Session V41: Superconductor-Insulator Transitions

Superconducting transition in narrow aluminum strips

We have studied the superconducting transition in highly conducting granular aluminum strips. The samples were fabricated using electron beam lithography and thermal evaporation. Measurements of resistance and voltage noise as a function of temperature, current and magnetic field show an evolution of different dynamic regimes as the width of the samples is decreased and they become quasi-one dimensional.   

Superconducting properties of V-Ti nanowires fabricated by molecular-templating technique

A series of V-Ti nanowires with nominal composition V$_{70}$Ti$_{30 }$was fabricated by sputter co-deposition of vanadium and titanium on top of suspended fluorinated carbon nanotubes. The V-Ti films with thickness 15-20 nm fabricated at the same conditions were superconducting with critical temperature about 5 K. We observed that nanowires with the length about 110 nm and the nominal thickness of 20 nm are superconducting with resistance versus temperature dependence described well by the theory of the thermally activated phase slips. Thinner and longer wires displayed either insulating or mixed behavior. We argue that the possible reason for the discrepancy is incomplete crystallization of V-Ti alloy on top a carbon nanotube.   

Suppression of superconductivity in amorphous Mo-Ge films doped with magnetic Gd atoms

A series of amorphous MoGe-Gd films with thickness in the range 4-60 nm was fabricated by simultaneous co-sputtering from Mo, Ge and Gd targets. The ratio of Mo and Ge was kept constant at $Mo_{79} Ge_{21} $, but the Gd content was varied by changing the power and inclination of the sputtering gun. For undoped films, the critical temperature decreased monotonically with film thickness from 60nm to 4nm. Addition of Gd atoms to the alloy strongly suppressed superconductivity. Remarkably the critical concentration of magnetic impurities, 0.6 at {\%} of Gd, was found to be the same for films with different thickness.   

Indirect Magnetic-Field-Tuned Superconductor-Insulator Transitions of Quasi-Two Dimensional Metal Films

Homogeneous films of amorphous bismuth have been continuously tuned from the superconducting state by increasing a perpendicular magnetic field. Electrical transport and Hall measurements show that the non-superconducting states of the films are quantum-corrected metals. In the vicinity of transition field, the resistance can be scaled with critical exponent product $\nu $z=0.4 at high temperatures but this form fails at lower temperatures where the resistance is a non-monotonic function of temperature. This suggests that a two-phase regime develops near criticality and the transition becomes indirect from superconductor to insulator with this two-phase regime in between at nonzero temperature. We also compare the magnitoresistance of homogeneous and granular bismuth films.   

Further Analysis of a Cooper Pair Insulator

Amorphous thin films of Bi deposited on a substrate with a Nano-Honeycomb (NHC) array of holes can exhibit a Cooper Pair Insulator (CPI) phase [1]. The transport in this state is dominated by the incoherent tunneling of Cooper Pairs between localized states. The resistivity is activated in temperature, and the magnetoresistance (MR) near the thickness-tuned Superconductor-Insulator Transition (SIT) exhibits a giant peak, as is found in thin films of InO$_{x}$ and TiN. In an effort to learn how the localization of pairs develops, we have investigated films deposited on substrates with different hole radii, order in the hole arrays, and surface roughness. We will present our latest findings on the common features describing the CPI phase, and how the above variations influence its properties and those of the thickness-tuned SIT in these amorphous films. [1] M. D. Stewart Jr., A. Yin, J. M. Xu, and J. M. Valles Jr., \textit{Science} \textbf{318}, 1273 (2007).   

Nernst signal generated by superconducting fluctuations in low-Tc disordered superconductors

In amorphous superconducting thin films of Nb$_{0.15}$Si$_{0.85}$ [1][2] and InOx [3][4], a finite Nernst coefficient can be detected in a wide range of temperature and magnetic field. Due to the negligible contribution of normal quasi-particles, superconducting fluctuations easily dominate the Nernst response in the entire range of study. In the vicinity of the critical temperature and in the zero-field limit, the magnitude of the signal is in quantitative agreement with what is theoretically expected for the Gaussian fluctuations of the superconducting order parameter. Even at higher temperatures and finite magnetic field, the Nernst coefficient is set by the size of superconducting fluctuations. The Nernst coefficient emerges as a direct probe of the ghost critical field, the normal-state mirror of the upper critical field. Moreover, upon leaving the normal state with fluctuating Cooper pairs, we show that the temperature evolution of the Nernst coefficient is different whether the system enters a vortex solid, a vortex liquid or a phase-fluctuating superconducting regime. [1] A. Pourret \textit{et al.}, Nature Physics 2, 683 - 686 (2006) [2] A. Pourret \textit{et al.}, Phys. Rev. B. \textbf{76}, 214504 (2007) [3] P. Spathis \textit{et al.}, Europhys.~Lett. \textbf{83}, 57005 (2008) [4] A. Pourret \textit{et al}., New Journal of Physics \textbf{11, }055071 (2009)   

