Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session V33: Superconductivity: Complex Order Parameter |
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Sponsoring Units: DCMP Chair: Suk Bum Chung, Stanford University Room: 403 |
Thursday, March 19, 2009 8:00AM - 8:12AM |
V33.00001: Topological Superconductivity and Superfluidity Taylor Hughes, Xiao-Liang Qi, S. Raghu, Shou-Cheng Zhang We construct time reversal invariant topological superconductors and superfluids in two and three dimensions. These states have a full pairing gap in the bulk, gapless counter-propagating Majorana states at the boundary, and a pair of Majorana zero modes associated with each vortex. The superfluid $^3$He B-phase provides a physical realization of the topological superfluidity, with experimentally measurable surface states protected by time- reversal symmetry. We show that the time reversal symmetry naturally emerges as a supersymmetry, which changes the parity of the fermion number associated with each time-reversal invariant vortex and connects each vortex with its superpartner. [Preview Abstract] |
Thursday, March 19, 2009 8:12AM - 8:24AM |
V33.00002: Observing Majorana Zero Modes in a $p_x+ip_y$ Superconductor at High Temperature by Tunneling Spectroscopy Yaacov E. Kraus, Assa Auerbach, Herbert A. Fertig, Steven H. Simon Directly observing a zero energy Majorana state in the vortex core of a chiral superconductor by tunneling spectroscopy requires energy resolution better than the spacing between core states $\Delta^2_0/\epsilon_F$. We show\footnote{arXiv:0811.2557, Phys. Rev. Lett. in press} that nevertheless, its existence can be clearly detected by comparing the temperature broadened tunneling conductance of a vortex with that of an antivortex even at temperatures $T \gg \Delta^2_0/\epsilon_F$. The Bogoliubov-de-Gennes (BdG) equation of a $p_x+ip_y$ superconductor is solved numerically on a sphere with vortex-antivortex pair at the poles. The robustness of the exponentially Majorana mode energy is verified by including a moderate white noise potential. [Preview Abstract] |
Thursday, March 19, 2009 8:24AM - 8:36AM |
V33.00003: Frequency dependence of the intrinsic Hall conductivity in a chiral $p+ip$ superconductor with impurities Pavel Nagornykh, Roman Lutchyn, Victor Yakovenko We calculate frequency dependence of the intrinsic Hall conductivity induced by impurity scattering in a chiral $p_x+ip_y$ superconductor. We find that, at large frequencies compared to the superconducting gap ($\Omega\gg\Delta$), the real part of the intrinsic Hall conductivity at zero temperature is proportional to $\Delta/\Omega^3\log(\Omega/2\Delta)$. Using our results for the Hall conductivity, we estimate the Kerr angle and compare it with the experimental data on $\rm Sr_2RuO_4$ by Xia et al., Phys. Rev. Lett. 97, 167002 (2006). [Preview Abstract] |
Thursday, March 19, 2009 8:36AM - 8:48AM |
V33.00004: Electromagnetic response of time reversal invariant triplet superconductors Rahul Roy, Catherine Kallin, John Berlinsky We study the effective action of time reversal invariant triplet superconductors in two and three dimensions and obtain the electromagnetic response. The B-phase of Helium 3 and its two dimensional analog are topologically non-trivial phases. The two dimensional triplet superconductor may be regarded as two copies of a chiral $p_x + i p_y $ superconductor. We discuss signatures of the non-trivial topology in the effective action and in the electromagnetic response. [Preview Abstract] |
Thursday, March 19, 2009 8:48AM - 9:00AM |
V33.00005: Microscopic analysis of the stability of half-quantum vortices in $p_x + ip_y$ superfluids in an annular geometry. Victor Vakaryuk We present a microscopic analysis of the thermodynamic stability of a half-quantum vortex (HQV) in $p_x + i p_y$ variant of equal-spin-pairing state which, under suitable conditions, is believed to be realized in $\rm Sr_2RuO_4$ and $^3$He-A. Our approach is based on a description of the HQV in terms of a BCS-like wave function with a spin-dependent boost. Stability criterion is found by comparing energies of half- and full-quantum vortices with appropriate account taken of Fermi liquid corrections. While we confirm earlier phenomenological findings by Suk Bum Chung et al.~(2007) for the stability of the HQV in the annular geometry, we also predict a novel feature that the HQV, if exists, should be accompanied by a non-zero spin polarization of the system. [Preview Abstract] |
