Accessing Ultrafast Spin-Transport Dynamics in Copper Using Broadband Terahertz Spectroscopy.

We study the spatiotemporal dynamics of ultrafast electron spin transport across nanometer-thick copper layers using ultrabroadband terahertz emission spectroscopy. Our analysis of temporal delays, broadening, and attenuation of the spin-current pulse reveals ballisticlike propagation of the pulse peak, approaching the Fermi velocity, and diffusive features including a significant velocity dispersion. A comparison to the frequency-dependent Fick's law identifies the diffusion-dominated transport regime for distances >2 nm. These findings lay the groundwork for designing future broadband spintronic devices.

Terahertz Spin-Conductance Spectroscopy: Probing Coherent and Incoherent Ultrafast Spin Tunneling.

Thin-film stacks F|H consisting of a ferromagnetic-metal layer F and a heavy-metal layer H are spintronic model systems. Here, we present a method to measure the ultrabroadband spin conductance across a layer X between F and H at terahertz frequencies, which are the natural frequencies of spin-transport dynamics. We apply our approach to MgO tunneling barriers with thickness d = 0-6 Å. In the time domain, the spin conductance Gs has two components. An instantaneous feature arises from processes like coherent spin tunneling. Remarkably, a longer-lived component is a hallmark of incoherent resonant spin tunneling mediated by MgO defect states, because its relaxation time grows monotonically with d to as much as 270 fs at d = 6.0 Å. Our results are in full agreement with an analytical model. They indicate that terahertz spin-conductance spectroscopy will yield new and relevant insights into ultrafast spin transport in a wide range of spintronic nanostructures.

Non-Abelian Holonomy of Majorana Zero Modes Coupled to a Chaotic Quantum Dot.

If a quantum dot is coupled to a topological superconductor via tunneling contacts, each contact hosts a Majorana zero mode in the limit of zero transmission. Close to a resonance and at a finite contact transparency, the resonant level in the quantum dot couples the Majorana modes, but a ground-state degeneracy per fermion parity subspace remains if the number of Majorana modes coupled to the dot is five or larger. Upon varying shape-defining gate voltages while remaining close to resonance, a nontrivial evolution within the degenerate ground-state manifold is achieved. We characterize the corresponding non-Abelian holonomy for a quantum dot with chaotic classical dynamics using random matrix theory and discuss measurable signatures of the non-Abelian time evolution.

Fermi-Arc Metals.

We predict a novel metallic state of matter that emerges in a Weyl-semimetal superstructure with spatially varying Weyl-node positions. In the new state, the Weyl nodes are stretched into extended, anisotropic Fermi surfaces, which can be understood as being built from Fermi arclike states. This "Fermi-arc metal" exhibits the chiral anomaly of the parental Weyl semimetal. However, unlike in the parental Weyl semimetal, in the Fermi-arc metal the "ultraquantum state," in which the anomalous chiral Landau level is the only state at the Fermi energy, is already reached for a finite energy window at zero magnetic field. The dominance of the ultraquantum state implies a universal low-field ballistic magnetoconductance and the absence of quantum oscillations, making the Fermi surface "invisible" to de Haas-van Alphen and Shubnikov-de Haas effects, although it signifies its presence in other response properties.

Nucleation of Ergodicity by a Single Mobile Impurity in Supercooled Insulators.

We consider a disordered Hubbard model and show that, at sufficiently weak disorder, a single spin-down mobile impurity can thermalize an extensive initially localized system of spin-up particles. Thermalization is enabled by resonant processes that involve correlated hops of the impurity and localized particles. This effect indicates that Anderson localized insulators behave as "supercooled" systems, with mobile impurities acting as ergodic seeds. We provide analytical estimates, supported by numerical exact diagonalization, showing how the critical disorder strength for such mechanism depends on the particle density of the localized system. In the U→∞ limit, doublons are stable excitations, and they can thermalize mesoscopic systems by a similar mechanism. The emergence of an additional conservation law leads to an eventual localization of doublons. Our predictions apply to fermionic and bosonic systems and are readily accessible in ongoing experiments simulating synthetic quantum lattices with tunable disorder.

Femtosecond formation dynamics of the spin Seebeck effect revealed by terahertz spectroscopy.

