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The existence of pure spin currents in absence of any driving external field is commonly considered an exotic phenomenon appearing only in quantum materials, such as topological insulators. We demonstrate instead that equilibrium spin currents are a rather general property of materials with non-negligible spin-orbit coupling (SOC). Equilibrium spin currents can be present at the surfaces of a slab. Yet, we also propose the existence of global equilibrium spin currents, which are net bulk spin currents along specific crystallographic directions of solid-state materials. Equilibrium spin currents are allowed by symmetry in a very broad class of systems having gyrotropic point groups. The physics behind equilibrium spin currents is uncovered by making an analogy between electronic systems with SOC and non-Abelian gauge theories. The electron spin can be seen as analogous to the color degree of freedom in SU(2) gauge theories and equilibrium spin currents can then be identified with diamagnetic color currents appearing as the response to a effective non-Abelian magnetic field generated by the SOC. Equilibrium spin currents are not associated with spin transport and accumulation, but they should nonetheless be carefully taken into account when computing transport spin currents. We provide quantitative estimates of equilibrium spin currents for a number of different systems, specifically the Au(111) and Ag(111) metallic surfaces presenting Rashba-type surface states, nitride semiconducting nanostructures, and bulk materials, such as the prototypical gyrotropic medium tellurium. In doing so, we also point out the limitations of model approaches showing that first-principles calculations are needed to obtain reliable predictions. We therefore use density functional theory computing the so-called bond currents, which represent a powerful tool to deeply understand the relation between equilibrium currents, electronic structure, and crystal point group., A.D. was funded through the EU Marie Sklodowska-Curie individual fellowship SPINMAN (ID No. SEP-210189940) during the very initial stage this work. The development of the work was then supported by the Science Foundation Ireland (SFI) Royal Society University Research Fellowship URF-R1-191769 and by the European Commission H2020-EU.1.2.1 FET-Open project INTERFAST (ID No. 965046). I.V.T. acknowledges support by Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19) and the Spanish MICINN Project No. PID2020-112811GB-I00. I.R. acknowledges the support of the U.K. Department of Business, Energy and Industrial Strategy (BEIS). A.R. was supported by the European Research Council (Grant No. ERC-2015-AdG694097), the Cluster of Excellence “CUI: Advanced Imaging of Matter” of the Deutsche Forschungsgemeinschaft (DFG)-EXC 2056 (Project ID No. 390715994), SFB925 “Light induced dynamics and control of correlated quantum systems” and partially by the Federal Ministry of Education and Research Grant No. RouTe-13N14839.

We consider the ground state of an electron gas embedded in a quantum gyrotropic cavity. We show that the light-matter interaction leads to a nontrivial topology of the many-body electron-photon wave function characterized by a nonzero Berry curvature. Physically, the latter manifests as the anomalous Hall effect, appearance of equilibrium edge/surface currents and orbital magnetization induced by vacuum fluctuations. Remarkably, closed analytical expressions for the anomalous Hall conductivity and macroscopic magnetization are obtained for the interacting many-body case.

We study a periodic arrangement of magnetic regions in a quasi-one-dimensional superconducting wire. Due to the local exchange field, each region supports Andreev bound states that hybridize, forming Bloch bands in the subgap spectrum of what we call the Andreev crystal (AC). As an illustration, ACs with ferromagnetic and antiferromagnetic alignment of the magnetic regions are considered. We relate the spectral asymmetry index of a spin-resolved Hamiltonian to the spin polarization and identify it as the observable that quantifies the closing and reopening of the excitation gap. In particular, antiferromagnetic ACs exhibit a sequence of gapped phases separated by gapless Dirac phase boundaries. Heterojunctions between antiferromagnetic ACs in neighboring phases support spin-polarized bound states at the interface. In close analogy to the charge fractionalization in Dirac systems with a mass inversion, we find a fractionalization of the interface spin., We acknowledge funding from the Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN; Projects No. FIS2016-79464-P and No. FIS2017-82804-P). I.V.T. acknowledges support from Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19). The work of F.S.B. is partially funded by the European Research Council under EU’s Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED).

We present an exhaustive study of Andreev crystals (ACs)—quasi-one-dimensional superconducting wires with a periodic distribution of magnetic regions. The exchange field in these regions is assumed to be much smaller than the Fermi energy. Hence, the transport through the magnetic region can be described within the quasiclassical approximation. In the first part of the paper, by assuming that the separation between the magnetic regions is larger than the coherence length, we derive the effective nearest-neighbor tight-binding equations for ACs with a helical magnetic configuration. The spectrum within the gap of the host superconductor shows a pair of energy-symmetric bands. By increasing the strength of the magnetic impurities in ferromagnetic ACs, these bands cross without interacting. However, in any other helical configuration, there is a value of the magnetic strength at which the bands touch each other, forming a Dirac point. Further increase of the magnetic strength leads to a system with an inverted gap. We study junctions between ACs with inverted spectrum and show that junctions between (anti)ferromagnetic ACs (always) never exhibit bound states at the interface. In the second part, we extend our analysis beyond the nearest-neighbor approximation by solving the Eilenberger equation for infinite ACs and junctions between semi-infinite ACs with collinear magnetization. From the obtained quasiclassical Green functions, we compute the local density of states and the local spin polarization in anti- and ferromagnetic ACs. We show that these junctions may exhibit bound states at the interface and fractionalization of the surface spin polarization., M.R. and F.S.B. acknowledge funding by the Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) (Project FIS2017-82804-P), and EU’s Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED). I.V.T. acknowledges support by Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19)

