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Non-reciprocal systems can be thought of as disobeying Newtons third law - an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest towards such systems. On a fundamental level, they can be a basis of describing non-equilibrium and active states of matter, with applications ranging from physics to social sciences. However, often the first step to understanding complex nonlinear models is to linearize about the steady states. It is thus useful to develop a careful understanding of linear non-reciprocal systems, similar to our understanding of Gaussian systems in equilibrium statistical mechanics. In this work we explore simplest linear non-reciprocal models with noise and spatial extent. We describe their regions of stability and show how non-reciprocity can enhance the stability of a system. We demonstrate the appearance of exceptional and critical exceptional points with the respective enhancement of fluctuations for the latter. We show how strong non-reciprocity can lead to a finite-momentum instability. Finally, we comment how non-reciprocity can be a source of colored, $1/f$ type noise., Comment: 11 pages, 6 figures

Charge transport in solids at low temperature reveals a material's mesoscopic properties and structure. Under a magnetic field, Shubnikov-de Haas (SdH) oscillations inform complex quantum transport phenomena that are not limited by the ground state characteristics. Here, in elemental metal Cr with two incommensurately superposed lattices of ions and a spin-density-wave ground state, we reveal that the phases of several low-frequency SdH oscillations in sigma_xx (rho_xx) and sigma_yy (rho_yy) are opposite, contrast with oscillations from normal cyclotron orbits that maintain identical phases. We trace the origin of the low frequency SdH oscillations to quantum interference effects arising from the incommensurate orbits of Cr's superposed reciprocal lattices, and explain the observed pi-phase shift by the reconnection of anisotropic joint open and closed orbits.

Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional point. Here we ask how dynamics in the vicinity of such a bifurcation are influenced by noise. A pitchfork bifurcation can be used to induce bifurcation behavior. We model a limit cycle with the normal form of the Hopf oscillator, couple it to the pitchfork, and investigate the resulting dynamical system in the presence of noise. We show that the generating functional for the averages of the dynamical variables factorizes between the pitchfork and the oscillator. The statistical properties of the pitchfork in the presence of noise in its various regimes are investigated and a scaling theory is developed for the correlation and response functions. The analysis is done by perturbative calculations as well as numerical means. Finally, observables illustrating the coupling of a system with a limit cycle to a pitchfork are discussed and the phase-phase correlations are shown to exhibit non-diffusive behavior with universal scaling., Comment: 10 pages, 8 figures

Previously, we introduced a method for systematically correcting a quasiparticle green's function via a power series expansion. Here we present an ODE based formalisms of power series correction that goes beyond the cumulant approximation and implement it to 1D Holstein chain for a wide range of coupling strengths in a scalable and inexpensive fashion at both zero and finite temperature. We show that this first differential formalism of the power series is both qualitatively and quantitatively in excellent agreement with exact diagonalization results on 1D Holstein chain with dispersive bosons for a large range of electron-boson coupling strength. We investigate carrier mass growth rate and carrier energy displacement across a wide range of coupling strength. Finally, we present a heuristic argument which predicts most of the rich satellite structure without explicit calculation.

Doped SrTi1-xNbxO3 exhibits superconductivity and a mid-infrared optical response reminiscent of copper-oxide superconductors. Strangely, its plasma frequency, omega_p, increases by a factor of ~3 when cooling from 300 K to 20 K, without any accepted explanation. Here, we present momentum-resolved electron energy loss spectroscopy (M-EELS) measurements of SrTi1-xNbxO3 at nonzero momentum, q. We find that the infrared feature previously identified as a plasmon is present at large q in insulating SrTiO3, where it exhibits the same temperature dependence and may be identified as an anharmonic, multiphonon background. Doping with Nb increases its peak energy and total spectral weight, drawing this background to lower q where it becomes visible in IR optics experiments. We conclude that the "plasmon" in doped SrTi1-xNbxO3 is not a free-carrier mode, but a composite excitation that inherits its unusual properties from the lattice anharmonicity of the insulator., Comment: 5 pages, 4 figures

