Spin-polarized Local Density Of States Research Articles

Exciting odd-frequency equal-spin triplet correlations at metal-superconductor interfaces

We predict the occurrence of odd frequency equal-spin-triplet correlations at a normal metal-superconductor junction. This result is significant because equal-spin-triplet correlations are associated with the presence of dissipation-less pure spin current. Inserting a spin-flipper at the interface of a normal metal-superconductor junction excites equal-spin-triplet correlations. The existence of odd frequency equal-spin-triplet correlations in absence of odd frequency mixed spin-triplet correlations is the main take-home message of this work. It tallies well with the measured local magnetization density of states and spin-polarized local density of states at the interface. The importance of spin-flip scattering to the obtained results is manifest when we compare our normal metal-spin flipper-superconductor junction to other hybrid junctions where either only spin mixing or both spin mixing and spin-flip scattering are present.

Learning pairing symmetries in disordered superconductors using spin-polarized local density of states

We construct an artificial neural network to study the pairing symmetries in disordered superconductors. For Hamiltonians on square lattice with s-wave, d-wave, and nematic pairing potentials, we use the spin-polarized local density of states near a magnetic impurity in the clean system to train the neural network. We find that, when the depth of the artificial neural network is sufficient large, it will have the power to predict the pairing symmetries in disordered superconductors. In a large parameter regime of the potential disorder, the artificial neural network predicts the correct pairing symmetries with relatively high confidences.

Odd-frequency superconductivity near a magnetic impurity in a conventional superconductor

Superconductor-ferromagnetic heterostructures have been suggested as one of the most promising alternatives of realizing odd-frequency superconductivity. In this work we consider the limit of shrinking the ferromagnetic region to the limit of a single impurity embedded in a conventional superconductor, which gives raise to localized Yu-Shiba-Rusinov (YSR) bound states with energies inside the superconducting gap. We demonstrate that all the sufficient ingredients for generating odd-frequency pairing are present at the vicinity of these impurities. We investigate the appearance of all possible pair amplitudes in accordance with the Berezinskii $SP^{\ast}OT^{\ast} = -1$ rule, being the symmetry under the exchange of spin, spatial, orbital (in our case $O=+1$) and time index, respectively. We study the spatial and frequency dependence of of the possible pairing amplitudes, analyzing their evolution with impurity strength and identifying a reciprocity between different symmetries related through impurity scattering. We show that the odd-frequency spin-triplet pairing amplitude dominates at the critical impurity strength, where the YSR states merge at the middle of the gap, while the even components cancel out close to the impurity. We also show that the spin-polarized local density of states exhibits the same spatial and frequency behavior as the odd-$\omega$ spin-triplet component at the critical impurity strength.

Visualizing pairing symmetry in nematic superconductors using spin-polarized spectroscopy of magnetic impurities

We study the spin-polarized spectral properties of Yu–Shiba–Rusinov resonance states induced by magnetic impurities in 2- and 3-dimensional nematic superconductors: few layer Bi2Te3 grown on FeTe0.55Se0.45 (2D) and CuxBi2Se3 (3D). We focus on the relationship between pairing symmetry and the spatial structure of spin-polarized spectroscopy. We calculate the spin-polarized local density of states (SP LDOS) and the corresponding Fourier transformation using the T-matrix method for both the 2- and 3-dimensional materials. Various situations with different impurity orientations and different SP LDOSs have been investigated. We find that, like the quasiparticle interference spectrum, the spin-polarized spectroscopy can be applied to distinguish threefold rotation symmetric pairings, e.g. the plain s-wave pairing, chiral p -wave pairing, etc, and nematic pairings in these materials.

Probing chiral edge states in topological superconductors through spin-polarized local density of state measurements

We show that spin-polarized local density of states (LDOS) measurements can uniquely determine the chiral nature of topologically protected edge states surrounding a ferromagnetic island embedded in a conventional superconductor with spin-orbit coupling. The spin-polarized LDOS show a strong spin-polarization directly tied to the normal direction of the edge, with opposite polarizations on opposite sides of the island, and with a distinct oscillatory pattern in energy.

