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DOE OSTI2023

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 timescales. 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 V⁢O 2 . We then apply our trained convolutional neural network architecture to new optical microscope images of a different V⁢O 2 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 for using the model to control the pattern formation via, e.g., tailored hysteresis protocols. Finally, we also introduce a distribution-based confidence measure on the results of a multilabel classifier, which does not rely on adversarial training. In addition, we propose a machine-learning-based criterion for diagnosing a physical system's proximity to criticality.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Imitation of spin density wave order in Cu 3 Nb 2 O 8

Spin density waves, based on modulated local moments, are usually associated with metallic materials, but have recently been reported in insulators which display coupled magnetic and structural order parameters. Here, we discuss one such example, the multiferroic Cu 3 Nb 2 O 8 , which is reported to undergo two magnetic phase transitions, first to an unknown antiferromagnetic phase at $T_N$ ≈ 26.5 K , and then to a helicoidal structure coupled to an electric polarization below $T_2$ ≈ 24 K which breaks the crystallographic inversion symmetry. By analogy with other complex oxides, one might naturally expect this intermediate phase to be a spin density wave phase. We apply spherical polarimetry to confirm the low-temperature magnetic structure, yet only observe a single magnetic phase transition to helicoidal order. We argue that the reported unknown phase actually supports an imitation spin density wave which originates from a decoupling of the components of the magnetic order parameter, as allowed by symmetry and driven by thermal fluctuations. This provides a mechanism for the magnetic, but not nuclear, structure to break inversion symmetry thereby creating an intermediate phase in the proximity of $T_N$ which imitates a spin density wave. As the temperature is reduced, this intermediate structure destabilizes the crystal such that a structural chirality is induced, as reflected by the emergence of the electric polarization, and the imitation spin density wave relaxes into a generic helicoid. This scenario in which critical fluctuations allow the magnetic structure to break inversion symmetry while the crystal structure remains centrosymmetric might be relevant to other complex multiferroics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Predicting the superconducting critical temperature in transition metal carbides and nitrides using machine learning

Transition metal carbides and nitrides have unique mechanical and chemical characteristics. At low temperatures many of them also exhibit superconductivity, which can be controlled by substitutions into both the transition metal and carbon/nitrogen sites. To investigate the factors governing the superconducting state, we apply machine learning methods. Here we collected a dataset containing 147 materials, which was used to create a pipeline for predicting their superconducting critical temperature. When this pipeline is applied to a randomly selected test set, it shows a good performance, with of 0.82 and RMSE of 1.9 K. To explore the limits of the machine learning approach, we also use it to predict entire substitution series within the dataset. This represents a realistic test for the predictive models, which can be extremely useful when applied to new substitutions in materials systems. The performance of the pipeline in this case is much more uneven, with good predictions for some series, while for others the model shows minimal predictive power. We discuss possible reasons for these results, as well as methods to estimate the performance of machine learning on new substitution series.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Density functionals combined with van der Waals corrections for graphene adsorbed on layered materials