We study a class of bifurcations generically occurring in dynamical systems with non-mutual couplings ranging from models of coupled neurons to predator-prey systems and non-linear oscillators. In these bifurcations, extended attractors such as limit cycles, limit tori, and strange attractors merge and split in a similar way as fixed points in a pitchfork bifurcation. We show that this merging and splitting coincides with the coalescence of covariant Lyapunov vectors with vanishing Lyapunov exponents, generalizing the notion of exceptional points to non-linear dynamical systems. We distinguish two classes of bifurcations, corresponding respectively to continuous and discontinuous behaviors of the covariant Lyapunov vectors at the transition. We outline some physical consequences of generalized exceptional points on the dynamics of the system, including non-reciprocal responses, the destruction of isochrons, and enhanced sensitivity to noise. We illustrate our results with concrete examples from neuroscience, ecology, and physics. When applied to interpret existing experimental observations, our analysis suggests a simple explanation for the non-trivial phase delays observed in the population dynamics of plankton communities and the recently measured statistics of rotation reversals for a solid body immersed in a Rayleigh-B\'enard convection cell., Comment: 32 pages, 16 figures

We consider a standard Ginzburg-Landau model of a ferroelectric whose electrical polarization is coupled to gradients of elastic strain. At the harmonic level, such flexoelectric interaction is known to hybridize acoustic and optic phonon modes and lead to phases with modulated lattice structures that precede the symmetry broken state for sufficiently large couplings. Here, we use the we use the self-consistent phonon approximation to calculate the effects of thermal and quantum polarization fluctuations on the bare modes to show that such long-range modulated order is unstable at all temperatures. We discuss the implications for the nearly ferroelectric SrTiO$_3$ and KTaO$_3$, and propose that these systems are melted versions of an underlying modulated state which is dominated by non-zero momentum thermal fluctuations except at the very lowest temperatures., Comment: 17 pages, 3 figures, 1 table, supplementary information included

Inspired by the recent experimental observation of strongly coupled polaritons in a Moir\'e heterobilayer, we study a model of dipole-interacting excitons localized on sites of a lattice and coupled to planar cavity photons. We calculate the phase diagram of this system by computing fluctuations around the mean field and determining the stability of the excitation spectrum. We find that the transition from the normal state to a polariton condensate is intermediated by a series of ordered states at partial fillings of the exciton lattice, stabilized by the exciton interactions. In particular we predict a supersolid phase in which a polariton condensate coexists with spatial order., Comment: 5 pages, 4 figures

Insulating-metallic transition mediated by substitutional atoms is predicted in a series of two-dimensional carbon-based structures. Introducing Si atoms in selected sites of tetrahexcarbon [Carbon 137 (2018) 266] according to rational chemical rules, metallicity by trivial band inversion without band gap opening is induced. Additional substitution of remaining C atoms by BN dimers introduces no changes in the metallic properties. A series of isomorphous two-dimensional materials with isoelectronic structures derived by exchanging group IV elements exhibiting various band gaps is obtained. Dynamical stability is verified with phonon analysis and beyond the harmonic approximation with molecular dynamics up to room temperature. The semi-metallic compounds have well-nested pockets of carriers and are good candidates for the formation of an excitonic insulator., Comment: 7 pages, 5 figures

Cubic energy materials such as thermoelectrics or hybrid perovskite materials are often understood to be highly disordered. In GeTe and related IV-VI compounds, this is thought to provide the low thermal conductivities needed for thermoelectric applications. Since conventional crystallography cannot distinguish between static disorder and atomic motions, we develop the energy-resolved variable-shutter pair distribution function technique. This collects structural snapshots with varying exposure times, on timescales relevant for atomic motions. In disagreement with previous interpretations, we find the time-averaged structure of GeTe to be crystalline at all temperatures, but with anisotropic anharmonic dynamics at higher temperatures that resemble static disorder at fast shutter speeds, with correlated ferroelectric fluctuations along the $<$100$>$c direction. We show that this anisotropy naturally emerges from a Ginzburg-Landau model that couples polarization fluctuations through long-range elastic interactions. By accessing time-dependent atomic correlations in energy materials, we resolve the long-standing disagreement between local and average structure probes, and show that spontaneous anisotropy is ubiquitous in cubic IV-VI materials., Comment: Published version, substantial changes, many references removed due to journal limits :-( Please see the supporting information online. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format (see conditions)

