We measure temperature dependent quasiparticle fluctuations in a small Al volume, embedded in a NbTiN superconducting microwave resonator. The resonator design allows for read-out close to equilibrium. By placing the Al film on a membrane, we enhance the fluctuation level and separate quasiparticle from phonon effects. When lowering the temperature, the recombination time saturates and the fluctuation level reduces a factor $\sim$100. From this we deduce that the number of free quasiparticles is still thermal. Therefore, the theoretical, inverse relation between quasiparticle number and recombination time is invalid in this experiment. This is consistent with quasiparticle trapping, where on-trap recombination limits the observed quasiparticle lifetime.
There has been an intense search in recent years for long-lived spin-polarized carriers for spintronic and quantum-computing devices. Here we report that spin polarized quasi-particles in superconducting aluminum layers have surprisingly long spin-lifetimes, nearly a million times longer than in their normal state. The lifetime is determined from the suppression of the aluminum's superconductivity resulting from the accumulation of spin polarized carriers in the aluminum layer using tunnel spin injectors. A Hanle effect, observed in the presence of small in-plane orthogonal fields, is shown to…
We study the kinetics of the quasiparticle capture and emission process in a small superconducting island (Cooper-pair box) connected by a tunnel junction to a massive superconducting lead. At low temperatures, the charge on the box fluctuates between two states, even and odd in the number of electrons. Assuming that the odd-electron state has the lowest energy, we evaluate the distribution of lifetimes of the even- and odd-electron states of the Cooper-pair box. The lifetime in the even-electron state is an exponentially distributed random variable corresponding to a homogenous Poisson proces…
The scattering cross section of a Coulomb potential screened by a charged Bose gas (CBG) is calculated both above and below the Bose-Einstein condensation temperature, using the variable phase method. In contrast with the BCS superconductor, the screened scattering potential and quasiparticle lifetime are found to be very different in the superconducting and normal states. We apply the result to explain the appearence of a sharp peak in the ARPES spectra in some cuprates below the superconducting transition.
Scanning tunneling spectroscopy measurements of superconducting thin lanthanum films grown on a normal metal tungsten substrate reveal an extraordinarily large broadening of the coherence peaks. The observed broadening corresponds to very short electron-like quasiparticle lifetimes in the tunneling process. A thorough analysis considering the different relaxation processes reveals that the dominant mechanism is an efficient quasiparticle relaxation at the interface between the superconducting film and the underlying substrate. This process is of general relevance to scanning tunneling spectros…
Based on Quasiparticle Interference(QPI) around a point impurity, we demonstrate an analysis scheme that extracts the lifetime of a quasiparticle by using the Local Density of States(LDOS) data around the impurity in a Scanning Tunneling Microscopy(STM) experiment. This data analysis scheme would augment the Fourier-Transform Scanning Tunneling Spectroscopic method which provides us with the quasiparticle dispersion. Thus, point impurities can be used as probes to extract quasiparticle lifetimes from STM experiments and this would complement other experimental methods such as Angle Resolved Ph…
We have measured the number of quasiparticles and their lifetime in aluminium superconducting microwave resonators. The number of excess quasiparticles below 160 mK decreases from 72 to 17 $μ$m$^{-3}$ with a 6 dB decrease of the microwave power. The quasiparticle lifetime increases accordingly from 1.4 to 3.5 ms. These properties of the superconductor were measured through the spectrum of correlated fluctuations in the quasiparticle system and condensate of the superconductor, which show up in the resonator amplitude and phase respectively. Because uncorrelated noise sources vanish, fluctuatio…
When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at 2$Δ$. We show that a phonon bandgap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon bandgap can be realized and matched to the recombination energy with a phononic crystal, a periodically-patterned dielectric membrane. We discuss in detail the non-equilibrium quasiparticle and phonon distributions that arise in a supercondu…
Quasiparticle excitations can compromise the performance of superconducting devices, causing high frequency dissipation, decoherence in Josephson qubits, and braiding errors in proposed Majorana-based topological quantum computers. Quasiparticle dynamics have been studied in detail in metallic superconductors but remain relatively unexplored in semiconductor-superconductor structures, which are now being intensely pursued in the context of topological superconductivity. To this end, we introduce a new physical system comprised of a gate-confined semiconductor nanowire with an epitaxially grown…
The attractive Hubbard model on a 2-D square lattice is studied at low electronic densities using the ladder approximation for the pair susceptibility. This model includes (i) the short coherence lengths known to exist experimentally in the cuprate superconductors, and (ii) two-particle bound states that correspond to electron pairs. We study the quasiparticle lifetimes in both non self-consistent and self-consistent theories, the latter including interactions between the pairs. We find that if we include the interactions between pairs the quasiparticle lifetimes vary approximately linearly wi…
We have measured the complex conductivity of a BSCCO(2212) thin film between 0.2 and 1.0 THz. We find the conductivity in the superconducting state to be well described as the sum of contributions from quasiparticles, the condensate, and order parameter fluctuations which draw 30% of the spectral weight from the condensate. An analysis based on this decomposition yields a quasiparticle scattering rate on the order of k_(B)*T/(hbar) for temperatures below Tc.
