Bulletin of the American Physical Society
APS March Meeting 2012
Volume 57, Number 1
Monday–Friday, February 27–March 2 2012; Boston, Massachusetts
Session P23: Superconductivity Theory II: pwave, chiral, and topological 
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Sponsoring Units: DCMP Chair: Herbert Fotso, Georgetown University Room: 255 
Wednesday, February 29, 2012 8:00AM  8:12AM 
P23.00001: Spinorbit induced mixedparity pairing in Sr$_2$RuO$_4$: a selfconsistent quantum manybody analysis John Deisz , Tim Kidd The unusual superconducting state in Sr$_2$RuO$_4$ has long been viewed as being analogous to a superfluid state in liquid $^3$He. Nevertheless, calculations based on a pure oddparity state are presently unable to completely reconcile the properties of Sr$_2$RuO$_4$. Using a selfconsistent quantum manybody scheme that employs realistic parameters, we are able to model several signature properties of the normal and superconducting states of Sr$_2$RuO$_4$ such as the weak temperature dependence of the spin susceptibility below $T_c$. However, we find that the dominant component of the model superconducting state is of even parity and closely related to superconducting state for the high$T_c$ cuprates although a smaller oddparity component is induced by spinorbit coupling. This mixed parity pairing state provides an alternative scenario for understanding the complex phenomena measured in Sr$_2$RuO$_4$. [Preview Abstract] 
Wednesday, February 29, 2012 8:12AM  8:24AM 
P23.00002: Spin and charge collective excitations in the multiband superconductivity of Sr2RuO4 Suk Bum Chung , Srinivas Raghu , Steve Kivelson Multiband superconductors with weak interband pair scattering can support soft collective modes. In the case of spinsinglet superconductivity, interband pair scattering leads to fluctuations of the relative phase of the order parameter on the different bands. However, when the superconductivity is spintriplet, the interband pair scattering gives rise to fluctuations of both the relative phase and the relative spin on the different bands. One possible example of a multiband triplet superconductor is a recently proposed model [1] of the superconductivity in Sr$_2$RuO$_4$ in which the pairing occurs primarily on the two quasi1D bands. We show that the collective excitations arising from relative spin fluctuations can lead to a double resonance peak in the presence of an oscillating magnetic field. We discuss how the presence or absence of such collective modes can yield clear information concerning the precise microscopic structure of the order parameter. \\ \\ $[1]$ S. Raghu, A. Kapitulnik, and S. Kivelson, Phys. Rev. Lett. {\bf 105}, 136401 (2010) [Preview Abstract] 
Wednesday, February 29, 2012 8:24AM  8:36AM 
P23.00003: Dynamics of domain walls in chiral pwave superconductors Kirill Samokhin Twofold degeneracy of the ground state of chiral $p$wave superconductors or superfluids with $k_x\pm ik_y$ order parameter makes it possible for domain walls separating regions of opposite chirality to exist. In addition to affecting the scattering spectrum in the bulk, the domain walls also carry localized lowenergy fermionic quasiparticles, whose energy essentially depends on the Josephson phase difference between the domains. Dynamical properties of the domain walls are determined by the transitions between different quasiparticle states induced by the domain wall motion. We present a microscopic calculation of the viscous friction coefficient and the effective mass of the domain walls. [Preview Abstract] 
Wednesday, February 29, 2012 8:36AM  8:48AM 
P23.00004: Stability of topological defects in chiral superconductors: London theory Victor Vakaryuk We examine thermodynamic stability of chiral domain walls and vortices  topological defects which can exist in chiral superconductors. Using London theory it is demonstrated that at sufficiently small applied and chiral fields the existence of domain walls and vortices in the sample is not favored and the sample's configuration is a single domain. The particular chirality of the singledomain configuration is neither favored nor disfavored by the applied field. Increasing the field leads to an entry of a domain wall loop or a vortex into the sample. Formation of a straight domain wall is never preferred in equilibrium. Values of the entry (critical) fields for both types of defects, as well as the equilibrium size of the domain wall loop, are calculated. The applicability of these results to $\rm Sr_2RuO_4$  a tentative chiral superconductor  is discussed. [Preview Abstract] 
Wednesday, February 29, 2012 8:48AM  9:00AM 