Signatures of phase fluctuations in the superfluid density through the field-tuned superconductor-insulator transition

The superconductor-insulator transition in amorphous two-dimensional metal films remains mysterious because the nature and role of superconducting fluctuations have not been conclusively identified, despite the central role they play in various exotic electronic states that have been proposed for these systems. This is partly because most of our current understanding of amorphous two-dimensional superconductors originates from conventional electrical transport data, which is focused on measuring dissipation. Instead, we use a two-coil mutual inductance technique to measure the superfluid density of both amporphous $MoGe$ and $InOx$ thin films through the field-tuned superconductor-insulator transition. We find that superconducting phase fluctuations leave a signature in the superfluid density, which we track up to the point that the magnetic field completely suppresses the superfluid response.   

Enhancement of superconductivity by a parallel magnetic field in 2-D superconductors

We report on the observation of significant enhancement of superconductivity by an applied \textit{parallel} magnetic field in two different 2-D superconducting systems: ultrathin, homogeneously disordered amorphous Pb films and the 2-D electron gas at the heteroepitaxial interface of 8 u.c. LaAlO$_{3}$ on TiO$_{2}$ terminated SrTiO$_{3}$. For both systems, we observe that the mean field T$_{c}$ is increased by a parallel magnetic field, while any perpendicular magnetic field results in a reduction of T$_{c}$. In the case of ultrathin $a$-Pb films, the magnitude of the T$_{c}$ enhancement is studied as the film thickness (zero-field T$_{c})$ is varied \textit{in situ}; the T$_{c}$ enhancement shows a strong non-monotonic dependence on the film thickness, peaking at 13{\%} in 8 T parallel field for a film with zero-field T$_{c}$ of 2.504 K. A comparison between the enhancement effect observed in ultrathin $a$-Pb films and the LaAlO$_{3}$/SrTiO$_{3}$ interface is presented. We will discuss the possible origin of the parallel magnetic field enhancement of superconductivity in these disparate systems.   

Spectroscopic signatures of FFLO physics in disordered superconductors in the presence of spin-exchange fields

We present Bogoliubov-de Gennes (BdG) results on the disordered attractive Hubbard model with a Zeeman field [1,2]. Near the Chandrasekhar-Clogston field scale, we find disordered Larkin-Ovchinnikov states, which have an inhomogeneous electronic structure involving unpolarized superconducting regions and polarized insulating regions. The former regions have a gapped local density of states (LDOS), whereas the latter regions contribute states within the gap. The total density of states has a soft gap and provides a distinct signature of modulated superconducting phases. Our results may help to understand the origin of the finite density of states at zero-bias in tunneling experiments on exchange-biased superconducting films [3]. \\ $[1]$ Y. L. Loh and N. Trivedi, arxiv:0907:0679 \\ $[2]$ Q. Cui and K. Yang, Phys. Rev. B 78, 054501 (2008) \\ $[3]$ G. Catelani, Y. M. Xiong, X. S. Wu, and P. W. Adams, Phys. Rev. B 80, 054512 (2009)   

Effect of phase fluctutations on the spectral function of disordered s-wave superconductors

We extract the dynamical properties of a disordered s-wave superconductor using a combination of auxiliary field Quantum Monte Carlo and analytic continuation methods. By comparing with self-consistent Bogoliubov-de Gennes mean field theory for the same disorder realizations, we are able to obtain fundamentally new insights into the roles of amplitude and phase fluctuations across the disorder-driven superconductor-insulator transition. The disordered superconductor is found to self-organize into local superconducting puddles embedded in an insulating matrix [1]. At finite temperature, the density of states shows coherence peaks below $T_c$, but only a pseudogap above $T_c$. Finally, we discuss the behavior of both local and global densities of states in connection to recent scanning tunneling spectroscopy experiments in thin superconducting films [2].\\[4pt] [1] A. Ghosal et al., Phys. Rev. Lett. 81 3940 (1998);Phys. Rev. B 65, 014501 (2001).\\[0pt] [2] Sacepe et al, Phys. Rev. Lett. 101, 157006 (2008).   