Standard density functionals like Perdew-Burke-Ernzerhof (PBE) or Strongly Constrained and Appropriately Normed (SCAN) need a correction to account for long-range van der Waals (vdW) interaction. The damped Zaremba-Kohn model (dZK) starts from a formula for the vdW interaction of a distant atom with a solid surface, both with known dielectric properties, damps this formula at short range, and then treats an adsorbed molecule or atomic layer as a collection of renormalized atoms. Here, we extend this model to graphene adsorbed on semiconducting layered materials [bulk graphite and hBN, and multilayer transition metal dichalcogenides (TMD)] by including the C 4 asymptotic term and multiple electrostatic image effects due to the two surfaces of the substrate slabs in the vdW calculations. The resulting SCAN-vdW-dZK and PBE-vdW-dZK give approximately the same results for the systems considered here, in agreement with available reference values. The predicted binding energies are roughly 25% lower than those from SCAN+rVV10 (revised Vydrov and Van Voorhis 2010), and ~15% lower than those from PBE+rVV10. Since SCAN+rVV10 usually overbinds, the predicted binding energies by SCAN-vdW-dZK and PBE-vdW-dZK are expected to be closer to the true values. The predicted equilibrium binding distances from SCAN-vdW-dZK and PBE-vdW-dZK are slightly larger (~ 0.1 Å) than those from SCAN+rVV10, and close to those from SCAN. The binding energy depends upon the number of substrate layers more strongly in vdW-dZK than in rVV10. The C 4 -term contributions can be 40% of the total vdW interactions, and the C 5 term contributes about 10%. The effects of images and the back surfaces of slabs can contribute about 4–10%. The vdW interaction energy power laws from the vdW-dZK model for graphene adsorbed on multilayer MoS 2 show slowly varying decay to the pairwise exponent –4 with increasing separation $\textit{D}$, very similar to those obtained from the random-phase approximation and renormalization group approaches by Ambrosetti et al. Both the PBE-vdW-dZK and SCAN-vdW-dZK give a greater increase in interlayer binding energy when the TMD substrate changes from monolayer to four-layer for the graphene/TMD adsorption systems. This is consistent with the relevant electron-energy-loss spectroscopy experimental results showing increased dielectric response from the substrate with increasing substrate layer number.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Absence of bulk charge density wave order in the normal state of UTe 2

A spatially modulated superconducting state, known as pair density wave (PDW), is a tantalizing state of matter with unique properties. Recent scanning tunneling microscopy (STM) studies revealed that spin-triplet superconductor UTe 2 hosts an unprecedented spin-triplet, multi-component PDW whose three wavevectors are indistinguishable from a preceding charge-density wave (CDW) order that survives to temperatures well above the superconducting critical temperature, T c . Whether the PDW is the mother or a subordinate order remains unsettled. Here, based on a systematic search for bulk charge order above T c using resonant elastic X-ray scattering (REXS), we show that the structure factor of charge order previously identified by STM is absent in the bulk within the sensitivity of REXS. Our results invite two scenarios: either the density-wave orders condense simultaneously at T c in the bulk, in which case PDW order is likely the mother phase, or the charge modulations are restricted to the surface.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Unified ab initio description of Fröhlich electron-phonon interactions in two-dimensional and three-dimensional materials

Ab initio calculations of electron-phonon interactions including the polar Fröhlich coupling have advanced considerably in recent years. The Fröhlich electron-phonon matrix element is by now well understood in the case of bulk three-dimensional (3D) materials. In the case of two-dimensional (2D) materials, the standard procedure to include Fröhlich coupling is to employ Coulomb truncation, so as to eliminate artificial interactions between periodic images of the 2D layer. While these techniques are well established, the transition of the Fröhlich coupling from three to two dimensions has not been investigated. Furthermore, it remains unclear what error one makes when describing 2D systems using the standard bulk formalism in a periodic supercell geometry. In this work, we generalize previous work on the ab initio Fröhlich electron-phonon matrix element in bulk materials by investigating the electrostatic potential of atomic dipoles in a periodic supercell consisting of a 2D material and a continuum dielectric slab. We obtain a unified expression for the matrix element, which reduces to the existing formulas for three-dimensional and 2D systems when the interlayer separation tends to zero or infinity, respectively. This expression enables an accurate description of the Fröhlich matrix element in 2D systems without resorting to Coulomb truncation. We validate our approach by direct ab initio density-functional perturbation theory calculations for monolayer BN and MoS 2 , and we provide a simple expression for the 2D Fröhlich matrix element that can be used in model Hamiltonian approaches. The formalism outlined in this work may find applications in calculations of polarons, quasiparticle renormalization, transport coefficients, and superconductivity, in 2D and quasi-2D materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Discovery and Investigation of Topological Superconductivity

During the period of the grant DOE DESC0014335, the PI worked on a range of material systems from the triplet superconductor UTe 2 to Sr 2 RuO 4 and superconductivity in Weyl semimetals. DOE funding has resulted in a total of nine papers. Papers have been published in the following journals: Nature, Science, PNAS, Nature Physics, Nature Communications, Phys. Rev. B, and npj Quantum materials. No funds are expected to remain at the end of this project. Below is a description of our scientific findings during this period.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Use of Refractory-Volatile Element Deep Eutectic Regions to Grow Single Crystalline Intermetallic Compounds

