Session D21: Multiband Superconductivity, mostly MgB2

STS studies of the pi-band superconductivity in MgB$_2$ in a transverse field

Since being discovered MgB$_2$ has become the paradigm for two-band/two-gap superconductivity. Early scanning tunneling spectroscopy (STS) measurements, showed a rapid suppression of the superconductivty in the isotropic $\pi$-band for modest applied fields $H \parallel c$. These measurements were performed with the tunnel current ($I_t$) parallel to the crystalline $c$-axis which couple, almost exclusively, to the $\pi$-band, and with the suppression attributed to vortex core overlap. Here we report STS measurements performed in a transverse field, such that $I_t \parallel c \perp H$. In this configuration no vortices are cutting through the image plane, and instead the superconducting phase is affected by the Meissner currents running within one penetration depth of the sample surface. Within this field orientation we observe far less suppression of the superconducting state in the $\pi$-band compared to the earlier measurements with $H \parallel c$. A clear gap is seen up to $H= 0.9$~T.   

Measurement of penetration depth of MgB$_{2}$ using DC SQUID

Penetration depth is an important parameter for the design of Rapid Single Flux Quantum (RSFQ) circuits. For MgB$_{2}$, different values from 40 nm to 150 nm have been reported by different groups. We have measured the penetration depth of MgB$_{2}$ using MgB$_{2}$ DC SQUIDs. The SQUID was made using MgB$_{2}$/MgO/MgB$_{2}$ Josephson junctions with epitaxial MgB$_{2}$ electrodes deposited via Hybrid Physical-Chemical Vapor Deposition. The MgO was deposited by RF Magnetron Sputtering of an MgO target. The device shows good voltage modulation above 150 $\mu$V. The working temperature for these SQUIDs ranges from below 10K to 37K, with the optimum voltage modulation near 35K. The results will be discussed in comparison to the penetration depth reported by other measurement techniques.   

Effect of scattering on the gap distribution in tunneling spectra of MgB$_{2}$/I/Pb junctions

We fabricated MgB$_{2}$/Native oxide/Pb planar tunneling junctions using the MgB$_{2}$ films grown by the hybrid physical-chemical vapor deposition technique (HPCVD). Both $\pi $ ($\sim $1.8 meV) and $\sigma $ gaps ($\sim $7.9 meV) were observed in spectra due to tunneling from side of $c$-oriented MgB$_{2}$ grains on film surface on SiC (0001) substrates. We have previously observed a distribution of energy gap values within both bands in clean HPCVD films with long electron mean free path. Here we report an investigation of the tunneling spectra by systematically varying the MgB$_{2}$ film thickness and the thickness of native oxide barrier. We found the MgB$_{2} \quad \pi $ gap distribution range narrows from $\sim $1.7 meV to $\sim $1.4 meV together with a loss of fine peak structures, as the MgB$_{2}$ film thickness decreases from 100 nm to 33 nm, in which the electron mean free path is limited by the thickness. In addition, fine peak structures also smear out when the junction resistance is large. The results show electron scattering from both inside the film and on the surface can smear out the gap distribution structures in tunneling spectra.   

Vortex Lattice Transition Dynamics in MgB$_2$

We present small-angle neutron scattering (SANS) studies of the vortex lattice (VL) in MgB$_{2}$ with $H \parallel c$. This material has three different VL phases, all with triangular symmetry but oriented differently with respect to the crystalline axes. Furthermore, a high degree of metastability between the VL phases of MgB$_{2}$ has been observed as the sample is cooled or heated across the equilibrium phase transitions. Here we present detailed studies of how the metastable (MS) VL phases transition to the ground state (GS), either driven by small changes of the DC magnetic field or by a transverse AC field. Our results show that the MS VL is not due to vortex pinning, and results are inconsistent with predictions based on the Bean model. Instead, we speculate that a ``jamming'' of counter rotated VL domains is responsible for the VL metastability. This is further supported by a power law dependence of the GS VL domain population upon the number of applied AC cycles. This work was supported by the Department of Energy, Basic Energy Sciences under Award No. DE-FG02-10ER46783.   

