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Resistive switching in thin films has been widely studied in a broad range of materials. Yet the mechanisms behind electroresistive switching have been persistently difficult to decipher and control, in part due to their non-equilibrium nature. Here, we demonstrate new experimental approaches that can probe resistive switching phenomena, utilizing amorphous TaO$_x$ as a model material system. Specifically, we apply Scanning Microwave Impedance Microscopy (sMIM) and cathodoluminescence (CL) microscopy as direct probes of conductance and electronic structure, respectively. These methods provide direct evidence of the electronic state of TaO$_x$ despite its amorphous nature. For example CL identifies characteristic impurity levels in TaO$_x$, in agreement with first principles calculations. We applied these methods to investigate He-ion-beam irradiation as a path to activate conductivity of materials and enable electroforming-free control over resistive switching. However, we find that even though He-ions begin to modify the nature of bonds even at the lowest doses, the films conductive properties exhibit remarkable stability with large displacement damage and they are driven to metallic states only at the limit of structural decomposition. Finally, we show that electroforming in a nanoscale junction can be carried out with a dissipated power of < 20 nW, a much smaller value compared to earlier studies and one that minimizes irreversible structural modifications of the films. The multimodal approach described here provides a new framework toward the theory/experiment guided design and optimization of electroresistive materials.

The pairing symmetry of the superconducting order parameter in iron-based superconductors has been a subject of debate, with various models proposing s-wave, d-wave, and mixed combinations as possible candidates. Here we probe the pairing symmetry of FeSe utilizing the new methodology of Tunneling Andreev Reflection (TAR). TAR directly exploits the transparency-dependence of tunneling current to disentangle contributions of single-particle current and Andreev reflection. These measurements provided new direct evidence in favor of the sign-changing nature of the superconducting order in FeSe, in a distinctly complementary approach to nanoscale imaging of quasiparticle interference. Crucially TAR can also probe higher-order contributions to Andreev reflection. Quantitative comparison of the experimental signatures of higher-order Andreev reflections with those in concomitant tight-binding simulations revealed new evidence in support of the nodal gap structure of superconductivity in FeSe. Finally, the effect of structural topological defects can be directly probed with TAR owing to its atomic spatial resolution. In particular, we find that superconductivity is completely suppressed along the twin boundary while its electronic structure is characterized by a V-shaped signature of a pseudogap state. Our findings provide new insight into the pairing symmetry of an unconventional superconductor, demonstrating the potential of differential tunneling Andreev reflection to reveal microscopic properties of emerging quantum materials.

Smart electronic circuits that support neuromorphic computing on the hardware level necessitate materials with memristive, memcapacitive, and neuromorphic-like functional properties; in short, the electronic response must depend on the voltage history, thus enabling learning algorithms. Here we demonstrate volatile ferroelectric switching of Sn$_2$P$_2$S$_6$ at room temperature and see that initial polarization orientation strongly determines the properties of polarization switching. In particular, polarization switching hysteresis is strongly imprinted by the original polarization state, shifting the regions of non-linearity toward zero-bias. As a corollary, polarization switching also enables effective capacitive switching, approaching the sought-after regime of memcapacitance. Landau-Ginzburg-Devonshire simulations demonstrate that one mechanism by which polarization can control the shape of the hysteresis loop is the existence of charged domain walls decorating the periphery of the repolarization nucleus. These walls oppose the growth of the switched domain and favor back-switching, thus creating a scenario of controlled volatile ferroelectric switching. Although the measurements were carried out with single crystals, prospectively volatile polarization switching can be tuned by tailoring sample thickness, domain wall mobility and electric fields, paving way to non-linear dielectric properties for smart electronic circuits.

