Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session A25: Superconductivity: Odd Parity 
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Sponsoring Units: DCMP Chair: Daniel Agterberg, University of Wisconsin, Milwaukee Room: 324 
(Author Not Attending)

A25.00001: Identifying detrimental effects for multiband superconductivity  Application to Sr$_2$RuO$_4$ Aline Ramires, Manfred Sigrist Spin polarization and antisymmetric spinorbit coupling are detrimental to Cooper pairing in the spin singlet and spin triplet channel, respectively. These are the wellknown features of paramagnetic limiting and selection rules in noncentrosymmetric superconductors. We propose a general scheme to probe the compatibility of arbitrary pairing states with given normal state properties in model systems. This yields a universal criterion which we validate with results based on weak coupling analysis of the stability of different superconducting gaps under timereversal and inversion symmetry breaking fields. Our criterion does, however, not address directly any aspects concerned with the pairing mechanism. A merit of the criterion is that it can be easily applied to the stability analysis of superconducting states in multiband systems, to establish gap structures favourable within a given complex band structure. As such it can serve as a tool to identify nontrivial mechanisms to suppress superconductivity under various external influences, in particular, magnetic fields or distortions. We apply our criterion to the multiband superconductor Sr$_2$RuO$_4$ with the aim to explore possible explanations for the limiting feature observed in the inplane upper critical field. [Preview Abstract] 
Monday, March 14, 2016 8:12AM  8:24AM 
A25.00002: Experimentally observable signatures of oddfrequency pairing in multiband superconductors Lucia Komendova, Alexander V. Balatsky, Annica M. BlackSchaffer We report on how hybridization (singlequasiparticle scattering) between two superconducting bands induces oddfrequency superconductivity in a multiband superconductor. Using the Green's functions formalism we derived the oddfrequency pairing correlation and its full frequency dependence. We found that the density of states is modified, at higher energies, from the sum of the two BCS spectra to also include additional hybridization gaps with strong coherence peaks when oddfrequency pairing is present. These gaps constitute clear experimentally measurable signatures of oddfrequency pairing in multiband superconductors. [1] L. Komendova, A. V. Balatsky, and A. M. BlackSchaffer, Phys. Rev. B 92, 094517 (2015). [Preview Abstract] 
Monday, March 14, 2016 8:24AM  8:36AM 
A25.00003: Oddparity superconductivity in the vicinity of inversion symmetry breaking in spinorbitcoupled systems Vladyslav Kozii, Liang Fu We study superconductivity in spinorbitcoupled systems in the vicinity of inversion symmetry breaking. We find that due to the presence of spinorbit coupling, fluctuations of the incipient paritybreaking order generate an attractive pairing interaction in an oddparity pairing channel, which competes with the $s$wave pairing. We show that Coulomb repulsion or an external Zeeman field suppresses the $s$wave pairing and promotes the oddparity superconducting state. Our work provides a new mechanism for oddparity pairing and opens a route to novel topological superconductivity. [Preview Abstract] 
Monday, March 14, 2016 8:36AM  8:48AM 
A25.00004: Triplet p$_z$wave pairing in quasionedimensional A$_2$Cr$_3$As$_3$ superconductors (A = K,Rb,Cs) Fan Yang, Xianxin Wu, Jiangping Hu, Congcong Le, Heng Fan We construct minimum effective models to investigate the pairing symmetry in the newly discovered quasionedimensional superconductor K$_2$Cr$_3$As$_3$. We show that a minimum threeband model based on the d$_{z^2}$ , d$_{xy}$ ,and d$_{x^2y^2}$ orbitals of one Cr sublattice can capture the band structures near Fermi surfaces. In both weak and strong coupling limits, the standard random phase approximation and meanfield solutions consistently yield the triplet pzwave pairing as the leading pairing symmetry for physically realistic parameters. The triplet pairing is driven by the ferromagnetic fluctuations within the sublattice. The gap function of the pairing state possesses line gap nodes on the k$_z$ = 0 plane on the Fermi surfaces.Experimental consequences of the triplet p$_z$wave pairing are also discussed, including the NMR, superfluid density and phasesensitive dc SQUID experiments. [Preview Abstract] 
Monday, March 14, 2016 8:48AM  9:00AM 
A25.00005: Leggett modes in the multiband superconductor Sr2RuO4 Wen Huang, Manfred Sigrist, Catherine Kallin Sr$_2$RuO$_4$ is a prototypical multiband superconductor, with three bands crossing the Fermi level. These bands exhibit distinct dimensional characteristics, with one quasi2D $\gamma$band and two quasi1D $\alpha$ and $\beta$ bands. As a consequence, the superconducting order parameter on the $\gamma$ and $\alpha/\beta$bands may only be weakly Josephsoncoupled, in contrast to the stronger coupling between the quasi1D bands. In this work, we study the Leggett modes associated with the relative phase fluctuations between the bands. We show that a soft Leggett mode exists in the case of comparatively weaker interband Josephson coupling between the $\gamma$ and $\alpha/\beta$bands. We further analyze the dependence of the interband Josephson coupling on spinorbit coupling, and discuss the possibility of an exotic timereversal symmetry breaking phase when the Josephson coupling is comparable between all pairs of bands. [Preview Abstract] 