We investigate the complex conductivity of a highly disordered MoC superconducting film with $k_Fl\approx 1$, where $k_F$ is the Fermi wavenumber and $l$ is the mean free path, derived from experimental transmission characteristics of coplanar waveguide resonators in a wide temperature range below the superconducting transition temperature $T_c$. We find that the original Mattis-Bardeen model with a finite quasiparticle lifetime, $τ$, offers a perfect description of the experimentally observed complex conductivity. We show that $τ$ is appreciably reduced by scattering effects. Characteristics …
We have directly measured quasiparticle number fluctuations in a thin film superconducting Al resonator in thermal equilibrium. The spectrum of these fluctuations provides a measure of both the density and the lifetime of the quasiparticles. We observe that the quasiparticle density decreases exponentially with decreasing temperature, as theoretically predicted, but saturates below 160 mK to 25-55 per cubic micron. We show that this saturation is consistent with the measured saturation in the quasiparticle lifetime, which also explains similar observations in qubit decoherence times.
The paramagnon contribution to the quasiparticle inelastic scattering rate in disordered superconductors is presented. Using Anderson's exact eigenstate formalism, it is shown that the scattering rate is Stoner enhanced and is further enhanced by the disorder relative to the clean case in a manner similar to the disorder enhancement of the long-range Coulomb contribution. The results are discussed in connection with the possibility of conventional or unconventional superconductivity in the borocarbides. The results are compared to recent tunneling experiments on LuNi$_{2}$B$_{2}$C.
We argue that the well known Dynes formula [Dynes R C {\it et al.} 1978 {\it Phys. Rev. Lett.} {\bf 41} 1509] for the superconducting quasiparticle density of states, which tries to incorporate the lifetime broadening in an approximate way, cannot be justified microscopically for conventional superconductors. Instead, we propose a new simple formula in which the energy gap has a finite imaginary part $-Δ_2$ and the quasiparticle energy is real. We prove that in the quasiparticle approximation 2$Δ_2$ gives the quasiparticle decay rate at the gap edge for conventional superconductors. This concl…
Studying the nodal quasiparticles in superconducting cuprates by photoemission with highly improved momentum resolution, we show that a new "kink" feature in the scattering rate is a key to uncover the nature of electron correlations in these compounds. Our data provide evidence that the main doping independent contribution to the scattering can be well understood in terms of the conventional Fermi liquid model, while the additional doping dependent contribution has a magnetic origin. This sheds doubt on applicability of a phonon-mediated pairing mechanism to high temperature superconductors.
