$ spaces are obtained in closed analytical forms in all these systems. A careful analysis reveals that, for the 1D QHO, IR in both coordinate spaces increase linearly with quantum number $n$. Likewise, for 3D QHO and PHP, it varies with single power of radial quantum number $n_{r}$ in both spaces. But, in H atom they depend on both principal ($n$) and azimuthal ($l$) quantum numbers. However, at a fixed $l$, IR (in conjugate spaces) initially advance with rise of $n$ and then falls off; also for a given $n$, it always decreases with $l$.

Superconducting gap anisotropy sensitive to nematic domains in FeSe

The structure of the superconducting gap in unconventional superconductors holds a key to understand the momentum-dependent pairing interactions. In superconducting FeSe, there have been controversial results reporting nodal and nodeless gap structures, raising a fundamental issue of pairing mechanisms of iron-based superconductivity. Here, by utilizing polarization-dependent laser-excited angle-resolved photoemission spectroscopy, we report a detailed momentum dependence of the gap in single- and multi-domain regions of orthorhombic FeSe crystals. We confirm that the superconducting gap has a twofold in-plane anisotropy, associated with the nematicity due to orbital ordering. In twinned regions, we clearly find finite gap minima near the vertices of the major axis of the elliptical zone-centered Fermi surface, indicating a nodeless state. In contrast, the single-domain gap drops steeply to zero in a narrow angle range, evidencing for nascent nodes. Such unusual node lifting in multi-domain regions can be explained by the nematicity-induced time-reversal symmetry breaking near the twin boundaries.

Extracting the mass dependence and quantum numbers of short-range correlated pairs fromA(e,e′p)andA(e,e′pp)scattering

The nuclear mass dependence of the number of short-range correlated (SRC) proton-proton (pp) and proton-neutron (pn) pairs in nuclei is a sensitive probe of the dynamics of short-range pairs in the ground state of atomic nuclei. This work presents an analysis of electroinduced single-proton and two-proton knockout measurements off 12C, 27Al, 56Fe, and 208Pb in kinematics dominated by scattering off SRC pairs. The nuclear mass dependence of the observed A(e,e'pp)/12C(e,e'pp) cross-section ratios and the extracted number of pp- and pn-SRC pairs are much softer than the mass dependence of the total number of possible pairs. This is in agreement with a physical picture of SRC affecting predominantly nucleon-nucleon pairs in a nodeless relative-S state of the mean-field basis.

Disorder-induced topological change of the superconducting gap structure in iron pnictides.

In superconductors with unconventional pairing mechanisms, the energy gap in the excitation spectrum often has nodes, which allow quasiparticle excitations at low energies. In many cases, such as in d-wave cuprate superconductors, the position and topology of nodes are imposed by the symmetry, and thus the presence of gapless excitations is protected against disorder. Here we report on the observation of distinct changes in the gap structure of iron-pnictide superconductors with increasing impurity scattering. By the successive introduction of nonmagnetic point defects into BaFe2(As(1-x)P(x))(2) crystals via electron irradiation, we find from the low-temperature penetration depth measurements that the nodal state changes to a nodeless state with fully gapped excitations. Moreover, under further irradiation the gapped state evolves into another gapless state, providing bulk evidence of unconventional sign-changing s-wave superconductivity. This demonstrates that the topology of the superconducting gap can be controlled by disorder, which is a strikingly unique feature of iron pnictides.

Pairing Symmetry of Heavy Fermion Superconductivity in the Two-Dimensional Kondo—Heisenberg Lattice Model

In the two-dimensional Kondo—Heisenberg lattice model away from half-filled, the local antiferromagnetic exchange coupling can provide the pairing mechanism of quasiparticles via the Kondo screening effect, leading to the heavy fermion superconductivity. We find that the pairing symmetry strongly depends on the Fermi surface (FS) structure in the normal metallic state. When JH/JK is very small, the FS is a small hole-like circle around the corner of the Brillouin zone, and the s-wave pairing symmetry has a lower ground state energy. For the intermediate coupling values of JH/JK, the extended s-wave pairing symmetry gives the favored ground state. However, when JH/JK is larger than a critical value, the FS transforms into four small hole pockets crossing the boundary of the magnetic Brillouin zone, and the d-wave pairing symmetry becomes more favorable. In that regime, the resulting superconducting state is characterized by either a nodal d-wave or nodeless d-wave state, depending on the conduction electron filling factor as well. A continuous phase transition exists between these two states. This result may be related to the phase transition of the nodal d-wave state to a fully gapped state, which has recently been observed in Yb-doped CeCoIn5.

