Session H10: Josephson Effects

Suppression of macroscopic quantum tunneling in a large Josephson junction coupled to a resonator

We calculated the zero-temperature macroscopic quantum tunneling rate of a current-biased Josephson junction weakly coupled to a resonator. We allow for the effects of environmental dissipation on both the junction and the resonator, and we consider both cases of weak and strong junction damping. We find that coupling to the resonator has a suppressive effect on the junction's tunneling: the stronger the coupling strength between the junction and resonator, the greater the reduction of the tunneling rate. Including damping to the junction also suppresses tunneling, but damping the resonator partially {\it counteracts} the suppression provided directly by the junction-resonator coupling. Modeling the dependence of the junction-resonator coupling on the resonator's frequency $\omega_R$ in a power law fashion $U_{int}\propto(\omega_{R})^n$, we find that for $0 [Preview Abstract]

Identifying the Odd-Frequency Superconducting State by a Field-Induced Josephson Effect

The prevalent symmetry in known superconductors may be described as odd under exchange of spin coordinates, and even under an exchange of spatial or time coordinates of the electrons constituting the Cooper pair. However, other types of pairing are also permitted by the governing Pauli principle. Among these is the so-called odd-frequency pairing state, which has been predicted to arise both in N/S and F/S proximity systems. Extending the possible pairing states compatible with the Pauli-principle will likely have impact on a wide range of sub-disciplines in physics, ranging from astrophysics to extremely compressed quantum liquids. Recent experiments report that such an odd-frequency superconducting bulk state may be realized in certain heavy-fermion compounds. While the Josephson current normally only flows between superconductors with the same symmetries with respect to frequency, we demonstrate that an exchange field may induce a current between diffusive even- and odd-frequency superconductors. This suggests a way to identify the possible existence of bulk odd-frequency superconductors.   

Tunable current-phase relation in double-dot Josephson junctions

The current-phase relation $I(\varphi)$ for a Josephson junction contains information about the microscopic nature of the Cooper pair transfer. In particular, junctions more complicated than the single tunnel junction exhibit characteristic non-sinusoidal forms. Here, we investigate the Josephson effect in a superconducting double dot device, similar to the devices studied experimentally by Y.\ A.\ Pashkin et al.\ [1] and E.\ Bibow et al.\ [2]. In the vicinity of a charge degeneracy line, the system reduces to a two-level system equivalent to a charge qubit. In this regime, we find that the interplay between sequential tunneling and cotunneling of Cooper pairs leads to a strongly non-sinusoidal current- phase relation, tunable via gate electrodes. We propose the measurement of $I(\varphi)$ in a SQUID configuration, analyze the implications of flux noise, and compare our results to different types of Josephson junctions such as single-dot systems and microbridges. [1] Y.\ A.\ Pashkin et al., Nature (London) \textbf{421} (2003), 823 [2] E.\ Bibow, P.\ Lafarge, L.\ L\'{e}vy, Phys.\ Rev.\ Lett.\ \textbf{88} (2002), 017003   

Spontaneous spin accumulation in singlet-triplet Josephson junctions

We show that the Andreev bound states in Josephson junctions between singlet $s$-wave and triplet $p$-wave superconductors carry a net magnetic moment. This magnetic moment depends on the relative phase between the superconductors constituting the junction and changes sign when the relative phase shifts by $\pi$. We estimate the net magnetization of such junctions and suggest several realistic experiments to detect this magnetization. We also discuss possible magnetization flip in such junctions in the presence of an applied bias voltage.   

Small Josephson junctions in asymmetric SQUIDs.

Ultra-small Josephson junctions are known to be susceptible to quantum fluctuations in the phase difference across the junction, resulting in an effective suppression of the critical current. We have investigated a method for stabilizing this phase difference by shunting a small junction (with a critical current I$_{01} \quad \approx $ 1 nA) with an additional capacitance and incorporating the junction in a dc SQUID loop. The second junction in the Al/AlO$_{x}$/Al SQUID has a much larger critical current (I$_{02}$ $\approx $ 1 $\mu $A ), producing a SQUID that is highly asymmetric. Our results show that the SQUID inductively couples the phase differences of the large and small junctions, leading to reduced phase fluctuations, and thus allowing accurate measurement of the small junction's critical current at millikelvin temperatures. This work was supported by the National Science Foundation and the Laboratory for Physical Sciences.   