The insulating state of quench-condensed ultrathin Be and its relationship to the magnetic-field-tuned superconductor-insulator transition

The temperature dependence of the resistance of quench-condensed ultrathin and highly insulating Be films displays an Arrhenius behavior indicative of the existence of an energy gap that is much larger than the superconducting gap energy measured in the superconducting films. A large high-field negative magnetoresisatnce is also observed in highly insulating films, suggesting a reduction of this gap energy by the magnetic field. With increasing film thickness, this gap energy decreases and, eventually, the insulating state gives way to superconductivity in a thickness-tuned insulator-to-superconductor transition. For superconducting films not far from the thickness-tuned transition, the application of a magnetic field leads to a sharp field-tuned superconductor-to-insulator transition and a negative magnetoresistance at high fields. These results, as well as other results from InOx and TiNx films, are used to discuss the relationship between the insulator-to-superconductor transition and the insulator-to-metal transition. It is suggested that sharp field-tuned superconductor-to-insulator transitions occur in films in which the insulator-to-superconductor transition precedes the insulator-to-metal transition as the film thickness is increased (the level of disorder is reduced). This work was supported by the NSF under the grant No. DMR-0606529.   

Quantum critical behavior on mesoscopic length scales across the superconductor-insulator transition

Recent studies of superconductor-insulator transition in 2D films provided new and exciting results, especially the novel transport behavior found on the insulating side of the transition. Here we present results from a study on the magnetic field tuned transition in 2D films when the length and width of the samples are varied from mm to sub-$\mu$m scales. Films of amorphous indium oxide are patterned into Hall bars of different sizes using standard optical and electron beam lithography and low temperature/high magnetic field transport measurements are conducted. We find that the low temperature transport behavior of the samples, on either side of the transition, depend systematically on the physical dimensions of the Hall bars and the application of perpendicular magnetic field appears to enhance this dimensional dependence.   

Phase diagram of a disordered system near superconductor-insulator transition

Experiments show that, in systems displaying the superconductor-insulator transition, Cooper pairs are conserved in the insulator state. We study the localized states of the Cooper pairs in the random potential and their transformations under the action of a strong magnetic field. Depending on dimensionality of the system and direction of magnetic field, the Bose-insulator of localized Cooper pairs, can either transit to Fermi-insulator and then to metal, or directly transit to metal. The resistance first strongly grows and then, at the field increasing, strongly decreases. This behavior of resistance was found in experiments   

Emergence of superconducting textures in two dimensions

Self-organized regular patterns are ubiquitous in nature, and one of their most celebrated manifestations is the Abrikosov vortex lattice: under an applied magnetic field, the homogeneous superconductivity becomes unstable and cast itself into a regular texture of the normal filaments, called Abrikosov vortices, immersed into a superconducting matrix. In this presentation I show that the interplay between the superconducting order parameter and elastic fields, which are intimately connected to the very existence of the superconductivity itself, can result in a novel superconducting state dual to the Abrikosov state: a regular texture of superconducting islands. The fact that both patterns emerge within the framework of the Ginzburg-Landau description of superconductivity indicates that the formation of regular structures may be a generic feature of any phase transition. Emergence of superconducting island arrays is not specific to the effect of the elastic forces, but can be caused by any inherent mechanism generating long-range non-local interactions in the Ginzburg-Landau functional. In particular, our findings suggest that the formation of superconducting island textures is a possible scenario for the superconductor-to-insulator transition in thin films. Additionally these self-organized regular arrays can be viewed as an array of coupled superconducting grains which from Josephson junctions. [see: arXiv:0910.0659]   

Effect of weak disorder on the superconducting transition

We investigate the effects of weak static potential disorder on the superconducting transition in a model of zero range electron-electron attraction and Gaussian random potential acting on otherwise free electrons. We integrate out the electron degrees of freedom to obtain a Ginzburg Landau like functional for the free energy in terms of the space ($\vec{r}$) and time ($\tau$) dependent complex pair amplitude $\Delta(\vec{r},\tau)\exp[i\phi (\vec{r},\tau)]$. We show that the uniform term of order $\Delta^2$ in this functional goes to zero at a temperature $T_c^{\textrm{BCS}}(1-\alpha (k_F\ell) ^{-2})$ for $k_F\ell \gg 1$, where $k_F\ell$ is the dimensionless electron mean free path in terms of the Fermi wavevector $k_F$. The $(k_F\ell)^{-2}$ term arises from a novel disorder induced dynamic pairbreaking process; its origin and the value of the coefficient $\alpha (\sim 1)$ will be discussed. We also show that the superconductivity causing nonzero stiffness condition of the phase gradient $\partial \phi$ has a contribution of order $(k_F\ell)^{-2}$ which reduces it. Our results raise the possibility that with such increasing disorder, as the superconducting coherence length decreases, the phase stiffness decreases with respect to the BCS value. This implies the existence of temperature region with ``pre-existing'' Cooper pairs but no phase coherence, and a pseudogap. Our results are compared with old and new data on disordered superconductors.