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DOE OSTI2020

First-principles calculation of the configurational energy density of states for a solid-state ion conductor with a variant of the Wang and Landau algorithm

In this work, a variant of the Wang and Landau algorithm for calculation of the configurational energy density of states is proposed. The algorithm was developed for the purpose of using first-principles simulations, such as density functional theory, to calculate the partition function of disordered sublattices in crystal materials. The expensive calculations of first-principles methods make a parallel algorithm necessary for a practical computation of the configurational energy density of states within a supercell approximation of a solid-state material. The algorithm developed in this work is tested with the two-dimensional (2d) Ising model to bench mark the algorithm and to help provide insight for implementation to a materials science application. Tests with the 2d Ising model revealed that the algorithm has good performance compared to the original Wang and Landau algorithm and the 1/$\textit{t}$ algorithm, in particular the short iteration performance. Further, a proof of convergence is presented within an adiabatic assumption, and the analysis is able to correctly predict the time dependence of the modification factor to the density of states. The algorithm was then applied to the lithium and lanthanum sublattice of the solid-state lithium ion conductor Li 0.5 La 0.5 TiO 3 . This was done to help understand the disordered nature of the lithium and lanthanum. The results find, overall, that the algorithm performs very well for the 2d Ising model and that the results for Li 0.5 La 0.5 TiO 3 are consistent with experiment while providing additional insight into the lithium and lanthanum ordering in the material. The primary result is that the lithium and lanthanum become more mixed between layers along the c axis for increasing temperature. In part, the simulation of the disordered Li 0.5 La 0.5 TiO 3 system serves as a benchmark for what size systems are currently and in the near future practical to calculate with density functional theory methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Melting of spatially modulated phases at domain wall/surface junctions in antiferrodistortive multiferroics

A physical understanding of the nature of spatially modulated phases (SMPs) in rare-earth-doped antiferrodistortive (AFD) multiferroics and how they behave close to surfaces and interfaces is lacking. Here the emergence of the antiferroelectric (AFE), ferroelectric (FE), or ferrielectric (AFE-FE) spatial modulation in the vicinity of the morphotropic phase transition in La x Bi 1 – x Fe O 3 ( x ~ 0.2 ) is explored on the atomic level using high-resolution scanning transmission electron microscopy (HRSTEM). The suppression, or “melting,” of the AFE-type SMP in the vicinity of the AFD twin wall/surface junction is revealed by HRSTEM in La 0.22 Bi 0.78 Fe O 3 films and explained by the hybrid approach combining Landau-Ginzburg-Devonshire (LGD) phenomenology and the semimicroscopic four-sublattice model (FSM). The LGD-FSM approach reduces the problem of AFE (or AFE-FE) SMP emergence and stability to the thermodynamic analysis of the free-energy functional with AFE, FE, and AFD long-range order parameters and two master parameters: the FE-AFE coupling strength between four neighboring A sites and the nonstoichiometry factor, which are proportional to the variations of La concentration in La x Bi 1 – x Fe O 3 films. Finally, we establish that the surface-induced melting of SMPs and the associated broadening of AFE AFD domain walls minimize the film free energy under certain conditions imposed on the master parameters and gradient energy below the critical value. The observed behavior provides insight into the origin of SMPs in AFD multiferroics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Topological symplectic Kondo effect

Multiple conduction channels interacting with a quantum impurity—a spin in the conventional “multichannel Kondo effect” or a topological mesoscopic device (“topological Kondo effect”)—has been proposed as a platform to realize anyonic quasiparticles. However, the above implementations require either perfect channel symmetry or the use of Majorana fermions. Here, in this work, we propose a Majorana-free mesoscopic setup which implements the Kondo effect of the symplectic Lie group and can harbor emergent anyons (including Majorana fermions, Fibonacci anyons, and parafermions) even in the absence of perfect channel symmetry. In addition to the detailed prescription of the implementation, we present the strong coupling solution by mapping the model to the multichannel Kondo effect associated to an internal symmetry and exploit conformal field theory to predict the nontrivial scaling of a variety of observables, including conductance, as a function of temperature. This work does not only open the door for robust Kondo-based anyon platforms, but also sheds light on the physics of strongly correlated materials with competing order parameters.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

