Spin Transport in Half-Metallic Ferromagnet-Superconductor Junctions

We investigate the charge and spin transport in half-metallic ferromagnet ($F$) and superconductor ($S$) nanojunctions. We utilize a self-consistent microscopic method that can accommodate the broad range of energy scales present, and ensures proximity effects that account for the interactions at the interfaces are accurately determined. Two experimentally relevant half-metallic junction types are considered: The first is a $F_1 F_2 S$ structure, where a half-metallic ferromagnet $F_1$ adjoins a weaker conventional ferromagnet $F_2$. The current is injected through the $F_1$ layer by means of an applied bias voltage. The second configuration involves a $S F_1 F_2 F_3 S$ Josephson junction whereby a phase difference $\Delta\varphi$ between the two superconducting electrodes generates the supercurrent flow. In this case, the central half-metallic $F_2$ layer is surrounded by two weak ferromagnets $F_1$ and $F_3$. By placing a ferromagnet with a weak exchange field adjacent to an $S$ layer, we are able to optimize the conversion process in which opposite-spin triplet pairs are converted into equal-spin triplet pairs that propagate deep into the half-metallic regions in both junction types. For the tunnel junctions, we study the bias-induced local magnetization, spin currents, and spin transfer torques for various orientations of the relative magnetization angle $\theta$ in the $F$ layers. We find that the bias-induced equal-spin triplet pairs are maximized in the half-metal for $\theta\approx90^\circ$ and as part of the conversion process, are anticorrelated with the opposite-spin pairs. We show that the charge current density is maximized, corresponding to the occurrence of a large amplitude of equal-spin triplet pairs, when the exchange interaction of the weak ferromagnet is about $0.1E_F.

Quantum phase transitions in superconductor--quantum-dot--superconductor Josephson structures with attractive intradot interaction

We theoretically study the superconducting proximity effect in a quantum dot coupled to two superconducting leads when the intradot interaction between electrons is made attractive. Because of the superconducting proximity effect, the electronic states for the embedded quantum dot are either spin-polarized states with an odd occupation number or BCS-like states with an even occupation number. We show that in the presence of an external magnetic field, the system can exhibit quantum phase transitions of fermion parity associated with the occupation number. In this work, we adopt a self-consistent theoretical method to extend our considerations beyond the so-called superconducting atomic limit in which the superconducting gap for the leads is assumed to be the largest energy scale. The method enables us to numerically investigate the electronic structure of the dot as results of the attractive interaction. For energy phase diagrams in the regime away from the atomic limit, we find a reentrant behavior where a BCS-like phase of the dot exists in an intermediate range of the hybridization strength between the quantum dot and the leads. We also consider Josephson current phase relations and identify a number of examples showing $0-\pi$ phase transitions that may offer important switching effects

Full proximity treatment of topological superconductors in Josephson-junction architectures

Experiments on planar Josephson junction architectures have recently been shown to provide an alternative way of creating topological superconductors hosting accessible Majorana modes. These zero-energy modes can be found at the ends of a one-dimensional channel in the junction of a two-dimensional electron gas (2DEG) proximitized by two spatially separated superconductors. The channel, which is below the break between the superconductors, is not in direct contact with the superconducting leads, so that proximity coupling is expected to be weaker and less well-controlled than in the simple nanowire configuration widely discussed in the literature. This provides a strong incentive for this paper which investigates the nature of proximitization in these Josephson architectures. At a microscopic level we demonstrate how and when it can lead to topological phases. We do so by going beyond simple tunneling models through solving self-consistently the Bogoliubov-de Gennes equations of a heterostructure multicomponent system involving two spatially separated $s$-wave superconductors in contact with a normal Rashba spin-orbit-coupled 2DEG. Importantly, within our self-consistent theory we present ways of maximizing the proximity-induced superconducting gap by studying the effect of the Rashba spin-orbit coupling, chemical potential mismatch between the superconductor and 2DEG, and sample geometry on the gap. Finally, we note (as in experiment) a Fulde-Ferrell-Larkin-Ovchinnikov phase is also found to appear in the 2DEG channel, albeit under circumstances which are not ideal for topological superconducting phase.Comment: 19 pages, 14 figure

Charge and Spin Currents in Ferromagnetic Josephson junctions

We determine, using a self consistent method, the charge and spin currents in ballistic Josephson junctions consisting of ferromagnetic ($F$) layers sandwiched between superconducting ($S$) electrodes ($SFS$-type junctions). When there are two $F$ layers, we also consider the experimentally relevant configuration where a normal ($N$) nonmagnetic spacer layer separates them. We study the current-phase relationships as functions of geometrical parameters that are accessible experimentally including the angles that characterize the relative orientation of the magnetization in the $F$ layers. Our self-consistent method ensures that the proper charge conservation laws are satisfied. As we vary the phase difference $\Delta\varphi$ between the two outer $S$ electrodes, multiple harmonics in the current phase relations emerge, their extent depends on the interface scattering strength and the relative $F$ layer widths and magnetization orientations. By manipulating the relative $F$ layer magnetization orientations, we find that the charge supercurrent can reverse directions or vanish altogether. These findings are discussed in the context of the generation and long-range nature of triplet pair correlation. We also investigate the spin currents and associated spin transfer torques throughout the junction. For noncollinear relative magnetizations, the non-conserved spin currents in a given $F$ region gives rise to net torques that can switch directions at particular magnetic configurations or $\Delta\varphi$ values. The details of the spin current behavior are shown to depend strongly on the degree of magnetic inhomogeneity in the system.Comment: 14 figures include