Monday, March 14, 2016 9:00AM  9:12AM 
A25.00006: Microscopic model of the Knight shift in anisotropic and correlated metals Richard Klemm, Bianca Hall We present a microscopic model of nuclear magnetic resonance in metals. The spins of the spin1/2 local nucleus and its surrounding orbital electrons interact with the arbitrary constant ${\bf B}_0$ and perpendicular timeoscillatory magnetic inductions ${\bf B}_1(t)$ and with each other via an anisotropic hyperfine interaction. An Andersonlike Hamiltonian describes the excitations of the relevant occupied local orbital electrons into the conduction bands, each band described by an anisotropic effective mass with corresponding Landau orbits and an anisotropic spin ${\bf g}$ tensor. Local orbital electron correlation effects are included using the meanfield decoupling procedure of Lacroix. The Knight resonance frequency and corresponding linewidth shifts are evaluated to leading orders in the hyperfine and Anderson excitation interactions. While respectively proportional to $(B_1/B_0)^2$ and a constant for weak $B_0 >> B_1$, both highly anisotropic shifts depend strongly upon ${\bf B}_0$ when a Landau level is near the Fermi energy. Electron correlations affect the anisotropy of the linewidth shift. [Preview Abstract] 
Monday, March 14, 2016 9:12AM  9:24AM 
A25.00007: Oddfrequency Superconductivity in Driven Systems Christopher Triola, Alexander Balatsky We show that Berezinskii’s classification of the symmetries of Cooper pair amplitudes in terms of parity under transformations that invert spin, space, time, and orbital degrees of freedom holds for driven systems even in the absence of translation invariance. We then discuss the conditions under which pair amplitudes which are odd in frequency can emerge in driven systems. Considering a model Hamiltonian for a superconductor coupled to an external driving potential, we investigate the influence of the drive on the anomalous Green’s function, density of states, and spectral function. We find that the anomalous Green’s function develops odd in frequency component in the presence of an external drive. Furthermore we investigate how these oddfrequency terms are related to satellite features in the density of states and spectral function. Supported by US DOE BES E 304. [Preview Abstract] 
Monday, March 14, 2016 9:24AM  9:36AM 
A25.00008: Majorana zero modes in $p+ip$ superconducting rings with half quantum flux in the presence of a $d$soliton Ali Beyramzadeh Moghadam, Kirill Shtengel Halfinteger flux quantization has been observed in mesoscopic rings of superconducting $\text{Sr}_2\text{RuO}_4$ \footnote{J. Jang et al. Science \textbf{331}, 186 (2011)}. This finding suggests a chiral $p+ip$ nature of the superconducting order parameter. Under the assumption that the $d$vector (which parametrizes the triplet pairing) lies in the plane of a 2D superconductor, such rings are expected to support Majorana zero modes at their inner and outer edges. However, such modes have not been directly observed in experiments. More recently, H.Y. Kee and M. Sigrist argued that the spinorbit coupling in such systems can stabilize a different spin texture, also consistent with halfquantum vortices\footnote{H.Y. Kee, M. Sigrist, arXiv:1307.5859}. That spin texture is characterized by the presence of a socalled $d$soliton \textendash a radial domain wall between the regions where the $d$vector is oriented in the positive and negative $z$directions. Our theoretical investigation of superconducting rings with $d$solitons confirms the existence of two Majorana zero modes, one at each boundary. Furthermore, the presence of a $d$soliton enhances the hybridization between the localized Majorana modes at the inner and outer boundaries. [Preview Abstract] 
Monday, March 14, 2016 9:36AM  9:48AM 
A25.00009: Scanning SQUID Microscopy of Sr$_2$RuO$_4$ Under Anisotropic Strain Christopher A. Watson, Hilary Noad, Alexandra Gibbs, Andrew P. Mackenzie, Clifford W. Hicks, Kathryn A. Moler The proposed $p_x \pm ip_y$ topological superconducting state of Sr$_2$RuO$_4$ has motivated a great deal of experimental effort. While some experimental results are consistent with this order parameter, others are not, and the question of the order parameter remains unsettled. Furthermore, it is possible that multiple order parameters are nearly degenerate, such that perturbing the sample may induce a change in order parameter. It was recently demonstrated that T$_c$ is strongly enhanced under anisotropic strain with $<$100$>$ principle axes; the dependence on strain was essentially quadratic, but with an anomaly at low strains. In this work, we will use a scanning SQUID susceptometer to study the local diamagnetic response of the superconducting state as a function of temperature and applied strain. We will investigate the homogeneity of the superconductivity and the precise dependence of T$_c$ on strain without inhomogeneityrelated broadening. [Preview Abstract] 
Monday, March 14, 2016 9:48AM  10:00AM 
