Hidden quasi-one-dimensional superconductivity in Sr₂RuO₄

Weyl Fermions and broken symmetry phases of laterally confined3He films

Broken symmetries in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. The Fermionic spectrum of confined (quasi-2D)3He-A consists of branches of chiral edge states. The negative energy states are related to the ground-state angular momentum,Lz=(N/2)ℏ, forN/2Cooper pairs. The power law suppression of the angular momentum,Lz(T)≃(N/2)ℏ[1-23(πT/Δ)2]for0⩽T≪Tc, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the chiral edge Fermions. We discuss the effects of wave function overlap, and hybridization between edge states confined near opposing edge boundaries on the edge currents, ground-state angular momentum and ground-state order parameter of superfluid3He thin films. Under strong lateral confinement, the chiral A phase undergoes a sequence of phase transitions, first to a pair density wave (PDW) phase with broken translational symmetry atDc2∼16ξ0. The PDW phase is described by a periodic array of chiral domains with alternating chirality, separated by domain walls. The period of PDW phase diverges as the confinement lengthD→Dc2. The PDW phase breaks time-reversal symmetry, translation invariance, but is invariant under the combination of time-reversal and translation by a one-half period of the PDW. The mass current distribution of the PDW phase reflects this combined symmetry, and originates from the spectra of edge Fermions and the chiral branches bound to the domain walls. Under sufficiently strong confinement a second-order transition occurs to the non-chiral 'polar phase' atDc1∼9ξ0, in which a single p-wave orbital state of Cooper pairs is aligned along the channel.

Effect of nonequilibrium order parameter on the optical response of superconductor Sr2RuO4

The breaking of time reversal symmetry of the superconducting pairings is expected to manifest itself through characteristic transport properties such as a non-zero Kerr angle which provides fingerprint of the quantum anomalous Hall state. In this work, we theoretically study the Kerr effect or the Hall-type response and also consider how this response is modified by the nonequilibrium shape of order parameter of the superconducting state due to the influence of the electromagnetic radiation for the most favorable candidates of chiral superconducting order parameters and of the non-chiral states in strontium ruthenate (Sr₂RuO₄). The unique sensitivity of the Hall-type response introduced above to different types of pairings can be used to identify the most favored pairing which is a serious doubt on the superconducting state of this material.

The superconductivity of Sr2RuO4 under c-axis uniaxial stress

Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor Sr₂RuO₄ can be tuned through a single Van Hove point, resulting in strong enhancement of both T_c and H_c2. Out-of-plane (c axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, by pushing it towards two Van Hove points simultaneously. Here, we achieve a record uniaxial stress of 3.2 GPa along the c axis of Sr₂RuO₄. H_c2 increases, as expected for increasing density of states, but unexpectedly T_c falls. As a first attempt to explain this result, we present three-dimensional calculations in the weak interaction limit. We find that within the weak-coupling framework there is no single order parameter that can account for the contrasting effects of in-plane versus c-axis uniaxial stress, which makes this new result a strong constraint on theories of the superconductivity of Sr₂RuO₄.

In the superconductor Sr2RuO4, in-plane strain is known to enhance both the superconducting transition temperature Tc and upper critical field Hc2, but the effect of out-of-plane strain has not been studied. Here, the authors find that Hc2 is enhanced under out-of-plane strain, but Tc unexpectedly decreases.

High-sensitivity heat-capacity measurements on Sr2RuO4 under uniaxial pressure

A key question regarding the unconventional superconductivity of [Formula: see text] remains whether the order parameter is single- or two-component. Under a hypothesis of two-component superconductivity, uniaxial pressure is expected to lift their degeneracy, resulting in a split transition. The most direct and fundamental probe of a split transition is heat capacity. Here, we report measurement of heat capacity of samples subject to large and highly homogeneous uniaxial pressure. We place an upper limit on the heat-capacity signature of any second transition of a few percent of that of the primary superconducting transition. The normalized jump in heat capacity, [Formula: see text], grows smoothly as a function of uniaxial pressure, favoring order parameters which are allowed to maximize in the same part of the Brillouin zone as the well-studied van Hove singularity. Thanks to the high precision of our measurements, these findings place stringent constraints on theories of the superconductivity of [Formula: see text].

Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging

Sr₂RuO₄ has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap [Formula: see text] on each band i that encodes its unknown superconducting order parameter. However, because the energy scales are so low, it has never been possible to directly measure the [Formula: see text] of Sr₂RuO₄ Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband [Formula: see text] At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors [Formula: see text] consistent with eight gap nodes/minima that are all closely aligned to the [Formula: see text] crystal lattice directions on both the α and β bands. Taking these observations in combination with other very recent advances in directional thermal conductivity [E. Hassinger et al., Phys. Rev. X 7, 011032 (2017)], temperature-dependent Knight shift [A. Pustogow et al., Nature 574, 72-75 (2019)], time-reversal symmetry conservation [S. Kashiwaya et al., Phys. Rev B, 100, 094530 (2019)], and theory [A. T. Rømer et al., Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising, T. Scaffidi, F. Flicker, G. F. Lange, S. H. Simon, Phys. Rev. Res. 1, 033108 (2019); and O. Gingras, R. Nourafkan, A. S. Tremblay, M. Côté, Phys. Rev. Lett. 123, 217005 (2019)], the BQPI signature of Sr₂RuO₄ appears most consistent with [Formula: see text] having [Formula: see text] [Formula: see text] symmetry.

Superconducting Symmetries of Sr_{2}RuO_{4} from First-Principles Electronic Structure

Although correlated electronic-structure calculations explain very well the normal state of Sr_{2}RuO_{4}, its superconducting symmetry is still unknown. Here we construct the spin and charge fluctuation pairing interactions based on its correlated normal state. Correlations significantly reduce ferromagnetic in favor of antiferromagnetic fluctuations and increase interorbital pairing. From the normal-state Eliashberg equations, we find spin-singlet d-wave pairing close to magnetic instabilities. Away from these instabilities, where charge fluctuations increase, we find two time-reversal symmetry-breaking spin triplets: an odd-frequency s wave, and a doubly degenerate interorbital pairing between d_{xy} and (d_{yz},d_{xz}).

Time Reversal Symmetry Breaking Superconductors: Sr2RuO4 and Beyond

Recent work done on the time reversal symmetry (TRS) breaking superconductors is reviewed in this paper. The special attention is paid to Sr 2 RuO 4 believed to be spin triplet chiral p-wave superconductor which break TRS and is expected to posses non-trivial topological properties. The family of TRS breaking superconductors is growing relatively fast, with many of its newly discovered members being non-centrosymmetric. However not only Sr 2 RuO 4 but also many other superconductors which possess center of inversion also break TRS. The TRS is often identified by means of the muon spin relaxation ( μ SR) and the Kerr effect. Both methods effectively measure the appearance of the spontaneous bulk magnetic field below superconducting transition temperature. This compound provides an example of the material whose many band, multi-condensate modeling has enjoyed a number of successes, but the full understanding has not been achieved yet. We discuss in some details the properties of the material. Among them is the Kerr effect and by understanding has resulted in the discovery of the novel mechanism of the phenomenon. The mechanism is universal and thus applicable to all systems with multi-orbital character of states at the Fermi energy.

Spin Fluctuations in Sr_{2}RuO_{4} from Polarized Neutron Scattering: Implications for Superconductivity

Triplet pairing in Sr_{2}RuO_{4} was initially suggested based on the hypothesis of strong ferromagnetic spin fluctuations. Using polarized inelastic neutron scattering, we accurately determine the full spectrum of spin fluctuations in Sr_{2}RuO_{4}. Besides the well-studied incommensurate magnetic fluctuations, we do find a sizable quasiferromagnetic signal, quantitatively consistent with all macroscopic and microscopic probes. We use this result to address the possibility of magnetically driven triplet superconductivity in Sr_{2}RuO_{4}. We conclude that, even though the quasiferromagnetic signal is stronger and sharper than previously anticipated, spin fluctuations alone are not enough to generate a triplet state strengthening the need for additional interactions or an alternative pairing scenario.