Ferroelectric domain wall motion is fundamental to the switching properties of ferroelectric devices and is influenced by a wide range of factors including spatial disorder within the material and thermal noise. We build a Landau-Ginzburg-Devonshire (LGD) model of 180${}^{\circ}$ ferroelectric domain wall motion that explicitly takes into account the presence of both spatial and temporal disorder. We demonstrate both creep flow and linear flow regimes of the domain wall dynamics by solving the LGD equations in a Galilean frame moving with the wall velocity $v$. Thermal noise plays a key role in the wall depinning process at small fields $E$. We study the scaling of the velocity $v$ with the applied DC electric field $E$ and show that noise strongly affects domain wall velocities. We also show that the domain wall widens significantly in the presence of thermal noise, especially as the material temperature $T$ approaches the critical temperature $T_c$. These calculations therefore point to the potential of noise and disorder to become control factors for the switching properties of ferroelectric materials, for example for advancement of microelectronic applications., Comment: 10 pages, 7 figures

Ferroelectric domain walls have emerged as one of the most fascinating objects in condensed matter physics due to the broad variability of functional behaviors they exhibit. However, the vast majority of domain walls studies have been focused on bias-induced dynamics and transport behaviors. Here, we introduce the scanning probe microscopy approach based on piezoresponse force microscopy (PFM) with a dynamically heated probe, combining local heating and local biasing of the material. This approach is used to explore the thermal polarization dynamics in soft Sn2P2S6 ferroelectrics, and allows for the exploration of phase transitions at individual domain walls. The strong and weak modulation regimes for the thermal PFM are introduced. The future potential applications of heated probe approach for functional SPM measurements including piezoelectric, elastic, microwave, and transport measurements are discussed.

Despite multiple efforts, there exist many unsolved fundamental problems related with detection and analysis of internal polarization structure and related phase transitions in ferroelectric domain walls. Their solution can be very important for the progress in domain wall nanoelectronics and related applications in advanced memories and other information technologies. Here, we theoretically study the features of phase transitions in the domain walls, which are potentially detectable by the scanning probe capacitance microwave microscopy. The finite element modelling based on the Landau-Ginzburg-Devonshire theory is performed for the capacitance changes related with the domain wall motion in a multiaxial ferroelectric BaTiO$_3$., Comment: 8 pages, 4 figures, 1 table

Direct detection of superconductivity has long been a key strength of point-contact Andreev reflection. However, its applicability to atomic-scale imaging is limited by the mechanical contact of the Andreev probe. To this end, we present a new method to probe Andreev reflection in a tunnel junction, leveraging tunneling spectroscopy and junction tunability to achieve quantitative detection of Andreev scattering. This method enables unambiguous assignment of superconducting origins of current-carrying excitations as well as detection of higher order Andreev processes in atomic-scale junctions. We furthermore revealed distinct sensitivity of Andreev reflection to natural defects, such as step edges, even in classical superconductors. The methodology opens a new path to nanoand atomic-scale imaging of superconducting properties, including disordered superconductors and proximity to phase transitions.

The van der Waals layered material CuInP2S6 features interesting functional behavior, including the existence of four uniaxial polarization states, polarization reversal against the electric field through Cu ion migration, a negative-capacitance regime, and reversible extraction of Cu ions. At the heart of these characteristics lies the high mobility of Cu ions, which also determines the spontaneous polarization. Therefore, Cu migration across the lattice results in unusual ferroelectric behavior. Here, we demonstrate how the interplay of polar and ionic properties provides a path to ionically controlled ferroelectric behavior, achieved by applying selected DC voltage pulses and subsequently probing ferroelectric switching during fast triangular voltage sweeps. Using current measurements and theoretical calculations, we observe that increasing DC pulse duration results in higher ionic currents, the build-up of an internal electric field that shifts polarization loops, and an increase in total switchable polarization by ~50% due to the existence of a high polarization phase which is stabilized by the internal electric field. Apart from tuning ferroelectric behavior by selected square pulses, hysteretic polarization switching can even be entirely deactivated and reactivated, resulting in three-state systems where polarization switching is either inhibited or can be performed in two different directions.

