arXiv subjects

E. W. Carlson

Publications and source records attributed to E. W. Carlson.

At least 19 recordsLinked to original sources

arXiv2025

Accurate prediction of macroscopic transport from microscopic imaging via critical fractals at the Mott transition

Vanadium dioxide (VO$_2$) exhibits hysteresis in resistance while undergoing a thermally driven insulator-metal transition (IMT). Understanding the nonequilibrium effects in resistance is of great interest, as VO$_2$ is a strong candidate for brain-inspired computing, which is more energy efficient for AI tasks compared to traditional computing. Accurate models of the connection between microscopic and macroscopic transport properties and microscopic imaging of VO$_2$ will allow us to better utilize VO$_2$ in future applications. However, predictions of macroscopic resistance of VO$_2$ that quantitatively match observations using spatially resolved data have not yet been achieved. Here, we demonstrate an accurate prediction of the macroscopic resistance of VO$_2$ throughout the entire temperature range of interest, by developing a multiscale resistor network model incorporating the assumption of fractal sub-pixel structure of the optical data, where the configuration of insulating and metallic domains within each pixel are drawn from the random field Ising model near criticality. This strongly indicates that the observed fractal, power law structure of metallic and insulating domains extends down to much smaller length scales than the current record for experimental resolution of this system, and that the two-dimensional random field Ising model near criticality is a suitable model for describing the metal and insulator patches of VO$_2$ down to scales that approach the unit cell.

cond-mat.str-el↗

arXiv2025

Effects of Interactions and Defect Motion on Ramp Reversal Memory in Locally Phase Separated Materials

The ramp-reversal memory (RRM) effect in metal-insulator transition metal oxides (TMOs), a non-volatile resistance change induced by repeated temperature cycling, has attracted considerable interest in neuromorphic computing and non-volatile memory devices. Our previously introduced defect motion model successfully explained RRM in vanadium dioxide (VO$_2$), capturing observed critical temperature shifts and memory accumulation throughout the sample. However, this approach lacked interactions between metallic and insulating domains, whereas the RRM only appears when TMOs are brought into the metal-insulator coexistence regime. Here, we extend our model by combining the Random Field Ising Model with defect diffusion-segregation, thereby enabling accurate hysteresis modeling while predicting the relationship between RRM and domain interactions. Our simulations demonstrate that maximum RRM occurs when the turnaround temperature approaches the warming branch inflection point, consistent with experimental observations on VO$_2$. Most significantly, we find that increasing nearest-neighbor interactions enhances the maximum memory effect, thus providing a clear mechanism for optimizing RRM performance. Since our model employs minimal assumptions, we predict that RRM should be a widespread phenomenon in materials exhibiting patterned phase coexistence of electronic domains. This work not only advances fundamental understanding of memory behavior in TMOs but also establishes a much-needed theoretical framework for optimizing device applications.

cond-mat.mtrl-sci↗

arXiv2022

Deep Learning Hamiltonians from Disordered Image Data in Quantum Materials

The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate pattern formation on the observable surface. This rich spatial structure contains information about interactions, dimensionality, and disorder -- a spatial encoding of the Hamiltonian driving the pattern formation. Image recognition techniques from machine learning are an excellent tool for interpreting information encoded in the spatial relationships in such images. Here, we develop a deep learning framework for using the rich information available in these spatial correlations in order to discover the underlying Hamiltonian driving the patterns. We first vet the method on a known case, scanning near-field optical microscopy on a thin film of VO2. We then apply our trained convolutional neural network architecture to new optical microscope images of a different VO2 film as it goes through the metal-insulator transition. We find that a two-dimensional Hamiltonian with both interactions and random field disorder is required to explain the intricate, fractal intertwining of metal and insulator domains during the transition. This detailed knowledge about the underlying Hamiltonian paves the way to using the model to control the pattern formation via, e.g., tailored hysteresis protocols. We also introduce a distribution-based confidence measure on the results of a multi-label classifier, which does not rely on adversarial training. In addition, we propose a new machine learning based criterion for diagnosing a physical system's proximity to criticality.

cond-mat.str-el↗

arXiv2022

Critical Nematic Correlations Throughout the Doping Range in BSCCO

Charge modulations have been widely observed in cuprates, suggesting their centrality for understanding the high-$T_c$ superconductivity in these materials. However, the dimensionality of these modulations remains controversial, including whether their wavevector is unidirectional or bidirectional, and also whether they extend seamlessly from the surface of the material into the bulk. Material disorder presents severe challenges to understanding the charge modulations through bulk scattering techniques. We use a local technique, scanning tunneling microscopy, to image the static charge modulations on Bi$_{2-z}$Pb$_z$Sr$_{2-y}$La$_y$CuO$_{6+x}$. By comparing the phase correlation length $ξ_{\mathrm{CDW}}$ with the orientation correlation length $ξ_{\mathrm{orient}}$, we show that the charge modulations are more consistent with an underlying unidirectional wave vector. Using cluster techniques, we show that these locally 1D charge modulations are actually a bulk effect resulting from 3D criticality throughout the entire superconducting doping range.