From nodeless clouds and vortices to gray ring solitons and symmetry-broken states in two-dimensional polariton condensates

We consider the existence, stability and dynamics of the nodeless state and fundamental nonlinear excitations, such as vortices, for a quasi-two-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of interesting features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose–Einstein condensates (BECs). For sizeable parameter ranges, in line with earlier findings, the nodeless state becomes unstable towards the formation of stable nonlinear single or multi-vortex excitations. The potential instability of the single vortex is also examined and is found to possess similar characteristics to those of the nodeless cloud. We also report that, contrary to what is known, e.g., for the atomic BEC case, stable stationary gray ring solitons (that can be thought of as radial forms of Nozaki–Bekki holes) can be found for polariton condensates in suitable parametric regimes. In other regimes, however, these may also suffer symmetry-breaking instabilities. The dynamical, pattern-forming implications of the above instabilities are explored through direct numerical simulations and, in turn, give rise to waveforms with triangular or quadrupolar symmetry.

Origin of pressure induced second superconducting dome in Ay Fe2−xSe2 [A = K, (Tl,Rb)

Recent observation of a pressure induced second superconducting phase in AyFe2−xSe2 [A = K, (Tl,Rb)] calls for the models of superconductivity that are rich enough to allow for multiple superconducting phases. We propose the model where pressure induces renormalization of band parameters in such a way that it leads to changes in Fermi surface topology even for a fixed electron number. We develop a low-energy effective model, derived from first-principles band-structure calculation at finite pressure, to suggest the phase assignment where a low pressure superconducting state with no hole pocket at the Γ point is a nodeless d-wave state. It evolves into a s± state at higher pressure when the Fermi surface topology changes and the hole pocket appears. We analyze the pairing interactions using a five band tight binding fitted band structure and find that a strong pairing strength is dependent on pressure. We also evaluate the energy and momentum dependence of neutron spin resonances in each of the phases as verifiable predictions of our proposal.

Electron-boson coupling and two superconducting gaps in optimally electron-doped BaFe1.9Ni0.1As2single crystals

We report a systematic investigation on c-axis point-contact Andreev reflection (PCAR) in BaFe$_{2-x}$Ni$_x$As$_2$ superconducting single crystals from underdoped to overdoped regions (0.075 $\leq x\leq 0.15$). At optimal doping ($x=0.1$) the PCAR spectrum feature the structures of two superconducting gap and electron-boson coupling mode. In the $s\pm$ scenario, quantitative analysis using a generalized Blonder-Tinkham-Klapwijk (BTK) formalism with two gaps: one isotropic and another angle dependent, suggest a nodeless state in strong-coupling limit with gap minima on the Fermi surfaces. Upon crossing above the optimal doping ($x > 0.1$), the PCAR spectrum show an in-gap sharp narrow peak at low bias, in contrast to the case of underdoped samples ($x < 0.1$), signaling the onset of deepened gap minima or nodes in the superconducting gap. This result provides evidence of the modulation of the gap amplitude with doping concentration, consistent with the calculations for the orbital dependent pair interaction mediated by the antiferromagnetic spin fluctuations.

D-wave superconductivity induced by short-range antiferromagnetic correlations in the two-dimensional Kondo lattice model

The possible heavy fermion superconductivity is carefully reexamined in the two-dimensional Kondo lattice model with an antiferromagnetic Heisenberg superexchange between local magnetic moments. In order to establish an effective mean field theory in the limit of the paramagnetic heavy Fermi liquid and near the half-filling case, we find that the spinon singlet pairing from the local antiferromagnetic short-range correlations can reduce the ground state energy substantially. In the presence of the Kondo screening effect, the Cooper pairs between the conduction electrons is induced. Depending on the ratio of the Heisenberg and the Kondo exchange couplings, the resulting superconducting state is characterized by either a d-wave nodal or d-wave nodeless state, and a continuous phase transition exists between these two states. These results are related to some quasi-two dimensional heary fermion superconductors.

Millimeter-wave study of London penetration depth temperature dependence in Ba(Fe0.926Co0.074)2As2 single crystal

In-plane surface Ka-band microwave impedance of optimally doped single crystals of the Fe-based superconductor Ba(Fe0.926Co0.074)2As2 (Tc = 22.8 K) was measured. Sensitive sapphire disk quasi-optical resonator with high-Tc cuprate conducting endplates was developed specially for Fe-pnictide superconductors. It allowed finding temperature variation of London penetration depth in a form of power law, namely Δλ(T) ∼ Tn with n = 2.8 from low temperatures up to at least 0.6Tc consisted with radio-frequency measurements. This exponent points towards nodeless state with pairbreaking scattering, which can support one of the extended s-pairing symmetries. The dependence λ(T) at low temperatures is well described by one superconducting small-gap (Δ≅0.75 in kTc units, where k is Boltzmann coefficient) exponential dependence.

Symmetry analysis of possible superconducting states in KxFeySe2superconductors

A newly discovered family of Fe-based superconductors is isostructural with the so-called 122 family of Fe pnictides but has a qualitatively different doping state. Early experiments indicate that superconductivity is nodeless, yet prerequisites for the ${s}_{\ifmmode\pm\else\textpm\fi{}}$ nodeless state (generally believed to be realized in Fe superconductors) are missing. It is tempting to assign a $d$-wave symmetry to the new materials, and it does seem, at first glance, that such a state may be nodeless. Yet a more careful analysis shows that it is not possible, given the particular 122 crystallography. If indeed superconductivity in this system is nodeless, the possible choice of admissible symmetries is severely limited: it is either a conventional single-sign ${s}_{+}$ state or another ${s}_{\ifmmode\pm\else\textpm\fi{}}$ state, different from the one believed to be present in other Fe-based superconductors.