We derive a kinetic theory capable of dealing both with large spin-orbit coupling and Kondo screening in dilute magnetic alloys. We obtain the collision integral non-perturbatively and uncover a contribution proportional to the momentum derivative of the impurity scattering S-matrix. The latter yields an important correction to the spin diffusion and spin-charge conversion coefficients, and fully captures the so-called side-jump process without resorting to the Born approximation (which fails for resonant scattering), or to otherwise heuristic derivations. We apply our kinetic theory to a quantum impurity model with strong spin-orbit, which captures the most important features of Kondo-screened Cerium impurities in alloys such as La$_{1-x}$Cu$_6$. We find 1) a large zero-temperature spin Hall conductivity that depends solely on the Fermi wave number and 2) a transverse spin diffusion mechanism that modifies the standard Fick's diffusion law. Our predictions can be readily verified by standard spin-transport measurements in metal alloys with Kondo impurities., Comment: 5 + 25 pages, 2 figures

We present a theory of magnetic response in finite-size two-dimensional superconductors with Rashba spin-orbit coupling. The interplay between the latter and an in-plane Zeeman field leads on the one hand to an out-of-plane spin polarization which accumulates at the edges of the sample over the superconducting coherence length, and on the other hand, to circulating supercurrents decaying away from the edge over a macroscopic scale. In a long finite stripe of width W, both the spin polarization and the currents contribute to the total magnetic moment induced at the stripe ends. These two contributions scale with powers of W such that for sufficiently large samples it can be detected by current magnetometry techniques., We acknowledge funding by the Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) (Projects No. FIS2016-79464-P and No. FIS2017-82804-P), by Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19), and by EU’s Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED).

The Eilenberger equation is a standard tool in the description of superconductors with an arbitrary degree of disorder. It can be generalized to systems with linear-in-momentum spin-orbit coupling (SOC), by exploiting the analogy of SOC with a non-Abelian background field. Such a field mixes singlet and triplet components and yields the rich physics of magnetoelectric phenomena. In this work we show that the application of this equation extends further, beyond superconductivity. In the normal state, the linearized Eilenberger equation describes the coupled spin-charge dynamics. Moreover, its resolvent corresponds to the so-called Cooperons, and can be used to calculate the weak-localization corrections. Specifically, we show how to solve this equation for any source term and provide a closed-form solution for the case of Rashba SOC. We use this solution to address several problems of interest for spintronics and superconductivity. First, we study spin injection from ferromagnetic electrodes in the normal state, and describe the spatial evolution of spin density in the sample, and the complete crossover from the diffusive to the ballistic limit. Second, we address the so-called superconducting Edelstein effect, and generalize the previously known results to arbitrary disorder. Third, we study weak-localization correction beyond the diffusive limit, which can be a valuable tool in experimental characterization of materials with very strong SOC. We also address the so-called pure gauge case where the persistent spin helices form. Our work establishes the linearized Eilenberger equation as a powerful and a very versatile method for the study of materials with spin-orbit coupling, which often provides a simpler and more intuitive picture compared to alternative methods., We acknowledge funding from Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) (Projects No. FIS2016-79464-P and No. FIS2017-82804- P). I.V.T. acknowledges support by Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19). S.I. and F.S.B acknowledge funding from EUs Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED).

We present a theoretical study of nonlocal magnetoelectric effects in diffusive hybrid structures with an intrinsic linear-in-momentum spin-orbit coupling (SOC) which is assumed to be spatially inhomogeneous. Our analysis is based on the SU(2)-covariant drift-diffusion equations from which we derive boundary conditions at hybrid interfaces for SOC of any kind. Within this formulation, the spin current is covariantly conserved when the spin relaxation is only due to the intrinsic SOC. This conservation leads to the absence of spin Hall (SH) currents in homogeneous systems. If, however, extrinsic sources of spin relaxation (ESR), such as magnetic impurities and/or a random SOC at nonmagnetic impurities, are present the spin is no longer covariantly conserved, and SH currents appear. We apply our model to describe nonlocal transport in a two-dimensional system with an interface separating two regions: one normal region without intrinsic SOC and one with a Rashba SOC. We first explore the inverse spin-galvanic effect, i.e., a spin polarization induced by an electric field. We demonstrate how the spatial behavior of such spin density depends on both the direction of the electric field and the strength of the ESR rate. We also study the spin-to-charge conversion, and compute the charge current and the distribution of electrochemical potential in the whole system when a spin current is injected into the normal region. In systems with an inhomogeneous SOC varying in one spatial direction, we find an interesting nonlocal reciprocity between the spin density induced by a charge current at a given point in space, and the spatially integrated current induced by a spin density injected at the same point., We acknowledge funding by the Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) (Projects No. FIS2016-79464-P and No. FIS2017- 82804-P) and by Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No.IT1249-19)

Breaking of the inversion symmetry at the interface between different materials may dramatically enhance spin-orbit interaction in the vicinity of the interface. We incorporate the effects of this interfacial spin-orbit coupling (ISOC) into the standard drift-diffusion theory by deriving generalized boundary conditions for diffusion equations. Our theoretical scheme is based on symmetry arguments, providing a natural classification and parametrization of all spin-charge and spin-spin conversion effects that occur due to ISOC at macroscopically isotropic interfaces between nonmagnetic materials. We illustrate our approach with specific examples of spin-charge conversion in hybrid structures. In particular, for a lateral metal-insulator structure we predict an ``ISOC-gating'' effect which can be used to detect spin currents in metallic films with weak bulk SOC.