Understanding the transfer of spin angular momentum is essential in modern magnetism research. A model case is the generation of magnons in magnetic insulators by heating an adjacent metal film. Here, we reveal the initial steps of this spin Seebeck effect with <27 fs time resolution using terahertz spectroscopy on bilayers of ferrimagnetic yttrium iron garnet and platinum. Upon exciting the metal with an infrared laser pulse, a spin Seebeck current js arises on the same ~100 fs time scale on which the metal electrons thermalize. This observation highlights that efficient spin transfer critically relies on carrier multiplication and is driven by conduction electrons scattering off the metal-insulator interface. Analytical modeling shows that the electrons' dynamics are almost instantaneously imprinted onto js because their spins have a correlation time of only ~4 fs and deflect the ferrimagnetic moments without inertia. Applications in material characterization, interface probing, spin-noise spectroscopy and terahertz spin pumping emerge.

Reflection-Symmetric Second-Order Topological Insulators and Superconductors.

Second-order topological insulators are crystalline insulators with a gapped bulk and gapped crystalline boundaries, but with topologically protected gapless states at the intersection of two boundaries. Without further spatial symmetries, five of the ten Altland-Zirnbauer symmetry classes allow for the existence of such second-order topological insulators in two and three dimensions. We show that reflection symmetry can be employed to systematically generate examples of second-order topological insulators and superconductors, although the topologically protected states at corners (in two dimensions) or at crystal edges (in three dimensions) continue to exist if reflection symmetry is broken. A three-dimensional second-order topological insulator with broken time-reversal symmetry shows a Hall conductance quantized in units of e^{2}/h.

Parity Anomaly and Spin Transmutation in Quantum Spin Hall Josephson Junctions.

We study the Josephson effect in a quantum spin Hall system coupled to a localized magnetic impurity. As a consequence of the fermion parity anomaly, the spin of the combined system of impurity and spin-Hall edge alternates between half-integer and integer values when the superconducting phase difference across the junction advances by 2π. This leads to characteristic differences in the splittings of the spin multiplets by exchange coupling and single-ion anisotropy at phase differences, for which time-reversal symmetry is preserved. We discuss the resulting 8π-periodic (or Z_{4}) fractional Josephson effect in the context of recent experiments.

Scattering matrix formulation of the topological index of interacting fermions in one-dimensional superconductors.

We construct a scattering matrix formulation for the topological classification of one-dimensional superconductors with effective time-reversal symmetry in the presence of interactions. For an isolated system, Fidkowski and Kitaev have shown that such systems have a Z_{8} topological classification. We here show that these systems have a unitary scattering matrix at zero temperature when weakly coupled to a normal-metal lead, with a topological index given by the trace of the Andreev-reflection matrix, trr_{he}. With interactions, trr_{he} generically takes on the finite set of values 0, ±1, ±2, ±3, and ±4. We show that the two topologically equivalent phases with trr_{he}=±4 support emergent many-body end states, which we identify to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-Fermi-liquid fixed point where a multiple-channel Kondo effect develops. Our results connect the topological index to transport properties, thereby highlighting the experimental signatures of interacting topological phases in one dimension.

Quantum transport of disordered Weyl semimetals at the nodal point.

Weyl semimetals are paradigmatic topological gapless phases in three dimensions. We here address the effect of disorder on charge transport in Weyl semimetals. For a single Weyl node with energy at the degeneracy point and without interactions, theory predicts the existence of a critical disorder strength beyond which the density of states takes on a nonzero value. Predictions for the conductivity are divergent, however. In this work, we present a numerical study of transport properties for a disordered Weyl cone at zero energy. For weak disorder, our results are consistent with a renormalization group flow towards an attractive pseudoballistic fixed point with zero conductivity and a scale-independent conductance; for stronger disorder, diffusive behavior is reached. We identify the Fano factor as a signature that discriminates between these two regimes.

Magnetic coupling of Gd3N@C80 endohedral fullerenes to a substrate.

Using magnetic endohedral fullerenes for molecular spintronics requires control over their encapsulated magnetic moments. We show by field-dependent x-ray magnetic circular dichroism measurements of Gd3N@C80 endohedral fullerenes adsorbed on a Cu surface that the magnetic moments of the encapsulated Gd atoms lie in a 4f7 ground state and couple ferromagnetically to each other. When the molecules are in contact with a ferromagnetic Ni substrate, we detect two different Gd species. The more abundant one couples antiferromagnetically to the Ni, whereas the other one exhibits a stronger and ferromagnetic coupling to the substrate. Both of these couplings to the substrate can be explained by an indirect exchange mechanism mediated by the carbon cage. The origin of the distinctly different behavior may be attributed to different orientations and thus electronic coupling of the carbon cage to the substrate, as revealed by scanning tunneling microscopy of the fullerenes on Cu.