Compounds containing both refractory and volatile elements present a unique challenge for crystal growth, given the conflicting realities of high melting temperatures and high vapor pressures. Nevertheless, the discovery of superconductivity in FeAs and FeSe based materials and a Weyl semimetal state in TaP are motivations to explore compounds containing such pairs. Here, we discuss use of the low-melting single phase liquid regions above deep M-X eutectics (M=transition metal, X=P, S) as the basis for high temperature solutions for growing intermetallic compounds containing volatile-refractory pairs. We show that Ni-P, Pd-P, Pt-P, and Pd-S compositions form single phase melts at moderate temperatures below 1000 °C and with minimal vapor pressure. We first present the simple case of growing Ni 2 P from Ni-P and next discuss the more complicated growth of RPd 3 S 4 (R=La, Ce, Nd, Eu) from a Pd-S melt. We show how frit-disc alumina crucible sets allow for contamination-free capture of decanted liquid and its reuse in subsequent experiments, demonstrating a fractionation of the CePd 3 S 4 growth to determine the optimal conditions for crystal growth. We conclude by using the single phase liquid regions above the Pt-P and Pd-P eutectics to grow single crystals of MPt 5 P (M=Mn, Fe) and MnPd 5 P. As these materials have primarily been studied in polycrystalline form, we give an overview of the magnetic and transport properties of our single crystals. The examples outlined here illustrate the utility of using the single phase liquid above deep metal-X eutectics for solution growth and materials discovery.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Understanding the Reactions Between Fe and Se Binary Diffusion Couples

Spurred by recent discoveries of high-temperature superconductivity in Fe-Se based materials, the magnetic, electronic, and catalytic properties of iron-chalcogenides have drawn significant attention. Furthermore, much remains to be understood about the sequence of phase formation in these systems. In this work, we shed light on this issue by preparing a series of binary Fe-Se ultrathin diffusion couples via designed thin film precursors and investigating their structural evolution as a function of composition and annealing temperature. Two previously unreported Fe-Se phases crystallized during the deposition process on a nominally room-temperature Si substrate in the 27-33% and 37-47% Fe (atomic percent) composition regimes. Both phases completely decompose after annealing to 200°C in a nitrogen glovebox. At higher temperatures, the sequence of phase formation is governed by Se loss in the annealing process, consistent with what would be expected from the phase diagram. Films rich in Fe (53-59% Fe) crystalized during deposition as β-FeSe (P4/nmm) with preferred c-axis orientation to the amorphous SiO 2 substrate surface, providing a means to non-epitaxial self-assembly of crystallographically aligned, iron-rich β-FeSe for future research. Our findings suggest the crystallization of binary Fe-Se compounds at room temperature via near diffusionless transformations should be a significant consideration in future attempts to prepare metastable ternary and higher order compounds containing Fe and Se.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Straintronic Effect on Phonon-Mediated Superconductivity of Nb 2 CT 2 (T = O, S, Se, or Te) MXenes

Here, the electronic structures, phonon dispersions, and electron–phonon coupling of Nb 2 CT 2 (T = O, S, Se, or Te) MXenes were investigated via first-principles calculations. Different models of Nb 2 CT 2 were constructed, and the results show that the low-energy models of Nb 2 CT 2 are intrinsic phonon-mediated superconductors. Of the four Nb 2 CT 2 MXenes, Nb 2 CO 2 MXene exhibits the largest superconducting critical temperature ($T_c$) of 14.43 K. The existence of soft modes induced by Kohn anomalies and the contribution of Nb atoms to the Fermi level lead to strong electron–phonon coupling (λ = 0.92) in Nb 2 CO 2 MXene. The $T_c$ of Nb 2 CO 2 is further enhanced by biaxial tensile strain and reaches up to 18.28 K under 4% tensile strain. The predicted $T_c$ of Nb 2 CS 2 is 4.5 K, which is comparable with experimental data. These findings will further stimulate the search for superconducting MXenes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Make Selenium Reactive Again: Activating Elemental Selenium for Synthesis of Metal Selenides Ranging from Nanocrystals to Large Single Crystals