In the context of a single electron two orbital Holstein system coupled to dispersionless bosons, we develop a general method to correct single particle Green's function using a power series correction(PSC) scheme. We then outline the derivations of various flavors of cumulant approximation through the PSC scheme and explain the assumptions and approximations behind them. Finally, we compute and compare PSC spectral function with cumulant and exact diagonalized spectral functions and elucidate three regimes of this problem - two that cumulant explains and one where cumulant fails. We find that the exact and the PSC spectral functions match within spectral broadening across all three regimes., Comment: 13 pages, 7 figures

Following a resurgence of interest in dilute superconductivity in polar semiconductors, we perform a variational calculation to probe the existence of Fr{\"o}hlich bipolarons in these materials. Our solution is capable of interpolating between the weak- and strong-coupling limits of the electron-phonon interaction. We predict bipolaron formation in solely the strong-coupling regime, and we are not aware of any existing materials at these parameter values. However, imposing an extrinsic electron size constraint to mimic confinement on the sub-micron scale produces binding in new parts of the phase diagram, including at weak coupling, within reach of the near-ferroelectric perovskites., Comment: 12 pages, 9 figures

We analyze a minimal model of SrTiO3, such as has been historically used to analyze the superconducting state. Treating the electron-phonon and electron-electron interactions on an equal footing, we calculate the normal state properties, focusing on the spectral function. We find a density-driven crossover caused mostly by the adiabaticity of the bosonic modes, but the spectral features of our theory are dominated by coupled plasmon-phonon oscillations rather than the bare phonon features seen in experiment., Comment: 5 pages, 4 figures

We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the solutions of the PD and classical equations, the objective is to minimize their mismatch on an overlap of the PD and classical domains, and the controls are virtual volume constraints and boundary conditions applied at the local-nonlocal interface. Our numerical tests performed on three-dimensional geometries illustrate the consistency and accuracy of our method, its numerical convergence, and its applicability to realistic engineering geometries. We demonstrate the coupling strategy as a means to reduce computational expense by confining the nonlocal model to a subdomain of interest, and as a means to transmit local (e.g., traction) boundary conditions applied at a surface to a nonlocal model in the bulk of the domain., Comment: 25 pages, 11 figures

A detailed exploration of the $f$-atomic orbital occupancy space for UO$_2$ is performed using a first principles approach based on density functional theory (DFT), employing a full hybrid functional within a systematic basis set. Specifically, the PBE0 functional is combined with an occupancy biasing scheme implemented in a wavelet-based algorithm which is adapted to large supercells. The results are compared with previous DFT+U calculations reported in the literature, while dynamical mean field theory (DMFT) is also performed to provide a further base for comparison. This work shows that the computational complexity of the energy landscape of a correlated $f$-electron oxide is much richer than has previously been demonstrated. The resulting calculations provide evidence of the existence of multiple previously unexplored metastable electronic states of UO$_2$, including those with energies which are lower than previously reported ground states.

Out of equilibrium, the lack of reciprocity is the rule rather than the exception. Non-reciprocal interactions occur, for instance, in networks of neurons, directional growth of interfaces, and synthetic active materials. While wave propagation in non-reciprocal media has recently been under intense study, less is known about the consequences of non-reciprocity on the collective behavior of many-body systems. Here, we show that non-reciprocity leads to time-dependent phases where spontaneously broken symmetries are dynamically restored. The resulting phase transitions are controlled by spectral singularities called exceptional points. We describe the emergence of these phases using insights from bifurcation theory and non-Hermitian quantum mechanics. Our approach captures non-reciprocal generalizations of three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Collective phenomena in these non-reciprocal systems range from active time-(quasi)crystals to exceptional-point enforced pattern-formation and hysteresis. Our work paves the way towards a general theory of critical phenomena in non-reciprocal matter., Comment: Supplementary movies at https://home.uchicago.edu/~vitelli/videos.html

In the mixed-valence manganites, a near-infrared laser typically melts the orbital and spin order simultaneously, corresponding to the photoinduced $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ excitations in the Mott-Hubbard bands of manganese. Here, we use ultrafast methods -- both femtosecond resonant x-ray diffraction and optical reflectivity -- to demonstrate that the orbital response in the layered manganite Nd$_{1-x}$Sr$_{1+x}$MnO$_{4}$ ($\it{x}$ = 2/3) does not follow this scheme. At the photoexcitation saturation fluence, the orbital order is only diminished by a few percent in the transient state. Instead of the typical $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ transition, a near-infrared pump in this compound promotes a fundamentally distinct mechanism of charge transfer, the $d^{0}$ $ \xrightarrow{}$ $d^{1}L$, where $\it{L}$ denotes a hole in the oxygen band. This novel finding may pave a new avenue for selectively manipulating specific types of order in complex materials of this class.

