Coherence Peak Research Articles

Robustness of Yu-Shiba-Rusinov resonances in the presence of a complex superconducting order parameter

Robust quantum systems rely on having a protective environment with minimized relaxation channels. Superconducting gaps play an important role in the design of such environments. The interaction of localized single spins with a conventional superconductor generally leads to intrinsically extremely narrow Yu-Shiba-Rusinov (YSR) resonances protected inside the superconducting gap. However, this may not apply to superconductors with nontrivial, energy dependent order parameters. Exploiting the Fe-doped two-band superconductor NbSe$_2$, we show that due to the nontrivial relation between its complex valued and energy dependent order parameters, YSR states are no longer restricted to be inside the gap. They can appear outside the gap (i. e. inside the coherence peaks), where they can also acquire a substantial intrinsic lifetime broadening. T-matrix scattering calculations show excellent agreement with the experimental data and relate the intrinsic YSR state broadening to the imaginary part of the host's order parameters. Our results suggest that non-thermal relaxation mechanisms contribute to the finite lifetime of the YSR states, even within the superconducting gap, making them less protected against residual interactions than previously assumed. YSR states may serve as valuable probes for nontrivial order parameters promoting a judicious selection of protective superconductors.

Lifthitz Transition and Shadow Gap in Li(Fe1−xCox)As Investigated by STM/STS

Recently, APRES experiments reported a superconducting (SC) gap opened on a shallow insulating band in Co-doped LiFeAs (Miao et al. 6:6056, 2015). Theoretically, this particular SC gap is characterized by asymmetric density of states (DOS) and vanishing of SC coherence peak, addressed as shadow gap. Using the scanning tunneling microscopy/spectroscopy (STM/STS), 1% and 3% Co-doped LiFeAs were studied. The Co dopants were atomically resolved. STS results at the Co sites on both samples showed no bound states. Negligible difference between spectra at Co sites and defect-free area was observed, suggesting weak impurity potentials of the Co dopants. Similar to LiFeAs, two SC coherence peaks at Δα = 5.6 meV and Δβ = 2.5 meV were observed in STS spectra of the 1% doped sample, which were the SC gaps of the inner hole band α and the outer hole band β. In the SC state, spectra of 3% Co-doped sample showed a broad peak at E1 = − 7.2 meV and other two peaks at ± 3.9 meV. Above Tc, the peak at E1 shifts to − 4.8 meV, and the peaks at ± 3.9 meV vanish. We showed that the distinct difference of STS results in 1% and 3% Co-doped LiFeAs was caused by Lifthitz transition and shadow gap on the shallow band. By fitting the spectra at low energies, we found the anisotropy of the β band was greatly increased when shadow gap opens on the shallow α band.

Theory of coherent phase modes in insulating Josephson junction chains

Recent microwave reflection measurements of Josephson junction chains have suggested the presence of nearly coherent collective charge oscillations deep in the insulating phase. Here we develop a qualitative understanding of such coherent charge modes by studying the local dynamical polarizability of the insulating phase of a finite length sine-Gordon model. By considering parameters near the noninteracting fermion limit where the charge operator dominantly couples to soliton-antisoliton pairs of the sine-Gordon model, we find that the local dynamical polarizability shows an array of sharp peaks in frequency representing coherent phase oscillations on top of an incoherent background. The strength of the coherent peaks relative to the incoherent background increases as a power law in frequency as well as exponentially as the Luttinger parameter approaches a critical value. The dynamical polarizability also clearly shows the insulating gap. We then compare the results in the high frequency limit to a perturbative estimate of phase-slip-induced decay of plasmons in the Josephson junction chain.

Detection of Bosonic Mode as a Signature of Magnetic Excitation in One-Unit-Cell FeSe on SrTiO3.

