We calculate within a mean-field theory the spectral signatures of various striped d-wave superconducting phases. We consider both in-phase and anti-phase modulations of the superconducting order across a stripe boundary, and the effects of coexisting inhomogeneous orders, including spin stripes, charge stripes, and modulated d-density-wave. We find that the anti-phase modulated d-wave superconductor exhibits zero-energy spectral weight, primarily along extended arcs in momentum space. Concomitantly, a Fermi surface appears and typically includes both open segments and closed pockets. When weak homogeneous superconductivity is also present the Fermi surface collapses onto nodal points. Among them are the nodal points of the homogeneous d-wave superconductor, but others typically exist at positions which depend on the details of the modulation and the band structure. Upon increasing the amplitude of the constant component these additional points move towards the edges of the reduced Brillouin zone where they eventually disappear. The above signatures are also manifested in the density of states of the clean, and the disordered system. While the presence of coexisting orders changes some details of the spectral function, we find that the evolution of the Fermi-surface and the distribution of the low-energy spectral weight are largely unaffected by them.
We investigate the one-dimensional $p$-wave superconducting model with periodically modulated hopping and show that under time-reversal symmetry, the number of the Majorana zero modes (MZMs) strongly depends on the modulation period. If the modulation period is odd, there can be at most one MZM. However if the period is even, the number of the MZMs can be zero, one and two. In addition, the MZMs will disappear as the chemical potential varies. We derive the condition for the existence of the MZMs and show that the topological properties in this model are dramatically different from the one wit…
By spatially mapping the Doppler effect of an in-plane magnetic field on the quasiparticle tunneling spectrum, we have laterally imaged the vortex lattice in superconducting 2H-NbSe2. Cryomagnetic scanning tunneling spectroscopy was performed at 300 mK on the ab-surface oriented parallel to the field H. Conductance images at zero bias show stripe patterns running along H, with the stripe separation varying as H^-0.5. Regions of higher zero-bias conductance show lower gap-edge conductance, consistent with spectral redistribution by spatially-modulated superfluid momentum. Our results are interp…
Low-energy incommensurate (IC) magnetic fluctuations in the multiband superconductor Sr$_2$RuO$_4$ is investigated by high-resolution inelastic neutron scattering measurements and random phase approximation (RPA) calculations. Below $T_\text{c}$, the substantial spin gap is observed at $\mathbf{Q}_\text{IC}=(0.3, 0.3, L)$ where the quasi-one-dimensional $α$ and $β$ sheets consisting of the Fermi surfaces are in good nesting conditions. $L$ modulated intensity of the low-energy IC magnetic fluctuations and our RPA calculations indicate that the superconducting gaps regarding the $α$ and $β$ she…
In a very interesting recent Letter\cite{berg}, the authors suggested that a novel form of superconducting state is realized in La$_{2-x}$Ba$_x$CuO$_4$ with $x$ close to 1/8. This suggestion was based on experiments\cite{li} on this compound which found predominantly two-dimensional (2D) characters of the superconducting state, with extremely weak interplane coupling. Later this specific form of superconducting state was termed striped superconductors\cite{berg08}. The purpose of this note is to point out that the suggested form\cite{berg} of the superconducting order parameter can be detected…
A simple theoretical model is proposed to describe the recent experimental results on formation of induced superconducting state and anomalous tunneling characteristics in selectively doped multilayered nanostructures based on La$_2$CuO$_4$ perovskite. In particular, it is shown that the structure composed from the nominally non-superconducting (undoped and overdoped) layers turns to be superconducting with superconductivity confined to narrow regions near the interfaces, in agreement with the experimental observations.