Semiclassical theory of speckle correlations.

Coherent wave propagation in random media results in a characteristic speckle pattern, with spatial intensity correlations with short-range and long-range behavior. Here, we show how the speckle correlation function can be obtained from a ray picture for two representative geometries, namely a chaotic cavity and a random waveguide. Our calculation allows us to study the crossover between a "ray limit" and a "wave limit," in which the Ehrenfest time τ(E) is larger or smaller than the typical transmission time τ(D), respectively. Remarkably, long-range speckle correlations persist in the ray limit τ(E)≫τ(D).

Enhanced zero-bias Majorana peak in the differential tunneling conductance of disordered multisubband quantum-wire/superconductor junctions.

A recent experiment Mourik et al. [Science 336, 1003 (2012)] on InSb quantum wires provides possible evidence for the realization of a topological superconducting phase and the formation of Majorana bound states. Motivated by this experiment, we consider the signature of Majorana bound states in the differential tunneling conductance of multisubband wires. We show that the weight of the Majorana-induced zero-bias peak is strongly enhanced by mixing of subbands, when disorder is added to the end of the quantum wire. We also consider how the topological phase transition is reflected in the gap structure of the current-voltage characteristic.

Probability distribution of Majorana end-state energies in disordered wires.

One-dimensional topological superconductors harbor Majorana bound states at their ends. For superconducting wires of finite length L, these Majorana states combine into fermionic excitations with an energy ε(0) that is exponentially small in L. Weak disorder leaves the energy splitting exponentially small, but affects its typical value and causes large sample-to-sample fluctuations. We show that the probability distribution of ε(0) is log normal in the limit of large L, whereas the distribution of the lowest-lying bulk energy level ε(1) has an algebraic tail at small ε(1). Our findings have implications for the speed at which a topological quantum computer can be operated.

Interaction correction to the conductance of a ballistic conductor.

In disordered metals, electron-electron interactions are the origin of a small correction to the conductivity, the "Altshuler-Aronov correction." Here we investigate the Altshuler-Aronov correction deltaG{AA} of a conductor in which the electron motion is ballistic and chaotic. We consider the case of a double quantum dot, which is the simplest example of a ballistic conductor in which deltaG{AA} is nonzero. The fact that the electron motion is ballistic leads to an exponential suppression of deltaG{AA} if the Ehrenfest time is larger than the mean dwell time tau{D} or the inverse temperature h/T.

Interplay of Ehrenfest and dephasing times in ballistic conductors.

Quantum interference corrections in ballistic conductors require a minimal time: the Ehrenfest time. In this Letter, we investigate the fate of the interference corrections to quantum transport in bulk ballistic conductors if the Ehrenfest time and the dephasing time are comparable.

Sloppy-model universality class and the Vandermonde matrix.

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy: the system behavior depends only on a few "stiff" combinations of the parameters and is unchanged as other "sloppy" parameter combinations vary by orders of magnitude. We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.

Ehrenfest time and the coherent backscattering off ballistic cavities.

If the Ehrenfest time tau(E) of a ballistic cavity is not negligible in comparison to its dwell time tau(D), the weak localization correction to the cavity's transmission is suppressed proportional to exp(-tau(E/tau(D). At the same time, quantum interference enhances the probability of reflection into the mode of incidence by a factor two. This "enhanced backscattering" does not depend on the Ehrenfest time. We show that, in addition to the diagonal enhanced backscattering, there are off-diagonal contributions to coherent backscattering that become relevant if tau(E) > or = tau(D).

Spectral form factor near the Ehrenfest time.

We calculate the Ehrenfest-time dependence of the leading quantum correction to the spectral form factor of a ballistic chaotic cavity using periodic orbit theory. For the case of broken time-reversal symmetry, when the quantum correction to the form factor involves two small-angle encounters of classical trajectories, our result differs from that previously obtained using field-theoretic methods [Tian and Larkin, Phys. Rev. B 70, 035305 (2004)]. While we believe that the existing field-theoretic calculation is technically flawed, the question whether the field theoretic and periodic-orbit approaches agree when more than one small-angle encounter of classical orbits is involved remains unanswered.