The Kerr rotation in the unconventional superconductor Sr2_2RuO4_4

The interpretation of Kerr rotation measurements in the superconducting phase of Sr$_2$RuO$_4$ is a controversial topic. Both intrinsic and extrinsic mechanisms have been proposed, and it has been argued that the intrinsic response vanishes by symmetry. We focus on the intrinsic contribution and clarify several conflicting results in the literature. On the basis of symmetry considerations and detailed calculations we show that the intrinsic Kerr signal is not forbidden in a general multi- band system but has a rich structure in the near infrared regime. We distinguish different optical transitions determined by the superconducting gap (far infrared) and the inter orbital coupling of the normal state (near infrared). We argue that the low frequency transitions do not contribute to the Hall conductivity while only the inter-orbital transitions in the near infrared regime contribute. Finally, we discuss the difficulties to connect the calculations for the optical Hall conductivity to the experimental measurement of the Kerr angle. We will compare different approximations which might lead to conflicting results.Comment: 9 pages, 8 figures, 1 tabl

On calculating the Berry curvature of Bloch electrons using the KKR method

We propose and implement a particularly effective method for calculating the Berry curvature arising from adiabatic evolution of Bloch states in wave vector k space. The method exploits a unique feature of the Korringa-Kohn-Rostoker (KKR) approach to solve the Schr\"odinger or Dirac equations. Namely, it is based on the observation that in the KKR method k enters the calculation via the structure constants which depend only on the geometry of the lattice but not the crystal potential. For both the Abelian and non-Abelian Berry curvature we derive an analytic formula whose evaluation does not require any numerical differentiation with respect to k. We present explicit calculations for Al, Cu, Au, and Pt bulk crystals.Comment: 13 pages, 5 figure

Gauge freedom for degenerate Bloch states

In nonmagnetic crystals with inversion symmetry the electronic bands are twofold degenerate. As a consequence, any orthonormalized linear combination of the two corresponding eigenfunctions can represent the electron wave function. A priori it is not obvious which superposition, gauge, should be chosen to calculate a quantity which is not gauge invariant within a certain approximation. Here we consider gauge options appropriate under particular physical conditions

The Fermi Surface Effect on Magnetic Interlayer Coupling

The oscillating magnetic interlayer coupling of Fe over spacer layers consisting of Cu$_{x}$Pd$_{1-x}$ alloys is investigated by first principles density functional theory. The amplitude, period and phase of the coupling, as well as the disorder-induced decay, are analyzed in detail and the consistency to the Ruderman-Kittel-Kasuya-Yoshida (RKKY) theory is discussed. For the first time an effect of the Fermi surface nesting strength on the amplitude is established from first principles calculations. An unexpected variation of the phase and disorder-induced decay is obtained and the results are discussed in terms of asymptotics

Spin-Orbit Coupling and Symmetry of the Order Parameter in Strontium Ruthenate

Determination of the orbital symmetry of a state in spin triplet Sr$_2$RuO$_4$ superconductor is a challenge of considerable importance. Most of the experiments show that the chiral state of the $\hat{z} (k_x \pm ik_y)$ type is realized and remains stable on lowering the temperature. Here we have studied the stability of various superconducting states of Sr$_2$RuO$_4$ in the presence of spin-orbit coupling. Numerically we found that the chiral state is never the minimum energy. Alone among the five states studied it has $=0$ and is therefore not affected to linear order in the coupling parameter $\lambda$. We found that stability of the chiral state requires spin dependent pairing interactions. This imposes strong constraint on the pairing mechanism.Comment: 4 pages, 4 figure

First-principles calculations of the Berry curvature of Bloch states for charge and spin transport of electrons

Recent progress in wave packet dynamics based on the insight of Berry pertaining to adiabatic evolution of quantum systems has led to the need for a new property of a Bloch state, the Berry curvature, to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principle calculations of the Berry curvature. Finally, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties such as the anomalous and spin Hall conductivity as well as the anomalous Nernst conductivity and discuss the influence of the Berry curvature on the de Haas–van Alphen oscillation

Preparation, physical characterization and catalytic properties of unsupported Pt–Rh catalyst