Theory of Chiral p-Wave Superconductivity with Near Nodes for Sr_{2}RuO_{4}

We use the functional renormalization group method to study a three-orbital model for superconducting Sr_{2}RuO_{4}. Although the pairing symmetry is found to be a chiral p wave, the atomic spin-orbit coupling induces near nodes for quasiparticle excitations. Our theory explains a major experimental puzzle between a d-wavelike feature observed in thermal experiments and the chiral p-wave triplet pairing revealed in nuclear-magnetic resonance and the Kerr effect.

Possible Three-Dimensional Nematic Odd-Parity Superconductivity in Sr_{2}RuO_{4}

The superconducting pairing in Sr_{2}RuO_{4} is widely considered to be chiral p wave with d[over →]_{k}∼(k_{x}+ik_{y})z[over ^], which belongs to the E_{u} representation of the crystalline D_{4h} group. However, this superconducting order appears hard to reconcile with a number of key experiments. In this Letter, based on symmetry analysis we discuss the possibility of odd-parity pairing with inherent three-dimensional character enforced by the interorbital interlayer coupling and the sizable spin-orbit coupling in the material. We focus on a yet unexplored E_{u} pairing, which contains finite (k_{z}x[over ^], k_{z}y[over ^]) component in the gap function. Under appropriate circumstances a novel time-reversal invariant nematic pairing can be realized. This nematic superconducting state could make contact with some puzzling observations on Sr_{2}RuO_{4}, such as the absence of spontaneous edge current and no evidence of split transitions under uniaxial strains.

Odd-Frequency Superconductivity in Sr_{2}RuO_{4} Measured by Kerr Rotation

We establish the existence of bulk odd-frequency superconductivity in Sr_{2}RuO_{4} and show that an intrinsic Kerr effect is direct evidence of this state. We use both general two- and three-orbital models, as well as a realistic tight-binding description of Sr_{2}RuO_{4} to demonstrate that odd-frequency pairing arises due to finite hybridization between different orbitals in the normal state, and is further enhanced by finite interorbital pairing.

Topological superconductivity in monolayer transition metal dichalcogenides

Theoretically, it has been known that breaking spin degeneracy and effectively realizing spinless fermions is a promising path to topological superconductors. Yet, topological superconductors are rare to date. Here we propose to realize spinless fermions by splitting the spin degeneracy in momentum space. Specifically, we identify monolayer hole-doped transition metal dichalcogenide (TMD)s as candidates for topological superconductors out of such momentum-space-split spinless fermions. Although electron-doped TMDs have recently been found superconducting, the observed superconductivity is unlikely topological because of the near spin degeneracy. Meanwhile, hole-doped TMDs with momentum-space-split spinless fermions remain unexplored. Employing a renormalization group analysis, we propose that the unusual spin-valley locking in hole-doped TMDs together with repulsive interactions selectively favours two topological superconducting states: interpocket paired state with Chern number 2 and intrapocket paired state with finite pair momentum. A confirmation of our predictions will open up possibilities for manipulating topological superconductors on the device-friendly platform of monolayer TMDs.

Absence of a Large Superconductivity-Induced Gap in Magnetic Fluctuations of Sr_{2}RuO_{4}

Inelastic neutron scattering experiments on Sr_{2}RuO_{4} determine the spectral weight of the nesting induced magnetic fluctuations across the superconducting transition. There is no observable change at the superconducting transition down to an energy of ∼0.35  meV, which is well below the 2Δ values reported in several tunneling experiments. At this and higher energies magnetic fluctuations clearly persist in the superconducting state. Only at energies below ∼0.3  meV can evidence for partial suppression of spectral weight in the superconducting state be observed. This strongly suggests that the one-dimensional bands with the associated nesting fluctuations do not form the active, highly gapped bands in the superconducting pairing in Sr_{2}RuO_{4}.

First-Principles Correlated Approach to the Normal State of Strontium Ruthenate

The interplay between multiple bands, sizable multi-band electronic correlations and strong spin-orbit coupling may conspire in selecting a rather unusual unconventional pairing symmetry in layered Sr2RuO4. This mandates a detailed revisit of the normal state and, in particular, the T-dependent incoherence-coherence crossover. Using a modern first-principles correlated view, we study this issue in the actual structure of Sr2RuO4 and present a unified and quantitative description of a range of unusual physical responses in the normal state. Armed with these, we propose that a new and important element, that of dominant multi-orbital charge fluctuations in a Hund's metal, may be a primary pair glue for unconventional superconductivity. Thereby we establish a connection between the normal state responses and superconductivity in this system.