The inertness of elemental selenium is a significant obstacle in the synthesis of selenium-containing materials at low reaction temperatures. Over the years, several recipes have been developed to overcome this hurdle; however, most of the methods are associated with the use of highly toxic, expensive, and environmentally harmful reagents. As such, there is an increasing demand for the design of cheap, stable, and nontoxic reactive selenium precursors usable in the low-temperature synthesis of transition metal selenides with vast applications in nanotechnology, thermoelectrics, and superconductors. Herein, a novel synthetic route has been developed for activating elemental selenium by using a solvothermal approach. By comprehensive 77 Se NMR, Raman, and infrared spectroscopies and gas chromatography–mass spectrometry, we show that the activated Se solution contained HSe – , [Se–Se] 2– , and Se 2– ions, as well as dialkyl selenide (R 2 Se) and dialkyl diselenide (R–Se–Se–R) species in dynamic equilibrium. This also corresponded to the first observation of naked Se 2 2– in solution. The versatility of the developed Se precursor was demonstrated by the successful synthesis of (i) the polycrystalline room-temperature modification of the β-Ag 2 Se thermoelectric material; (ii) large single crystals of superconducting β-FeSe; (iii) CdSe nanocrystals with different particle sizes (3–10 nm); (iv) nanosheets of PtSe 2 ; and (v) mono- and dibenzyl selenides and diselenides at room temperature. In conclusion, The simplicity and diversity of the developed Se activation method holds promise for applied and fundamental research.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Quantum interference of currents in an atomtronic SQUID

Quantum interference of currents is the most important and well known quantum phenomenon in a conventional superconducting quantum interference device (SQUID). Here, we report the observation of quantum interference of currents in an atomtronic SQUID. Analogous to a conventional SQUID, currents flowing through two junctions in an atomtronic SQUID interfere due to the phase difference from rotation. This interference results in modulation of critical currents. This modulation was observed for three different radii with clear modulation periods which were measured to be consistent with fundamental rotation rates. This observation shows the possibility of studying various interesting SQUID physics with an atomtronic SQUID and especially, macroscopic quantum phenomena with currents may be realized with an atomtronic SQUID toward the goal of quantum metrology of rotation sensing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Spatially dispersing Yu-Shiba-Rusinov states in the unconventional superconductor FeTe 0.55 Se 0.45

By using scanning tunneling microscopy (STM) we find and characterize dispersive, energy-symmetric in-gap states in the iron-based superconductor FeTe 0.55 Se 0.45 , a material that exhibits signatures of topological superconductivity, and Majorana bound states at vortex cores or at impurity locations. We use a superconducting STM tip for enhanced energy resolution, which enables us to show that impurity states can be tuned through the Fermi level with varying tip-sample distance. We find that the impurity state is of the Yu-Shiba-Rusinov (YSR) type, and argue that the energy shift is caused by the low superfluid density in FeTe 0.55 Se 0.45 , which allows the electric field of the tip to slightly penetrate the sample. We model the newly introduced tip-gating scenario within the single-impurity Anderson model and find good agreement to the experimental data.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Theory of optical responses in clean multi-band superconductors

Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a dirty-limit theory by Mattis and Bardeen for over 60 years. Here we show, by investigating the selection rules imposed by particle-hole symmetry and unitary symmetries, that intrinsic momentum-conserving optical excitations can occur in clean multi-band superconductors when one of the following three conditions is satisfied: (i) inversion symmetry breaking, (ii) symmetry protection of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling with unbroken time reversal and inversion symmetries. This result indicates that clean-limit optical responses are common beyond the straightforward case of broken inversion symmetry. We apply our theory to optical responses in FeSe, a clean multi-band superconductor with inversion symmetry and significant spin-orbit coupling. This result paves the way for studying clean-limit superconductors through optical measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Unconventional supercurrent phase in Ising superconductor Josephson junction with atomically thin magnetic insulator