We analyze the dynamics of a superconducting qubit and the phenomenon of multiorder Rabi oscillations in the presence of a time-modulated external field. Such a field is also presented as a bichromatic field consisting of two spectral components, which are symmetrically detuned from the qubit resonance frequency. This approach leads to obtaining qualitative quantum effects beyond those for the case of monochromatic excitation of qubits. We calculate Floquet states and quasienergies of the composite system "superconducting qubit plus time-modulated field" for various resonant regimes. We analyz…
The interface between the insulating oxides LaAlO3 and SrTiO3 exhibits a superconducting two-dimensional electron system that can be modulated by a gate voltage. While gating of the conductivity has been probed extensively and gating of the superconducting critical temperature has been demonstrated, the question whether, and if so how, the gate tunes the superfluid density and superconducting order parameter is unanswered. We present local magnetic susceptibility, related to the superfluid density, as a function of temperature, gate voltage and location. We show that the temperature dependence…
We report magnetoresistance measurements through Nb films having a periodic thickness modulation. The cylinder shaped large-thickness regions of the sample, which form a square lattice, act as repulsive centers for the superconducting vortices. For low driving currents along one of the axes of the square lattice, the resistivity $ρ$ increases monotonously with increasing magnetic field $B$ and the $ρ$--$B$ characteristics are approximately piecewise linear. The linear $ρ$ vs $B$ segments change their slope at matching fields where the number of vortices is an integer or a half integer times th…
The role of antiferromagnetic spin correlations in high-temperature superconductors remains a matter of debate. We present inelastic neutron scattering evidence that gapless spin fluctuations coexist with superconductivity in La$_{1.905}$Ba$_{0.095}$CuO$_4$. Furthermore, we observe that both the low-energy magnetic spectral weight and the spin incommensurability are enhanced by the onset of superconducting correlations. We propose that the coexistence occurs through intertwining of spatial modulations of the pair wave function and the antiferromagnetic correlations. This proposal is also direc…
Recent low-temperature scanning tunnelling spectroscopy experiments on the surface of BSCCO-2212 have revealed a strong positive correlation between the position of localized resonances at -960 meV identified with interstitial oxygen dopants and the size of the local spectral gap. We review efforts to understand these correlations within a model where the dopants modulate the pair interaction on an atomic scale. We provide further evidence for this model by comparing the correlations between the dopants and the local density of states with experimental results.
We establish the quasi-one-dimensional Li purple bronze as a photoemission paradigm of Luttinger liquid behavior. We also show that generalized signatures of electron fractionalization are present in the angle resolved photoemission spectra for quasi-two-dimensional purple bronzes and certain cuprates. An important component of our analysis for the quasi-two-dimensional systems is the proposal of a ``melted holon'' scenario for the k-independent background that accompanies but does not interact with the peaks that disperse to define the Fermi surface.
Scanning tunneling spectroscopy applied to the high-$T_{c}$ cuprates has revealed significant spatial inhomogeneity on the nanoscale. Regions on the order of a coherence length in size show variations of the magnitude of the superconducting gap of order $\pm20%$ or more. An important unresolved question is whether or not these variations are also present in the bulk, and how they influence superconducting properties. As many theories and data analyses for high-$T_{c}$ superconductivity assume spatial homogeneity of the gap magnitude, this is a pressing question. We consider the far-infrared op…
We have studied the magnetic field or disorder induced insulating and metallic phases in amorphous Ta superconducting thin films. The evolution of the nonlinear transport in the insulating phase exhibits a non-monotonic behavior as the magnetic field is increased. We suggest that this observation could be an evidence of the presence of localized Cooper pairs in the insulating phase. As the metallic phase intervenes the superconducting and insulating states in Ta films, this result further reveals that Cooper pairs also exist in the metallic ground state.