Two-dimensional chiral topological superconductivity in Shiba lattices

The chiral p-wave superconductor is the archetypal example of a state of matter that supports non-Abelian anyons, a highly desired type of exotic quasiparticle. With this, it is foundational for the distant goal of building a topological quantum computer. While some candidate materials for bulk chiral superconductors exist, they are subject of an ongoing debate about their actual paring state. Here we propose an alternative route to chiral superconductivity, consisting of the surface of an ordinary superconductor decorated with a two-dimensional lattice of magnetic impurities. We furthermore identify a promising experimental platform to realize this proposal.

Chiral p-wave superconductors may form the basis for topological quantum computers however one has yet to be identified. Here, the authors propose that such a state may be created by a two-dimensional array of magnetic adatoms on the surface of a superconductor with strong spin-orbit coupling.

Strain Control of Fermiology and Many-Body Interactions in Two-Dimensional Ruthenates

Here we demonstrate how the Fermi surface topology and quantum many-body interactions can be manipulated via epitaxial strain in the spin-triplet superconductor Sr_{2}RuO_{4} and its isoelectronic counterpart Ba_{2}RuO_{4} using oxide molecular beam epitaxy, in situ angle-resolved photoemission spectroscopy, and transport measurements. Near the topological transition of the γ Fermi surface sheet, we observe clear signatures of critical fluctuations, while the quasiparticle mass enhancement is found to increase rapidly and monotonically with increasing Ru-O bond distance. Our work demonstrates the possibilities for using epitaxial strain as a disorder-free means of manipulating emergent properties, many-body interactions, and potentially the superconductivity in correlated materials.

Chiral superconductors

Chiral superconductivity is a striking quantum phenomenon in which an unconventional superconductor spontaneously develops an angular momentum and lowers its free energy by eliminating nodes in the gap. It is a topologically non-trivial state and, as such, exhibits distinctive topological modes at surfaces and defects. In this paper we discuss the current theory and experimental results on chiral superconductors, focusing on two of the best-studied systems, Sr2RuO4, which is thought to be a chiral triplet p-wave superconductor, and UPt3, which has two low-temperature superconducting phases (in zero magnetic field), the lower of which is believed to be chiral triplet f-wave. Other systems that may exhibit chiral superconductivity are also discussed. Key signatures of chiral superconductivity are surface currents and chiral Majorana modes, Majorana states in vortex cores, and the possibility of half-flux quantum vortices in the case of triplet pairing. Experimental evidence for chiral superconductivity from μSR, NMR, strain, polar Kerr effect and Josephson tunneling experiments are discussed.

Large Chern Number and Edge Currents in Sr2RuO4

We show from a weak-coupling microscopic calculation that the most favored chiral superconducting order parameter in Sr2RuO4 has a Chern number of |C|=7. The two dominant components of this order parameter are given by sin(3k(x))+isin(3k(y)) and sin(k(x))cos(k(y))+isin(k(y))cos(k(x)) and lie in the same irreducible representation E(u) of the tetragonal point group as the usually assumed gap function, sin(k(x))+isin(k(y)). While the latter gap function leads to C=1, the two former lead to C=-7, which is also allowed for an E_{u} gap function since the tetragonal symmetry only fixes C modulo 4. Since it was shown that the edge currents of a |C|>1 superconductor vanish exactly in the continuum limit, and can be strongly reduced on the lattice, this form of order parameter could help resolve the conflict between experimental observation of time-reversal symmetry breaking and yet the absence of observed edge currents in Sr2RuO4.

Chiral d-wave superconductivity in doped graphene

A highly unconventional superconducting state with a spin-singlet dx2-y2+/-idxy-wave, or chiral d-wave symmetry has recently been suggested to emerge from electron-electron interactions in doped graphene. It has been argued that graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverge, is particularly likely to be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss the multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review the means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.

Is the anisotropy of the upper critical field of Sr2RuO4 consistent with a helical p-wave state?