Thursday, March 19, 2009 9:00AM - 9:12AM |
V33.00006: Josephson tunneling studies of odd-parity superconductivity in Sr$_2$RuO$_4$ Ronald Myers, Ying Liu, D. Fobes, Z. Mao, H. Yaguchi, Y. Maeno In the recent phase-sensitive work that provided the most unambiguous evidence for odd-parity superconductivity in Sr$_2$RuO$_4$, we used Au$_{0.5}$In$_{0.5}$ as the s-wave superconducting counter electrode in the SQUID structure. However, Au$_{0.5}$In$_{0.5}$ has a T$_c$ less than that of Sr$_2$RuO$_4$, making detection of the pairing symmetry near the T$_c$ of Sr$_2$RuO$_4$ inaccessible to the phase sensitive measurements. To go beyond this limit and open up possibilities of several other experiments involving Josephson tunneling into Sr$_2$RuO$_4$, we seek an alternative material system with an s-wave superconductor of T$_c$ $>$ 1.5K that would exhibit Josephson coupling with Sr$_2$RuO$_4$. An Ag/Pb/Ag trilayer has been chosen for this purpose. Ag/Pb/Ag-Sr$_2$RuO$_4$ tunneling devices were prepared that showed a suppressed superconducting gap feature of Sr$_2$RuO$_4$, suggesting the presence of superconductivity at the polished ac face of a Sr$_2$RuO$_4$ crystal. However, no Josephson coupling between Ag/Pb/Ag and Sr$_2$RuO$_4$ was detected. More experiments are currently underway, and new results will be presented. [Preview Abstract] |
Thursday, March 19, 2009 9:12AM - 9:24AM |
V33.00007: Measurements of superconducting energy gap in individual Ru islands embedded in Sr$_{2}$RuO$_{4}$ Yiqun Ying, B. Clouser, R. Myers, N. Staley, Ying Liu, D. Fobes, Z.Q. Mao, Y. Xin, L. Allard We report our tunneling measurements on individual single-crystalline Ru islands embedded in a bulk Sr$_{2}$RuO$_{4}$ single crystal. Tunneling junctions were prepared on large (micron size) and small (submicron size) Ru islands by fabricating tunneling windows using quartz filaments as shadow masks. Our measurements revealed the presence of an energy gap below a temperature close to the $T_{c}$ of bulk Ru. In the zero temperature limit, the gap was found to be 0.07 meV for large Ru islands, consistent with our measurements on bulk polycrystalline Ru. However, in small Ru islands a gap of 0.1 meV, clearly larger than that seen in large Ru islands, was observed. The difference in energy gap may reflect difference in pairing state in Ru islands of different sizes. Above the $T_{c}$ of Ru but below the $T_{c}$ of Sr$_{2}$RuO$_{4}$, we detected no proximity induced energy gap. This observation is unexpected as our Z-contrasted transmission electron microscope study showed that the interface between a Ru island and Sr$_{2}$RuO$_{4}$ is atomically sharp, which appears to rule out the suppression of the proximity effect by disorder. We argue that these observations are associated with chiral p-wave superconductivity in Sr$_{2}$RuO$_{4}$. [Preview Abstract] |
Thursday, March 19, 2009 9:24AM - 9:36AM |
V33.00008: Magnetic response of Sr$_{2}$RuO$_{4}$ nanocrystals: search for chiral currents and fractional vortices D. J. Bahr, M. J. A. Stoutimore, R. Budakian, D. J. Van Harlingen, Y. Maeno The ruthenate superconductor Sr$_{2}$RuO$_{4}$ may have a chiral order parameter of the form p$_{x}\pm $ip$_{y,}$, making it a candidate for nucleation of excitations with non-Abelian statistics that could enable topologically protected quantum computing. To test this scenario, we have measured the magnetic response of Sr$_{2}$RuO$_{4}$ nanocrystals to search for spontaneous chiral currents and half-integer vortices. Each nanocrystal (1$\mu $m x 1$\mu $m x 0.5$\mu $m) was extracted from a large single crystal with bulk transition temperature in the range 1.2K-1.4K. We then glued it into the pickup loop of a flux transformer or a gradiometer that is inductively coupled to a dc-SQUID magnetometer. We have observed the diamagnetic screening of the crystal and the entry of discrete vortices in an applied magnetic field. We report on our search for spontaneously generated currents, chiral domain dynamics and the nucleation of half-integer vortices, which we should be sensitive to due to the small size of the crystal. [Preview Abstract] |