We compare the quasiparticle lifetime behavior in the unitary limit of two unconventional superconductors dressed by non-magnetic impurity scattering to differentiate an anomalous functional behavior in its shape when the disorder concentration is changed in a triplet paired model with respect to the well behave singlet model. For singlet paired superconductors, the functional shape of the lifetime due to elastic scattering around the nodal regions does not change with the change of the disorder concentration, but for a triplet model with a tiny gap, an anomalous drop in shape is observed only…
We measure the Shubnikov-de Haas effect in thin-film Sr$_2$RuO$_4$ grown on an (LaAlO$_3$)$_{0.29}$-(SrAl$_{1/2}$Ta$_{1/2}$O$_3$)$_{0.71}$ (LSAT) substrate. We detect all three known Fermi surfaces and extract the Fermi surface volumes, cyclotron effective masses, and quantum lifetimes. We show that the electronic structure is nearly identical to that of single-crystal Sr$_2$RuO$_4$, and that the quasiparticle lifetime is consistent with the Tc of comparably clean, single-crystal Sr$_2$RuO$_4$. Unlike single-crystal Sr$_2$RuO$_4$, where the quantum and transport lifetimes are roughly equal, we…
We study the dynamical quasiparticle scattering by spin and charge fluctuations in Fe-based pnictides within a five-orbital model with on-site interactions. The leading contribution to the scattering rate is calculated from the second-order diagrams with the polarization operator calculated in the random-phase approximation. We find one-particle scattering rates which are highly anisotropic on each Fermi surface sheet due to the momentum dependence of the spin susceptibility and the multi-orbital composition of each Fermi pocket. This fact, combined with the anisotropy of the effective mass, p…
A new generation of angular-resolved photoemission spectroscopy (ARPES) measurements on the cuprate superconductors offer the promise of enhanced momentum and energy resolution. In particular, the energy and temperature dependence of the on-shell nodal (k_x=k_y) quasiparticle scattering rate can be studied. In the superconducting state, low temperature transport measurements suggest that one can describe nodal quasiparticles within the framework of a BCS d-wave model by including forward elastic scattering and spin-fluctuation inelastic scattering. Here, using this model, we calculate the temp…
We report new time-resolved data of quasiparticle relaxation and Cooper pair recombination dynamics in YBa_2Cu_3O_{7-δ}, measured as a function of temperature and doping δusing femtosecond optical spectroscopy. The data show the existence of a normal state pseudo-gap for in-plane charge excitations below T* and an unusual divergence of the quasiparticle relaxation time in the superconducting state τ_s with δtowards optimum doping. In the underdoped state, no change in the amplitude of the induced transmission (which is proportional to the DOS at E_F), or relaxation time τ_s is observed at T_c.…
Scanning tunnelling spectroscopy (STS) measurements find that the surface of Bi-2212 is characterized by nanoscale sized regions, "gap patches," which have different magnitudes for the d-wave energy gap. Recent studies have shown that the tunnelling conductance can be fit using a BCS-type density of states for a d-wave superconductor with a local quasiparticle scattering rate. The fit is made with a scattering rate which varies linearly with energy and has a slope that is positively correlated with the local value of the gap. We revisit a model of quasiparticle scattering by impurities and spi…
We show that low-energy spectral features in the cuprates can be separated into different components by the measurement of the recombination dynamics of different low-energy excitations in real-time using femtosecond laser spectroscopy. Quasiparticle (QP) recombination across the gap and intra-gap localized state relaxation processes exhibit qualitatively different time- and temperature-dependences. The relaxation measurements also show the existence of two distinct coexisting energy gaps near optimum doping and in the overdoped region, one more or less temperature independent (which exists ab…
We present a circuit QED experiment in which a separate transmission line is used to address a quasi-lumped element superconducting microwave resonator which is in turn coupled to an Al/AlO$_{x}$/Al Cooper-pair box (CPB) charge qubit. In our measurements we find a strong correlation between the measured lifetime of the CPB and the coupling between the qubit and the transmission line. By monitoring perturbations of the resonator's 5.44 GHz resonant frequency, we have measured the spectrum, lifetime ($T_{1}$), Rabi, and Ramsey oscillations of the CPB at the charge degeneracy point while the CPB …