We study theoretically the spectral and transport properties of a superconducting wire with a magnetic defect. We start by modelling the system as a one dimensional magnetic Josephson junction and derive the equation determining the full subgap spectrum in terms of the normal-state transfer matrix for arbitrary length and exchange field of the magnetic region. We demonstrate that the quantum phase transition predicted for a short-range magnetic impurity, and associated with a change of the total spin of the system, also occurs in junctions of finite length. Specifically, we find that the total spin changes discontinuously by integer jumps when bounds states cross the Fermi level. The spin can be calculated by using a generalization of Friedel sum rule for the superconducting state, which we also derive. With these tools, we analyze the subgap spectrum of a junction with the length of the magnetic region smaller than the superconducting coherence length and demonstrate how phase transitions also manifest as change of the sign of the supercurrent., 7 pages, 3 figures

Although equilibrium spin currents (ESCs) may exist in materials with spin-orbit coupling, they are not transport currents and cannot lead to spin accumulation in the presence of time-reversal symmetry. It is for this reason that the detection of ESCs has remained elusive. Here we show that in a nanowire with spin-orbit coupling, breaking the time-reversal symmetry by a Zeeman field leads to a bulk equilibrium spin current which manifests itself in a sizable edge spin polarization, transverse to the Zeeman field. The net accumulated spin does not depend on specific properties of the wire ends, being fully determined by the bulk spin current. This bulk-boundary correspondence is a universal property that occurs in both the normal and superconducting states independently of the degree of disorder. The transverse edge spin polarization is strongly enhanced in the superconducting state when the Zeeman energy is of the order of the induced superconducting gap. This leads to a hitherto unknown transverse magnetic susceptibility that can be much larger than the longitudinal, and it drastically changes the paramagnetic response of the nanowire., We acknowledge funding from the Spanish Ministerio de Ciencia, Innovacion y Universidades (MICINN; Projects No. FIS2016-79464-P and No. FIS2017-82804- P). I.V.T. acknowledges support from Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249- 19). F.S.B. acknowledges funding from the EU’s Horizon 2020 innovation program under Grant Agreement No. 800923 (SUPERTED).

We present and experimentally verify a universal theoretical framework for the description of spin-charge interconversion in non-magnetic metal/insulator structures with interfacial spin–orbit coupling (ISOC). Our formulation is based on drift-diffusion equations supplemented with generalized boundary conditions. The latter encode the effects of ISOC and relate the electronic transport in such systems to spin loss and spin-charge interconversion at the interface. We demonstrate that the conversion efficiency depends solely on these interfacial parameters. We apply our formalism to two typical spintronic devices that exploit ISOC: a lateral spin valve and a multilayer Hall bar, for which we calculate the non-local resistance and the spin Hall magnetoresistance, respectively. Finally, we perform measurements on these two devices with a BiOx/Cu interface and verify that transport properties related to the ISOC are quantified by the same set of interfacial parameters., C.S-F., F.S.B., and I.V.T. acknowledge funding from the Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) (Project Nos. FIS2016–79464-P and FIS2017–82804-P) and Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT1249-19). The work of F.S.B. is partially funded by EU's Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED). The work at nanoGUNE is supported by Intel Corporation through the Semiconductor Research Corporation under MSR-INTEL TASK No. 2017-IN-2744 and the “FEINMAN” Intel Science Technology Center and by the Spanish MICINN under the Maria de Maeztu Units of Excellence Programme (No. MDM-2016–0618) and under Project Nos. MAT2015–65159-R and RTI2018–094861-B-100. V.T.P. acknowledges postdoctoral fellowship support from the “Juan de la Cierva–Formación” program by the Spanish MICINN (Grant No. FJCI-2017-34494). E.S. thanks the Spanish MECD for a Ph.D. fellowship (Grant No. FPU14/03102).

Here an approach is presented for reconstructing the distribution of electronic internal quantum pressure in the electronic continuum of solids from the experimental electron density. Using the formalism of the density functional theory, the spatial inner-crystal map of the quantum pressure is obtained. The results are visualized via the indicator of quantum pressure focusing (IQPF) which reveals the regions where the pressure is concentrated or depleted due to quantum effects. IQPF contains all quantum electron-shell structure-forming contributions resulting from kinetic, exchange and correlation effects, and presents a clear picture of the chemical bond features in crystals with different type of bonding mechanisms.

The Exact Factorization framework is extended and utilized to introduce the electronic-states of correlated electron-photon systems. The formal definitions of an exact scalar potential and an exact vector potential that account for the electron-photon correlation are given. Inclusion of these potentials to the Hamiltonian of the uncoupled electronic system leads to a purely electronic Schr\"odinger equation that uniquely determines the electronic states of the complete electron-photon system. For a one-dimensional asymmetric double-well potential coupled to a single photon mode with resonance frequency, we investigate the features of the exact scalar potential. In particular, we discuss the significance of the step-and-peak structure of the exact scalar potential in describing the phenomena of photon-assisted delocalization and polaritonic squeezing of the electronic excited-states. In addition, we develop an analytical approximation for the scalar potential and demonstrate how the step-and-peak features of the exact scalar potential are captured by the proposed analytical expression.

We present a theoretical study of diffusive superconducting systems with extrinsic spin-orbit coupling and arbitrarily strong impurity potential. We derive from a microscopic Hamiltonian a diffusion equation for the quasi-classical Green function, and demonstrate that all mechanisms related to the spin-orbit coupling are expressed in terms of three kinetic coefficients: the spin Hall angle, the spin current swapping coefficient, and the spin relaxation rate due to Elliott-Yafet mechanism. The derived diffusion equation contains a hitherto unknown term describing a spin-orbit torque that appears exclusively in the superconducting state. As an example, we provide a qualitative description of a magnetic vortex in a superconductor with triplet correlations, and show that the novel term describes a spin torque proportional to the vector product between the spectral angular momentum of the condensate and the triplet vector. Our equation opens up the possibility to explore spintronic effects in superconductors with no counterparts in the normal metallic state., C.H. acknowledges funding by Ministry of Science and Technology, Taiwan (Project No. 107- 2917-I-564-009) C.H. and F.S.B. acknowledge funding by the Spanish Ministerio de Economía y Competitividad (MINECO) (Projects No. FIS2014-55987-P and FIS2017-82804-P). I.V.T. acknowledges the support by Spanish Ministerio de Economia y Competitividad (MINECO) (Project No. FIS2016-79464-P) and by the Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT578-13).