Microwave measurements have recently been successfully applied to measure ferroelectric materials on the nanoscale, including detection of polarization switching and ferroelectric domain walls. Here we discuss the question whether scanning probe microscopy (SPM) operating at microwave frequency can identify the changes associated with the soft phonon dynamics in a ferroic. The analytical expressions for the electric potential, complex impedance and dielectric losses are derived and analyzed, since these physical quantities are linked to experimentally-measurable properties of the ferroic. As a ferroic we consider virtual or proper ferroelectric with an optic phonon mode that softens at a Curie point. We also consider a decay mechanism linked to the conductance of the ferroic, and thus manifesting itself as the dielectric loss in the material. Our key finding is that the influence of the soft phonon dispersion on the surface potential distribution, complex impedance and dielectric losses are evidently strong in the vicinity (10-30 K) of the Curie temperature. Furthermore, we quantified how the spatial distribution and frequency spectra of the complex impedance and the dielectric losses react on the dynamics of the soft phonons near the Curie point. These results set the stage for characterization of polar phase transitions with nanoscale microwave measurements, providing a complementary approach to well established electromechanical measurements for fundamental understanding of ferroelectric properties as well as their applications in telecommunication and computing., Comment: 26 pages, including 4 figures and the supplementary materials

Rapid proliferation of hyperspectral imaging in scanning probe microscopies creates unique opportunities to systematically capture and categorize higher dimensional datasets, toward new insights into electronic, mechanical and chemical properties of materials with nano- and atomic-scale resolution. Here we demonstrate similarity learning for tunneling spectroscopy acquired on superconducting material (FeSe) with sparse density of imperfections (Fe vacancies). Popular methods for unsupervised learning and discrete representation of the data in terms of clusters of characteristic behaviors were found to produce inconsistencies with respect to capturing the location and tunneling characteristics of the vacancy sites. To this end, we applied a more general, non-linear similarity learning. This approach was found to outperform several widely used methods for dimensionality reduction and produce a clear differentiation of the type of tunneling spectra. In particular, significant spectral weight transfer likely associated with the electronic reconstruction by the vacancy sites, is systematically captured, as is the spatial extent of the vacancy region. Given that a great variety of electronic materials will exhibit similarly smooth variation of the spectral responses due to random or engineered inhomogeneities in their structure, we believe our approach will be useful for systematic analysis of hyperspectral imaging with minimal prior knowledge, as well as prospective comparison of experimental measurements to theoretical calculations with explicit consideration of disorder.

Using Landau-Ginsburg-Devonshire approach and available experimental results we reconstruct the thermodynamic potential of the layered ferroelectric CuInP$_2$S$_6$ (CIPS), which is expected to be applicable a wide range of temperatures and applied pressures. The analysis of temperature dependences of the dielectric permittivity and lattice constants for different applied pressures unexpectedly reveals the critically important role of the nonlinear electrostriction in this material. With the nonlinear electrostriction included we calculated temperature and pressure phase diagrams and spontaneous polarization of bulk CIPS. Using the coefficients of the reconstructed four-well thermodynamic potential, we study the strain-induced phase transitions in thin epitaxial CIPS films, as well as the stress-induced phase transitions in CIPS nanoparticles, which shape varies from prolate needles to oblate disks. We reveal the strong influence of the mismatch strain, elastic stress and shape anisotropy on the polar properties and phase diagrams of nanoscale CIPS. Also, we derived analytical expressions, which allow the elastic control of the nanoscale CIPS polar properties. Hence obtained results can be of particular interest for the strain-engineering of nanoscale layered nanoferroelectrics., Comment: 23 pages including 6 figures and 2 appendixes

Compressed sensing (CS) is a valuable technique for reconstructing measurements in numerous domains. CS has not yet gained widespread adoption in scanning tunneling microscopy (STM), despite potentially offering the advantages of lower acquisition time and enhanced tolerance to noise. Here we applied a simple CS framework, using a weighted iterative thresholding algorithm for CS reconstruction, to representative high-resolution STM images of superconducting surfaces and adsorbed molecules. We calculated reconstruction diagrams for a range of scanning patterns, sampling densities, and noise intensities, evaluating reconstruction quality for the whole image and chosen defects. Overall we find that typical STM images can be satisfactorily reconstructed down to 30\% sampling - already a strong improvement. We furthermore outline limitations of this method, such as sampling pattern artifacts, which become particularly pronounced for images with intrinsic long-range disorder, and propose ways to mitigate some of them. Finally we investigate compressibility of STM images as a measure of intrinsic noise in the image and a precursor to CS reconstruction, enabling a priori estimation of the effectiveness of CS reconstruction with minimal computational cost.