The parity modulation of the ground state of a superconducting island is a direct consequence of the presence of the Cooper pair condensate preferring an even number of charge carriers. The addition energy of an odd, unpaired quasiparticle equals to the superconducting gap, $Δ$, suppressing single electron hopping in the low temperature limit. Controlling the quasiparticle occupation is of fundamental importance for superconducting qubits as single electron tunneling results in decoherence. In particular, topological quantum computation relies on the parity control and readout of Majorana boun…
We directly observe low-temperature non-equilibrium quasiparticle tunneling in a pair of charge qubits based on the single Cooper-pair box. We measure even- and odd-state dwell time distributions as a function of temperature, and interpret these results using a kinetic theory. While the even-state lifetime is exponentially distributed, the odd-state distribution is more heavily weighted to short times, implying that odd-to-even tunnel events are not described by a homogenous Poisson process. The mean odd-state dwell time increases sharply at low temperature, which is consistent with quasiparti…
We have calculated the non-equilibrium quasiparticle and phonon distributions $f(E)$, $n(Ω)$, where $E$ and $Ω$ are the quasiparticle and phonon energies respectively, generated by the photons of the probe signal of a low temperature superconducting resonator SR operating well-below its transition temperature $T_c$ as the absorbed probe power per unit volume $P_{abs}$ was changed. The calculations give insight into a rate equation estimate which suggests that the quasiparticle distributions can be driven far from the thermal equilibrium value for typical readout powers. From $f(E)$ the driven …
Present computations of the gap of color superconductivity in weak coupling assume that the quarks which participate in the condensation process are infinitely long-lived. However, the quasiparticles in a plasma are characterized by having a finite lifetime. In this article we take into account this fact to evaluate its effect in the computation of the color gap. By first considering the Schwinger-Dyson equations in weak coupling, when one-loop self-energy corrections are included, a general gap equation is written in terms of the spectral densities of the quasiparticles. To evaluate lifetime …
The quasiparticle lifetime and the related transport relaxation times are the fundamental quantities which must be known in order to obtain a description of the transport properties of the high T_c superconductors. Studies of these quantities have been undertaken previously for the d-wave, high T_c superconductors for the case of temperature-independent elastic impurity scattering. However, much less is known about the temperature-dependent inelastic scattering. Here we give a detailed description of the characteristics of the temperature-dependent quasiparticle-quasiparticle scattering in d-w…
We illustrate the importance of many-body effects in the Fourier transformed local density of states (FT-LDOS) of d-wave superconductors from a model of electrons coupled to an Einstein mode with energy Omega_0. For bias energies significantly larger than Omega_0 the quasiparticles have short lifetimes due to this coupling, and the FT-LDOS is featureless if the electron-impurity scattering is treated within the Born approximation. In this regime it is important to include boson exchange for the electron-impurity scattering which provides a `step down' in energy for the electrons and allows for…
We examine the macroscopic quantum tunneling (MQT) in high-Tc superconductor Josephson junctions with a d-wave order parameter. Using microscopic Hamiltonian and the functional integral method, we analytically obtain the MQT rate (the inverse lifetime of the metastable state) for the c-axis twist Josephson junctions. In the case of the zero twist angle, the system shows the super-Ohmic dissipation due to the presence of the nodal quasiparticle tunneling. Therefore, the MQT rate is strongly suppressed in compared with the finite twist angle cases.
Low temperature thermal conductivity, $κ$, of optimally-doped Bi2212 was studied before and after the introduction of point defects by electron irradiation. The amplitude of the linear component of $κ$ remains unchanged, confirming the universal nature of heat transport by zero-energy quasiparticles. The induced decrease in the absolute value of $κ$ at finite temperatures allows us to resolve a nonuniversal term in $κ$ due to conduction by finite-energy quasiparticles. The magnitude of this term provides an estimate of the quasiparticle lifetime at subkelvin temperatures.