Theoretical analysis for spin-polarized local density of states in the vortex state of helical p-wave superconductors

Based on the quasi-classical Eilenberger theory, we calculate the site-dependence of order-parameter and spin-polarized local density of states (LDOS) in the vortex lattice state of helical p-wave superconductors. The spin-polarized LDOS is induced around the vortex core by the vorticity coupling to the chirality of up-spin pair or down-spin pair. In order to distinguish the d-vector symmetry, we investigate the magnetic eld effect on the spatial structure of the spin-polarized LDOS.

Spin-polarized local density of states around vortex in helical p-wave superconductors

Based on the quasi-classical Eilenberger theory, we investigate the magnetic field dependence of order-parameters and spin-polarized local density of states (LDOS) in the vortex lattice state of helical p-wave superconductors. The spin-polarized LDOS is induced by the vorticity coupling to the chirality of up-spin pair or down-spin pair, even when Knight shift does not change. We clarify the instability of the helical p-wave state at high field, and that the spin-polarized LDOS shows the unique behaviors of the helical p-wave state.

Spin-polarized local density of states in the vortex state of helical p -wave superconductors

Properties of the vortex state in helical p-wave superconductor are studied by the quasi-classical Eilenberger theory. We confirm the instability of the helical p-wave state at high fields and that the spin-polarized local density of states M(E,r) appears even when Knight shift does not change. This is because the vorticity couples to the chirality of up-spin pair or down-spin pair of the helical state. In order to identify the helical p-wave state at low fields, we investigate the structure of the zero-energy M (E = 0, r) in the vortex states, and also the energy spectra of M (E, r).

Skyrmion-induced bound states in a p -wave superconductor

In s-wave systems, it has been theoretically shown that a ferromagnetic film hosting a skyrmion can induce a bound state embedded in the opposite-spin continuum. In this work, we consider a case of skyrmion-induced state in a p-wave superconductor. We find that the skyrmion induces a bound state that generally resides \emph{within} the spectral gap and is isolated from all other states, in contrast to the case of conventional superconductors. To this end, we derive an approximate expression for the $T$-matrix, through which we calculate the spin-polarized local density of states which is observable in scanning tunneling microscopy measurements. We find the unique spectroscopic features of the skyrmion-induced bound state and discuss how our predictions could be employed as novel experimental probes for p-wave superconducting states.

Skyrmion-induced bound states in a superconductor

We consider a superconductor proximity coupled to a two-dimensional ferromagnetic film with a skyrmion texture. Using the $T$-matrix calculations and numerical modeling we calculate the spin-polarized local density of states in the superconductor in the vicinity of the skyrmion. We predict the skyrmion bound states that are induced in the superconductor, similar to the well-known Yu-Shiba-Rusinov states. The bound-state wave functions have spatial power-law decay. It is suggested that superconductivity could facilitate an effective long-range interaction between skyrmions when bound-state wave functions overlap.

Spin-polarized edge currents and Majorana fermions in one- and two-dimensional topological superconductors

We investigate the persistent currents, spin-polarized local density of states, and spectral functions of topological superconductors constructed by placing ferromagnetic impurities on top of an s-wave superconductor with Rashba spin-orbit interaction. We solve self-consistently for the superconducting order parameter and investigate both two-dimensional blocks and one-dimensional wires of ferromagnetic impurities, with the magnetic moments pointing both perpendicular and parallel to the surface. We find that the topologically protected edge states of ferromagnetic blocks give rise to spin-polarized edge currents, but that the total persistent current flows in opposite direction to what is expected from the dispersion relation of the edge states. We also show that the Majorana fermions at the end points of one-dimensional wires are spin-polarized, which can be directly related to the spin-polarization of the edge currents of two-dimensional blocks. Connections are also made to the physics of the Yu-Shiba-Rusinov states for zero-dimensional impurities.

