We have constructed a phase diagram in temperature-magnetic field-disorder space for homogeneously disordered superconducting tantalum thin films. Phases are phenomenologically identified by the nonlinear transport characteristics that are unique in each phase. The resulting phase diagram shows that a direct superconductor-insulator transition is prohibited at any disorder because the superconducting phase is completely surrounded by the intervening metallic phase.
Many disordered superconducting films exhibit smeared tunneling spectra with evident in-gap states. We demonstrated 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 Gamma 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 Delta and the larger the Gamma. MoC films of 3 nm thickness deposited simultaneously on silicon and sapphire substrates reveal very similar scalar d…
The suppression of superconductivity in disordered systems is a fundamental problem of condensed matter physics. Here we investigate the superconducting niobium-titanium-nitride (Nb_{1-x}Ti_{x}N) thin films grown by atomic layer deposition (ALD) where disorder is controlled by the slight tuning of the ALD process parameters. We observe the smooth crossover from the disorder-driven superconductor-normal metal transition (often reffered to as fermionic mechanism) to the case where bosonic mechanism dominates and increasing disorder leads to formation of metal with Cooper pairing. We show that, i…
It is now well known that the properties of the disordered s wave superconductors can deviate significantly from the prediction of standard Bardeen-Cooper-Schrieffer (BCS) theory. By measuring the temperature dependence of the resonance frequency, $f_0$, of microwave resonators made from disordered NbTiN and TiN thin films, at low temperatures, below half of the superconducting critical temperature, $T_c$, Driessen et al. \cite{driessen2012PRL} demonstrated that $f_0$ vanishes faster than predicted from the BCS theory. Here, we report on the temperature dependence of $f_0$ of microwave resonat…
We study the two-dimensional superconductor-insulator transition (SIT) in thin films of tantalum nitride. At zero magnetic field, films can be disorder-tuned across the SIT by adjusting thickness and film stoichiometry; insulating films exhibit classical hopping transport. Superconducting films exhibit a magnetic field-tuned SIT, whose insulating ground state at high field appears to be a quantum-corrected metal. Scaling behavior at the field-tuned SIT shows classical percolation critical exponents $z ν\approx$ 1.3, with a corresponding critical field $H_c \ll H_{c2}$. The Hall effect shows a …
Mesoscopic fluctuations of the local density of states encode multifractal correlations in disorderedelectron systems. We study fluctuations of the local density of states in a superconducting state of weakly disordered films. We perform numerical computations in the framework of the disordered attractive Hubbard model on two-dimensional square lattices. Our numerical results are explained by an analytical theory. The numerical data and the theory together form a coherent picture of multifractal correlations of local density of states in weakly disordered superconducting films.
We report on the study of phonon properties and electron-phonon coupling in thin NbTiN films, which are intensively exploited in superconducting devices. Studied NbTiN films with thicknesses less than 10~nm are disordered with respect to electron transport, the Ioffe-Regel parameter of $k_F l_e = 2.5-3.0$ ($k_F$ is the Fermi wave vector and $l_e$ is the electron mean free path), and inelastic electron-phonon interaction, the product $q_T l_e \ll 1$ ($q_T$ is the wave vector of a thermal phonon). By means of magnetoconductance and photoresponse techniques, we derived the inelastic electron-phon…
We report on the inelastic-scattering rate of electrons on phonons and relaxation of electron energy studied by means of magnetoconductance, and photoresponse, respectively, in a series of strongly disordered superconducting NbN films. The studied films with thicknesses in the range from 3 to 33 nm are characterized by different Ioffe-Regel parameters but an almost constant product q_Tl(q_T is the wave vector of thermal phonons and l is the elastic mean free path of electrons). In the temperature range 14-30 K, the electron-phonon scattering rates obey temperature dependencies close to the pow…
We experimentally investigated the detection performance of highly disordered NbxTi1-xN based superconducting nanowire single photon detectors (SNSPDs). The dependence on the composition of the transition temperature Tc for NbxTi1-xN films show a dome-like behavior on the Nb content, with a maximal Tc at xNb~0.65 , and the Nb0.65Ti0.35N films also combine relatively large sheet resistance and intermediate residual resistivity ratio. Moreover, 60-nm-wide and 7-nm-thick Nb0.65Ti0.35N nanowires show a switching current as high as 14.5 uA, and saturated intrinsic detection efficiency with a platea…
Terahertz Electrodynamics and Kinetic Inductance of Disordered Titanium-Vanadium Alloy Thin Films