Magneto-optical response, i.e. optical response in the presence of a magnetic field, is commonly used for characterization of materials and in optical communications. However, quantum mechanical description of electric and magnetic fields in crystals is not straightforward as the position operator is ill defined. We present a reformulation of the density matrix perturbation theory for time-dependent electromagnetic fields under periodic boundary conditions, which allows us to treat the orbital magneto-optical response of solids at the \textit{ab initio} level. The efficiency of the computational scheme proposed is comparable to standard linear-response calculations of absorption spectra and the results of tests for molecules and solids agree with the available experimental data. A clear signature of the valley Zeeman effect is revealed in the continuum magneto-optical spectrum of a single layer of hexagonal boron nitride. The present formalism opens the path towards the study of magneto-optical effects in strongly driven low-dimensional systems., Comment: 12 pages, 3 figures

Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice this normally means optimizing the value of some observable, a so called merit function. In consequence, a key part of the theory is a set of equations, which provides the gradient of the merit function with respect to parameters that control the shape of the driving field. We show that these equations can be straightforwardly derived using the standard linear response theory, only requiring a minor generalization -- the unperturbed Hamiltonian is allowed to be time-dependent. As a result, the aforementioned gradients are identified with certain response functions. This identification leads to a natural reformulation of QOCT in term of the Keldysh contour formalism of the quantum many-body theory. In particular, the gradients of the merit function can be calculated using the diagrammatic technique for non-equilibrium Green's functions, which should be helpful in the application of QOCT to computationally difficult many-electron problems., Comment: 7 pages

The inversion symmetry breaking at the interface between different materials generates a strong interfacial spin-orbit coupling (ISOC) that may influence the spin and charge transport in hybrid structures. Here we use a simple analytically solvable model to study in the ballistic approximation various spin transport phenomena induced by ISOC in a bilayer metallic system. In this model a nonequilibrium steady state carrying a spin current is created by applying a spin-dependent bias across the metallic junction. Physical observables are then calculated using the scattering matrix approach. In particular we calculate the absorption of the spin current at the interface (the interface spin loss) and study the interface spin-to-charge conversion. The latter consists of an in-plane interface charge current generated by the spin-dependent bias applied to the junction, which can be viewed as a spin-galvanic effect mediated by ISOC. Finally, we demonstrate that ISOC leads to an interfacial spin-current swapping; that is, the ``primary'' spin current flowing through the spin-orbit active interface is necessarily accompanied by a ``secondary'' swapped spin current flowing along the interface and polarized in the direction perpendicular to that of the primary current. Using the exact spin continuity equation, we relate the swapping effect to the interfacial spin loss and argue that this effect is generic and independent of the ballistic approximation used for specific calculations.

The Usadel equation is the standard theoretical tool for the description of superconducting structures in the diffusive limit. Here I derive the Usadel equation for gyrotropic materials with a generic linear in momentum spin-orbit coupling. It accounts for the spin-charge/singlet-triplet coupling and in the normal state reduces to the system of spin-charge diffusion equations describing various magneto-electric effects, such as the spin Hall effect (SHE), the spin-galvanic effect (SGE) and their inverses. Therefore the derived Usadel equation establishes a direct connection of these effects to their superconducting counterparts. The working power of the present formalism is illustrated on the example of the bulk SGE., Comment: 5 pages

We derive the Bloch equations for the spin dynamics of a two-dimensional electron gas in the presence of spin-orbit coupling. For the latter we consider both the intrinsic mechanisms of structure inversion asymmetry (Rashba) and bulk inversion asymmetry (Dresselhaus), and the extrinsic ones arising from the scattering from impurities. The derivation is based on the SU(2) gauge-field formulation of the Rashba-Dresselhaus spin-orbit coupling. Our main result is the identification of a new spin-generation torque arising from the Elliot-Yafet process, which opposes a similar term arising from the Dyakonov-Perel process. The new spin-generation torque contributes to the current-induced spin polarization (CISP) -- also known as the Edelstein or inverse spin-galvanic effect. As a result, the behavior of the CISP turns out to be more complex than one would surmise from consideration of the internal Rashba-Dresselhaus fields alone. In particular, the symmetry of the current-induced spin polarization does not necessarily coincide with that of the internal Rashba-Dresselhaus field, and an out-of-plane component of the CISP is generally predicted, as observed in recent experiments. We also discuss the extension to the three-dimensional electron gas, which may be relevant for the interpretation of experiments in thin films., Comment: 11 pages, 2 figures

I.V.T. acknowledges funding by the Spanish MINECO (FIS2013-46159-C3-1-P) and “Grupos Consolidados UPV/EHU del Gobierno Vasco” (IT-578-13). The work of E.Y.S. was supported by the University of Basque Country UPV/EHU under program UFI 11/55, FIS2015-67161-P (MINECO/FEDER) grant, and “Grupos Consolidados UPV/EHU del Gobierno Vasco” (IT-472-10).