Rh was deposited on a parent platinum black catalyst by an underpotential deposition method. Mean particle size and bulk composition of this Rh–Pt sample was determined by TEM and EDS. No individual Rh grains could be observed, but Rh was present in the near-surface regions, according to energy-filtered TEM images. The surface-sensitive cyclic voltammetry indicated 15–20% Rh on the surface. XPS, in turn, detected ∼2–2.5% Rh in the information depth. The Rh–Pt catalyst was tested in methylcyclopentane hydrogenative ring-opening reaction between 468 and 603 K and 8 to 64 kPa H2 pressure (with 1.3 kPa MCP). The parent Pt black as well as a Rh black catalyst was also studied for comparison. MCP produced ring opening and hydrogenolysis products. The ring-opening products (ROP) consisted of 2- and 3-methylpentane (2MP and 3MP) as well as hexane (nH). These were the main products, together with some fragments and unsaturated hydrocarbons. The amount of the latter class increased at higher temperatures. The selectivities of ROP, fragments, and benzene over Rh–Pt catalyst as a function of temperature were between the values observed on Pt and Rh. The hydrogen pressure dependence of selectivities on Rh–Pt was more similar to that observed on Pt. Four subsequent treatments with O2 and H2 up to T = 673 K were applied on the bimetallic catalyst, followed by XPS and catalytic runs, respectively. These treatments promoted structural rearrangement, with XPS detecting less Rh in the near surface region, partly as oxidized Rh after O2 treatment. The catalytic behavior became more Pt-like on these structural and composition changes. We concluded that adding a relatively small amount of Rh to Pt creates bimetallic active sites with properties different from those of its components, behaving as a true bimetallic catalyst

Preparation, physical characterization and catalytic properties of unsupported Pt–Rh catalyst

Rh was deposited on a parent platinum black catalyst by an underpotential deposition method. Mean particle size and bulk composition of this Rh–Pt sample was determined by TEM and EDS. No individual Rh grains could be observed, but Rh was present in the near-surface regions, according to energy-filtered TEM images. The surface-sensitive cyclic voltammetry indicated 15–20% Rh on the surface. XPS, in turn, detected ∼2–2.5% Rh in the information depth. The Rh–Pt catalyst was tested in methylcyclopentane hydrogenative ring-opening reaction between 468 and 603 K and 8 to 64 kPa H2 pressure (with 1.3 kPa MCP). The parent Pt black as well as a Rh black catalyst was also studied for comparison. MCP produced ring opening and hydrogenolysis products. The ring-opening products (ROP) consisted of 2- and 3-methylpentane (2MP and 3MP) as well as hexane (nH). These were the main products, together with some fragments and unsaturated hydrocarbons. The amount of the latter class increased at higher temperatures. The selectivities of ROP, fragments, and benzene over Rh–Pt catalyst as a function of temperature were between the values observed on Pt and Rh. The hydrogen pressure dependence of selectivities on Rh–Pt was more similar to that observed on Pt. Four subsequent treatments with O2 and H2 up to T = 673 K were applied on the bimetallic catalyst, followed by XPS and catalytic runs, respectively. These treatments promoted structural rearrangement, with XPS detecting less Rh in the near surface region, partly as oxidized Rh after O2 treatment. The catalytic behavior became more Pt-like on these structural and composition changes. We concluded that adding a relatively small amount of Rh to Pt creates bimetallic active sites with properties different from those of its components, behaving as a true bimetallic catalyst

Interlayer Coupling and p-wave Pairing in Strontium Ruthenate

On the basis of a three orbital model and an effective attractive interaction between electrons we investigate the possible superconducting states, with $p$ and $f$-wave internal symmetry, of Sr$_2$RuO$_4$. For an orbital dependent interaction which acts between in plane and out of plane nearest neighbour Ruthenium atoms we find a state for which the gap in the quasi-particle spectra has a line node on the $\alpha$ and $\beta$ sheets of the Fermi Surface, but it is complex with no nodes on the $\gamma$-sheet. We show that this state is consistent with all the available experimental data. In particular, we present the results of our calculations of the specific heat and penetration depth as functions of the temperature.Comment: 4 pages, 5 figure

Magnetic field induced rotation of the d-vector in the spin triplet superconductor Sr2_2RuO4_4

In zero magnetic field the superconductor Sr$_2$RuO$_4$ is believed to have a chiral spin triplet pairing state in which the gap function d-vector is aligned along the crystal c-axis. Using a phenomenological but orbital specific description of the spin dependent electron-electron attraction and a realistic quantitative account of the electronic structure in the normal state we analyze the orientation of the spin triplet Cooper pair d-vector in response to an external c-axis magnetic field. We show that for suitable values of the model parameters a c-axis field of only 20 mT is able to cause a reorientation phase transition of the d-vector from along $c$ to the $a-b$ plane, in agreement with recent experiments.Comment: 6 pages, 7 figures. Submitted Phys Rev