We report the discovery of superconductivity in binary alloy Sn$_{1-x}$Sb$_{x}$ with $x$ in the range of 0.43 to 0.6, which possesses a modulated rhombohedral structure due to the incommensurate ordering of Sn and Sb layers along the $c$-axis. The specific heat measurements indicate a weakly coupled, fully gapped superconducting state in this homogeneity range with a maximum bulk $T_{\rm c}$ of 1.58 K at $x$ = 0.46, though the electronic specific heat and Hall coefficients remain nearly $x$-independent. The nonmonotonic dependence of the bulk $T_{\rm c}$ is discussed in relation to the effects…
Photoexcitations on a superconductor using ultrafast nir-infrared (NIR) pulses, whose energy is much higher than the superconducting energy gap, are expected to suppress/destroy superconductivity by breaking Cooper pairs and excite quasiparticles from occupied state to unoccupied state far above the Fermi level. This appears to be true only for small pumping fluence. Here we show that the intense NIR pumping has different effect. We perform an intense NIR pump, c-axis terahertz probe measurement on an electron-doped cuprate superconductor Pr$_{0.88}$LaCe$_{0.12}$CuO$_4$ with T$_c$=22 K. The me…
Usually, the superconducting quantum interference device (SQUID) consists of two Josephson junctions and the interference therein is modulated by a magnetic flux. In this work, we propose an electrically modulated SQUID consisting of single Josephson junction coupled by a time-reversal breaking Weyl semimetal thin film. For a low Fermi energy, the Josephson current is only mediated by Fermi arc surface states, and has an arbitrary ground-state phase difference \phi0 which is directly proportional to the product of the transverse electric field and the cross section area of the junction.For a s…
We study the effect of thermal phase fluctuation on the electron spectral function $A(k,ω)$ in a d-wave superconductor with Monte Carlo simulation. The phase degree of freedom is modeled by a XY-type model with build-in d-wave character. We find a ridge-like structure emerges abruptly on the underlying Fermi surface in $A(k,ω=0)$ above the KT-transition temperature of the XY model. Such a ridge-like structure, which shares the same characters with the Fermi arc observed in the pseudogap phase of the underdoped cuprates, is found to be caused by the vortex-like phase fluctuation of the XY model…
The binary ruthenate, RuO$_2$, has been the subject of intense interest due to its itinerant antiferromagnetism and strain-induced superconductivity. The strain mechanism and its effect on the microscopic electronic states leading to the normal and superconducting state, however, remain undisclosed. Here, we investigate highly-strained epitaxial (110) RuO$_2$ films using polarization-dependent oxygen K-edge X-ray absorption spectroscopy (XAS). Through the detection of pre-edge peaks, arising from O:$2p$ - Ru:$4d$ hybridization, we uncover the effects of epitaxial strain on the orbital/electron…
Terahertz reflectance spectra of the Ca-intercalated graphite CaC6 reveal a superconducting gap below 11K. The gap signature lacks a sharp onset to full reflectivity at 2Delta, but rather shows a distribution of gap values consistent with an anisotropic gap. The experimental data were successfully fitted to the gap distribution obtained from density functional calculations by Sanna et al. (Phys.Rev. B75, 020511, 2007). The temperature dependence of the superconducting gap is characteristic for a BCS type superconductor.
Motivated by numerical evidence of the valence bond groundstate of the two-dimensional Heisenberg pyrochlore lattice, we argue using a $t$-$J$ model that it evolves under doping into novel phases characterized by superconductivity coexisting with the underlying valence-bond solid order. A fermionic mean-field theory supplemented by exact diagonalization results provide strong arguments in favor of the stability of such supersolid phases. The resemblance with modulated superconducting patterns in high-$T_c$ cuprates as well as possible relevance to frustrated noncuprate superconductors such as …
Recent advances in the experimental growth and control of disordered thin films, heterostructures, and interfaces provide a fertile ground for the observation and characterisation of the collective superconducting excitations emerging below $T_c$ after breaking the $U(1)$ gauge symmetry. Here we combine THz experiments in a nano-structured granular Al thin film and theoretical calculations to demonstrate the existence of optically-active phase modes, which represent the Goldstone excitations of the broken gauge symmetry. By measuring the complex transmission trough the sample we identify a siz…