A25.00010: Realization of a mixedsymmetry superconducting gap in correlated organic metals Michaela Altmeyer, Daniel Guterding, Harald O. Jeschke, Sandra Diehl, Torsten Methfessel, Ulrich Tutsch, Harald Schubert, Michael Lang, Jens M\"uller, Michael Huth, Martin Jourdan, HansJoachim Elmers, Roser Valenti Recent scanning tunneling spectroscopy measurements on the organic charge tranfer salt $\kappa$(BEDTTTF)$_2$Cu[N(CN)$_2$]Br show clear evidence of a highly anisotropic gap structure. Based on an {\it ab initio} derived model Hamiltonian we employ random phase approximation spin fluctuation theory yielding a composite order parameter of (extended) s+d$_{x^2y^2}$ symmetry. Taking explicitly also the shape of the Fermi surface into account we calculate STS spectra that are in excellent agreement to the experimental observations [1]. Moreover we determine the minimal tight binding model to describe the general lattice structure of these compounds accurately and generate a phase diagram for the gap symmetry by varying the hopping parameters. Based on {\it ab initio} derived parameter sets we predict the gap symmetry of other superconducting $\kappa$ charge transfer salts. [Preview Abstract] 
Monday, March 14, 2016 10:00AM  10:12AM 
A25.00011: Quasiparticles near domain walls in hexagonal superconductors Soumya Mukherjee, Kirill Samokhin We calculate the energy spectrum of quasiparticles trapped by a domain wall separating different time reversal symmetrybreaking ground states in a hexagonal superconductor, such as UPt$_3$. The bound state energy is found to be strongly dependent on the gap symmetry, the domain wall orientation, the quasiparticle's direction of semiclassical propagation, and the phase difference between the domains. We calculate the corresponding density of states and show how one can use its prominent features, in particular, the zeroenergy singularity, to distinguish between different pairing symmetries. [Preview Abstract] 
Monday, March 14, 2016 10:12AM  10:24AM 
A25.00012: Dynamic Quantum Phase Transitions in Holographic Superconductors Moon Jip Park, Matthew Gilbert A nonequilibrium quench that crosses a quantum critical point is known to exhibit distinct behavior from trivial quench. This is readily apparent via examination of the Loschmidt echo that contains the YangLee (YL) zeros in the nonequilibrium quench within the vanishing returning rate of ground state when the quantum critical point is crossed. While previous studies on the dynamical quenches are restricted within noninteracting systems, we use of the Loschmidt echo to understand quenches within strongly interacting conformal field theories using holographic mapping. We show that the free energy of the gravitational dual possesses YL zeros at the superconducting critical temperature. We argue that, on the gravitational side, the presence of YL zeros implies that the free energy is invariant under a set of discrete deformations of the metric characterized by the time at which the returning rate vanishes. We illustrate these ideas using a holographic superconductor constructed via the coupling of AdS gravity with a Maxwell field and charged scalar. [Preview Abstract] 
Monday, March 14, 2016 10:24AM  10:36AM 
A25.00013: Knight shift and spin relaxation in the single band 2D Hubbard model. James LeBlanc, Xi Chen, Emanuel Gull We study in detail the roles of spin and charge fluctuations in the single band 2D Hubbard model. Using dynamical mean field theory and cluster extensions such as the dynamical cluster approximation (DCA), we compute the full two particle susceptibilities in the spin and charge representations. By performing analytic continuations we obtain the temperature and doping dependence of the spinlattice relaxation ($T_1^{1}$) and knight shift in the 2D Hubbard model relevant to NMR results on doped cuprates and connect these to RPA results in weak coupling limits. [Preview Abstract] 
Monday, March 14, 2016 10:36AM  10:48AM 
A25.00014: Magnetism and experimental consequences of $p_z$wave spin triplet state in quasionedimensional A$_2$Cr$_3$As$_3$ superconductors Xianxin Wu, Fan Yang, Congcong Le, Jing Yuan, Shengshan Qin, Heng Fan, Jiangping Hu The recently discovered quasione dimensional superconductors A$_2$Cr$_3$As$_3$(A=K,Rb,Cs), are found to possess strong frustrated magnetic fluctuations and are nearby a novel inout coplanar magnetic ground state. Then, we find that the triplet $p_z$wave pairing is strongly favored. Finally, with $p_z$ wave pairing state, we obtain the specific heat, superfluid density, Knight shift and spin relaxation rate and find that all these properties at low temperature ($T\ll T_c$) show powerlaw behaviors and are consistent available experiments. Particularly, the superfluid density determined by the $p_z$wave pairing state in this quasione dimensional system is anisotropic: the inplane superfluid density varies as $\Delta \rho_{\parallel} \sim T$ but the outplane one varies as $\Delta \rho_{\perp} \sim T^3$ at low temperature. The anisotropic upper critical field reported in experiment is consistent with the $S_z=0$ (i.e,($\uparrow\downarrow+\downarrow\uparrow$)) $p_z$wave pairing state. We also suggest the phasesensitive dcSQUID measurements to pin down the triplet $p_z$wave pairing state. References: [1] X. Wu et al., Chin. Phys. Lett. 32, 057401 (2015). [2] X. Wu et al., Phys. Rev. B 92,104511 (2015). [3] X. Wu et al., arXiv: 1507.07451 (2015) [Preview Abstract] 
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