Non-linear Time Effects in Superconducting Polycrystalline MgB$_{2}$

The time evolution of the voltage response (V-t curves) to a symmetric bi-directional square wave (BSW) current with long periods (P) applied to the MgB$_{2}$ sample was investigated at low dissipation levels. It was observed that regular sinusoidal-like voltage oscillations evolve at certain ranges of the amplitude (I$_{BSW})$ and period (P$_{I})$ of the BSW current, external magnetic field (H), and temperature (T). The regular sinusoidal-like oscillations were interpreted in terms of the dynamic competition between pinning and depinning processes. In this process, the interaction between flux lines and pinning centers could be elastic coupling because of rigidity of flux line lattice in MgB$_{2}$. We suggest that the oscillating mode can be related to the drifting of flux lines which are in motion. In this case, due to the strong pinning and complex relaxation effects, the majority of flux lines traversing the sample does not leave it entirely and remains in an oscillating mode by moving forth and back as a function of time. We suggest that the flux dynamics associated with the oscillating mode is the ordered motion of defective flux line system. Fast Fourier Transform analysis of V-t oscillations showed that the period of oscillations is comparable to that of the BSW current. The oscillating mode was also discussed in terms of sliding charge density waves (CDWs).   

Study of MgB$_{2}$ Films for RF Cavity Applications

Magnesium diboride (MgB$_{2})$ is a promising superconducting material for RF cavity applications due to its high critical temperature $T_{c}$ and large thermodynamic critical field $H_{c}$. Using Hybrid Physical-Chemical Vapor Deposition (HPCVD), we have grown 2"-diameter MgB$_{2}$ films on sapphire and metal substrates, including molybdenum, niobium, tantalum, and stainless steel. Measured by DC magnetization, the $T_{c}$'s of these films were between 38.2 to 39.2 K; the upper critical field $H_{c2}$'s were about 7 T, in consistent with previously reported value of clean MgB$_{2}$ films; the zero-field critical current density $J_{c}$'s were above 10$^{7}$ A/cm$^{2}$ and were suppressed rapidly by increasing applied magnetic field, indicating a lack of pinning in clean MgB$_{2}$ films. Multilayered MgB$_{2}$/MgO films were also investigated to prevent vortex penetrating the MgB$_{2}$ layer and increase the vortex penetration field (H$_{c1})$ following Gurevich's theoretical work [1]. The RF properties of these films were studied. \\[4pt] [1] A. Gurevich, \textit{Appl. Phys. Lett.} 88, 012511 (2006).   

Mesoscopic Nonlinear Electrodynamic Response of the Two Band Superconductor MgB$_{2}$

Multi-gap superconductors are expected to have exotic physics associated with internal coupling between the multiple order parameters. 10 years after its discovery, MgB$_{2}$ is a two gap superconductor that still attracts much attention for both fundamental and practical reasons. A microwave measurement of the temperature dependent third harmonic response P$_{3f}$ (T) is performed by applying a strong and localized (mesoscopic) RF magnetic field on high quality MgB$_{2}$ films. Comparing to the P$_{3f}$ (T) result on Nb thin films, the low temperature nonlinearity of MgB$_{2}$ shows a complete harmonic cancelation at a temperature near the transition temperature of the proximity-induced $\pi $ band. One possibility is that this phenomenon is due to an additional intrinsic nonlinearity arising from Josephson coupling between the $\sigma $ and $\pi $ bands. This nonlinear response then interferes with other nonlinear mechanisms coming from moving vortices and the intrinsic nonlinear Meissner effect of the two-gap system. To investigate further, we measure the magnitude and phase of the nonlinear response and compare to models of the three nonlinearity mechanisms.   

Superconducting-to-Normal Switching and I-V Experiments showing Multiple Tunneling Channels in a Multi-Gap Superconductor

Magnesium diboride is a BCS superconductor with many interesting properties, notably its two superconducting energy gaps associated with the disconnected sheets of its Fermi surface. A heterojunction, using the dual-gap MgB$_{2}$ and a single-gap superconductor as its superconducting electrodes, provides a system well-suited for exploring the unique properties of MgB$_{2}$, by exhibiting multiple tunneling channels. We present data from superconducting-to-normal state switching experiments and tunneling spectroscopy experiments to temperatures as low as 20mK that indicate multiple tunneling channels in this multiple-gap superconductor. We describe features of escape rates and I-V curves that may be consistent with recent published theoretical work on macroscopic quantum tunneling in multi-gap superconductors.   