cond-mat.supr-con↗

arXiv2018

Connecting Complex Electronic Pattern Formation to Critical Exponents

Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it pertains to those geometric clusters (defined as connected sets of nearest-neighbor aligned spins) in the context of Ising models. We show how data from surface probes can be used to distinguish whether electronic patterns observed at the surface of a material are confined to the surface, or whether the patterns originate in the bulk. Whereas thermodynamic critical exponents are derived from the behavior of Fortuin-Kasteleyn (FK) clusters, critical exponents can be similarly defined for geometric clusters. We find that these geometric critical exponents are not only distinct numerically from the thermodynamic and uncorrelated percolation exponents, but that they separately satisfy scaling relations at the critical fixed points discussed in the text. We furthermore find that the two-dimensional (2D) cross-sections of geometric clusters in the three-dimensional (3D) Ising model display critical scaling behavior at the bulk phase transition temperature. In particular, we show that when considered on a 2D slice of a 3D system, the pair connectivity function familiar from percolation theory displays more robust critical behavior than the spin-spin correlation function, and we calculate the corresponding critical exponent. We discuss the implications of these two distinct length scales in Ising models. We also calculate the pair connectivity exponent in the clean 2D case. These results extend the theory of geometric criticality in the clean Ising universality classes, and facilitate the broad application of geometric cluster analysis techniques to maximize the information that can be extracted from scanning image probe data in condensed matter systems.

cond-mat.str-el↗

arXiv2018

Classifying surface probe images in strongly correlated electronic systems via machine learning

Scanning probe experiments such as scanning tunneling microscopy (STM) and atomic force microscopy (AFM) on strongly correlated electronic systems often reveal complex pattern formation on multiple length scales. By studying the universal scaling in these images, we have shown in several distinct correlated electronic systems that the pattern formation is driven by proximity to a disorder-driven critical point, revealing a unification of the pattern formation in these materials. As an alternative approach to this image classification problem of novel materials, here we report the first investigation of the machine learning method to determine which underlying physical model is driving pattern formation in a system. Using a neural network architecture, we are able to achieve 97% accuracy on classifying configuration images from three models with Ising symmetry. This investigation also demonstrates that machine learning can capture the implicit universal behavior of a physical system. This broadens our understanding of what machine learning can do, and we expect more synergy between machine learning and condensed matter physics in the future.

cond-mat.str-el↗

arXiv2015

Random Field Driven Spatial Complexity at the Mott Transition in VO2

We report the first application of critical cluster techniques to the Mott metal-insulator transition in vanadium dioxide. We show that the geometric properties of the metallic and insulating puddles observed by scanning near-field infrared microscopy are consistent with the system passing near criticality of the random field Ising model as temperature is varied. The resulting large barriers to equilibrium may be the source of the unusually robust hysteresis phenomena associated with the metal-insulator transition in this system.

cond-mat.str-el↗

arXiv2014

Decoding Spatial Complexity in Strongly Correlated Electronic Systems

Inside the metals, semiconductors, and magnets of our everyday experience, electrons are uniformly distributed throughout the material. By contrast, electrons often form clumpy patterns inside of strongly correlated electronic systems (SCES) such as colossal magnetoresistance materials and high temperature superconductors. In copper-oxide based high temperature superconductors, scanning tunneling microscopy (STM) has detected an electron nematic on the surface of the material, in which the electrons form nanoscale structures which break the rotational symmetry of the host crystal. These structures may hold the key to unlocking the mystery of high temperature superconductivity in these materials, but only if the nematic also exists throughout the entire bulk of the material. Using newly developed methods for decoding these surface structures, we find that the nematic indeed persists throughout the bulk of the material. We furthermore find that the intricate pattern formation is set by a delicate balance among disorder, interactions, and material anisotropy, leading to a fractal nature of the cluster pattern. The methods we have developed can be extended to many other surface probes and materials, enabling surface probes to determine whether surface structures are confined only to the surface, or whether they extend throughout the material.

cond-mat.str-el↗

arXiv2012

Tunable nano Peltier cooling device from geometric effects using a single graphene nanoribbon