P23.00005: Intrinsic Hall effect in a multiband chiral superconductor Edward Taylor , Catherine Kallin We identify an intrinsic, dissipationless Hall effect in multiband chiral superconductors in the absence of a magnetic field (i.e., an \emph{anomalous} quantum Hall effect). Similarly to its analog in ferromagnets, this effect arises from interband transitions when timereversal symmetry is spontaneously broken. We discuss the implications of this effect for the putative chiral $p$wave superconductor, $\mathrm{Sr}_2\mathrm{RuO}_4$, and show that it can be of the right order of magnitude to contribute significantly to the polar Kerr rotation observed in experiments, depending on the structure of the order parameter across the bands. [Preview Abstract] 
Wednesday, February 29, 2012 9:00AM  9:12AM 
P23.00006: Topologically protected surface Majorana arcs and bulk Weyl fermions in ferromagnetic superconductors Sumanta Tewari , Jay Sau A number of ferromagnetic superconductors have been recently discovered which are believed to be in the socalled ``equal spin pairing'' (ESP) state. In the ESP state the Cooper pairs condense forming order parameters $\Delta_{\uparrow,\uparrow}, \Delta_{\downarrow\downarrow}$, which are decoupled in the spinsector. We show that these 3D systems generically support topologically protected surface Majorana arcs and bulk Weyl fermions as gapless excitations. Similar protected lowenergy exotic quasiparticles should also appear in the recently discovered noncentrosymmteric superconductors in the presence of a Zeeman field. The protected surface arcs can be probed by angleresolved photoemission (ARPES) as well as fourier transform scanning tunneling spectroscopty (FTSTS) experiments. [Preview Abstract] 
Wednesday, February 29, 2012 9:12AM  9:24AM 
P23.00007: Thermodynamic signatures of halfquantum vortices in $p+ip$ Josephson junction arrays Graham Krahn , Kirill Shtengel A very interesting type of excitation in a chiral pwave superconductor is a halfquantum vortex. As the name suggests, they carry half of a superconducting flux quantum, and are only possible in superconductors with spintriplet pairing. An astonishing feature of these excitations is the presence of topologically protected Majorana zero modes. Single halfquantum vortices were recently discovered (J. Jang et al, Science \textbf{331}(6014): 186188) in superconducting mesoscopic rings made of Sr$_2$RuO$_4$, yet to this date they have not been observed in macroscopic samples. We propose a method for detecting halfquantum vortices in Josephson junction arrays, which could host a large number of these vortices. Contrary to a 3D setting, we argue that halfquantum vortices can be energetically preferable in quasi2D chiral spintriplet superconductors. As a result, halfquantum vortices rather than full vortices could drive a BerezinskiiKosterlitzThouless transition (which manifests itself as a resistive transition). We propose to look for their signatures by comparing transition temperatures in $p+ip$ Josephson junction arrays in a transverse magnetic field in both unfrustrated and frustrated cases. [Preview Abstract] 
Wednesday, February 29, 2012 9:24AM  9:36AM 
P23.00008: Scattering theory of chiral Majorana fermion interferometry Jian Li , Genevi\`eve Fleury , Markus Buttiker Using scattering theory, we investigate interferometers composed of chiral Majorana fermion modes coupled to normal metal leads. We advance an approach in which also the basis states in the normal leads are written in terms of Majorana modes. As a consequence the scattering at the junctions of the lead to the Majorana mode couples modes effectively only pairwise irrespective of the number of normal scattering modes. We demonstrate that the charge current can also be expressed in terms of interference between pairs of Majorana modes. These two basic facts permit a treatment and understanding of current and noise signatures of chiral Majorana fermion interferometry in an especially elegant way. As a particular example of applications, in FabryPerottype interferometers where chiral Majorana modes form loops, resonances (antiresonances) upon such loops always lead to peaked (suppressed) Andreev differential conductances and negative (positive) crosscorrelations originate purely from twoMajoranafermion exchange. These investigations are intimately related to current and noise signatures of Majorana bound states. [Preview Abstract] 
Wednesday, February 29, 2012 9:36AM  9:48AM 
P23.00009: Probing Majorana fermions in onedimensional topological superconductors using nonequilibrium transport: an openquantumsystem study Dibyendu Roy , Carlos J. Bolech , Nayana Shah We study onedimensional topological superconductors using an openquantumsystem approach based on Langevin equations. We go beyond a lowenergy effective model of Majorana fermions, to derive different nonequilibrium transport properties exactly in these systems. The role of the coupling between the superconducting wire and metallic leads in physical experiments to detect Majorana bound states is also examined. [Preview Abstract] 