A "fingerprint" of Cooper pairing mediated by collective bosonic excitation mode is the reconstruction of the quasiparticle-density-of-states (DOS) spectrum with an additional "dip-hump" structure located outside the superconducting coherence peak. Here, we report an in situ scanning tunneling spectroscopy study of one-unit-cell (1-UC) FeSe film on a SrTiO3(001) substrate. In the quasiparticle-DOS spectrum, the bosonic excitation mode characterized by the dip-hump structure is detected outside the larger superconducting gap. Statistically, the excitation mode shows an anticorrelation with pairing strength in magnitude and yields an energy scale upper-bounded by twice the superconducting gap. The observation coincides with the characteristics of magnetic resonance in cuprates and iron-based superconductors. Furthermore, the local response of superconducting spectra to magnetically distinct Se defects all exhibits the induced in-gap quasiparticle bound states, indicating an unconventional sign-reversing pairing over the Fermi surface in 1-UC FeSe. These results clarify the magnetic nature of the bosonic excitation mode and reveal a signature of electron-magnetic-excitation coupling in 1-UC FeSe/SrTiO3(001) besides the previously established pairing channel of electron-phonon interaction.

Absence of strong localization at low conductivity in the topological surface state of low-disorder Sb2Te3

We present low-temperature transport measurements of a gate-tunable thin film topological insulator system that features high mobility and low carrier density. Upon gate tuning to a regime around the charge neutrality point, we infer an absence of strong localization even at conductivities well below $e^2/h$, where two dimensional electron systems should conventionally scale to an insulating state. Oddly, in this regime the localization coherence peak lacks conventional temperature broadening, though its tails do change dramatically with temperature. Using a model with electron-impurity scattering, we extract values for the disorder potential and the hybridization of the top and bottom surface states.

Study of broadband multimode light via non-phase-matched sum frequency generation

We propose non-phase-matched sum frequency generation (SFG) as a method for characterizing broadband multimode light. Both the central wavelength and the bandwidth are in this case not limited by the phase matching condition. As an example, we consider bright squeezed vacuum (BSV) generated through high-gain parametric down conversion (PDC). In the spectrum of SFG from BSV, we observe the coherent peak and the incoherent background. We show that the ratio of their widths is equal to the number of frequency modes in BSV, which in the case of low-gain PDC gives the degree of frequency entanglement for photon pairs. By generating the sum frequency in the near-surface region of a nonlinear crystal, we increase the SFG efficiency and get rid of the modulation caused by chromatic dispersion, known as Maker fringes. This allows one to use non-phasematched SFG as a wavelength-independent autocorrelator. Furthermore, we demonstrate efficient non-phase-matched three- and four-frequency summation of broadband multimode light, hardly possible under phase matching. We show that the latter contains the coherent peak while the former does not.

Cooper Pair Density of Bi2Sr2CaCu2O8+ x in Atomic scale at 4.2 K.

In pursuit of the elusive mechanism of high- T C superconductors (HTSC), spectroscopic imaging scanning tunneling microscopy (SI-STM) is an indispensable tool for surveying local properties of HTSC. Since a conventional STM utilizes metal tips, which allow the examination of only quasiparticles and not superconducting (SC) pairs, Josephson tunneling using STM has been demonstrated by many authors in the past. An atomically resolved scanning Josephson tunneling microscopy (SJTM), however, was realized only recently on Bi2Sr2CaCu2O8+ x (Bi-2212) below 50 mK and on the Pb(110) surface at 20 mK. Here we report the atomically resolved SJTM on Bi2Sr2CaCu2O8+ x at 4.2 K using Bi-2212 tips created in situ. The I- V characteristics show clear zero bias conductance peaks following Ambegaokar-Baratoff (AB) theory. A gap map was produced for the first time using an atomically resolved Josephson critical current map I C( r) and AB theory. Surprisingly, we found that this new gap map is anticorrelated to the gap map produced by a conventional method relying on the coherence peaks. Quasiparticle resonance due to a single isolated zinc atom impurity was also observed by SJTM, indicating that atomically resolved SJTM was achieved at 4.2 K. Our result provides a starting point for realizing SJTM at even higher temperatures, rendering possible investigation of the existence of SC pairs in HTSC above the T C.