We present a method to identify distinct tunneling modes in tunable superconducting tunnel junction composed of superconducting tip and sample in scanning tunneling microscope. Combining the measurement of the relative decay constant of tunneling current extracted from I-V-z spectroscopy with its statistical analysis over the atomic disorders in the sample surface, we identified the crossover of tunneling modes between single quasiparticle tunneling, multiple Andreev reflection, and Josephson tunneling with respect to the bias voltage. The method enables one to determine the particular tunneling regime independently of the spectral shapes, and to reveal the intrinsic modulation of Andreev reflection and Josephson current that would be crucial for quantum device application of superconductors.

Recently, a layered ferroelectric CuInP2Se6 was shown to exhibit domain walls with locally enhanced piezoresponse - a striking departure from the observations of nominally zero piezoresponse in most ferroelectrics. Although it was proposed that such "bright" domain walls are phase-boundaries between ferri- and antiferroelectrically ordered regions of the materials, the physical mechanisms behind the existence and response of these boundaries remain to be understood. Here, using Landau-Ginzburg-Devonshire phenomenology combined with four sub-lattices model, we describe quantitatively the bright-contrast and dark-contrast domain boundaries between the antiferroelectric, ferroelectric or ferrielectric long-range ordered phases in a layered ferroelectric-antiferroelectric ferroics, such as CuInP2(S1-ySey)6, Comment: 22 pages, 5 figures, 1 Appendix

With the advent of increasingly elaborate experimental techniques in physics, chemistry and materials sciences, measured data are becoming bigger and more complex. The observables are typically a function of several stimuli resulting in multidimensional data sets spanning a range of experimental parameters. As an example, a common approach to study ferroelectric switching is to observe effects of applied electric field, but switching can also be enacted by pressure and is influenced by strain fields, material composition, temperature, time, etc. Moreover, the parameters are usually interdependent, so that their decoupling toward univariate measurements or analysis may not be straightforward. On the other hand, both explicit and hidden parameters provide an opportunity to gain deeper insight into the measured properties, provided there exists a well-defined path to capture and analyze such data. Here, we introduce a new, two-dimensional approach to represent hysteretic response of a material system to applied electric field. Utilizing ferroelectric polarization as a model hysteretic property, we demonstrate how explicit consideration of electromechanical response to two rather than one control voltages enables significantly more transparent and robust interpretation of observed hysteresis, such as differentiating between charge trapping and ferroelectricity. Furthermore, we demonstrate how the new data representation readily fits into a variety of machinelearning methodologies, from unsupervised classification of the origins of hysteretic response via linear clustering algorithms to neural-network-based inference of the sample temperature based on the specific morphology of hysteresis.

Using a local real-space microscopy probe, we discover evidence of nanoscale interlayer defects along the c-crystallographic direction in BaFe2As2 (122) based iron-arsenide superconductors. We find ordered 122 atomic arrangements within the ab-plane, and within regions of ~10 to 20 nm size perpendicular to this plane. While the FeAs substructure is very rigid, Ba ions are relatively weakly bound and can be displaced from the 122, forming stacking faults resulting in the physical separation of the 122 between adjacent ordered domains. The evidence for interlayer defects between the FeAs superconducting planes gives perspective on the minimal connection between interlayer chemical disorder and high-temperature superconductivity. In particular, the Cooper pairs may be finding a way around such localized interlayer defects through a percolative path of the ordered layered 122 lattice that may not affect Tc.