Free Electron Laser Utilization Laboratory, Raja Ramanna Center for Advanced Technology（自由电子激光利用实验室，拉贾·拉曼纳先进技术中心）；Homi Bhabha National Institute（霍米·巴哈国家研究所）
A tractable framework for phase transitions in phase-fluctuating disordered 2D superconductors: applications to bilayer MoS$_2$ and disordered InO$_x$ thin films
Superconductor insulator transition in transverse magnetic field is studied in the highly disordered MoC film with the product of the Fermi momentum and the mean free path $k_F*l$ close to unity. Surprisingly, the Zeeman paramagnetic effects dominate over orbital coupling on both sides of the transition. In superconducting state it is evidenced by a high upper critical magnetic field $B_{c2}$, by its square root dependence on temperature, as well as by the Zeeman splitting of the quasiparticle density of states (DOS) measured by scanning tunneling microscopy. At $B_{c2}$ a logarithmic anomaly …
We experimentally study the ghost critical field (GCF), a magnetic field scale for the suppression of superconducting fluctuations, using Hall effect and magnetoresistance measurements on a disordered superconducting thin film near its transition temperature $T_c$. We observe an increase in the Hall effect with a maximum in field that tracks the upper critical field below $T_c$, vanishes near $T_c$, and returns to higher fields above $T_c$. Such a maximum has been observed in studies of the Nernst effect and identified as the GCF. Magnetoresistance measurements near $T_c$ indicate quenching of…
We use sub-Kelvin scanning tunneling spectroscopy to investigate the suppression of superconductivity in homogeneously disordered ultrathin MoC films. We observe that the superconducting state remains spatially homogeneous even on the films of 3 nm thickness. The vortex imaging suggests the global phase coherence in our films. Upon decreasing thickness, when the superconducting transition drops from 8.5 to 1.2 K, the superconducting energy gap follows perfectly Tc. All this is pointing to a two-stage fermionic scenario of the superconductor-insulator transition (SIT) via a metallic state as an…
Suppression of the critical temperature in homogeneously disordered superconducting films is a consequence of the disorder-induced enhancement of Coulomb repulsion. We demonstrate that for the majority of thin films studied now this effect cannot be completely explained in the assumption of two-dimensional diffusive nature of electrons motion. The main contribution to the $T_c$ suppression arises from the correction to the electron-electron interaction constant coming from small scales of the order of the Fermi wavelength that leads to the critical temperature shift $δT_c/T_{c0} \sim - 1/k_Fl$…
We investigate the magnetic field evolution of the superconducting state in a strongly disordered NbN thin film which exhibits a magnetic field tuned superconductor to insulator-like transition, employing low temperature scanning tunneling spectroscopy (STS). Transport measurements of the sample reveals a characteristic magnetic field, which separates the low field state where resistance decreases with decreasing temperature, i.e. dR/dT > 0 and a high-field state where dR/dT < 0. However, STS imaging of the superconducting state reveals a smooth evolution across this field and the presence of …
The resistivity tensor correlations $ρ_{xy}$($B$)$\sim$ $[ρ_{xx}(B)]^β$ for the mixed state magnetic field dependencies of the resistivity tensor of electron-doped Nd$_{2-x}$Ce$_x$CuO$_{4+δ}$/SrTiO$_3$ single crystal films near the antiferromagnetic (AF) - superconducting (SC) phase transition and with varying degree of disorder ($δ$) were studied. The decrease of $β$ from 1.2$\pm$0.2 at $x$ = 0.14 to 0.6$\pm$0.1 at $x$ = 0.15 points out on the evidence of the change from the anisotropic $s$ - wave to the $d$ - wave pairing symmetry in the external magnetic field at the transition from underdo…
"The non-contact broadband transmission line flip-chip spectroscopy technique is utilized to probe resonances of mm-sized square kinetic planar resonators made from strongly disordered molybdenum carbide films, in the GHz frequency range. The temperature dependence of the resonances was analyzed by the complex conductivity of disordered superconductor, as proposed in Ref. arXiv:1407.2402 , which involves the Dynes superconducting density of states. The obtained Dynes broadening parameters relate reasonably to the ones estimated from scanning tunneling spectroscopy measurements. The eigenmodes …
Disordered thin films close to the superconducting-insulating phase transition (SIT) hold the key to understanding quantum phase transition in strongly correlated materials. The SIT is governed by superconducting quantum fluctuations, which can be revealed for example by tunneling measurements. These experiments detect a spectral gap, accompanied by suppressed coherence peaks that do not fit the BCS prediction. To explain these observations, we consider the effect of finite-range superconducting fluctuations on the density of states, focusing on the insulating side of the SIT. We perform a con…