Manifestation of electron correlation effect in 5f states of uranium compounds revealed by 4d–5f resonant photoelectron spectroscopy

We have elucidated the nature of the electron correlation effect in uranium compounds by imaging the partial $\mathrm{U}~5f$ density of states (pDOS) of typical itinerant, localized, and heavy fermion uranium compounds by using the $\mathrm{U}~4d-5f$ resonant photoemission spectroscopy. Obtained $\mathrm{U}~5f$ pDOS exhibit a systematic trend depending on the physical properties of compounds. The coherent peak at the Fermi level can be described by the band-structure calculation, but an incoherent peak emerges on the higher binding energy side ($\lesssim 1~\mathrm{eV}$) in the \Uf pDOS of localized and heavy fermion compounds. As the $\mathrm{U}~5f$ state is more localized, the intensity of the incoherent peak is enhanced and its energy position is shifted to higher binding energy. These behaviors are consistent with the prediction of the Mott metal-insulator transition, suggesting that the Hubbard-$U$ type mechanism takes an essential role in the $5f$ electronic structure of actinide materials.

Spin diffusion equation in superconductors in the vicinity of Tc

We microscopically derive the spin diffusion equation in an s-wave superconductor in the vicinity of the superconducting transition temperature Tc. Applying the general relation between the relaxation function and the response function to the present spin diffusion problem, we examine how the spin relaxation time and the spin diffusion coefficient are renormalized in the superconducting state. The analysis reveals that, below Tc, both the spin relaxation time and the spin diffusion coefficient are increased, resulting in an enhancement of the spin diffusion length. The present result may provide an explanation for the recent observation of an enhanced spin pumping signal below Tc in a Py/Nb/Pt system that is free from the coherence peak effect.

Observation of the coherent quasiparticle states in SrRu1–xIrxO3 films via polarization-dependent soft X-ray absorption spectroscopy

The electronic structures of SrRu1−xIrxO3 films (0≤x≤1) have been investigated by employing polarization-dependent soft X-ray absorption spectroscopy. In SrIrO3, the coherent quasi-particle peak at the Fermi level (EF) is clearly observed, reflecting the spin-orbit-coupled correlated metallic nature of SrIrO3. X-ray linear dichroism signals for x=0 and x=1 are negligibly weak, demonstrating the pseudo-cubic structure for SrRuO3 and the strong spin-orbit coupling in SrIrO3. In contrast, finite linear dichroism is observed for the intermediate x regime, indicating that the narrow dxz↓ and dyz↓ bands close to EF are occupied less than the wide dxy↓ band due to the enhanced in-plane hopping.

Smeared d‐Wave Anisotropy in a Monolayer Organic Superconductor

AbstractAn epitaxially grown monolayer of organic superconductor, (BETS)2GaCl4, on Ag(111) forms islands of uniform and mixed stacking of 2D stripes. A d‐wave superconducting gap of magnitude 2Δ = 14 meV is ubiquitously measured even though orientation directions of the molecular chains are altered in the inhomogeneous islands. Mixing of intrastripes antinodal states is manifested by smeared anisotropy of the low energy quasiparticle as well as features of multigaps in their density of states. Despite proximal convolution, the pronounced coherence peaks indicate well preserved superconducting state. The interplay between structural parameters and electronic properties makes single layer (BETS)2GaCl4 a unique playground to test the effect of confinement and symmetry variation on the superconducting ground state.

High-Stability Algorithm in White-Light Phase-Shifting Interferometry for Disturbance Suppression

A hybrid algorithm, combining a “Gauss-type” envelope algorithm with the Carré algorithm, is proposed for disturbance suppression. For white-light phase-shifting interferometry (WLPSI), this novel algorithm provides suitable performance in suppressing noise caused by external conditions, such as mechanical vibrations, low-reflectivity surfaces, and poor-contrast interferograms. The algorithm is mathematically derived, and simulation testing is performed at the micro level to demonstrate that the algorithm can position the coherence peak correctly under challenging conditions. At the macro level, the algorithm is further verified on standard samples, with the repeatability of the step height being less than 0.32% in a favorable environment and 0.59% in a noisy environment. The repeatability of the roughness was 0.23% in a favorable environment and 0.65% in a noisy environment. Note that “repeatability” = “standard deviation” / “dean value”, reflecting the stability as a percentage. The simulated and experimental results prove that the proposed algorithm is highly precise and robust. This algorithm reduces the environmental dependence of the performance of WLPSI instrumentation and expands its range of application.