The Higgs amplitude mode is a collective excitation studied and observed in a broad class of matter, including superconductors, charge density waves, antiferromagnets, 3He p-wave superfluid, and ultracold atomic condensates. In all the observations reported thus far, the amplitude mode was excited by perturbing the condensate out of equilibrium. Studying an exciton-polariton condensate, here we report the first observation of this mode purely driven by intrinsic quantum fluctuations without such perturbations. By using an ultrahigh quality microcavity and a Raman spectrometer to maximally reject photoluminescence from the condensate, we observe weak but distinct photoluminescence at energies below the condensate emission. We identify this as the so-called ghost branches of the amplitude mode arising from quantum depletion of the condensate into this mode. These energies, as well as the overall structure of the photoluminescence spectra, are in good agreement with our theoretical analysis.

Critical phenomena arise ubiquitously in various context of physics, from condensed matter, high energy physics, cosmology, to biological systems, and consist of slow and long-distance fluctuations near a phase transition or critical point. Usually, these phenomena are associated with the softening of a massive mode. Here we show that a novel, non-Hermitian-induced mechanism of critical phenomena that do not fall into this class can arise in the steady state of generic driven-dissipative many-body systems with coupled binary order parameters such as exciton-polariton condensates and driven-dissipative Bose-Einstein condensates in a double-well potential. The criticality of this ``critical exceptional point'' is attributed to the coalescence of the collective eigenmodes that convert all the thermal-and-dissipative-noise activated fluctuations to the Goldstone mode, leading to anomalously giant phase fluctuations that diverge at spatial dimensions $d\le 4$. Our dynamic renormalization group analysis shows that this gives rise to a strong-coupling fixed point at dimensions as high as $d<8$ associated with a new universality class beyond the classification by Hohenberg and Halperin, indicating how anomalously strong the many-body corrections are at this point. We find that this anomalous enhancement of many-body correlation is due to the appearance of a sound mode at the critical exceptional point despite the system's dissipative character., Comment: 16 pages, 3 figures including appendices

Mapping all the neurons in the brain requires automatic reconstruction of entire cells from volume electron microscopy data. The flood-filling network (FFN) architecture has demonstrated leading performance for segmenting structures from this data. However, the training of the network is computationally expensive. In order to reduce the training time, we implemented synchronous and data-parallel distributed training using the Horovod library, which is different from the asynchronous training scheme used in the published FFN code. We demonstrated that our distributed training scaled well up to 2048 Intel Knights Landing (KNL) nodes on the Theta supercomputer. Our trained models achieved similar level of inference performance, but took less training time compared to previous methods. Our study on the effects of different batch sizes on FFN training suggests ways to further improve training efficiency. Our findings on optimal learning rate and batch sizes agree with previous works., Comment: 9 pages, 10 figures

We report on superconductivity in single crystals of SrTiO$_{3-\delta}$ with carrier densities $\textit{n} < 1.4 \times10^{18}cm^{-3}$, where only a single band is occupied. For all samples in this regime, the resistive transition occurs at $T_{c} \approx 65 \pm 25 \ mK$. We observe a zero resistance state for $\textit{n}$ as low as $1.03 \times10^{17}cm^{-3}$, and a partial resistive transition for $\textit{n} = 3.85 \times10^{16}cm^{-3}$. We observe low critical current densities, relatively high and isotropic upper critical fields, and an absence of diamagnetic screening in these samples. Our findings suggest an inhomogeneous superconducting state, embedded within a homogeneous high-mobility 3-dimensional electron gas. $T_{c}$ does not vary appreciably when $\textit{n}$ changes by more than an order of magnitude, inconsistent with conventional superconductivity., Comment: 5 pages, 4 figures