A material with reversible temperature change capability under an external electric field, known as the electrocaloric effect (ECE), has long been considered as a promising solid-state cooling solution. However, electrocaloric (EC) performance of EC materials generally is not sufficiently high for real cooling applications. As a result, exploring EC materials with high performance is of great interest and importance. Here, we report on the ECE of ferroelectric materials with van der Waals layered structure (CuInP2S6 or CIPS in this work in particular). Over 60% polarization charge change is observed within a temperature change of only 10 K at Curie temperature. Large adiabatic temperature change (|{\Delta}T|) of 3.3 K, isothermal entropy change (|{\Delta}S|) of 5.8 J kg-1 K-1 at |{\Delta}E|=142.0 kV cm-1 at 315 K (above and near room temperature) are achieved, with a large EC strength (|{\Delta}T|/|{\Delta}E|) of 29.5 mK cm kV-1. The ECE of CIPS is also investigated theoretically by numerical simulation and a further EC performance projection is provided., Comment: 32 pages, 10 figures

Triboelectric charging strongly affects the operation cycle and handling of materials and can be used to harvest mechanical energy through triboelectric nanogenerator set-up. Despite ubiquity of triboelectric effects, a lot of mechanisms surrounding the relevant phenomena remain to be understood. Continued progress will rely on the development of rapid and reliable methods to probe accumulation and dynamics of static charges. Here, we demonstrate in-situ quantification of tribological charging with nanoscale resolution, that is applicable to a wide range of dielectric systems. We apply this method to differentiate between strongly and weakly charging compositions of industrial grade polymers. The method highlights the complex phenomena of electrostatic discharge upon contact formation to pre-charged surfaces, and directly reveals the mobility of electrostatic charge on the surface. Systematic characterization of commercial polyethylene terephthalate samples revealed the compositions with the best antistatic properties and provided an estimate of characteristic charge density up to 5x10-5 C/m2. Large-scale molecular dynamics simulations were used to resolve atomistic level structural and dynamical details revealing enrichment of oxygen containing groups near the air-interface where electrostatic charges are likely to accumulate.

The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations are expressed in terms of conditional law of a partially observed Markov diffusion process. It then follows that the adjoint time-inverse forward backward doubly stochastic differential equations governs the evolution of the unnormalized filtering density in the optimal filtering problem.

Analytical description of domain structure morphology and phase diagrams of ferroelectric nanoparticles is developed in the framework of Landau Ginzburg Devonshire approach. To model realistic conditions of incomplete screening of spontaneous polarization at the particle surface, it was considered covered by an ultra-thin layer of screening charge with finite screening length. The phase diagrams, calculated for spherical Sn2P2S6 nanoparticles in coordinates "temperature vs surface screening length" by finite element modeling, demonstrate the emergence of polydomain region at the tricritical point and its broadening with increasing the screening length for the particle radius over a critical value. Metastable and stable labyrinthine domain structures exist in Sn2P2S6 nanoparticles with radius 8 and 10 nm and more, similarly to the case of CuInP2S6 nanoparticles considered previously. We derived simple analytical expressions for the boundaries between paraelectric, single-domain and poly-domain ferroelectric phases, tricritical point and the necessary condition for the appearance of labyrinthine domains, and demonstrated their high accuracy in comparison with finite element modeling results. Analytical description shows that phase diagrams and domain morphologies, which are qualitatively similar to the ones calculated in this work, can be expected in other ferroelectric nanoparticles covered by the screening charges, being rather different for the ferroelectrics with the first and second order ferroelectric-paraelectric transitions respectively., Comment: 36 pages, 6 figures, 3 appendices

The interest in ferroelectric van der Waals crystals arises from the potential to realize ultrathin ferroic systems owing to the reduced surface energy of these materials and the layered structure that allows for exfoliation. Here, we quantitatively unravel giant negative electrostriction of van der Waals layered copper indium thiophosphate (CIPS), which exhibits an electrostrictive coefficient Q33 as high as -3.2 m4/C2 and a resulting bulk piezoelectric coefficient d33 up to -85 pm/V. As a result, the electromechanical response of CIPS is comparable in magnitude to established perovskite ferroelectrics despite possessing a much smaller spontaneous polarization of only a few uC/cm2. In the paraelectric state, readily accessible owing to low transition temperatures, CIPS exhibits large dielectric tunability, similar to widely-used barium strontium titanate, and as a result both giant and continuously tunable electromechanical response. The persistence of electrostrictive and tunable responses in the paraelectric state indicates that even few layer films or nanoparticles will sustain significant electromechanical functionality, offsetting the inevitable suppression of ferroelectric properties in the nanoscale limit. These findings can likely be extended to other ferroelectric transition metal thiophosphates and (quasi-) two-dimensional materials and might facilitate the quest towards novel ultrathin functional devices incorporating electromechanical response., Comment: Published version in Phys. Rev. Materials https://journals.aps.org/prmaterials/abstract/10.1103/PhysRevMaterials.3.024401