Thursday, March 19, 2009 9:36AM - 9:48AM |
V33.00009: Investigating magnetic order in Sr$_{2}$RuO$_{4}$ using cantilever torque magnetometry Raffi Budakian, Joonho Jang, Dale Van Harlingen, Yoshi Maeno Following the initial $\mu $SR and NMR studies suggesting that Sr$_{2}$RuO$_{4}$ is a spin-triplet superconductor, there has been a great deal of interest to understand the nature of the order parameter. Although Sr$_{2}$RuO$_{4}$ is similar in structure to the layered high-Tc cuprate superconductors, it is thought to possess chiral p$_{x}\pm $ip$_{y}$ pairing symmetry. The complex order parameter can give rise to a rich variety of new correlated states, such as domains having orbital order that possess a net magnetic moment and half-integer vortices with zero-energy modes. We have applied ultrasensitive cantilever torque magnetometry to measure the magnetic moment, susceptibility, and vortex entry into micron-size Sr$_{2}$RuO$_{4}$ in search of magnetic moments generated by chiral edge currents and fractional vortices. This talk will present recent data in this effort. [Preview Abstract] |
Thursday, March 19, 2009 9:48AM - 10:00AM |
V33.00010: Orbital magnetic moment in the chiral p-wave superconductor Sr2RuO4 James Annett, Karol Wysokinski, Balazs Gyorffy The existence and magnitude of a bulk orbital angular momentum of the condensate chiral a phase in superfluid helium-3 is a longstanding matter of controversy. The analogous problem in a chiral p-wave superconducting material is the existence of a finite orbital magnetic moment in the bulk. In Sr2RuO4 the existence of such an orbital moment is strongly suggested by experimental evidence for spontaneously time reversal symmetry breaking (TRSB) in the superconducting state, but the theories disagree on the expected magnitude of this moment. We show that a non-zero orbital magnetization density arises natually in a realistic band model for Sr2RuO4, and its temperature dependence is qualitatively similar to those of the muSr and Kerr effect experimental results. The simplest model which leads to the orbital moment requires at minimum two degenerate atomic orbitals per Ru, which correspond to the Ru d xz and d yz states. This is in contrast to the theories of orbital angular momentum in the isotropic superfluid 3-He, or models of orbital moment in Sr2RuO4 which assume only a single band at the Fermi level. The implications of this surprising result are explored. [Preview Abstract] |
Thursday, March 19, 2009 10:00AM - 10:12AM |
V33.00011: Absence of superconductivity in the half-filled anisotropic triangular lattice Hubbard model Hongtao Li, R.T. Clay, S. Mazumdar The superconducting $\kappa$-(BEDT-TTF)$_2$X salts, with one hole per molecular site and strong dimerization are widely thought to have an effective $\frac{1}{2}$-filled band. The presence of antiferromagnetism (AFM) near superconductivity (SC) in their pressure-temperature phase diagram has led to the suggestion suggest that the SC can be explained within an anisotropic triangular lattice $\frac{1}{2}$-filled band Hubbard Hamiltonian. In this model increasing frustration suppresses the AFM transition, and it has been suggested that d-wave SC appears near the metal/AFM interface. We performed exact diagonalizations on a 16-site periodic anisotropic triangular lattice and determined the full phase diagram. We confirm the Mott metal-insulator transition and AFM, change of the AFM wavevector for large anisotropy, and the presence of a non-magnetic insulating phase. We do not find any hint of long range superconducting correlations. In our results the Hubbard $U$ always suppresses the superconducting pair-pair correlations over their non-interacting value. We conclude that the Hubbard model is too simple to explain the SC in organic charge-transfer solids. [Preview Abstract] |
Thursday, March 19, 2009 10:12AM - 10:24AM |
V33.00012: Nuclear spin-lattice relaxation rate as a link between antiferromagnetism and superconductivity in organic conductors Claude Bourbonnais, Abdelouahab Sedeki The interdependence of antiferromagnetism and superconductivity in the Bechgaard salts series of organic conductors is examined in the light of the anomalous temperature dependence of the nuclear spin-lattice relaxation rate. We use the renormalization group approach to the electron gas model to demonstrate that the metallic state anomaly of the nuclear relaxation rate found in the Bechgaard salts and the mechanism of passage from antiferromagnetism to superconductivity can be both described within a unified framework. [Preview Abstract] |
