P. M. R. Brydon

Types of topological surface states in nodal noncentrosymmetric superconductors

origin appear at their surface. We show that the presence of certain inversion-type lattice symmetries can give rise to additional topological features of the gap nodes, resulting in surface states forming one-dimensional arcs connecting the projections of two nodal rings. In addition, we demonstrate that Majorana surface states can appear at time-reversal-invariant momenta of the surface Brillouin zone, even when the system is not fully gapped in the bulk. Within a continuum theory we derive the topological invariants that protect these different types of zero-energy surface states. We independently derive general conditions for the existence of zero-energy surface bound states using the complementary quasiclassical scattering theory, explicitly taking into account the effectsofspin-orbitsplittingofthebands.Wecomputesurfacebound-statespectraforvariouscrystalpoint-group symmetries and orbital-angular-momentum pairing states. Finally, we examine the signatures of the arc surface states and of the zero-energy surface flat bands in tunneling-conductance spectra and dicuss how topological phase transitions in noncentrosymmetric superconductors could be observed in experiments.

Topologically protected flat zero-energy surface bands in noncentrosymmetric superconductors

Nodal non-centrosymmetric superconductors (NCS) have recently been shown to be topologically non-trivial. An important consequence is the existence of topologically protected flat zero-energy surface bands, which are related to the topological characteristics of the line nodes of the bulk gap via a bulk-boundary correspondence [Schnyder and Ryu, arXiv:1011.1438]. In this paper we examine these zero-energy surface bands using a quasiclassical theory. We determine their spectrum and derive a general condition for their existence in terms of the sign change of the gap functions. A key experimental signature of the zero-energy surface bands is a zero-bias peak in the tunneling conductance, which depends strongly on the surface orientation. This can be used as a fingerprint of a topologically non-trivial NCS.

0- π Transition in Magnetic Triplet Superconductor Josephson Junctions

We examine a Josephson junction involving two arbitrary equal-spin-pairing unitary triplet superconductors and a ferromagnetic tunneling barrier. Using perturbation theory, we show how the interaction of the barrier moment with the spin of the tunneling triplet Cooper pairs can reverse the sign of the Josephson charge current. This also results in a Josephson spin current, which contains a phase-independent contribution due to reflection processes at the barrier. We verify our analytic predictions using a nonperturbative Bogoliubov-de Gennes method.

Interplay of ferromagnetism and triplet superconductivity in a Josephson junction

In this work we extend our earlier analysis of the novel Josephson effect in triplet superconductor-ferromagnet-triplet superconductor (TFT) junctions [Kastening et al., Phys. Rev. Lett. 96, 047009 (2006)]. In our more general formulation of the TFT junction, we allow for potential scattering at the barrier and an arbitrary orientation of the ferromagnetic moment. Several new effects are found upon the inclusion of these extra terms: for example, we find that a Josephson current can flow even when there is vanishing phase difference between the superconducting condensates on either side of the barrier. The critical current for a barrier with magnetization parallel to the interface is calculated as a function of the junction parameters, and is found to display strong nonanalyticities. Furthermore, the Josephson current switches identified in our previous work are found to be robust features of the junction, while the unconventional temperature dependence of the current is very sensitive to the extra terms in the barrier Hamiltonian.

Andreev spectroscopy and surface density of states for a three-dimensional time-reversal-invariant topological superconductor

A topological superconductor is a fully gapped superconductor that exhibits exotic zero-energy Andreev surface states at interfaces with a normal metal. In this paper we investigate the properties of a three-dimensional time-reversal invariant topological superconductor by means of a two-band model with unconventional pairing in both the interband and intraband channels. Due to the bulk-boundary correspondence the presence of Andreev surface states in this system is directly related to the topological structure of the bulk wave functions, which is characterized by a winding number. Using quasiclassical scattering theory we construct the spectrum of the Andreev bound states that appear near the surface and compute the surface density of states for various surface orientations. Furthermore, we consider the effects of band splitting, i.e., the breaking of an inversion-type symmetry, and demonstrate that in the absence of band splitting there is a direct transition between the fully gapped topologically trivial phase and the nontrivial phase whereas in the presence of band splitting there exists a finite region of a gapless nodal superconducting phase between the fully gapped topologically trivial and nontrivial phases.

Origin and Control of Spin Currents in a Magnetic Triplet Josephson Junction

We study the appearance of a Josephson spin current in a model triplet superconductor junction with a magnetically-active tunneling barrier. We find three distinct mechanisms for producing a spin current, and we provide a detailed discussion of the symmetry properties and the physical origins of each. By combining these three basic mechanisms, we find that it is possible to exercise fine control over the spin currents. In particular, we show that unlike the charge current, the spin currents on either side of the barrier need not be identical.

Inflated nodes and surface states in superconducting half-Heusler compounds

The half-Heusler superconductors such as YPtBi are multiorbital systems with both strong spin-orbit coupling and broken inversion symmetry. The spin-orbit coupling allows for the formation of Cooper pairs with effective spins larger than unity, which introduces novel pairing states. Some of these states display Fermi surfaces of Bogoliubov quasiparticles. On the other hand, the absence of inversion symmetry leads to topologically protected nodes associated with specific surface features as, for example, flat bands. The authors consider two likely pairing symmetries for this material, one that breaks time-reversal symmetry and one that does not, and find a rich variety of bulk nodes and surface states.

Edge Currents as a Signature of Flatbands in Topological Superconductors

We study nondegenerate flatbands at the surfaces of noncentrosymmetric topological superconductors by exact diagonalization of Bogoliubov-de Gennes Hamiltonians. We show that these states are strongly spin polarized and acquire a chiral dispersion when placed in contact with a ferromagnetic insulator. This chiral mode carries a large edge current which displays a singular dependence on the exchange-field strength. The contribution of other edge states to the current is comparably weak. We hence propose that the observation of the edge current can serve as a test of the presence of nondegenerate flatbands.

Spin-orbital coupling in a triplet superconductor-ferromagnet junction.

We study the interplay of spin and orbital degrees of freedom in a triplet superconductor-ferromagnet junction. Using a self-consistent spatially dependent mean-field theory, we show that increasing the angle between the ferromagnetic moment and the triplet vector order parameter enhances or suppresses the p-wave gap close to the interface, according to whether the gap antinodes are parallel or perpendicular to the boundary, respectively. The associated change in condensation energy establishes an orbitally dependent preferred orientation for the magnetization. When both gap components are present, as in a chiral superconductor, first-order transitions between different moment orientations are observed as a function of the exchange field strength.

Microscopically derived Ginzburg-Landau theory for magnetic order in the iron pnictides

We examine the competition of the observed stripe spin density wave (SDW) with other commensurate and incommensurate SDW phases in a two-band model of the pnictides. Starting from this microscopic model, we rigorously derive an expansion of the free energy in terms of the different order parameters at the mean-field level. We show that three distinct commensurate SDW states are possible and study their appearance as a function of the doping and the electronic structure. We show that the stripe phase is generally present, but its extent in the phase diagram depends strongly upon the number of hole Fermi pockets that are nested with the electron Fermi pockets. Electron pockets competing for the same portion of a hole pocket play a crucial role. We discuss the relevance of our results for the antiferromagnetism of the pnictides.