We calculate the angular and temperature T dependencies of the upper critical field Hc2(θ, ϕ, T) for the C4v point group helical p-wave states, assuming a single uniaxial ellipsoidal Fermi surface, Pauli limiting and strong spin-orbit coupling that locks the spin-triplet d-vectors onto the layers. Good fits to the Sr2RuO4 Hc2,a(θ, T) data of Kittaka et al (2009 Phys. Rev. B 80 174514) are obtained. Helical states with d(k) =kˆxxˆ −kˆyy and kˆyxˆ +kˆxy (or kˆxxˆ +kˆyyˆ and kˆyxˆ -kˆxyˆ ) produce Hc2(90°, ϕ, T) that greatly exceed (or do not exhibit) the fourfold azimuthal anisotropy magnitudes observed in Sr2RuO4 by Kittaka et al and by Mao et al (2000 Phys. Rev. Lett. 84 991), respectively.

Enhanced spin-triplet superconductivity near dislocations in Sr₂RuO₄

Superconductors with a chiral p-wave pairing are of great interest because they could support Majorana modes that could enable the development of topological quantum computing technologies that are robust against decoherence. Sr₂RuO₄ is widely believed to be a chiral p-wave superconductor. Yet, the mechanism by which superconductivity emerges in this, and indeed most other unconventional superconductors, remains unclear. Here we show that the local superconducting transition temperature in the vicinity of lattice dislocations in Sr₂RuO₄ can be up to twice that of its bulk. This is all the more surprising for the fact that disorder is known to easily quench superconductivity in this material. With the help of a phenomenological theory that takes into account the crystalline symmetry near a dislocation and the pairing symmetry of Sr₂RuO₄, we predict that a similar enhancement should emerge as a consequence of symmetry reduction in any superconductor with a two-component order parameter.

Spin-orbital entanglement and the breakdown of singlets and triplets in Sr2RuO4 revealed by spin- and angle-resolved photoemission spectroscopy

Spin-orbit coupling has been conjectured to play a key role in the low-energy electronic structure of Sr2RuO4. By using circularly polarized light combined with spin- and angle-resolved photoemission spectroscopy, we directly measure the value of the effective spin-orbit coupling to be 130±30  meV. This is even larger than theoretically predicted and comparable to the energy splitting of the dxy and dxz,yz orbitals around the Fermi surface, resulting in a strongly momentum-dependent entanglement of spin and orbital character in the electronic wavefunction. As demonstrated by the spin expectation value ⟨sk⃗·s-k⃗⟩ calculated for a pair of electrons with zero total momentum, the classification of the Cooper pairs in terms of pure singlets or triplets fundamentally breaks down, necessitating a description of the unconventional superconducting state of Sr2RuO4 in terms of these newly found spin-orbital entangled eigenstates.

Domain walls and their experimental signatures in s+is superconductors

Arguments were recently advanced that hole-doped Ba(1-x)K(x)Fe2As2 exhibits the s+is state at certain doping. Spontaneous breaking of time-reversal symmetry in the s+is state dictates that it possess domain wall excitations. Here, we discuss what are the experimentally detectable signatures of domain walls in the s+is state. We find that in this state the domain walls can have a dipolelike magnetic signature (in contrast to the uniform magnetic signature of domain walls p+ip superconductors). We propose experiments where quench-induced domain walls can be stabilized by geometric barriers and observed via their magnetic signature or their influence on the magnetization process, thereby providing an experimental tool to confirm the s+is state.

Predicted nucleation of domain walls in p(x)+ip(y) superconductors by a Z(2) symmetry-breaking transition in external magnetic fields

We show that time reversal symmetry-breaking p(x)+ip(y) wave superconductors undergo several phase transitions subjected to an external magnetic field or supercurrent. In such a system, the discrete Z(2) symmetry can recover before a complete destruction of the order parameter. The domain walls associated with Z(2) symmetry can be created in a controllable way by a magnetic field or current sweep according to the Kibble-Zurek scenario. Such domain wall generation can take place in exotic superconductors like Sr(2)RuO(4), thin films of superfluid (3)He-A, and some heavy fermion compounds.