It is well known that a current driven through a two-dimensional electron gas with Rashba spin-orbit coupling induces a spin polarization in the perpendicular direction (Edelstein effect). This phenomenon has been extensively studied in the linear response regime, i.e., when the average drift velocity of the electrons is a small fraction of the Fermi velocity. Here we investigate the phenomenon in the nonlinear regime, meaning that the average drift velocity is comparable to or exceeds the Fermi velocity. This regime is realized when the electric field is very large or when electron-impurity scattering is very weak. We consider the limiting case of a two-dimensional noninteracting electron gas with no impurities. In this case, the quantum kinetic equation for the density matrix is exactly and analytically solvable, reducing to a problem of spin dynamics for ``unpaired'' electrons near the Fermi surface. The crucial parameter is $\ensuremath{\gamma}=eE{L}_{s}/{E}_{F}$, where $E$ is the electric field, $e$ is the absolute value of the electron charge, ${E}_{F}$ is the Fermi energy, and ${L}_{s}=\ensuremath{\hbar}/(2m\ensuremath{\alpha})$ is the spin-precession length in the Rashba spin-orbit field with coupling strength $\ensuremath{\alpha}$. If $\ensuremath{\gamma}\ensuremath{\ll}1$, the evolution of the spin is adiabatic, resulting in a spin polarization that grows monotonically in time and eventually saturates at the maximum value $n(\ensuremath{\alpha}/{v}_{F})$, where $n$ is the electron density and ${v}_{F}$ is the Fermi velocity. If $\ensuremath{\gamma}\ensuremath{\gg}1$ the evolution of the spin becomes strongly nonadiabatic and the spin polarization is progressively reduced and eventually suppressed for $\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\infty}$. We also predict an inverse nonlinear Edelstein effect, in which an electric current is driven by a magnetic field that grows linearly in time. The ``conductivities'' for the direct and the inverse effects satisfy generalized Onsager reciprocity relations, which reduce to the standard ones in the linear response regime.

Ballistic Josephson junctions are studied in the presence of a spin-splitting field and spin-orbit coupling. A generic expression for the quasiclassical Green's function is obtained and with its help we analyze several aspects of the proximity effect between a spin-textured normal metal (N) and singlet superconductors (S). In particular, we show that the density of states may show a zero-energy peak which is a generic consequence of the spin dependent couplings in heterostructures. In addition, we also obtain the spin current and the induced magnetic moment in a SNS structure and discuss possible coherent manipulation of the magnetization which results from the coupling between the superconducting phase and the spin degree of freedom. Our theory predicts a spin accumulation at the S/N interfaces, and transverse spin currents flowing perpendicular to the junction interfaces. Some of these findings can be understood in the light of a non-Abelian electrostatics., F.K. is grateful for financial support from the Alexander von Humboldt foundation. This work was supported by the Spanish Ministerio de Economia y Competitividad (MINECO) through Projects No. FIS2014-55987-P and FIS2013-46159-C3-1-P, and the Basque Departamento de Educacion, UPV/EHU through Projects IT-756-13 and IT-578-13.

We present a theory of spin dynamics caused by spin-orbit coupling for two-dimensional gases of cold atoms and other quasiparticles with pseudospin 1/2 moving in orbital gauge fields. Our approach is based on the gauge transformation in the form of a SU(2) rotation gauging out the spin-orbit coupling. As a result, the analysis of the spin dynamics is reduced to calculation of the density-related susceptibility of the system without spin-orbit coupling at the wavevector determined by the spin-rotation length. This approach allows one to treat the spin dynamics in terms of the linear response theory for bosonic and fermionic ensembles. We study different regimes of irreversible spin relaxation and coherent spin dynamics in these systems. For bosonic gases the effects of low temperature are crucial due to accumulation of particles in the small-momentum subspace even if the Bose–Einstein condensation does not occur due to the system low dimensionality., We acknowledges funding by the Spanish MEC (FIS2010-21282-C02-01 and FIS2012-36673-C03-01) and “Grupos Consolidados UPV/EHU del Gobierno Vasco” (IT-319-07 and IT-472-10). The contribution of EYS was, in addition, supported by the University of Basque Country UPV/EHU under program UFI 11/55.

A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semiclassic limit. The spectrum of Andreev bound states is obtained from the single valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along such closed trajectories. For the demonstration, an Andreev-Wilson loop in the composite position–particle-hole–spin space is constructed and shown to depend on only two parameters, namely, a magnetic phase shift and a local precession axis for the spin. The details of the Andreev-Wilson loop can be extracted via measuring the spin-resolved density of states. A Josephson junction can thus be viewed as an analog computer of closed-path-ordered exponentials., The work of F. S. B. and F. K. was supported by Spanish Ministerio de Economía y Competitividad (MINECO) through Project No. FIS2014-55987-P and the Basque Government under UPV/EHU Project No. IT-756-13. I. V. T. acknowledges support from the Spanish Grant No. FIS2013-46159-C3-1-P and from the “Grupos Consolidados UPV/EHU del Gobierno Vasco” (Grant No. IT578-13).

Due to the spin-orbit coupling (SOC) an electric current flowing in a normal metal or semiconductor can induce a bulk magnetic moment. This effect is known as the Edelstein (EE) or magnetoelectric effect. Similarly, in a bulk superconductor a phase gradient may create a finite spin density. The inverse effect, also known as the spin-galvanic effect, corresponds to the creation of a supercurrent by an equilibrium spin polarization. Here, by exploiting the analogy between a linear-in-momentum SOC and a background SU(2) gauge field, we develop a quasiclassical transport theory to deal with magnetoelectric effects in superconducting structures. For bulk superconductors this approach allows us to easily reproduce and generalize a number of previously known results. For Josephson junctions we establish a direct connection between the inverse EE and the appearance of an anomalous phase shift ${\ensuremath{\varphi}}_{0}$ in the current-phase relation. In particular we show that ${\ensuremath{\varphi}}_{0}$ is proportional to the equilibrium spin current in the weak link. We also argue that our results are valid generically, beyond the particular case of linear-in-momentum SOC. The magnetoelectric effects discussed in this study may find applications in the emerging field of coherent spintronics with superconductors.