Thursday, March 19, 2009 10:24AM - 10:36AM |
V33.00013: New details in the phase diagram of $\lambda\textnormal{-}(\textnormal{BETS})_2\textnormal{Ga}\textnormal{Cl}_4$ made by advancing the art of RF penetration depth measurements in pulsed fields using a tunnel diode oscillator William A. Coniglio, Laurel E. Winter, Kyuil Cho, Braunen E. Smith, C.C. Agosta, L.K. Montgomery We report improvements to the Tunnel Diode Oscillator method of measuring the penetration depth of a superconductor at RF frequencies above 100 MHz. Optimizations to the circuit for high frequency and pulsed fields are briefly discussed as well as a digital demodulation technique for rendering the oscillation frequency with accuracy suitably better than the stability of the oscillator itself. Using a 390 MHz oscillator, we measured the penetration depth of $\lambda\textnormal{-}(\textnormal{BETS})_2\textnormal{Ga}\textnormal{Cl}_4$ with the magnetic field oriented parallel to the conducting planes of the sample using fields up to 21\,T and temperatures from 400\,mK to 5.5\,K. Our new data crunching techniques have allowed us to resolve two phase transitions between the superconducting and normal states as well as a third transition that appears at low temperature as an enhancement to the upper critical field. We explore the properties of the phase diagram in two samples. [Preview Abstract] |
Thursday, March 19, 2009 10:36AM - 10:48AM |
V33.00014: Upper Critical Field and Phase Diagram Studies for $\lambda$-(BETS)$_2$GaCl$_4$ Laurel E. Winter, William A. Coniglio, Kyuil Cho, Braunen E. Smith, C.C. Agosta, L.K. Montgomery The upper critical fields for the highly anisotropic organic superconductor $\lambda\textnormal{-}(\textnormal{BETS})_2\textnormal{Ga}\textnormal{Cl}_4$ have been studied by measuring the in-plane RF penetration depth with a tunnel diode oscillator technique in pulsed fields. At zero field we found a $T_c$ of 5 K. With the field perpendicular to the conducting layers we extrapolate $H_{c2,T=0}$ to 2.8 T and with the field parallel $H_{c2,T=0}$ is 11 T. With the field applied parallel to the conducting layers, for $T > 0.5T_c$ the $H_{c2}$ follows the superconducting gap function $\sqrt{1-\frac{T}{T_c}}$, then saturates below $0.5 T_c$. Below 0.35$T_c$ we see a clear enhancement of 1.5 T in $H_{c2}$ and in addition there is a second phase line at a lower field than $H_{c2}$. These features are both characteristic of the FFLO state. We will discuss this second phase line in relation to the Pauli Limit as calculated in a semi-empirical method and compare our phase diagram to previous results. [Preview Abstract] |
Thursday, March 19, 2009 10:48AM - 11:00AM |
V33.00015: Mesoscopic conductance oscillations in superconducting nanoparticle films Al-Amin Dhirani, Brian Lam Recent advances in nanoparticle synthesis yield control over key nanoparticle characteristics such as structure and chemical composition. This in turn enables fabrication of nanostructured materials with novel and controlled properties. We have found that superconducting 100 nm niobium nanoparticles can be sintered to make porous macroscopic films that routinely exhibit conductance oscillations as a function of bias voltage and magnetic field. We speculate the effect is related to electron-hole interference previously observed at interfaces between disordered normal materials and superconductor electrodes. Our results show that the oscillations in the present system are associated with nanoparticle state (superconducting vs. normal) and ubiquitous elastic scattering at length scales dictated by nanoparticle size. Robust observation of this mesoscopic interference phenomenon in a disordered, macroscopic system is remarkable. It is enabled by the present approach's ability to balance conterveiling considerations: sufficient disorder to induce elastic scattering and restricted averaging to limit dephasing. [Preview Abstract] |
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