Session D41: Ruthenates and Unconventional Superconducting Pairing

Domain walls and non-integral flux penetration in superconductors having broken time-reversal symmetry

$\textrm{Sr}_2\textrm{RuO}_4$ is a candidate material for realizing superconductivity that spontaneously breaks time-reversal symmetry~[1]. If this symmetry is in fact broken then the spatial pattern of the superconductivity may break up into domains that differ in their chirality, separated by domain walls. A consistent picture of how, where, or whether such domain walls form in $\textrm{Sr}_2\textrm{RuO}_4$ has, however, yet to emerge~[2]. It has been predicted that, owing to in-plane crystalline anisotropy, a domain wall may catalyze the dissociation of a unit-flux vortex (measured in units of the superconducting flux quantum $\Phi_0$) into two fractional-flux vortices, the fluxes of which sum to unity~[3]. In the present work, we consider a domain wall in which there is a relatively sharp bend through an angle $\Theta$. We show that, even in the absence of crystalline anisotropy, such a wall is penetrated by a magnetic field localized to the vicinity of the bend, of total, non-quantized flux $\Phi_{0}\Theta/\pi$. (Anisotropy, weak in $\textrm{Sr}_2\textrm{RuO}_4$, gives a small correction to this result.)\thinspace\ The observation of localized regions carrying non-integer flux would provide evidence for domain walls separating chiral domains of superconductivity. \par\noindent [1]~A.\ P.\ Mackenzie and Y.\ Maeno, Rev.\ Mod.\ Phys.\ {\bf 75\/}, 657 (2003). \hfil\break\noindent [2]~C.\ Kallin and A.\ J.\ Berslinsky, arXiv:0902.2170v1 (2009). \hfil\break\noindent [3]~M.\ Sigrist and D.] F.\ Agterberg, Prog.\ Theor.\ Phys {\bf 102\/}, 965 (1999).   

Effect of kinematic spin polarization in half-quantum vortex state on its stability

It has been shown recently [1] that a half-quantum vortex state in systems with equal spin pairing posses, in addition to a regular spin polarization produced by the Zeeman coupling, a spin polarization of purely kinematic nature. We discuss implications of such kinematic spin polarization on the stability of the half-quantum vortex and its possible experimental signatures in candidate equal spin pairing systems such as $\rm Sr_2RuO_4$. \par\noindent [1]~V.\ Vakaryuk and A.\ J.\ Leggett, Phys.\ Rev.\ Lett.\ {\bf 103}, 057003 (2009).   

Angular Momentum in a Chiral P-wave Superconductor

A chiral p-wave superconductor spontaneously breaks time reversal symmetry and is expected to have a spontaneous macroscopic angular momentum in the ground state. This angular momentum is not a topological invariant, but we find it is surprisingly robust to changes in the system parameters. We study the intrinsic angular momentum of the ground state, within Bogoliubov-deGennes theory, for a variety of geometries, including in a harmonic trap, and vary both the chiral p-wave pairing strength as well as the BCS cutoff parameter. We compare these results to the behaviour of the Hall viscosity, which has been proposed as a topological invariant for a chiral p-wave.   

Detection of Individual Vortices in Micron-Size Sr$_{2}$RuO$_{4}$ Rings by Phase-Locked Cantilever

We describe a feedback-based dynamic cantilever magnetometry technique capable of achieving high magnetic moment sensitivity with low applied fields. Using this technique, we have observed periodic entry of vortices into mesoscopic Sr$_{2}$RuO$_{4}$ rings. The quantized jump in the magnetic moment of the particle produced by individual vortices was measured with a resolution of $7\times 10^{-19}J/T$ at an applied field of 1 G.   

Magnetic response of Sr$_{2}$RuO$_{4}$ nanocrystals: search for chiral currents and fractional vortices

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 (2$\mu $m x 2$\mu $m x 0.5$\mu $m) was extracted from a large single crystal with bulk transition temperature in the range 1.2K-1.4K. It was then glued into the pickup loop of a flux transformer or a gradiometer that is inductively-coupled to a dc-SQUID magnetometer. We monitor the diamagnetic screening of the crystal and the entry of discrete vortices in perpendicular and parallel applied magnetic fields and as a function of temperature to search for the existence of half-quantum vortices in this system. We are also developing other techniques such as nanoscale Scanning SQUID Microscopy for probing the vortex dynamics in Sr$_{2}$RuO$_{4}$.   