The spatial distribution of the internal pressure of an electron fluid, which spontaneously arises at the formation of a molecule or a crystal, is linked to the main features of chemical bonding in molecular crystals. The local pressure is approximately expressed in terms of the experimental electron density and its derivatives using the density functional formalism and is applied to identify the bonding features in benzene, formamide and chromium hexacarbonyl. We established how the spatial regions of compression and stretching of the electron fluid in these solids reflect the typical features of chemical bonds of different types. Thus, the internal electronic pressure can serve as a bonding descriptor, which has a clear physical meaning and reveals the specific features of variety of the chemical bonds expressing them in terms of the electron density., 13 pages, 3 figures

We use analytic (current) density-potential maps of time-dependent (current) density functional theory (TD(C)DFT) to inverse engineer analytically solvable time-dependent quantum problems. In this approach the driving potential (the control signal) and the corresponding solution of the Schr\"odinger equation are parametrized analytically in terms of the basic TD(C)DFT observables. We describe the general reconstruction strategy and illustrate it with a number of explicit examples. First we consider the real space one-particle dynamics driven by a time-dependent electromagnetic field and recover, from the general TDDFT reconstruction formulas, the known exact solution for a driven oscillator with a time-dependent frequency. Then we use analytic maps of the lattice TD(C)DFT to control quantum dynamics in a discrete space. As a first example we construct a time-dependent potential which generates prescribed dynamics on a tight-binding chain. Then our method is applied to the dynamics of spin-1/2 driven by a time dependent magnetic field. We design an analytic control pulse that transfers the system from the ground to excited state and vice versa. This pulse generates the spin flip thus operating as a quantum NOT gate., Comment: 11 pages, 6 figures

arXiv:1409.4563v1, We present a full microscopic theory to describe the Josephson current through an extended superconductor-normal metal-superconductor (SNS) diffusive junction with an intrinsic spin-orbit coupling (SOC) in the presence of a spin-splitting field h. We demonstrate that the ground state of the junction corresponds to a finite intrinsic phase difference 0 < φ0 < 2π between the superconductor electrodes provided that both h and the SOC-induced SU(2) Lorentz force are finite. The nontrivial φ0 is closely related to the appearance of an equilibrium spin current in the normal metal with the spin projection parallel to the exchange field direction. In the particular case of a Rashba SOC we present analytic and numerical results for φ0 as a function of the strengths of the spin fields, the length of the junction, the temperature and the properties of SN interfaces., This work was supported by the Spanish Ministry of Economy and Competitiveness under Projects No. FIS2011-28851-C02-02, FIS2013-46159-C3-1-P, FIS2014-55987-P, and the Basque Government under UPV/EHU Project No. IT-756-13. IVT acknowledges funding by the Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT578-13).

We propose a practical approximation to the exchange-correlation functional of (time-dependent) density functional theory for many-electron systems coupled to photons. The (time non-local) optimized effective potential (OEP) equation for the electron- photon system is derived. We test the new approximation in the Rabi model from weak to strong coupling regimes. It is shown that the OEP (i) improves the classical description, (ii) reproduces the quantitative behavior of the exact ground-state properties and (iii) accurately captures the dynamics entering the ultra-strong coupling regime. The present formalism opens the path to a first-principles description of correlated electron-photon systems, bridging the gap between electronic structure methods and quantum optics for real material applications., Comment: 5 pages, 2 figures

We present a rigorous formulation of the time-dependent density functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally $v$-representable.

One of the most accepted models that describe the anomalous thermal behavior of amorphous materials at temperatures below 1 K relies on the quantum mechanical tunneling of atoms between two nearly equivalent potential energy wells forming a two-level system (TLS). Indirect evidence for TLSs is widely available. However, the atomistic structure of these TLSs remains an unsolved topic in the physics of amorphous materials. Here, using classical molecular dynamics, we found several hitherto unknown bistable structural motifs that may be key to understanding the anomalous thermal properties of amorphous alumina at low temperatures. We show through free energy profiles that the complex potential energy surface can be reduced to canonical TLSs. The tunnel splitting predicted from instanton theory, the number density, dipole moment, and coupling to external strain of the discovered motifs are consistent with experiments., We acknowledge financial support from the Marie Curie International Incoming Fellowship (Grant Agreement PIIF-GA-2012-326435 RespSpatDisp) and the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-267374), both within the 7th European Community Framework Programme. We also thank “ayuda para la Especializacion de Personal Investigador del Vicerrectorado de Investigacion UPV/EHU-2013”, Grupos Consolidados UPV/EHU del Gobierno Vasco (IT-578-13), and the Ikerbasque Foundation. This research was supported, in part, by a grant of computer time from the CUNY HPC under NSF Grants CNS-0855217, CNS-0958379, and ACI-1126113.

The broken inversion symmetry at the surface of a metallic film (or, more generally, at the interface between a metallic film and a different metallic or insulating material) greatly amplifies the influence of the spin-orbit interaction on the surface properties. The best known manifestation of this effect is the momentum-dependent splitting of the surface state energies (Rashba effect). Here we show that the same interaction also generates a spin-polarization of the bulk states when an electric current is driven through the bulk of the film. For a semi-infinite jellium model, which is representative of metals with a closed Fermi surface, we prove as a theorem that, regardless of the shape of the confinement potential, the induced surface spin density at each surface is given by ${\bf S} =-\gamma \hbar {\bf \hat z}\times {\bf j}$, where ${\bf j}$ is the particle current density in the bulk, ${\bf \hat z}$ the unit vector normal to the surface, and $\gamma=\frac{\hbar}{4mc^2}$ contains only fundamental constants. For a general metallic solid $\gamma$ becomes a material-specific parameter that controls the strength of the interfacial spin-orbit coupling. Our theorem, combined with an {\it ab initio} calculation of the spin polarization of the current-carrying film, enables a determination of $\gamma$, which should be useful in modeling the spin-dependent scattering of quasiparticles at the interface., Comment: 5 pages, 2 figures