Multilayer Structures in MgB2 superconducting thin films: influence on doping, pinning, and connectivity

Pinning force density, connectivity, and doping were investigated for MgB$_{2}$ superconducting thin films. Pulsed Laser Deposition (PLD) was used to produce MgB$_{2}$ thin films on Al$_{2}$O$_{3}$ (0001), MgO (111), YSZ (111), and SiC (0001) substrates. The MgB$_{2}$ target was manufactured through high pressure and high temperature induction heating that produced a highly dense material. ZrB$_{2}$, SiC, or C targets were alternated with the MgB$_{2}$ target to produce films with various levels of doping and/or pinning centers. X-ray diffraction (XRD) was used to determine the substitution, strain, and epitaxy. Surface microstructures and grain sizes were compared via scanning electron microscopy (SEM). Transmission electron microscopy (TEM) was employed on ion-milled samples representing cross-sections of the film to determine the oxide content of the films as well as to confirm if the added dopants modified the superconducting properties of the MgB$_{2}$ via atomic substitution or increases in strain. Normal-state resistivity measurements were taken on the films to determine the connectivity as compared to literature single crystal values. Magnetic $J_{c}$s were taken of the films to determine the influence of the microstructure on the pinning properties.   

Effect of Carbon Nanotubes on Transport Properties of MgB$_{2}$

Carbon nanotubes (CNT) and magnesium diboride (MgB$_{2})$ are two fascinating materials; with CNT exhibiting unique quantum electrical properties due to its 1-D structure and MgB$_{2}$ being a superconducting with transition temperature (T$_{c})$ at $\sim $40 K. We report preliminary results on the effect of carbon nanotubes on the temperature dependent (300K to 4K) thermoelectric power (TEP) and resistivity of MgB$_{2}$. The normalized resistance (R-R$_{300})$/R$_{300}$ shows very little dependence on the sample composition; however, the absolute resistance increases with increasing CNT concentration. At high CNT composition, the TEP mimic the characteristic TEP of CNT. However at low CNT composition, we see an upturn at about 30K.   

Applicability of two-component Ginzburg-Landau model in two-band systems

We report a microscopic derivation of the conditions under which the two-band superconductors can be described by a two-component Ginzburg-Landau (GL) field theory. We also investigate the conditions when multicomponent GL-like expansions fail and one should resort to a microscopic description. We show that besides being directly applicable at elevated temperatures, a version of a minimal two-component GL theory in certain cases also gives an unexpectedly accurate description of certain aspects of a two-band system even substantially far from $T_c$. This shows that two-component GL model can be used for addressing a wide range of questions in multiband systems.   

Inter-band scattering effects in the Chevrel phase superconductors

Recent scanning tunneling spectroscopy on the Chevrel phases SnMo$_6$S$_8$ and PbMo$_6$S$_8$ by Petrovi\'{c} et al.~(PRL \textbf{106}, 017003 (2011)) demonstrates clear signatures of multi-band superconductivity. In contrast with MgB$_2$, where there is extremely weak scattering between the $\sigma$ and $\pi$ bands, the inter-band scattering rate is relatively high compared to the intra-band scattering rate in the Chevrel phases. We calculate the quasi-classical Green's function in the presence of strong inter-band scattering and derive comparable results to the measured density of states. We make predictions for proposed measurements on the vortex cores.   

Collective modes in three-band superconductors with repulsive interband interactions

I consider a simple model of a three-band superconductor with repulsive interband interactions. In such a system frustration associated with the odd number of gaps leads to the possible existence of intrinsically complex time-reversal symmetry breaking (TRSB) order parameter. I show that in this state the fluctuations of the \emph{different} gaps are strongly coupled and this leads to the development of novel excitations, which mix the phase and amplitude oscillations. This is due to the non-trivial relative phase angle between the gaps. The energy of these excitations is less than $2 \Delta$ and thus they are true collective modes of the system.   

Cryomagnetic STM imaging of the subsurface vortex lattice in the multiband superconductor $2H$-NbSe$_2$

Using cryomagnetic scanning tunneling microscopy (STM) in a novel field geometry, we studied single crystals of the multiband superconductor $2H$-NbSe$_{2}$ under diamagnetically-induced superfluid momentum. Spectroscopy and conductance imaging were performed at 300 mK and in a field of up to 9 T, applied in the $ab$-plane.[1] Spatial maps of the Doppler effect on the quasiparticle tunneling spectrum revealed distinct stripe patterns that originate from in-plane vortices whose cores are buried in the bulk.[2] The stripe separation varies systematically as a function of the applied field. Our results are interpreted in terms of the interaction between vortical and screening currents, and demonstrate a general method for probing subsurface vortices, especially in emerging multiband superconductors such as the ferro-pnictides/chalcogenides.\\[4pt] [1] I. Fridman \emph{et al.}, arXiv:1110.6490 (2011) \\[0pt] [2] I. Fridman \emph{et al.}, Appl. Phys. Lett. \textbf{99}, 192505 (2011)