Proposed experiment to test existence of horizontal nodal lines in Sr$_{2}$RuO$_{4}$

Since the original proposal of an unconventional chiral order parameter in the ruthenate perovskite superconductor Sr$_{2}$RuO$_{4}$, much attention has been given to the possibility of horizontal nodal lines on the predominant $\gamma$ cylindrical Fermi surface given thermodynamic evidence, such as power law specific heat and spin relaxation rate behavior, for low-lying quasiparticle excitations in this material. Here I propose Andreev and tunneling spectroscopy experiments exploiting the peculiar Fermi surface topology of the normal electrode graphite to determine whether such nodal lines in fact exist.   

Investigations of the order parameter in $UPt_3$ single crystals

Long the paradigm for unconventional superconductivity, $UPt_3$ has been studied with great interest for more than two decades. Although much is known about the nature of the superconducting order, there are still basic questions that remain unanswered. One of the most interesting and elusive has been whether or not the superconducting state is chiral. Small angle neutron scattering (SANS) from the Abrikosov vortex lattice provides a tool to examine the vortex structure and thus both chirality and the nature of the B-C superconducting transition. Our recent SANS results on a high quality crystal are encouraging, with narrow rocking curves in the C-phase. Additionally, striking new Josephson interference experiments have shed light on the nodal structure of the superconducting gap. These SANS and Josephson interference experiments share samples prepared by UHV crystal growth and post-growth processing techniques, and provide guidance to sample preparation for future work.   

Observation of the transition between real and complex superconducting order parameter phases in UPt$_3$

The heavy fermion superconductor UPt$_3$ provides a rich system for studying the competition between superconductivity and other forms of electronic order because it has an unconventional pairing mechanism, coexistence of anti-ferromagnetism and superconductivity, and two distinct superconducting phases characterized by different order parameter symmetries. We have fabricated Josephson tunnel junctions on the as-grown surfaces of UPt$_3$ single crystals at a series of angles in the basal plane. By measuring their critical current, we map out the magnitude of the superconducting order parameter as a function of k-space direction and temperature. We observe a sharp node in the superconducting gap at 45$^{\circ}$ with respect to the a-axis in the high temperature phase and the onset of an out-of-phase component creating a complex order parameter in the low temperature phase.   

Microwave Spectroscopy of Heavy Fermion Superconductors at MilliKelvin Temperatures

Heavy fermion metals are of immense interest due to the extreme renormalization of quasiparticle mass, the possibility of non-Fermi-liquid physics, and the appearance of superconductivity on the verge of magnetic order, in the vicinity of quantum critical points. The nature of these unconventional pairing states allows, in some cases, for order parameter collective modes. We have setup a novel system for high-resolution microwave spectroscopy at milliKelvin temperatures, across the frequency range 2 to 40 GHz. We are using this to study the unconventional superconducting states in a number of Ce- and U-based heavy fermion compounds. I will present a brief overview of the microwave spectroscopy system, and a summary of measurements on a number of samples including CeCoIn$_{5}$, where we see the existence of two quasiparticle bands, the heavier of which is largely responsible for the superconductivity, and the lighter of which remains largely uncondensed even at low temperatures.   

Driving towards superconducting thin films of Sr2RuO4: A status report

Chiral p-wave superconductor Sr$_2$RuO$_4$ has attracted attention recently in the context of quantum computing because of the proposed possibility of using this exotic superconductor to make topologically protected qubits. To accomplish this, however, superconducting thin films of Sr$_2$RuO$_4$ are required. Our latest drive towards this long-standing goal has involved the growth of epitaxial thin films of Sr$_2$RuO$_4$ using molecular beam epitaxy (MBE) and the characterization by various techniques. We carried out electrical and magneto transport and scanning Raman spectroscopy measurements on c-axis oriented Sr$_2$RuO$_4$ films grown on (100) LSAT substrates, and demonstrated steady progress on improving the film quality. However, the lowest residual resistivity obtained so far suggests that the films are still not of sufficiently high quality to exhibit superconductivity, which will be confirmed by measurements down to dilution refrigerator temperatures. Nevertheless, interesting behavior, such as an unexpected linear temperature dependence in resistivity, has been found. Additional measurements, such as tunneling, are being pursued to clarify the origin of this observation. The work is supported by DOE, DOD ARO and NSF.   