Spin density wave fluctuations and p-wave pairing in Sr2RuO4

Recently, a debate has arisen over which of the two distinct parts of the Fermi surface of Sr(2)RuO(4) is the active part for the chiral p-wave superconductivity exhibited. Early theories proposed p-wave pairing on the two-dimensional γ band, whereas a recent proposal focuses on the one-dimensional (α, β) bands whose nesting pockets are the source of the strong incommensurate spin density wave (SDW) fluctuations. We apply a renormalization group theory to study quasi-one-dimensional repulsive Hubbard chains and explain the form of SDW fluctuations, reconciling the absence of long-range order with their nesting Fermi surface. The mutual exclusion of p-wave pairing and SDW fluctuations in repulsive Hubbard chains favors the assignment of the two-dimensional γ band as the source of p-wave pairing.

New directions in the pursuit of Majorana fermions in solid state systems

The 1937 theoretical discovery of Majorana fermions-whose defining property is that they are their own anti-particles-has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic 'topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to 'engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions-the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.

Upper critical magnetic field far above the paramagnetic pair-breaking limit of superconducting one-dimensional Li0:9Mo6O17 single crystals

The upper critical field H(c2) of purple bronze Li0:9Mo6O17 is found to exhibit a large anisotropy, in quantitative agreement with that expected from the observed electrical resistivity anisotropy. With the field aligned along the most conducting axis, H(c2) increases monotonically with decreasing temperature to a value 5 times larger than the estimated paramagnetic pair-breaking field. Theories for the enhancement of H(c2) invoking spin-orbit scattering or strong-coupling superconductivity are shown to be inadequate in explaining the observed behavior, suggesting that the pairing state in Li0:9Mo6O17 is unconventional and possibly spin triplet.

Intrinsic Hall effect in a multiband chiral superconductor in the absence of an external magnetic field

We identify an intrinsic Hall effect in multiband chiral superconductors in the absence of a magnetic field (i.e., an anomalous Hall effect). This effect arises from interband transitions involving time-reversal symmetry-breaking chiral Cooper pairs. We discuss the implications of this effect for the putative chiral p-wave superconductor, Sr2RuO4, and show that it can contribute significantly to Kerr rotation experiments. Since the magnitude of the effect depends on the structure of the order parameter across the bands, this result may be used to distinguish between different models proposed for the superconducting state of Sr2RuO4.

Chiral p-wave order in Sr2RuO4

Shortly after the discovery in 1994 of superconductivity in Sr(2)RuO(4), it was proposed on theoretical grounds that the superconducting state may have chiral p-wave symmetry analogous to the A phase of superfluid (3)He. Substantial experimental evidence has since accumulated in favor of this pairing symmetry, including several interesting recent results related to broken time-reversal symmetry (BTRS) and vortices with half of the usual superconducting flux quantum. Great interest surrounds the possibility of chiral p-wave order in Sr(2)RuO(4), since this state may exhibit topological order analogous to that of a quantum Hall state, and can support such exotic physics as Majorana fermions and non-Abelian winding statistics, which have been proposed as one route to a quantum computer. However, serious discrepancies remain in trying to connect the experimental results to theoretical predictions for chiral p-wave order. In this paper, I review a broad range of experiments on Sr(2)RuO(4) that are sensitive to p-wave pairing, triplet superconductivity and time-reversal symmetry breaking and compare these experiments to each other and to theoretical predictions. In this context, the evidence for triplet pairing is strong, although some puzzles remain. The 'smoking gun' experimental results for chiral p-wave order, those which directly look for evidence of BTRS in the superconducting state of Sr(2)RuO(4), are most perplexing when the results are compared with each other and to theoretical predictions. Consequently, the case for chiral p-wave superconductivity in Sr(2)RuO(4) remains unresolved, suggesting the need to consider either significant modifications to the standard chiral p-wave models or possible alternative pairing symmetries. Recent ideas along these lines are discussed.

Intrinsic optical dichroism in the chiral superconducting state of Sr2RuO4

We present an analysis of the Hall conductivity σ(xy)(ω,T) in time reversal symmetry breaking states of exotic superconductors. We find that the dichroic signal is nonzero in systems with interband order parameters. This new intrinsic mechanism may explain the Kerr effect observed in strontium ruthenate and possibly other superconductors. We predict coherence factor effects in the temperature dependence of the imaginary part of the ac Hall conductivity Imσ(xy)(ω,T), which can be tested experimentally.