Based on the phenomenon of curvature-induced doping in graphene we propose a class of Peltier cooling devices, produced by geometrical effects, without gating. We show how a graphene nanorib- bon laid on an array of curved nano cylinders can be used to create a targeted and tunable cooling device. Using two different approaches, the Nonequlibrium Green's Function (NEGF) method and experimental inputs, we predict that the cooling power of such a device can approach the order of kW/cm2, on par with the best known techniques using standard superlattice structures. The struc- ture proposed here helps pave the way toward designing graphene electronics which use geometry rather than gating to control devices.

cond-mat.mes-hall↗

arXiv2011

Spatial Complexity Due to Incipient Electronic Nematicity in Cuprates

Surface probes such as scanning tunneling microscopy (STM) have detected complex patterns at the nanoscale, indicative of electronic inhomogeneity, in a variety of high temperature superconductors. In cuprates, the pattern formation is associated with the pseudogap phase, a precursor to the high temperature superconducting state. Symmetry breaking (i.e. from C4 to C2) in the form of electronic nematicity has recently been implicated as a unifying theme of the pseudogap phase,[1] however the fundamental physics governing the nanoscale pattern formation has not yet been identified. Here we use universal cluster properties extracted from STM studies of cuprate superconductors in order to identify the fundamental physics controlling the complex pattern formation. We find that the pattern formation is set by a delicate balance between disorder and interactions, leading to a fractal nature of the cluster pattern. The method introduced here may be extended to a variety of surface probes, enabling the direct measurement of the dimension of the phenomenon being studied, in order to determine whether the phenomenon arises from the bulk of the material, or whether it is confined to the surface.

cond-mat.supr-con↗

arXiv2010

Quantum phase transitions in disordered dimerized quantum spin models and the Harris criterion

We use quantum Monte Carlo simulations to study effects of disorder on the quantum phase transition occurring versus the ratio g=J/J' in square-lattice dimerized S=1/2 Heisenberg antiferromagnets with intra- and inter-dimer couplings J and J'. The dimers are either randomly distributed (as in the classical dimer model), or come in parallel pairs with horizontal or vertical orientation. In both cases the transition violates the Harris criterion, according to which the correlation-length exponent should satisfy nu >= 1. We do not detect any deviations from the three-dimensional O(3) universality class obtaining in the absence of disorder (where nu = 0.71). We discuss special circumstances which allow nu<1 for the type of disorder considered here.

cond-mat.str-el↗

arXiv2010

Noise Predictions for STM in Systems with Local Electron Nematic Order

We propose that thermal noise in local stripe orientation should be readily detectable via STM on systems in which local stripe orientations are strongly affected by quenched disorder. Stripes, a unidirectional, nanoscale modulation of electronic charge, are strongly affected by quenched disorder in two-dimensional and quasi-two-dimensional systems. While stripe orientations tend to lock to major lattice directions, dopant disorder locally breaks rotational symmetry. In a host crystal with otherwise $C_4$ rotational symmetry, stripe orientations in the presence of quenched disorder map to the random field Ising model. While the low temperature state of such a system is generally a stripe glass in two dimensional or strongly layered systems, as the temperature is raised, stripe orientational fluctuations become more prevalent. We propose that these thermally excited fluctuations should be readily detectable in scanning tunneling spectroscopy as {\em telegraph noise} in the high voltage part of the local $I(V)$ curves. We predict the spatial, temporal, and thermal evolution of such noise, including the circumstances under which such noise is most likely to be observed. In addition, we propose an in-situ test, amenable to any local scanning probe, for assessing whether such noise is due to correlated fluctuations rather than independent switchers.

cond-mat.str-el↗

arXiv2009

Inward dispersion of the spin excitation spectrum of stripe-ordered La2NiO4+d

Polarized- and unpolarized-neutron scattering measurements of the spin excitation spectrum in the stripe-ordered phase of La2NiO4+d (d = 0.11) are presented. At low energies, the magnetic spectral weight is found to shift anomalously towards the two-dimensional antiferromagnetic wave vector, similar to the low-energy dispersions observed in cuprate superconductors. While spin-wave spectra in stripe phases can exhibit an apparent inward dispersion, we find that the peak shifts measured here cannot be accounted for by this effect. Possible extensions of the model are discussed.

cond-mat.str-el↗

arXiv2009

Magnetic Excitations of Undoped Iron Oxypnictides

We study the magnetic excitations of undoped iron oxypnictides using a three-dimensional Heisenberg model with single-ion anisotropy. Analytic forms of the spin wave dispersion, velocities, and structure factor are given. Aside from quantitative comparisons which can be made to inelastic neutron scattering experiments, we also give qualitative criteria which can distinguish various regimes of coupling strength. The magnetization reduction due to quantum zero point fluctuations shows clear dependence on the c-axis coupling.