ARPES Measurements of the Effects of Strain on the Electronic Structure of Sr$_{2}$RuO$_{4}$ and Sr$_{3}$Ru$_{2}$O$_{7}$

We report ARPES studies of the evolution of the Fermi surface of both single-layer (Sr$_{2}$RuO$_{4})$ and bilayer (Sr$_{3}$Ru$_{2}$O$_{7})$ strontium ruthenate as a function of strain. The technique of molecular beam epitaxy allows films of these materials to be grown on substrates with mismatched lattice constants, producing novel strained crystal states that can be probed \textit{in situ} with ARPES. These two materials have attracted attention recently for the correlated electronic states they support (spin-triplet superconductivity and an electronic nematic phase, respectively). In particular, Sr$_{3}$Ru$_{2}$O$_{7}$ contains a number of low-lying bands with hybridization gaps near $E_{F}$ that form a complex manifold of Fermi surface sheets. The evolution of these sheets with strain has implications for the microscopic origin of metamagnetism and nematicity in this material. Finally, for comparison with our measurements, we present density functional theory calculations of the electronic band structure of the crystals under compressive and tensile epitaxial strain.   

Reconstruction of SrRuO$_{3}$ Films During Pulsed Laser Deposition

SrRuO$_{3}$ (SRO) is a perovskite oxide conductor, widely used as an electrode in thin film systems due to its chemical and lattice compatibility. SRO thin films were grown on SrTiO$_{3}$ substrates by pulsed laser deposition and monitored with high-pressure reflection high-energy electron diffraction. High quality growth and flat films were confirmed with ex situ atomic force and scanning transmission electron microscopies. Oxygen growth pressures below $\sim $10 mtorr produced films that exhibited surface oxygen vacancies seen with scanning tunneling microscopy (STM). Typically, high oxygen pressures are employed to minimize oxygen vacancies, however for growth or post-annealing above $\sim $100 mtorr, in situ characterization by STM and low energy electron diffraction (LEED) revealed a surface reconstruction consisting of parallel rows with periodicity doubled in one direction. Density function theory (DFT) has found that additional oxygen can increase stability of a structure in which SrO rows buckle outward with excess oxygen bonding below. Reconstruction will affect film structures, interface properties, and screening.   

In situ Angle-resolved Photoemission Studies of Epitaxial SrRuO$_{3}$ Thin Films

We have performed high resolution angle-resolved photoemission spectroscopy (ARPES) studies of the electronic structure of epitaxial ferromagnetic SrRuO3 thin films grown in situ using molecular-beam epitaxy . We report the first observation of dispersive bands near the Fermi level and the Fermi surface (FS) topology. The measured FS shows good agreement with predictions from band structure calculations in the low-temperature ferromagnetic state. In addition, we address one of the open questions regarding SrRuO3 being the degree to which electron correlation affects its electron structure. Compared to the density functional calculations, our data show that the Ru t2g bands near the Fermi level are significantly renormalized by strong electron-electron correlations.   

Correlation driven metal insulator transition as a function of thickness in SrRuO3 thin films

Recently there has been debate on the existence of a fundamental thickness limit of a metallic ground state of SrRuO3 thin films and what mechanism drives the system to an insulating state at low thicknesses should there be a transition. We present further evidence that a fundamental thickness level does indeed exist and that the metal-to-insulator transition is in fact a transition from a conducting ferromagnetic state to an insulating anti-ferromagnetic state that occurs from 3 to 4 unit cell layers of SrRuO3. We show this in two steps, in the first step we do Density Functional calculations on SrRuO3 that show a ferromagnetic -- anti-ferromagnetic phase transition occurring in SrRuO3 at large values of the electron correlation correlation U. In the second step we use ruthenium 3d x-ray photoemission spectra obtained in situ to demonstrate that U increases for very thin films of SrRuO3, driving the metal-to-insulator transition.