Wednesday, February 29, 2012 9:48AM  10:00AM 
P23.00010: Majorana End States of Au Wires in Proximity to $d_{x^2y^2}$wave Superconductors Kam Tuen Law , Lok Man Wong We propose a one dimensional DIII class Hamiltonian which respects timereversal symmetry and supports zeroenergy double Majorana end states. Single Majorana end states can appear if timereversal symmetry is broken. Majorana fermions survive in the quasi1D regime when multiple transverse subbands of the wire are occupied. More importantly, this model can be realized by inducing $d_{x^2y^2}$wave superconductivity on a quantum wire with strong spinorbit coupling. We suggest Au wires deposited on doped LSCO realize this topological superconducting phase. The energy scales of this setup, an induced proximity gap of 10meV and the Rashba energy of 60meV, are two orders of magnitude larger than the corresponding energy scales in semiconductorbased proposals. [Preview Abstract] 
Wednesday, February 29, 2012 10:00AM  10:12AM 
P23.00011: Topological Josephson effect for arbitrary values of the tunnel coupling in the Kitaev model Flavio Nogueira , Ilya Eremin We investigate the Josephson effect for a setup with two lattice quantum wires featuring fused Majorana boundary modes at the tunnel junction. We show exactly that additional degeneracies occur when the size of the Josephson coupling attains a certain critical value, thus introducing additional energy level crossings. The physical consequences of these additional level crossings are discussed. It is shown that for this critical coupling the Andreev levels can be cast in the form $E_{m\sigma}=2\sigma\sqrt{2}w\cos(\phi/6\pi m/3)$, where $m=1,0,1$ and $\sigma=\pm 1$. The exact Josephson current exhibits the characteristic $4\pi$ periodicity along with additional features related to the extra crossings of Andreev levels at the critical value of the tunnel coupling. [Preview Abstract] 

P23.00012: ABSTRACT WITHDRAWN 
Wednesday, February 29, 2012 10:24AM  10:36AM 
P23.00013: Singleparticle offdiagonal long range order in $Pf$ wave function for topological superconductors Olexei Motrunich We ask what can be glimpsed about a fermion system from a boson wave function obtained as the absolute value of the fermion wave function in the particle number basis. We consider examples of spinless $p$wave superconductors in one and two dimensions and find that thus constructed wave function shows singleboson offdiagonal long range order when the fermion system is in the weakcoupling topological phase, but only pairboson order in the strongcoupling nontopological phase. We discuss implications when such fermion states are used as factors in trial wave functions e.g. from slavefermion construction. [Preview Abstract] 
Wednesday, February 29, 2012 10:36AM  10:48AM 
P23.00014: Topological Superconductivity in SpinOrbit Coupled Bands Aaron Farrell , Tami PeregBarnea Topological superconductors have nontrivial winding of their order parameter phase and are expected to support Majorana Fermions in their vortex cores. For this reason they have been sought after in the past couple of decades. Over the past few years, a new and promising route for realizing topological superconductors has opened due to recent advances in the field of topological insulators. The current proposals are based on semiconductor heterostructures. In the proposed devices, spinorbit coupled bands are Zeeman split by a magnetic field and superconductivity is induced by proximity to a conventional superconductor. This leads to heterostructures of two or three layers. This talk will focus on the prospect of realizing a topological superconductor in materials with inherent spinorbital coupling and an intrinsic tendency for superconductivity. The proposed device will allow simplification of recently suggested devices as the need for a superconducting layer will be eliminated. [Preview Abstract] 
Wednesday, February 29, 2012 10:48AM  11:00AM 
P23.00015: Theory of Superconductivity in Mesoscopic Systems Jiawei Huo , Weiqiang Chen , Srinivas Raghu , Fuchun Zhang By using Bogoliubovde Gennes (BdG) equations, we study superconducting (SC) states in a quasi 2dimensional system of radius $R$. It is shown that no vortices exist in $s$wave SC samples with $R < R_c\sim\xi(0)$, the $T=0$ coherence length. We predict that chiral $p$wave states exhibit superconductivity for $R < R_c$ only in the presence of a vortex with opposite chirality. This {\it reentrant} SC phase is a consequence of nonzero chirality of the pairing order parameter and implies the presence of chiral edge currents. Our study may be applied to sharply probing the pairing symmetry of unconventional superconductors. [Preview Abstract] 
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