Two-Dimensional Dilaton Gravity Theory and Lattice Schwarzian Theory

We report a holographic study of a two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the cases of non-vanishing and vanishing cosmological constants. Our result shows that the boundary theory of the two-dimensional dilaton gravity theory with the Dirichlet boundary condition for the case of non-vanishing cosmological constants is the Schwarzian term coupled to a dilaton field, while for the case of vanishing cosmological constant, a theory does not have a kinetic term. We also include the higher derivative term $R^2$, where $R$ is the scalar curvature that is coupled to a dilaton field. We find that the form of the boundary theory is not modified perturbatively. Finally, we show that a lattice holographic picture is realized up to the second-order perturbation of boundary cut-off $\epsilon^2$ under a constant boundary dilaton field and the non-vanishing cosmological constant by identifying the lattice spacing $a$ of a lattice Schwarzian theory with the boundary cut-off $\epsilon$ of the two-dimensional dilaton gravity theory.Comment: 15 pages, minor changes, references adde

Justification for the group-theoretical method as the right way to solve the infinite spherical well in quantum mechanics

Recently, the problem of the infinite spherical well was solved by the group-theoretical method to resolve all the peculiarities in the currently accepted solution [DOI: 10.13140/RG.2.2.18172.44162 (Researchgate, 2017)]. With a view to further justifying the group-theoretical method, the problem is first studied from the viewpoint of classical mechanics. Then the radial probability densities predicted by classical mechanics are compared with those predicted from solutions of the problem obtained by the group-theoretical method. The comparisons clearly indicate the convergence of predictions of quantum mechanics and classical mechanics in the limit of large eigen-energies. Therefore, the group-theoretical method is justified as the right way to solve the problem of the infinite spherical well.Comment: 13 pages, 9 figure

Two-dimensional spin-imbalanced Fermi gases at non-zero temperature: Phase separation of a non-condensate

We study a trapped two-dimensional spin-imbalanced Fermi gas over a range of temperatures. In the moderate temperature regime, associated with current experiments, we find reasonable semi-quantitative agreement with the measured density profiles as functions of varying spin imbalance and interaction strength. Our calculations show that, in contrast to the three-dimensional case, the phase separation which appears as a spin balanced core, can be associated with non-condensed fermion pairs. We present predictions at lower temperatures where a quasi-condensate will first appear, based on the pair momentum distribution and following the protocols of Jochim and collaborators. While these profiles also indicate phase separation, they exhibit distinctive features which may aid in identifying the condensation regime.Comment: 4 pages, 4 figur

Quasi-condensation in two-dimensional Fermi gases

In this paper we follow the analysis and protocols of recent experiments, combined with simple theory, to arrive at a physical understanding of quasi-condensation in two dimensional Fermi gases. We find that quasi-condensation mirrors Berezinskii-Kosterlitz-Thouless behavior in many ways, including the emergence of a strong zero momentum peak in the pair momentum distribution. Importantly, the disappearance of this quasi-condensate occurs at a reasonably well defined crossover temperature. The resulting phase diagram, pair momentum distribution, and algebraic power law decay are compatible with recent experiments throughout the continuum from BEC to BCS

Signatures of pairing and spin-orbit coupling in correlation functions of Fermi gases

We derive expressions for spin and density correlation functions in the (greatly enhanced) pseudogap phase of spin-orbit coupled Fermi superfluids. Density-density correlation functions are found to be relatively insensitive to the presence of these Rashba effects. To arrive at spin-spin correlation functions we derive new $f$-sum rules, valid even in the absence of a spin conservation law. Our spin-spin correlation functions are shown to be fully consistent with these $f$-sum rules. Importantly, they provide a clear signature of the Rashba band-structure and separately help to establish the presence of a pseudogap.Comment: 5 pages, 2 figures, with 5 page supplemen

Correcting inconsistencies in the conventional superfluid path integral scheme

In this paper we show how to redress a shortcoming of the path integral scheme for fermionic superfluids and superconductors. This approach is built around a simultaneous calculation of electrodynamics and thermodynamics. An important sum rule, the compressibility sum rule, fails to be satisfied in the usual calculation of the electromagnetic and thermodynamic response at the Gaussian fluctuation level. Here we present a path integral scheme to address this inconsistency. Specifically, at the leading order we argue that the superconducting gap should be calculated using a different saddle point condition modified by the presence of an external vector potential. This leads to the well known gauge-invariant BCS electrodynamic response and is associated with the usual (mean field) expression for thermodynamics. In this way the compressibility sum rule is satisfied at the BCS level. Moreover, this scheme can be readily extended to address arbitrary higher order fluctuation theories. At any level this approach will lead to a gauge invariant and compressibility sum rule consistent treatment of electrodynamics and thermodynamics.Comment: Comments welcome. Submitted directly to Phys. Rev. B Rapid Communication