Scanninng Josephson Tunneling Microscopy of Single Crystal Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ from a Conventional Superconducting Tip

Using a scanning tunneling microscope with superconducting Pb-coated tips (S-STM), we have observed the thermally fluctuated Josephson Effect between the tip and conventional superconductors. Such STM-based Josephson junctions are a powerful tool that can directly probe the phase of the superconducting condensate via the Josephson Effect as well as characterize the quasiparticle spectrum, both on a nanometer length scale. In this talk we present data from Josephson junctions formed between the S-STM tips and Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ single crystals. These results clearly show c-axis Josephson tunneling between a conventional superconductor and both overdoped and optimally doped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$. Josephson measurements at various surface locations indicate an inhomogeneous structure of the I$_{C}$R$_{N}$ product in overdoped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$. These local I$_{C}$R$_{N}$ data of the Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ are related to the local superconducting gap. This work is supported by DOE Grant No. DE-FG02-05ER46194.   

Thermal Management in Large Bi2212 Mesas used for Terahertz Sources

We report the intrinsic tunneling characteristics of 300x100x1 $\mu $m$^{3}$ mesas on Bi2212 single crystals that have recently shown high-power emission at terahertz frequencies due to the ac Josephson effect. Despite the large mesa volumes compared to those of others, there is an accessible range of voltages for which self-heating does not exceed T$_{c}$ and significant terahertz emission can be observed. We use a model of the current-voltage curve, I(V), based on (1) the low-current normal-state c-axis resistance of the mesa and (2) a temperature increase proportional to power, P=IV. We find that the local temperatures along the nonlinear I(V) are consistent with the observed unpolarized thermal radiation from the mesa, thus verifying the model.   

Quantized energy levels in quantum and classical regimes in current-biased intrinsic Josephson junction

The multiphoton transitions between quantized energy levels in the current-biased Bi$_{2}$Sr$_{2}$SrCaCu$_{2}$O$_{8+x}$ intrinsic Josephson junctions (IJJs) in the quantum and classical regimes are studied through the switching current distributions. The system shows the saturation behavior of the switching current distributions near $T^{\ast }\sim $0.8 K, which is the crossover temperature between classical and quantum nature of the system. We observe the multiphoton transitions between quantized energy levels in the quantum regime, which is manifested by the enhancement of the escape rate in the microwave radiation with frequencies of 12-16 GHz. This enhancement behavior keeps even in the classical regime and is washed out near T$\sim $2 K, of which thermal energy corresponds to the energy level spacing at the switching currents. This means that the existence of the quantized energy levels even in the classical regime of IJJs, due to the relatively large plasma frequency in the IJJs.   

Direct observation of a sin(2$\phi )$ component in the current-phase relation of superconductor-ferromagnet-superconductor (SFS) Josephson junctions

We present direct measurements of the current-phase relation (CPR) of SFS Josephson junctions in an rf-SQUID geometry. The junctions are fabricated from Nb-Cu$_{47}$Ni$_{53}$-Nb trilayers with a junction area of 2x2 $\mu $m$^{2}$ and a CuNi thickness of 7 nm. By measuring the magnetic flux through the rf-SQUID as a function of applied current, we observe transitions between an ordinary 0-Josephson junction state and a $\pi $-junction state characterized by a phase difference of $\pi $ in the ground state occurring at temperatures between 1.5 K and 3.5 K. Near this temperature crossover, we observe period-doubling of the CPR indicating the existence of a term proportional to sin(2$\phi )$. Work is underway to determine if this signifies an intrinsic second-order tunneling mechanism or is the result of junction inhomogeneities.   

Sub-Gap Currents in Nb/Al/AlOx/Nb Josephson Junctions and Their Dependence on the Method of Barrier Formation

Josephson tunnel-junctions have been fabricated using two different methods of barrier formation. Both types of devices start with single-crystal Nb/Al bi-layers grown by molecular beam epitaxy on A-plane sapphire. It is found that complete wetting of the Nb layer is achieved with 20 nm of Al evaporated at room temperature. The barrier is then formed either by thermal oxidation of the Al surface in molecular oxygen (the well-known process developed by Gurvitch et al.) or by co-depositing Al in an oxygen background of about 5 micro-torr. A Nb counter-electrode is deposited in situ by evaporation at room temperature. Josephson junctions fabricated from these multi-layers exhibit Fiske resonances and a reduced gap voltage due to the relatively thick Al layer. For devices tested at 4 K, the co-deposition process yields junctions that show a sub-gap current in agreement with theory and no measurable shunt conductance. In contrast, those devices with barriers formed by thermal oxidation show a small shunt conductance in addition to the predicted sub-gap current.   