Currents induced by magnetic impurities in superconductors with spin-orbit coupling.

We show that superconducting currents are generated around magnetic impurities and ferromagnetic islands proximity coupled to superconductors with finite spin-orbit coupling. Using the Ginzburg-Landau theory, T-matrix calculation, as well as self-consistent numerical simulation on a lattice, we find a strong dependence of the current on the direction and magnitude of the magnetic moment. We establish that in the case of point magnetic impurities, the current is carried by the induced Yu-Shiba-Rusinov (YSR) subgap states. In the vicinity of the phase transition, where the YSR states cross at zero energy, the current increases dramatically. Furthermore, we show that the currents are orthogonal to the local spin polarization and, thus, can be probed by measuring the spin-polarized local density of states.

First-principles study of magnetism at grain boundaries in iron and nickel

The geometric and magnetic structures of fully relaxed symmetrical tilt $\ensuremath{\Sigma}5(310)$ grain boundaries (GBs) in iron and $\ensuremath{\Sigma}5(210)$ GBs in nickel have been investigated using density-functional theory. We found for both GBs an enhancement of the local magnetic moments of atoms in the GB plane ($2.55\text{ }{\ensuremath{\mu}}_{B}$ for iron and $0.67\text{ }{\ensuremath{\mu}}_{B}$ for nickel) which is correlated with the larger local atomic volume compared to the bulk. At larger distances from the GB the variation of the local magnetic moments follows the changes in the exchange splitting in the spin-polarized local density of states imposed by the local variations in the atomic geometry. When Si and Sn impurity atoms in interstitial or substitutional positions appear at the $\ensuremath{\Sigma}5(310)$ GB in iron, the local magnetic moments of iron atoms are reduced for silicon and almost unchanged for tin. We also calculated the segregation enthalpies of both impurities and confirmed the experimental fact that silicon is a substitutional and tin an interstitial segregant; the calculated values of segregation enthalpy are in good agreement with experiment.

Atomic relaxations and magnetic states in a single-atom tunneling junction

A detailed theoretical investigation of structure, electronic and magnetic properties of a single atom magnetic junction is presented. Our studies are based on the density functional theory and the multiple scattering approach. We concentrate on a Cu tip interacting with the Co adatom on Cu(001), and study this junction for the tip-substrate distances ranging from the tunneling to the contact regime. We demonstrate that atomic structure of the tip and position of the adatom above the surface significantly depend on the tip-substrate distance. The adatom-surface distance is found to vary nonmonotonically as the tip approaches the surface. A pronounced change in the spin-polarized local density of states on the Co adatom, and a strong suppression of its magnetic moment are found when the tip is about $4\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$ away from the surface.

Aspects of spin-polarized scanning tunneling microscopy at the atomic scale: experiment, theory, and simulation

The principle and method of atomic-scale spin-polarized scanning tunneling microscopy is discussed, and its application to the case of the (0 1 0) surface of g-phase Mn3N2 is presented. For this surface, new proofs of the spinpolarized effect are presented, and it is also shown that the spin-polarized effect can turn on and off with small changes to the tip apex which can occur during scanning; this indicates that the tip magnetic density of states can and does change at certain points during the experiment. It is also shown how to model height profile data using spin-polarized local density of states of the sample. As well, it is shown how to relate the equation for the total spin-polarized height profile to those of the separated magnetic and non-magnetic height profiles. Comparison of the experimental height profiles to the simulated height profiles based on spin-polarized local densities of states calculated from first-principles density functional theory is shown. In particular, a comparison is made between the results of using the atom-superposition method vs. a full Tersoff–Hamman simulation method. For the case of the transition metal nitride system here, it is shown that the latter method is crucial for a full understanding due to the directionality of the atomic orbital lobes.