Ferroelectric materials have remained one of the foci of condensed matter physics and materials science for over 50 years. In the last 20 years, the development of voltage-modulated scanning probe microscopy techniques, exemplified by Piezoresponse force microscopy (PFM) and associated time and voltage spectroscopies, opened a pathway to explore these materials on a single-digit nanometer level. Consequently, domain structures, walls and polarization dynamics can now be imaged in real space. More generally, PFM has allowed studying electromechanical coupling in a broad variety of materials ranging from ionics to biological systems. It can also be anticipated that the recent Nobel prize in molecular electromechanical machines will result in rapid growth in interest in PFM as a method to probe their behavior on single device and device assembly levels. However, the broad introduction of PFM also resulted in a growing number of reports on nearly ubiquitous presence of ferroelectric-like phenomena including remnant polar states and electromechanical hysteresis loops in materials which are non-ferroelectric in the bulk, or in cases where size effects are expected to suppress ferroelectricity. While in certain cases plausible physical mechanisms can be suggested, there is remarkable similarity in observed behaviors, irrespective of the materials system. In this review, we summarize the basic principles of PFM, briefly discuss the features of ferroelectric surfaces salient to PFM imaging and spectroscopy, and summarize existing reports on ferroelectric like responses in non-classical ferroelectric materials. We further discuss possible mechanisms behind observed behaviors, and possible experimental strategies for their identification., Comment: 74 pages, 16 figures

Electronic interactions present in material compositions close to the superconducting dome play a key role in the manifestation of high-Tc superconductivity. In many correlated electron systems, however, the parent or underdoped states exhibit strongly inhomogeneous electronic landscape at the nanoscale that may be associated with competing, coexisting, or intertwined chemical disorder, strain, magnetic, and structural order parameters. Here we demonstrate an approach based on a combination of scanning tunneling microscopy/spectroscopy (STM/S) and advanced statistical learning for an automatic separation and extraction of statistically significant electronic behaviors in the spin density wave (SDW) regime of a lightly (~1%) gold-doped BaFe2As2. We show that the decomposed STS spectral features have a direct relevance to fundamental physical properties of the system, such as SDW-induced gap, pseudogap-like state, and impurity resonance states.

Graphene monolayers are known to display domains of anisotropic friction with twofold symmetry and anisotropy exceeding 200 percent. This anisotropy has been thought to originate from periodic nanoscale ripples in the graphene sheet, which enhance puckering around a sliding asperity to a degree determined by the sliding direction. Here we demonstrate that these frictional domains derive not from structural features in the graphene, but from self-assembly of atmospheric adsorbates into a highly regular superlattice of stripes with period 4 to 6 nm. The stripes and resulting frictional domains appear on monolayer and multilayer graphene on a variety of substrates, as well as on exfoliated flakes of hexagonal boron nitride. We show that the stripe-superlattices can be reproducibly and reversibly manipulated with submicron precision using a scanning probe microscope, allowing us to create arbitrary arrangements of frictional domains within a single flake. Our results suggest a revised understanding of the anisotropic friction observed in graphene and bulk graphite in terms of atmospheric adsorbates., Comment: This version contains new data which show that the stripes observed in AFM are adsorbates rather than structural ripples. We also clarify that the stripe axis is parallel to the axis of high friction, rather than perpendicular, as we previously claimed following others' studies; our revised conclusion is based on a more careful imaging sequence which avoided reorienting frictional domains