Based on the SU(2) lattice gauge theory formulation of the t-J model, we discuss possible signature of the unit cell doubling associated with the staggered flux (SF) state in the lightly doped spin liquid. Although the SF state appears only dynamically in a uniform d-wave superconducting (SC) state, a topological defect [SU(2) vortex] freezes the SF state inside the vortex core. Consequently, the unit cell doubling shows up in the hopping ($χ_{ij}$) and pairing ($Δ_{ij}$) order parameters of physical electrons. We find that whereas the center in the vortex core is a SF state, as one moves away…
We present a ^{115}In NMR study of the quasi two-dimensional heavy-fermion superconductor CeCoIn_5 believed to host a Fulde-Ferrel-Larkin-Ovchinnkov (FFLO) state. In the vicinity of the upper critical field and with a magnetic field applied parallel to the ab-plane, the NMR spectrum exhibits a dramatic change below T*(H) which well coincides with the position of reported anomalies in specific heat and ultrasound velocity. We argue that our results provide the first microscopic evidence for the occurrence of a spatially modulated superconducting order parameter expected in a FFLO state. The NMR…
We theoretically give an infinite number of metastable crystal structures for the superconducting sulfur hydride H$_{x}$S under pressure. It has been thought that theoretically predicted structures of H$_{2}$S and H$_{3}$S exhibit low and high $T_{\rm c}$ in the experiment, respectively. The newly found structures are long-period modulated crystals where slab-like H$_{2}$S and H$_{3}$S regions intergrow in a microscopic scale. The extremely small formation enthalpy for the H$_{2}$S--H$_{3}$S boundary indicated with the first-principles calculations suggests possible alloying of these phases th…
We present the first measurements of thermal signatures of the Little-Parks effect using a highly sensitive nanocalorimeter. Small variations of the heat capacity $C\_p$ of 2.5 millions of non interacting micrometer-sized superconducting rings threaded by a magnetic flux $Φ$ have been measured by attojoule calorimetry. This non-invasive method allows the measurement of thermodynamic properties -- and hence the probing of the energy levels -- of nanosystems without perturbing them electrically. It is observed that $C\_p$ is strongly influenced by the fluxoid quantization (Little-Parks effect) n…
Taking advantage of a novel multiprobe setup we have measured, on a unique sample, the ac-magnetic susceptibility, the resistivity, the ac-specific heat and the thermopower of the superconductor heavy fermion CeCu$_{2}$Si$_{2}$ under pressure up to 5.1 GPa. At the superconducting transition temperature $T_c$, the Meissner signal corresponds to that expected for the sample volume and coincides with the specific heat jump and the resistive transition completion temperatures. Differing from previous observations, here the susceptibility measurements did not reveal any anomaly in the vicinity of t…
Neutron and X-ray scattering studies have provided strong evidence for coupled spatial modulations of charge and spin densities in layered nickelates and cuprates. The accumulated results for La(2-x)Sr(x)NiO(4+d) are consistent with the strongly-modulated topological-stripe concept. Clues from Nd-doped La(2-x)Sr(x)CuO(4) suggest similar behavior for the cuprates. The experimental results are summarized, and features that conflict with an interpretation based on a Fermi-surface instability are emphasized. A rationalization for the differences in transport properties between the cuprates and nic…
Femtosecond pump-probe spectroscopy is applied to identify transient optical signatures of phase transitions in optimally doped YBa2Cu3O7-δ films. To elucidate the dynamics of superconducting and pseudogap phases, the slow thermal component is removed from the time-domain traces of photo-induced reflectivity in a high-flux regime with low frequency pulse rate. The rescaled data exhibit distinct signatures of the phase separation with abrupt changes at the onsets of TSC and TPG in excellent agreement with transport data. Compared to the superconducting phase, the response of the pseudogap phase…
We investigate phonon-mediated Cooper pairing in flat electronic band systems by solving the full-bandwidth multiband Eliashberg equations for superconductivity in magic angle twisted bilayer graphene using a realistic tight-binding model. We find that Cooper pairing away from the Fermi level contributes decisively to superconductivity by enhancing the critical temperature and ensures a robust finite superfluid density. We show that this pairing yields particle-hole asymmetric superconducting domes in the temperature-gating phase diagram and gives rise to distinct spectroscopic signatures in t…
We measured the far infrared reflectivity of two superconducting Pr(2-x)Ce(x)CuO(4) films above and below Tc. The reflectivity in the superconducting state increases and the optical conductivity drops at low energies, in agreement with the opening of a (possibly) anisotropic superconducting gap. The maximum energy of the gap scales roughly with Tc as 2 Delta_{max} / kB Tc ~ 4.7. We determined absolute values of the penetration depth at 5 K as lambda_{ab} = (3300 +/- 700) A for x = 0.15 and lambda_{ab} = (2000 +/- 300) A for x = 0.17. A spectral weight analysis shows that the Ferrell-Glover-Tin…