We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (~ 1 μs) and sets a bound for a weakly coupled island (> 10 μs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the r…
We investigate theoretically the magnetic spin-flip transitions of neutral atoms trapped near a superconducting slab. Our calculations are based on a quantum-theoretical treatment of electromagnetic radiation near dielectric and metallic bodies. Specific results are given for rubidium atoms near a niobium superconductor. At the low frequencies typical of the atomic transitions, we find that BCS theory greatly overestimates coherence effects, which are much less pronounced when quasiparticle lifetime effects are included through Eliashberg theory. At 4.2 K, the typical atomic spin lifetime is f…
Recent ARPES experiments show a narrow quasiparticle peak at the gap edge along the antinodal [1,0]-direction for the overdoped cuprate superconductors. We show that within weak coupling BCS theory for a d-wave superconductor the s-wave single-impurity scattering cross section vanishes for energies of the gap edge. This coherence effect occurs through multiple scattering off the impurity. For small impurity concentrations the spectral function has a pronounced increase of the (scattering) lifetime for antinodal quasiparticles but shows a very broad peak in the nodal direction, in qualitative a…
We implement dynamical decoupling techniques to mitigate noise and enhance the lifetime of an entangled state that is formed in a superconducting flux qubit coupled to a microscopic two-level system. By rapidly changing the qubit's transition frequency relative to the two-level system, we realize a refocusing pulse that reduces dephasing due to fluctuations in the transition frequencies, thereby improving the coherence time of the entangled state. The coupling coherence is further enhanced when applying multiple refocusing pulses, in agreement with our $1/f$ noise model. The results are applic…
Quasiparticle recombination in a superconductor with an s-wave gap is typically dominated by a phonon bottleneck effect. We have studied how a magnetic field changes this recombination process in metallic thin-film superconductors, finding that the quasiparticle recombination process is significantly slowed as the field increases. While we observe this for all field orientations, we focus here on the results for a field applied parallel to the thin film surface, minimizing the influence of vortices. The magnetic field disrupts the time-reversal symmetry of the pairs, giving them a finite lifet…
We show that recent measurements of the magnetic field dependence of the magnetization, specific heat and resistivity of overdoped $T_c \sim 17K$ $Tl_{2}Ba_{2}CuO_{6+δ}$ in the vicinity of the superconducting $H_{c2}$ imply that the vortex viscosity is anomalously small and that the material studied is inhomogeneous with small, a few hundred $Å$, regions in which the local $T_{c}$ is much higher than the bulk $T_{c}$. The anomalously small vortex viscosity can be derived from a microscopic model in which the quasiparticle lifetime varies dramatically around the Fermi surface, being small every…
A detailed study of the normal state photoemission lineshapes and quasiparticle dispersion for the single layer Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+δ}$ (Bi2201) superconductor is presented. We report the first experimental evidence of a double peak structure and a dip of spectral intensity in the energy distribution curves (EDCs) along the nodal direction. The double peak structure is well identified in the normal state, up to ten times the critical temperature. As a result of the same self-energy effect, a strong mass renormalization of the quasiparticle dispersion, i.e. kink, and an increase of th…
We present the results of a microscopic calculation of the longitudinal thermal conductivity of quasiparticles, $κ_{xx}$, in a 2D d-wave superconductor in the vortex state. Our approach takes into account both impurity scattering and a contribution to the thermal transport lifetime due to the scattering of quasiparticles off of vortices. We compare the results with the experimental measurements on high-T$_c$ cuprates and organic superconductors.
One of the key challenges in the field of high-temperature superconductivity is understanding the nature of fermionic quasiparticles. Experiments consistently demonstrate the existence of a second energy scale, distinct from the d-wave superconducting gap, that persists above the transition temperature into the "pseudogap" phase. One common class of models relates this energy scale to the quasiparticle gap due to a competing order, such as the incommensurate "checkerboard" order observed in scanning tunneling microscopy (STM) and resonant elastic X-ray scattering (REXS). In this paper we show …
Measurements of the temperature dependence of the quasiparticle (QP) dynamics in Hg1223 with femtosecond time-resolved optical spectroscopy are reported. From the temperature dependence of the amplitude of the photoinduced reflection, the existence of two gaps is deduced, one temperature dependent Dc that closes at Tc, and another temperature independent ''pseudogap'' Dp. The zero-temperature magnitudes of the two gaps are Dc/kTc = 6 +/- 0.5 and Dp/kTc = 6.4 +/- 0.5 respectively. The quasiparticle lifetime is found to exhibit a divergence as T -> Tc from below, which is attributed to the exist…
We show that low-lying excitations of a 2D BCS superconductor are significantly altered when coupled to an externally driven cavity, which induces controllable long-range attractive interactions between the electrons. We find that they combine non-linearly with intrinsic local interactions to increase the Bogoliubov quasiparticle excitation energies, thus enlarging the superconducting gap. The long-range nature of the driven-cavity-induced attraction qualitatively changes the collective excitations of the superconductor. Specifically, they lead to the appearance of additional collective excita…
When immersed in a see of cold electrons, local impurities give rise to density modulations known as Friedel oscillations. In spite of the generality of this phenomenon, the exact shape of these modulations is usually computed only for non-interacting electrons with a quadratic dispersion relation. In actual materials, one needs to take into account several additional factors, such as (i) the details of the band structure, (ii) the lifetime of quasiparticles, (iii) in superconductors, the presence of a pairing gap. Studying how these effects influence Friedel oscillations is a viable way to ac…