Abstract In two-dimensional (2D) NbSe 2 crystal, which lacks inversion symmetry, strong spin-orbit coupling aligns the spins of Cooper pairs to the orbital valleys, forming Ising Cooper pairs (ICPs). The unusual spin texture of ICPs can be further modulated by introducing magnetic exchange. Here, we report unconventional supercurrent phase in van der Waals heterostructure Josephson junctions (JJs) that couples NbSe 2 ICPs across an atomically thin magnetic insulator (MI) Cr 2 Ge 2 Te 6 . By constructing a superconducting quantum interference device (SQUID), we measure the phase of the transferred Cooper pairs in the MI JJ. We demonstrate a doubly degenerate nontrivial JJ phase ( ϕ ), formed by momentum-conserving tunneling of ICPs across magnetic domains in the barrier. The doubly degenerate ground states in MI JJs provide a two-level quantum system that can be utilized as a new dissipationless component for superconducting quantum devices. Our work boosts the study of various superconducting states with spin-orbit coupling, opening up an avenue to designing new superconducting phase-controlled quantum electronic devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Charge-neutral fermions and magnetic field-driven instability in insulating YbIr 3 Si 7

Kondo lattice materials, where localized magnetic moments couple to itinerant electrons, provide a very rich backdrop for strong electron correlations. They are known to realize many exotic phenomena, with a dramatic example being recent observations of quantum oscillations and metallic thermal conduction in insulators, implying the emergence of enigmatic charge-neutral fermions. Here, we show that thermal conductivity and specific heat measurements in insulating YbIr 3 Si 7 reveal emergent neutral excitations, whose properties are sensitively changed by a field-driven transition between two antiferromagnetic phases. In the low-field phase, a significant violation of the Wiedemann-Franz law demonstrates that YbIr 3 Si 7 is a charge insulator but a thermal metal. In the high-field phase, thermal conductivity exhibits a sharp drop below 300 mK, indicating a transition from a thermal metal into an insulator/semimetal driven by the magnetic transition. These results suggest that spin degrees of freedom directly couple to the neutral fermions, whose emergent Fermi surface undergoes a field-driven instability at low temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Anomalous transverse resistance in the topological superconductor β-Bi2Pd

Abstract A supercurrent flowing in a superconductor meets no resistance. Yet an electric field may still be established within the superconductor in the presence of dissipative processes, such as vortex motion. Here we report the observation of a transverse voltage drop in superconducting β- Bi 2 Pd thin films. Unlike the Hall effect in general or in other superconductors, the sign of the observed transverse voltage does not depend on the external magnetic field. Instead, it is dictated by the broken inversion symmetry on the film interfaces. This anomalous transverse voltage, or transverse resistance, is indicative of a chirality that likely resonates with the topological surface states reported in β- Bi 2 Pd.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Discovery of conjoined charge density waves in the kagome superconductor CsV3Sb5

Abstract The electronic instabilities in CsV 3 Sb 5 are believed to originate from the V 3 d -electrons on the kagome plane, however the role of Sb 5 p -electrons for 3-dimensional orders is largely unexplored. Here, using resonant tender X-ray scattering and high-pressure X-ray scattering, we report a rare realization of conjoined charge density waves (CDWs) in CsV 3 Sb 5 , where a 2 × 2 × 1 CDW in the kagome sublattice and a Sb 5 p -electron assisted 2 × 2 × 2 CDW coexist. At ambient pressure, we discover a resonant enhancement on Sb L 1 -edge (2 s →5 p ) at the 2 × 2 × 2 CDW wavevectors. The resonance, however, is absent at the 2 × 2 × 1 CDW wavevectors. Applying hydrostatic pressure, CDW transition temperatures are separated, where the 2 × 2 × 2 CDW emerges 4 K above the 2 × 2 × 1 CDW at 1 GPa. These observations demonstrate that symmetry-breaking phases in CsV 3 Sb 5 go beyond the minimal framework of kagome electronic bands near van Hove filling.

36 MATERIALS SCIENCE↗