cond-mat.supr-con↗

arXiv2008

Low energy spin waves and magnetic interactions in SrFe$_2$As$_2$

We report inelastic neutron scattering studies of magnetic excitations in antiferromagnetically ordered SrFe$_{2}$As$_{2}$ ($T_{N}=220$ K), the parent compound of the FeAs-based superconductors. At low temperatures (T=7 K), the spectrum of magnetic excitations $S(Q,\hbar ω)$ consists of a Bragg peak at the elastic position ($\hbar ω=0$ meV), a spin gap ($ Δ\leq 6.5$ meV), and sharp spin wave excitations at higher energies. Based on the observed dispersion relation, we estimate the effective magnetic exchange coupling using a Heisenberg model. On warming across $T_{N} $, the low temperature spin gap rapidly closes, with weak critical scattering and spin-spin correlations in the paramagnetic state. The antiferromagnetic order in SrFe$_{2}$As$_{2}$ is therefore consistent with a first order phase transition, similar to the structural lattice distortion.

cond-mat.supr-con↗

arXiv2008

Incompatibility of modulated checkerboard patterns with the neutron scattering resonance peak in cuprate superconductors

Checkerboard patterns have been proposed in order to explain STM experiments on the cuprates BSCCO and Na-CCOC. However the presence of these patterns has not been confirmed by a bulk probe such as neutron scattering. In particular, simple checkerboard patterns are inconsistent with neutron scattering data, in that they have low energy incommsensurate (IC) spin peaks rotated 45 degrees from the direction of the charge IC peaks. However, it is unclear whether other checkerboard patterns can solve the problem. In this paper, we have studied more complicated checkerboard patterns ("modulated checkerboards") by using spin wave theory and analyzed noncollinear checkerboards as well. We find that the high energy response of the modulated checkerboards is inconsistent with neutron scattering results, since they fail to exhibit a resonance peak at (pi,pi), which has recently been shown to be a universal feature of cuprate superconductors. We further argue that the newly proposed noncollinear checkerboard also lacks a resonance peak. We thus conclude that to date no checkerboard pattern has been proposed which satisfies both the low energy constraints and the high energy constraints imposed by the current body of experimental data in cuprate superconductors.

cond-mat.supr-con↗

arXiv2007

d+id'-wave Superconducting States in Graphene

We show that effective superconducting orders generally emerge at low energy in the superconducting state of graphene with conventionally defined pairing symmetry . We study such a particular interesting example, the $d_{x^2-y^2}+id'_{xy}$ spin singlet pairing superconducting state in graphene, which can be generated by electronic correlation as well as induced through a proximity effect with a d-wave superconductor. We find that effectively the d-wave state is a state with mixed s-wave and exotic $p+ip$-wave pairing orders at low energy. This remarkable property leads to distinctive superconducting gap functions and novel behavior of the Andreev conductance spectra.

cond-mat.mes-hall↗

arXiv2007

The Luttinger liquid kink

Although the Tomonaga-Luttinger liquid exhibits spin-charge separation and the electron is not an elementary excitation of the system, nevertheless an effective electronic dispersion may be defined by the frequency-dependent peak in the momentum distribution curve (MDC). The MDC is defined by considering the single hole spectral function $A^<(\vec{k},ω)$ as a function of $\vec{k}$ at a fixed frequency $ω$. We show the existence of a \emph{kink} in this dispersion for the spin-rotationally invariant Tomonaga-Luttinger liquid at finite temperature. In the repulsive regime where the charge velocity $v_{c}$ is greater than the spin velocity $v_{s}$, the low frequency effective electronic dispersion is linear in $\vec{k}$ and follows a velocity $v_l$ between the spin and charge velocities, $v_s < v_l < v_c$. The high frequency part (which is also linear in $\vec{k}$) disperses with the charge velocity $v_c$. The energy scale of the crossover between the two velocities defines a kink, $E_{\rm kink}$. In addition, the high energy dispersion extrapolates to the Fermi energy at a wavevector $k_{ex} \ne k_F$ which is shifted from the Fermi wavevector. The presence of such a kink is measurable with, {\em e.g.}, angle-resolved photoemission experiments, and may be used to test for the presence of Luttinger liquid behavior in systems in which the separate contributions from spin and charge to the MDC are not discernible due to strong interactions or low experimental resolution.

cond-mat.str-el↗