Ferromagnetic Josephson Junctions

Superconducting correlations cannot penetrate into a ferromagnet over a large distance due to the pair breaking effect of the exchange field. Ferromagnet/Superconductor (F/S) systems are often studied using weak ferromagnetic alloys with smaller exchange energy and correspondingly larger penetration depth. We are studying S/F/S junctions using the weak ferromagnetic alloy, CuNi [1]. The samples are fabricated by sputtering the S/F/S trilayer onto a Si substrate; they are subsequently patterned using trilayer photolithography and ion milling to obtain pillars of 50 micron diameter. Measurements performed on these pillars at 4K show the Josephson effect with the expected modulation of the critical current as a function of applied magnetic field. Because spin-flip scattering and spin-orbit scattering are strong in weak ferromagnetic alloys such as CuNi, there is an incentive to work with strong ferromagnets. The results from our CuNi data confirm the robustness of the sample fabrication technique and pave the way to future studies of Josephson junctions with strong ferromagnets such as Ni. [1] V. A. Oboznov, Phys. Rev. Lett. 96, 197003 (2006)   

I-V Characteristics vs. Spatial Dissipation Maps in YBCO Grain Boundary on Bicrystal Substrates

Grain boundary (GB) properties of YBCO films on SrTiO3 bicrystal substrates with 24 degree misorientations are examined by transport and scanning laser microscopy (SLM) techniques. Thermoelectric SLM clearly shows the location of grain boundaries, and variable temperature SLM confirms that GB has lower Tc. A series of I-V measured in superconducting states exhibit clear step-like features identified in earlier papers as sub-gap structures. The low temperature SLM shows a close relation between the step-like features and the local dissipation pattern in GB. We believe that the activation of Fiske steps is responsible for the step-like I-V, and SLM images show the spatial pattern of the self-excited resonance in GB. We will also discuss how Ca-doping and nanoparticle additions on YBCO affect the junction properties.   

Vibronic Effects in Superconducting Niobium Nanowires

Research of superconducting transport through microscopic objects with intrinsic vibrational degrees of freedom is a frontier research avenue. Here we report on experimental studies of a few-atom niobium nanowires prepared in a mechanically-controlled break junction set-up. We present evidence for the resonant interaction between the ac Josephson effect and the mechanical motion of atoms in niobium dimer nanowires at frequencies up to about 8~THz. This is application-rich, but a largely unexplored frequency range (``terahertz gap''), which interrogates the lowest frequency vibrational modes of complex organic and biological molecules. We also discuss supercondicting transport and noise in niobium nanowires with oxygen contamination.   

Fluxon dynamics in a Josephson junction parallel array

We present experimental measurements on the dynamics of fluxons in an array of Josephson junctions. Fluxons trapped in a parallel array of Josephson junctions upon cooldown experience a potential determined by the junction critical currents and the cell inductances. We probe the dynamics of the fluxon with switching current measurements, which allow determination of the transition rate of the fluxon from its pinned state to a running state. The transition to the running state is initiated by thermal activation at temperatures higher than the quantum crossover temperature for the junctions. Below the crossover, we observe an abrupt change in the critical force needed to move the fluxon. Quantum tunneling of the fluxons is a possible explanation for this observation. We present the data, numerical simulations, and a discussion of the results.   

Field-dependence of interlayer tunnelling in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$

Micron-scale `mesa' structures fabricated on the surface of single crystals of strongly anisotropic high-temperature superconducting (HTS) compounds form stacks of `intrinsic Josephson junctions' connected in series. Studying the current-voltage (I-V) characteristics of HTS mesas is now an established technique for obtaining important information regarding the electronic density of states (DoS) in these compounds, such as the magnitude $\Delta$ of the superconducting energy gap, and its symmetry in $k$-space. We have fabricated mesas on the HTS compound Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8}$ (Bi-2212) and studied these at a range of hole-doping levels, temperatures, and applied magnetic fields. Of particular interest is the field-dependent behaviour of the I-V characteristic at bias voltages much less than the sum-gap voltage 2$\Delta $/e, corresponding to quasiparticles near the gap nodes. We compare our results with predictions for the field-dependent DoS made by Volovik [1] in which the local energy is assumed to be Doppler shifted by the local superfluid velocity. We also discuss features seen in our tunnelling characteristics at voltages above 2$\Delta $/e, which may correspond to strong-coupling effects in Bi-2212. [1] G. E. Volovik, JETP Lett., 58: 469-473, 1993.