The optical conductivity of Ba(Fe$_{0.92}$Co$_{0.08}$)$_2$As$_2$ shows a clear signature of the superconducting gap, but a simple $s$-wave description fails in accounting for the low frequency response. This task is achieved by introducing an extra Drude peak in the superconducting state representing sub-gap absorption, other than thermally broken pairs. This extra peak and the coexisting $s$-wave response respect the total sum rule indicating a common origin for the carriers. We discuss the possible origins for this absorption as (i) quasiparticles due to pair-breaking from interband impurity…
The interplay of superconductivity with electronic and structural instabilities on the kagome lattice provides a fertile ground for the emergence of unusual phenomena. The vanadium-based kagome metals $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) exhibit superconductivity on an almost ideal kagome lattice, with the superconducting transition temperature $T_{\rm c}$ forming two domes upon pressure-tuning. The first dome arises from the competition between superconductivity and a charge-density-wave, whereas the origin for the second dome remains unclear. Herein, we show that the appearance of the second supe…
The Berezinskii-Kosterlitz-Thouless (BKT) transition is expected to have a clear signature on the specific heat. The singularity at the transition temperature $T_{BKT}$ is predicted to be immeasurable, and a broad non-universal peak is expected at $T>T_{BKT}$. Up to date this has not been observed in two-dimensional superconductors. We use a unique highly sensitive technique to measure the specific heat of ultrathin Pb films. We find that thick films exhibit a specific heat jump at $T_C$ that is consistent with BCS theory. As the film thickness is reduced below the superconducting coherence le…
We investigate the behavior of the Higgs (amplitude) mode when superconductivity emerges on a preexisting charge-density-wave state. We show that the weak overdamped square-root singularity of the amplitude fluctuations in a standard BCS superconductor is converted in a sharp, undamped power-law divergence in the coexisting state, reminiscent of the Higgs behavior in Lorentz-invariant theories. This effect reflects in a strong superconducting resonance in the Raman spectra, both for an electronic and a phononic mechanism leading to the Raman visibility of the Higgs. In the latter case, our res…
Superfluid dome in the spatially modulated two-dimensional XY model
Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Department of Chemistry, Duke University（杜克大学化学系）；Trans-scale Quantum Science Institute, The University of Tokyo（东京大学跨尺度量子科学研究所）
The compound IrTe2 is known to exhibit a transition to a modulated state featuring Ir-Ir dimers, with large associated atomic displacements. Partial substitution of Pt or Rh for Ir destabilizes the modulated structure and induces superconductivity. It has been proposed that quantum critical dimer fluctuations might be associated with the superconductivity. Here we test for such local dimer correlations and demonstrate their absence. X-ray pair distribution function approach reveals that the local structure of Ir0.95Pt0.05Te2 and Ir0.8Rh0.2Te2 dichalcogenide superconductors with compositions ju…
Recently RuB$_2$ was shown to be a possible two-gap, type-I superconductor. Temperature dependent heat capacity measurements revealed a two-gap superconducting ground state while magnetic field dependent magnetization measurements indicated surprising type-I superconductivity with a very low experimental critical field ($H_c$) $\sim$ 120 Oe. In this paper, we report direct spectroscopic evidence of two superconducting energy gaps in RuB$_2$. We have measured scanning tunnelling spectra exhibiting signature of two gaps on different grains of polycrystalline RuB$_2$, possibly originating from mu…
Signature of chiral superconducting order parameter evidenced in mesoscopic superconductors
Quantum Science Center of Guangdong-HongKong-Macau Greater Bay Area（粤港澳大湾区量子科学中心）；University of Science and Technology of China（中国科学技术大学）；The Chinese University of Hong Kong（香港中文大学）
We present tunneling data from optimally-doped, superconducting BaFe1.86Co0.14As2 and its parent compound, BaFe2As2. In the superconductor, clear coherence-like peaks are seen across the whole field of view, and their analysis reveals nanoscale variations in the superconducting gap value, Delta. The average magnitude of 2Delta is ~7.4 kBTC, which exceeds the BCS weak coupling value for either s- or d-wave superconductivity. The characteristic length scales of the deviations from the average gap value, and of an anti-correlation discovered between the gap magnitude and the zero bias conductance…