State-based peridynamic models provide an important extension of bond-based models that allow the description of general linearly elastic materials. Meshfree discretizations of these nonlocal models are attractive due to their ability to naturally handle fracture. However, singularities in the integral operators have historically proven problematic when seeking convergent discretizations. We utilize a recently introduced optimization-based quadrature framework to obtain an asymptotically compatible scheme able to discretely recover local linear elasticity as the nonlocal interaction is reduced at the same rate as the grid spacing. By introducing a correction to the definition of nonlocal dilitation, surface effects for problems involving bond-breaking and free surfaces are avoided without the need to modify the material model. We use a series of analytic benchmarks to validate the consistency of this approach, illustrating second-order convergence for the Dirichlet problem, and first-order convergence for problems involving curvilinear free surfaces and composite materials. We additionally illustrate that these results hold for material parameters chosen in the near-incompressible limit.

The magnetoresistance (MR) of a material is typically insensitive to reversing the applied field direction and varies quadratically with magnetic field in the low-field limit. Quantum effects [1], unusual topological band structures [2], and inhomogeneities that lead to wandering current paths [3, 4] can induce a crossover from quadratic to linear magnetoresistance with increasing magnetic field. Here we explore a series of metallic charge- and spin-density-wave systems that exhibit extremely large positive linear magnetoresistance. By contrast to other linear MR mechanisms, this effect remains robust down to miniscule magnetic fields of tens of Oersted at low temperature. We frame an explanation of this phenomenon in a semi-classical narrative for a broad category of materials with partially-gapped Fermi surfaces due to density waves.

The metal-semiconductor contact is a major factor limiting the shrinking of transistor dimension to further increase device performance. In-plane edge contacts have the potential to achieve lower contact resistance due to stronger orbital hybridization compared to conventional top contacts. However, a quantitative understanding of the electron transport properties in the edge contact is still lacking. In this work, we present full-band atomistic quantum transport simulations of the graphene/MoS$_2$ edge contact. By using a Wannier function basis to accurately describe the electronic bands, together with a full self-consistent solution of the electrostatics, we are able to efficiently model device structures on a micron scale, but with atomic level accuracy. We find that the potential barrier created by trapped charges decays fast with distance away from the interface, and is thus thin enough to enable efficient injection of electrons. This results in Ohmic behavior in its I-V characteristics, which agrees with experiments. Our results demonstrate the role played by trapped charges in the formation of a Schottky barrier, and how one can reduce the Schottky barrier height (SBH) by adjusting the relevant parameters of the edge contact system. Our framework can be extended conveniently to incorporate more general nanostructure geometries. For example, a full 3D solution of the electrostatics will also lead to better modeling of the electrical potential. Furthermore, better ab-initio calculations can be conveniently added to our methods to further improve their accuracy.

We propose a novel mechanism for a nonequilibrium phase transition in a $U(1)$-broken phase of an electron-hole-photon system, from a Bose-Einstein condensate of polaritons to a photon laser, induced by the non-Hermitian nature of the condensate. We show that a (uniform) steady state of the condensate can always be classified into two types, namely, arising either from lower or upper-branch polaritons. We prove (for a general model) and demonstrate (for a particular model of polaritons) that an exceptional point where the two types coalesce marks the endpoint of a first-order-like phase boundary between the two types, similar to a critical point in a liquid-gas phase transition. Since the phase transition found in this paper is not in general triggered by population inversion, our result implies that the second threshold observed in experiments is not necessarily a strong-to-weak-coupling transition, contrary to the widely-believed understanding. Although our calculation mainly aims to clarify polariton physics, our discussion is applicable to general driven-dissipative condensates composed of two complex fields., Comment: Revised version. 6 pages and 4 figures + 13 pages and 6 figures of Supplemental Material