We investigate the proximity effect in diffusive superconducting hybrid structures with a spin-orbit (SO) coupling. Our study is focused on the singlet-triplet conversion and the generation of long-range superconducting correlations in ferromagnetic elements. We derive the quasiclassical equations for the Green's functions including the SO coupling terms in form of a background SU(2) field. With the help of these equations, we first present an interesting complete analogy between the spin diffusion process in normal metals and the generation of the triplet components of the condensate in a diffusive superconducting structure in the presence of SO coupling. From this analogy it turns out naturally that the SO coupling is an additional source of the long-range triplet component (LRTC) besides the magnetic inhomogeneities studied in the past. This analogy opens a range of possibilities for the generation and manipulation of the triplet condensate in hybrid structures. In particular we demonstrate that a normal metal with SO coupling can be used as source of LRTC if attached to a superconductor-ferromagnet bilayer. We also demonstrate an explicit connection between an inhomogeneous exchange field and SO coupling mechanisms for the generation of the LRTC and establish the conditions for the appearance of the LRTC in different geometries. Our work gives a global description of the singlet-triplet conversion in hybrid structures in terms of generic spin fields and our results are particularly important for the understanding of the physics underlying spintronic devices with superconductors. © 2014 American Physical Society., The work of F.S.B was supported by the Spanish Ministry of Economy and Competitiveness under Project No. FIS2011-28851-C02-02 the Basque Government under UPV/EHU Project No. IT-756-13. I.V.T. acknowledges funding by the “Grupos Consolidados UPV/EHU del Gobierno Vasco” (IT-578-13) and Spanish MICINN (FIS2010-21282-C02-01).

In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of density-functional-type theories that describe the interaction of charged particles with photons and introduce the appropriate Kohn-Sham schemes. We show how the evolution of a system described by quantum electrodynamics in Coulomb gauge is uniquely determined by its initial state and two reduced quantities. These two fundamental observables, the polarization of the Dirac field and the vector potential of the photon field, can be calculated by solving two coupled, non-linear evolution equations without the need to explicitly determine the (numerically infeasible) many-body wave function of the coupled quantum system. To find reliable approximations to the implicit functionals we present the according Kohn-Sham construction. In the non-relativistic limit this density-functional-type theory of quantum electrodynamics reduces to the density-functional reformulation of the Pauli-Fierz Hamiltonian, which is based on the current density of the electrons and the vector potential of the photon field. By making further approximations, e.g. restricting the allowed modes of the photon field, we derive further density functional-type theories of coupled matter-photon systems for the corresponding approximate Hamiltonians. In the limit of only two sites and one mode we deduce the according effective theory for the two-site Hubbard model coupled to one photonic mode. This model system is used to illustrate the basic ideas of a density-functional reformulation in great detail and we present the exact Kohn-Sham potentials for our coupled matter-photon model system., MR acknowledges financial support by the Austrian Science Fonds (FWF projects J 3016-N16 and P 25739-N27). We further acknowledge financial support from the European Research Council Advanced Grant DYNamo (ERC-2010-AdG-267374), Spanish Grant (FIS2010-21282-C02-01), Grupos Consolidados UPV/EHU del Gobierno Vasco (IT578-13), Ikerbasque and the European Commission projects CRONOS (Grant number 280879-2 CRONOS CP-FP7)., Sí

We formulate diagrammatic rules for many-body perturbation theory which uses Kohn-Sham (KS) Green's functions as basic propagators. The diagram technique allows to study the properties of the dynamic nonlocal exchange-correlation (xc) kernel $f_{xc}$. We show that the spatial non-locality of $f_{xc}$ is strongly frequency-dependent. In particular, in extended systems the non-locality range diverges at the excitation energies. This divergency is related to the discontinuity of the xc potential., Comment: 4 RevTeX pages including 3 eps figures, submitted to Phys. Rev. Lett; revised version with new references

We address and quantify the role of nonadiabaticity (“memory effects”) in the exchange-correlation (xc) functional of time-dependent density functional theory (TDDFT) for describing nonlinear dynamics of many-body systems. Time-dependent resonant processes are particularly challenging for available TDDFT approximations, due to their strong nonlinear and nonadiabatic character. None of the known approximate density functionals are able to cope with this class of problems in a satisfactory manner. In this work we look at the prototypical example of the resonant processes by considering Rabi oscillations within the exactly soluble two-site Hubbard model. We construct the exact adiabatic xc functional and show that (i) it does not reproduce correctly resonant Rabi dynamics, and (ii) there is a sizable nonadiabatic contribution to the exact xc potential, which turns out to be small only at the beginning and at the end of the Rabi cycle when the ground-state population is dominant. We then propose a “two-level” approximation for the time-dependent xc potential which can capture Rabi dynamics in the two-site problem. It works well both for resonant and for detuned Rabi oscillations and becomes essentially exact in the linear response regime., We acknowledge financial support from the European Research Council Advanced Grant DYNamo (Grant No. ERC-2010-AdG-267374), Spanish Grant (Grant No. FIS2010-21282-C02-01), Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT578-13), and Ikerbasque and the European Commission projects CRONOS (Grant No. 280879-2 CRONOS CP-FP7).

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Spectrum of excitons in double-quantum-well structures is calculated in tilted magnetic field. It is shown that spectrum becomes asymmetric in quasimomentum if a transverse in respect to growth direction component of magnetic field is nonzero. A transition from $k$-space direct exciton ground state to $k$-space indirect one accompanied by sharp quenching of photoluminescense is described., Comment: LATEX, 15 pages, 2 eps figures. Submited to Sem. Sci. Tech

It is shown that electronic states of a new type, with energy in the band gap can exist at a heterointerface. The interfacial states may be associated with Tamm surface states in the materials forming the heterointerface, but they can appear even if there are no surface states in the initial materials. In the plane of the heterojunction, the energy spectrum of interfacial states forms a two-dimensional band.