We have developed and measured a high-gain quantum-limited microwave parametric amplifier based on a superconducting lumped LC resonator with the inductor L including an array of 8 superconducting quantum interference devices (SQUIDs). This amplifier is parametrically pumped by modulating the flux threading the SQUIDs at twice the resonator frequency. Around 5 GHz, a maximum gain of 31 dB, a product amplitude-gain x bandwidth above 60 MHz, and a 1 dB compression point of -123 dBm at 20 dB gain are obtained in the non-degenerate mode of operation. Phase sensitive amplification-deamplification i…
We present a theory for quasiparticle heat transport through superconducting weak links. The thermal conductance depends on the phase difference ($ϕ$) of the superconducting leads. Branch conversion processes, low-energy Andreev bound states near the contact and the suppression of the local density of states near the gap edge are related to phase-sensitive transport processes. Theoretical results for the influence of junction transparency, temperature and disorder, on the phase modulation of the conductance are reported. For high-transmission weak links, $D\to 1$, the formation of an Andreev b…
We study an ultra-cold atomic Fermi Gas with the atom-atom interaction modulated periodically in space. A novel ground state with cooper pairs occupying non-zero center of mass momenta is found. Such a state is closely related to the state proposed by Fulde, Ferrell, Larkin, and Ovchinnikov(FFLO). The resultant single particle excitations with momenta along the direction of the modulation shows multiple-gap structures. Such a system can be realized in experiment with a spatially modulated Feshbach resonance. Experimental signatures of such a state are discussed.
We present femtosecond time-resolved pump-probe spectroscopic studies of a pseudogap (PG) along with the superconducting (SC) gap in an overdoped iron pnictide Ca(Fe0.927Co0.073)2As2. It is seen that the temperature evolution of the photoexcited quasiparticle (QP) relaxation dynamics, coherently excited A1g-symmetric optical phonon and two acoustic phonon dynamics behave anomalously in the vicinity of the superconducting transition temperature Tc. A continuous change in the sign of the experimentally measured transient differential reflectivity Delta_R/R signal at the zero time-delay between t…
The effects of absence of inversion symmetry on superconducting states are investigated theoretically. In particular we focus on the noncentrosymmetric compounds which have the cubic symmetry $O$ like Li$_2$Pt$_3$B. An appropriate and isotropic spin-orbital interaction is added in the Hamiltonian and it acts like a magnetic monopole in the momentum space. The consequent pairing wavefunction has an additional triplet component in the pseudospin space, and a Zeeman magnetic field $\bf{B}$ can induce a collinear supercurrent $\bf{J}$ with a coefficient $κ(T)$. The effects of anisotropy embedded i…
Cavity spintronics recently heralded non-local magnonic signal transfer between magnetic samples. Here we show that by including superconductors in the cavity, we can make use of these principles to bring composite superconductor--ferromagnet systems to the macroscale. We analyze how a superconductor's a.c. conductivity influences the spin dynamics of a spatially separated magnet, and we discuss the potential impact on spintronic applications.
We present local tunneling spectroscopy experiments in the superconducting and ferromagnetic phases of the reentrant superconductor ErRh$_4$B$_{4}$. The tunneling conductance curves jump from showing normal to superconducting features within a few mK close to the ferromagnetic transition temperature, with a clear hysteretic behavior. Within the ferromagnetic phase, we do not detect any superconducting correlations. Within the superconducting phase we find a peculiar V-shaped density of states at low energies, which is produced by the magnetically modulated phase that coexists with superconduct…
Solutions of the Bogoliubov-de Gennes equations for the two-dimensional self-consistent Hubbard t-U-V model of superconductors with $d_{x^2-y^2}$ symmetry of the order parameter in the presence of a magnetic field are found. It is shown that spatial inhomogeneity of superconducting order parameter results in the emergence of stripe-like domains that are stabilized by applied magnetic field leading to emergence of space-modulated composite spin-charge-superconducting order parameter.
A possible superconducting gap signature with filling temperature around 40 K in hexagonal iron telluride islands
Peking University（北京大学）；ShanghaiTech University（上海科技大学）；Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；Beijing Academy of Quantum Information Sciences（北京量子信息科学研究院）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Hefei National Laboratory（合肥国家实验室）