We investigate theoretically nonequilibrium effects on photoluminescence and gain/absorption spectra of a driven-dissipative exciton-polariton condensate, by employing the combined Hartree-Fock-Bogoliubov theory with the generalized random phase approximation extended to the Keldysh formalism. Our calculated photoluminescence spectra is in semiquantitative agreement with experiments, where features such as a blue shift of the emission from the condensate, the appearance of the dispersionless feature of a diffusive Goldstone mode, and the suppression of the dispersive profile of the mode are obtained. We show that the nonequilibrium nature of the exciton-polariton condensate strongly suppresses the visibility of the Bogoliubov dispersion in the negative energy branch (ghost branch) in photoluminescence spectra. We also show that the trace of this branch can be captured as a hole burning effect in gain/absorption spectra. Our results indicate that the nonequilibrium nature of the exciton-polariton condensate strongly reduces quantum depletion, while a scattering channel to the ghost branch is still present., Comment: 25 pages, 21 figures

Perovskite structured materials contain myriad tunable ordered phases of electronic and magnetic origin with proven technological importance and strong promise for a variety of energy solutions. An always-contributing influence beneath these cooperative and competing interactions is the lattice, whose physics may be obscured in complex perovskites by the many coupled degrees of freedom which makes these systems interesting. Here we report signatures of an approach to a quantum phase transition very near the ground state of the nonmagnetic, ionic insulating, simple cubic perovskite material ScF3 and show that its physical properties are strongly effected as much as 100 K above the putative transition. Spatial and temporal correlations in the high-symmetry cubic phase determined using energy- and momentum-resolved inelastic X-ray scattering as well as X-ray diffraction reveal that soft mode, central peak and thermal expansion phenomena are all strongly influenced by the transition., Comment: 6 pages, 4 figures

The structural phase transitions of MF$_3$ (M=Al, Cr, V, Fe, Ti, Sc) metal trifluorides are studied within a simple Landau theory consisting of tilts of rigid MF$_6$ octahedra associated with soft antiferrodistoritive optic modes that are coupled to long-wavelength strain generating acoustic phonons. We calculate the temperature and pressure dependence of several quantities such as the spontaneous distortions, volume expansion and shear strains as well as $T-P$ phase diagrams. By contrasting our model to experiments we quantify the deviations from mean-field behavior and found that the tilt fluctuations of the MF$_6$ octahedra increase with metal cation size. We apply our model to predict giant barocaloric effects in Sc substituted TiF$_3$ of up to about $15\,$JK$^{-1}$kg$^{-1}$ for modest hydrostatic compressions of $0.2\,$GPa. The effect extends over a wide temperature range of over $140\,$K (including room temperature) due to a large predicted rate $dT_c/dP = 723\,$K GPa$^{-1}$, which exceeds those of typical barocaloric materials. Our results suggest that open lattice frameworks such as the trifluorides are an attractive platform to search for giant barocaloric effects., Comment: 11 pages, 8 figures

Motivated by recent experiments, we use the $+U$ extension of the generalized gradient approximation to density functional theory to study superlattices composed of alternating layers of LaNiO$_3$ and LaMnO$_3$. For comparison we also study a rocksalt ((111) double perovskite) structure and bulk LaNiO$_3$ and LaMnO$_3$. A Wannier function analysis indicates that band parameters are transferable from bulk to superlattice situations with the exception of the transition metal d-level energy, which has a contribution from the change in d-shell occupancy. The charge transfer from Mn to Ni is found to be moderate in the superlattice, indicating metallic behavior, in contrast to the insulating behavior found in recent experiments, while the rocksalt structure is found to be insulating with a large Mn-Ni charge transfer. We suggest a high density of cation antisite defects may account for the insulating behavior experimentally observed in short-period superlattices., Comment: 9 pages, 7 figures

Obtaining strong magnetoelectric couplings in bulk materials and heterostructures is an ongoing challenge. We demonstrate that manganite heterostructures of the form ${\rm (Insulator)/(LaMnO_3)_n/(CaMnO_3)_n/(Insulator)}$ show strong multiferroicity in magnetic manganites where ferroelectric polarization is realized by charges leaking from ${\rm LaMnO_3}$ to ${\rm CaMnO_3}$ due to repulsion. Here, an effective nearest-neighbor electron-electron (electron-hole) repulsion (attraction) is generated by cooperative electron-phonon interaction. Double exchange, when a particle virtually hops to its unoccupied neighboring site and back, produces magnetic polarons that polarize antiferromagnetic regions. Thus a striking giant magnetoelectric effect ensues when an external electrical field enhances the electron leakage across the interface., Comment: This version supersedes arXiv:1203.3283