Time-dependent (current) density functional theory for many-electron systems strongly coupled to quantized electromagnetic modes of a microcavity is proposed. It is shown that the electron-photon wave function is a unique functional of the electronic (current) density and the expectation values of photonic coordinates. The Kohn-Sham system is constructed, which allows to calculate the above basic variables by solving selfconsistent equations for noninteracting particles. We suggest possible approximations for the exchange-correlation potentials and discuss implications of this approach for the theory of open quantum systems., Comment: 4+ pages

We consider spin relaxation dynamics in cold Fermi gases with a pure-gauge spin-orbit coupling corresponding to recent experiments. We show that such experiments can give a direct access to the collisional spin drag rate, and establish conditions for the observation of spin drag effects. In the recent experiments the dynamics is found to be mainly ballistic leading to new regimes of reversible spin relaxation-like processes., Comment: 5 pages, 2 figures

Trabajo presentado al: "Deutsche Physikalische Gesellschaft Spring Meeting" celebrado en Regensburg (Alemania) del 10 al 15 de Marzo de 2013., The derivative discontinuity of the exchange-correlation (xc) energy of density functional theory (DFT) at integer particle number is absent in many popular local and semilocal approximations. In lattice DFT, approximations exist which exhibit a discontinuity in the xc potential at half filling but due to convergence problems of the Kohn-Sham (KS) self-consistency cycle, the use of these functionals is mostly restricted to situations where the local density is away from half filling. Here a numerical scheme for the self-consistent solution of the lattice KS Hamiltonian with a local xc potential with rapid (or quasidiscontinuous) density dependence is suggested. The problem is formulated in terms of finite-temperature DFT where the discontinuity in the xc potential emerges naturally in the limit of zero temperature. A simple parametrization is suggested for the xc potential of the uniform 1D Hubbard model at finite temperature obtained from the thermodynamic Bethe ansatz. The feasibility of the numerical scheme is demonstrated by application to a model of fermionic atoms in a harmonic trap. The corresponding density profile exhibits a plateau of integer occupation at low temperatures which melts away for higher temperatures.

The long-range proximity effect in superconductor-ferromagnet (S/F) hybrid nanostructures is observed if singlet Cooper pairs from the superconductor are converted into triplet pairs which can diffuse into the ferromagnet over large distances. It is commonly believed that this happens only in the presence of magnetic inhomogeneities. We show that there are other sources of the long-range triplet component (LRTC) of the condensate and establish general conditions for their occurrence. As a prototypical example, we consider first a system where the exchange field and spin-orbit coupling can be treated as time and space components of an effective SU(2) potential. We derive a SU(2) covariant diffusive equation for the condensate and demonstrate that an effective SU(2) electric field is responsible for the long-range proximity effect. Finally, we extend our analysis to a generic ferromagnet and establish a universal condition for the LRTC. Our results open a new avenue in the search for such correlations in S/F structures and make a hitherto unknown connection between the LRTC and Yang-Mills electrostatics. © 2013 American Physical Society., The work of F. S.B was supported by the Spanish Ministry of Economy and Competitiveness under Project No. FIS2011-28851-C02-02 and the Basque Government under UPV/EHU Project No. IT-366-07. I.V. T. acknowledges funding by the ‘‘Grupos Consolidados UPV/EHU del Gobierno Vasco’’ (IT-319-07) and the Spanish MICINN (FIS2010-21282-C02-01).

A time-dependent density functional theory (TDDFT) for a quantum many-body system on a lattice is formulated rigorously. We prove the uniqueness of the density-to-potential mapping and demonstrate that a given density is $v$-representable if the initial many-body state and the density satisfy certain well defined conditions. In particular, we show that for a system evolving from its ground state any density with a continuous second time derivative is $v$-representable and therefore the lattice TDDFT is guaranteed to exist. The TDDFT existence and uniqueness theorem is valid for any connected lattice, independently of its size, geometry and/or spatial dimensionality. The general statements of the existence theorem are illustrated on a pedagogical exactly solvable example which displays all details and subtleties of the proof in a transparent form. In conclusion we briefly discuss remaining open problems and directions for a future research., 12 pages, 1 figure

Interpretation of most experimental results in condensed matter physics does not require the knowledge of all microscopic details of complicated many-body dynamics.

In this paper we further explore and develop the quantum continuum mechanics (QCM) of Tao et al. [Phys. Rev. Lett. 103, 086401 (2009)] with the aim of making it simpler to use in practice. Our simplifications relate to the non-interacting part of the QCM equations, and primarily refer to practical implementations in which the groundstate stress tensor is approximated by its Kohn-Sham (KS) version. We use the simplified approach to directly prove the exactness of QCM for one-electron systems via an orthonormal formulation. This proof sheds light on certain physical considerations contained in the QCM theory and their implication on QCM-based approximations. The one-electron proof then motivates an approximation to the QCM (exact under certain conditions) expanded on the wavefunctions of the KS equations. Particular attention is paid to the relationships between transitions from occupied to unoccupied KS orbitals and their approximations under the QCM. We also demonstrate the simplified QCM semianalytically on an example system.

A general description of the phase separation (PS) in HTSC is presented based on a concept of “soft” dielectric ordering with respect to the addition of collectivized charge carriers. The possibility of the PS crucially depends on the properties of the screening ion subsystem. The interaction of electron and ion subsystems determines a large variety of manifestations of the PS under different experimental conditions. It is shown that the assumption of the existence of the PS makes it possible to explain on common grounds a number of experiments on different HTSC, which seem to be quite separate from each other, such as anomalous magnetoresistance at T T c in Ba 1- x K x BiO 3 , the appearance of midgap states in cuprate HTSC, the existence of two plateaus in the dependence of T c on composition x in YBa 2 Cu 3 O 6+ x , the appearence of photoinduced superconductivity in yttrium superconductors and others.