Visualization of the periodic modulation of Cooper pairing in a cuprate superconductor

A major obstacle in understanding the mechanism of Cooper pairing in the cuprates is the existence of various intertwined orders associated with spin, charge, and Cooper pairs. Of particular importance is the ubiquitous charge order features that have been observed in a variety of cuprates, especially in the underdoped regime of the phase diagram. To explain the origin of the charge order and its implication to the superconducting phase, many theoretical models have been proposed, such as charge stripes, electronic nematicity, and Fermi surface instability. A highly appealing physical picture is the so-called pair density wave (PDW), a periodic modulation of Cooper paring in space, which may also induce a charge order. To elucidate the existence and nature of the PDW order, here we use scanning tunneling microscopy (STM) to investigate a severely underdoped Bi2Sr2CaCu2O8+{\delta}, in which superconductivity just emerges on top of a pronounced checkerboard charge order. By analyzing the spatial distribution of the spectral features characteristic of superconductivity, we observe a periodic modulation of both the superconducting coherence peak and gap depth, demonstrating the existence of a density wave order of Cooper pairing. The PDW order has the same spatial periodicity as the charge order, and the amplitudes of the two orders exhibit clear positive correlation. These results shed important new lights on the origin of and interplay between the charge order and Cooper pairing modulation in the cuprates.

Temperature and frequency of complex conductivity, penetration depth and superfluid density of Ba(Fe1−xCox)2As2-superconductor in one- and two-gap models

The temperature and frequency dependence of complex dynamical conductivity $$\sigma = \sigma_{1} + i\sigma_{2}$$ , penetration depth, and superfluid density of Ba(Fe1−xCox)2As2 are calculated in the framework of one- and two-gap models at terahertz frequencies for a temperature range of 2 K < T < TC (TC = 22 K). In the single-gap model, an isotropic s-wave gap without any node and a d-wave gap with possible nodes are considered. In the two-gap model, one of the gaps was considered isotropic s-wave gap with amplitude $$\varDelta_{A} = 3\;{\text{meV}}$$ , while the other gap was supposed to be an anisotropic d-wave gap with possible nodes, and its rms amplitude was $$\varDelta_{0} = 8\;{\text{meV}}$$ . The interaction between the gaps is waived, since it is small, and its description is problematic. Comparing the result with the experimental data proves that the two-gap model consistently describes the optical characteristics of Ba(Fe1−xCox)2As2. In the two-gap model, the temperature dependence of $$\sigma_{1}$$ demonstrated a coherence peak at frequencies below 15 cm−1. The temperature dependence of the penetration depth calculated from $$\sigma_{2}$$ shows power-law behavior at low temperatures, and the superfluid density varies steeply near TC.

Time-dependent spectra of a three-level atom in the presence of electron shelving

We investigate time-dependent spectra of the intermittent resonance fluorescence of a single, laser-driven, three-level atom due to electron shelving. After a quasi-stationary state of the strong transition, a slow decay due to shelving leads to the steady state of the three-level system. The long-term stationary spectrum consists of a coherent peak, an incoherent Mollow-like structure, and a very narrow incoherent peak at the laser frequency. We find that in the ensemble average dynamics the narrow peak emerges during the slow decay regime, after the Mollow spectrum has stabilized, but well before an average dark time has passed. The coherent peak, being a steady state feature, is absent during the time evolution of the spectrum

Coherent multiple scattering of light in ( 2+1 ) dimensions

We formulate a multiple scattering theory of light in media spatially disordered along two directions and homogeneous along the third one, without making any paraxial approximation on the wave equation and fully treating the vector character of light. With this formalism, we calculate the distribution of transverse momenta of a beam as it evolves along the optical axis, and unveil a phenomenon not captured by the paraxial equation: a cross-over from a scalar to a vector regime, visible in the coherent backscattering peak as polarization gets randomized.