Nonlinear excitations, stability inversions, and dissipative dynamics in quasi-one-dimensional polariton condensates

We study the existence, stability, and dynamics of the ground state and nonlinear excitations, in the form of dark solitons, for a quasi-one-dimensional polariton condensate in the presence of nonresonant pumping and nonlinear damping. We find a series of remarkable features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates. For some sizable parameter ranges, the nodeless (``ground'') state becomes unstabletoward the formation of stable nonlinear single- or multi-dark-soliton excitations. It is also observed that for suitable parametric choices, the instability of single dark solitons can nucleate multi-dark-soliton states. Also, for other parametric regions, stable asymmetric sawtooth-like solutions exist. These are shown to emerge through a symmetry-breaking bifurcation from bubble-like solutions that we also explore. We also consider the dragging of a defect through the condensate and the interference of two initially separated condensates, both of which are capable of nucleating dark multisoliton dynamical states.

Andreev Bound States as a Phase-Sensitive Probe of the Pairing Symmetry of the Iron Pnictide Superconductors

A leading contender for the pairing symmetry in the Fe pnictide high-temperature superconductors is extended s wave s_{+/-}, a nodeless state in which the pairing changes sign between Fermi surfaces. Verifying such a pairing symmetry requires a special phase-sensitive probe that is also momentum selective. We show that the sign structure of s_{+/-} pairing can lead to surface Andreev bound states (ABS) at the sample edge. In the clean limit they only occur when the edge is along the nearest neighbor Fe-Fe bond, but not for a diagonal edge or a surface orthogonal to the c axis. In contrast to d-wave ABS, they are not at zero energy and, in general, do not produce a zero bias tunneling peak. Consequences for tunneling measurements are derived, within a simplified two-band model and also for a more realistic five-band model. In both cases, surface ABS are obtained.

Reply to “Comment on ‘Nodeless pairing state in single-crystalYBa2Cu3O7’ ”

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Fluxon pinning in the nodeless pairing state of superconducting YBa2Cu3O7

Positive-muon spin rotation (μ+SR) spectroscopy and magnetic moment measurements were used to probe fluxon (or vortex) formation in the superconducting mixed state of a high-purity YBa2Cu3O7 crystal. Random potentials caused by crystal-lattice defects pin fluxons. A fluxon lattice forms in an external magnetic field, and changes of thermal activation lead to fluxon pinning and depinning. The root second moment of the local magnetic field distribution (σ) determined by μ+SR contains information on the magnetic penetration depth and the pinning. Fluxon pinning leads to temperature-dependent transverse displacements of the fluxons that decrease σ and also fluctuations in the separation between fluxons that tend to increase σ. By accounting for the field-dependent and temperature-activated fluxon disorder, it is found that the experimental results for the penetration depth are consistent with a supercon-ducting order parameter of a strong-coupling two-fluid model, confirming that the superconductivity is nodeless with s-wave superconducting pairing. Quantitative results for fluxon displacements are discussed within the context of the fluxon field-temperature phase diagram.

Spin-Triplet Superconductivity Mediated by Phonons in Quasi-One-Dimensional Systems

We investigate the spin-triplet superconductivity mediated by phonons in quasi-one-dimensional (Q1D) systems with open Fermi surfaces. We obtain the ground state phase diagrams. It is found that spin-triplet superconductivity occurs for weak screening and strong on-site Coulomb interaction, even in the absence of any additional nonphonon pairing interactions. We find that the nodeless spin-triplet state is more favorable than the spin-triplet state with line nodes, for the parameter values of the Q1D superconductors (TMTSF)_2X. We also find that Q1D open Fermi surface, which is the specific feature of this system, plays an essential role in the pairing symmetry. We discuss the compatibility of the present results with the experimental results in these compounds.

Large amplitude spatial fluctuations in the boundary region of the Bose–Einstein condensate in the Gross–Pitaevskii régime

Abstract The Gross–Pitaevskii regime of a Bose–Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross–Pitaevskii equation is found which are characterised by pronounced large-amplitude oscillations close to the boundary of the condensate. The limiting case within this class is a nodeless ground state which is known from recent investigations as an extension of the Thomas–Fermi approximation. We have found the energies of the oscillatory states to lie above the ground state energy but recent experimental work, especially on spatially confined superconductors, indicates that such states may be easily occupied and made manifest at finite temperatures. We have also investigated their stability using a Poincare section analysis as well as a linear perturbation approach. Both these techniques demonstrate stability against small perturbations. Finally, we have discussed the relevance of these quasi-one-dimensional solutions in the context of the fully three-dimensional condensates. This has been argued on the basis of numerical work and asymptotic approximations.