Structural phase transition, precursory electronic anomaly, and strong-coupling superconductivity in quasi-skutterudite (Sr1−xCax)3Ir4Sn13 and Ca3Rh4Sn13**Project supported by the National Natural Science Foundation of China (Grant Nos. 11674377 and 11634015), the National Key R&D Program of China (Grant Nos. 2017YFA0302904 and 2016YFA0300502), and the Strategic Priority Research Program (B) of the Chinese Academy of Sciences (Grant No. XDB07020200). J. Y. is supported

The interplay between superconductivity and structural phase transition has attracted enormous interest in recent years. For example, in Fe-pnictide high temperature superconductors, quantum fluctuations in association with structural phase transition have been proposed to lead to many novel physical properties and even the superconductivity itself. Here we report a finding that the quasi-skutterudite superconductors (Sr1−xCax)3Ir4Sn13 (x = 0, 0.5, 1) and Ca3Rh4Sn13 show some unusual properties similar to the Fe-pnictides, through 119Sn nuclear magnetic resonance (NMR) measurements. In (Sr1−xCax)3Ir4Sn13, the NMR linewidth increases below a temperature T* that is higher than the structural phase transition temperature Ts. The spin-lattice relaxation rate (1/T1) divided by temperature (T), 1/T1T and the Knight shift K increase with decreasing T down to T*, but start to decrease below T*, and followed by more distinct changes at Ts. In contrast, none of the anomalies is observed in Ca3Rh4Sn13 that does not undergo a structural phase transition. The precursory phenomenon above the structural phase transition resembles that occurring in Fe-pnictides. In the superconducting state of Ca3Ir4Sn13, 1/T1 decays as exp(−Δ/kBT) with a large gap Δ = 2.21kBTc, yet without a Hebel–Slichter coherence peak, which indicates strong-coupling superconductivity. Our results provide new insight into the relationship between superconductivity and the electronic-structure change associated with structural phase transition.

On the origin of in-gap states in homogeneously disordered ultrathin films. MoC case

Many disordered superconducting films exhibit smeared tunneling spectra with evident in-gap states. We have found that the tunneling density of states in ultrathin MoC films is gapless and can be described by the Dynes version of the BCS density of states with a strong broadening parameter Γ accounting for the suppression of coherence peaks and increased in-gap states. The thinner the film, the lower the Tc and the superconducting energy gap Δ and the larger the Γ. MoC films of 3 nm thickness deposited simultaneously on silicon and sapphire substrates reveal very similar scalar disorder, evidenced by the equal sheet resistance, but exhibit different superconducting characteristics of Tc, Δ and Γ, suggesting that pair breaking responsible for the dissipation channel and the suppression of superconductivity originates on the film-substrate interface. It indicates that sapphire is a stronger pair breaker. Interface pair breaking can be operative in other cases as well.

Probe of spin dynamics in superconducting NbN thin films via spin pumping

The emerging field of superconductor (SC) spintronics has attracted intensive attentions recently. Many fantastic spin dependent properties in SC have been discovered, including the observation of large magnetoresistance, long spin lifetimes and the giant spin Hall effect in SC, as well as spin supercurrent in Josephson junctions, etc. Regarding the spin dynamic in SC films, few studies has been reported yet. Here, we report the investigation of the spin dynamics in an s-wave superconducting NbN film via spin pumping from an adjacent insulating ferromagnet GdN layer. A profound coherence peak of the Gilbert damping is observed slightly below the superconducting critical temperature of the NbN layer, which is consistent with recent theoretical studies. Our results further indicate that spin pumping could be a powerful tool for investigating the spin dynamics in 2D crystalline superconductors.

Spin-current coherence peak in superconductor/magnet junctions

Coherence peak effects in a superconductor induced by a thermal spin current are reported. We measured inverse spin Hall effects induced by spin injection from a ferrimagnetic insulator Y3Fe5O12 into a superconductor NbN using longitudinal spin Seebeck effects. In the vicinity of the superconducting transition temperature of the NbN, a large enhancement of the spin Seebeck voltage is observed, whose sign is opposite to that for the vortex Nernst effect, but is consistent with a calculation for a coherence peak effect in the superconductor NbN.