$\testit{d}$-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals

In this work, we uncover the properties of complex tensor ($\textit{d}$-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-$\frac{3}{2}$ fermions at a fourfold linear band-crossing point. Although the general theory of $\textit{d}$-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-$\frac{3}{2}$ nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a complex second-rank tensor order parameter. In the case of linear dispersion, for the chemical potential at the Fermi point and at strong coupling, the energetically preferred superconducting state is the uniaxial nematic state, which preserves time-reversal symmetry and provides a full (anisotropic) gap for quasiparticle excitations. In contrast, at a finite chemical potential, we find that the usual weak-coupling instability is toward the “cyclic state,” well known from the studies of multicomponent Bose-Einstein condensates, which breaks time-reversal symmetry maximally, has vanishing average value of angular momentum, and features 16 small Bogoliubov-Fermi surfaces. The Rarita-Schwinger-Weyl semimetals provide therefore the first example of weakly coupled, three-dimensional, isotropic $\textit{d}$-wave superconductors where the $\textit{d}$-wave superconducting phase is uniquely selected by the quartic expansion of the mean-field free energy, and is not afflicted by the accidental degeneracy first noticed by Mermin over 40 years ago. We discuss the appearance and stability of the Bogoliubov-Fermi surfaces in absence of inversion symmetry in the electronic Hamiltonian, as in the case at hand.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Semimetal–Mott insulator quantum phase transition of the Hubbard model on the honeycomb lattice

We take advantage of recent improvements in the grand canonical hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of U c /κ = 3.834(14) and the critical exponent zν = 1.185(43). Under the assumption that this corresponds to the expected antiferromagnetic Mott transition, we are also able to provide a preliminary estimate β = 1.095(37) for the critical exponent of the order parameter. We consider our findings in view of the SU(2) Gross-Neveu, or chiral Heisenberg, universality class. Here, we also discuss the computational scaling of the hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Atomic-scale visualization of a cascade of magnetic orders in the layered antiferromagnet GdTe3

Abstract GdTe 3 is a layered antiferromagnet which has attracted attention due to its exceptionally high mobility, distinctive unidirectional incommensurate charge density wave (CDW), superconductivity under pressure, and a cascade of magnetic transitions between 7 and 12 K, with as yet unknown order parameters. Here, we use spin-polarized scanning tunneling microscopy to directly image the charge and magnetic orders in GdTe 3 . Below 7 K, we find a striped antiferromagnetic phase with twice the periodicity of the Gd lattice and perpendicular to the CDW. As we heat the sample, we discover a spin density wave with the same periodicity as the CDW between 7 and 12 K; the viability of this phase is supported by our Landau free energy model. Our work reveals the order parameters of the magnetic phases in GdTe 3 and shows how the interplay between charge and spin can generate a cascade of magnetic orders.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Valley magnetism, nematicity, and density wave orders in twisted bilayer graphene

We analyze density wave and Pomeranchuk orders in twisted bilayer graphene. This complements our earlier analysis of the pairing instabilities. We assume that near half filling of either conduction or valence band, the Fermi level is close to Van Hove points, where the density of states diverges, and study potential instabilities in the particle-hole channel within a patch model with two valley degrees of freedom. The hexagonal symmetry of twisted bilayer graphene allows for either six or twelve Van Hove points. We consider both cases and find the same two leading candidates for particle-hole order. One is an SU(2)-breaking spin state with ferromagnetism within a valley. A subleading intervalley hopping induces antiferromagnetism between the valleys. The same state has also been obtained in strong-coupling approaches, indicating that this order is robust. Here, the other is a mixed state with 120° complex spin order and orthogonal complex charge order. In addition, we find a weaker but still attractive interaction in nematic channels, and discuss the type of a nematic order.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Order-Disorder Transitions in ( Ca x Sr 1 - x ) 3 Rh 4 Sn 13

The classification of structural phase transitions as displacive or order-disorder in character is usually based on spectroscopic data above the transition. Here, we use single crystal x-ray diffraction to investigate structural correlations in the quasiskutterudites, (Ca x Sr 1-x ) 3 Rh 4 Sn 13 , which have a quantum phase transition at x ~ 0.9. Three-dimensional pair distribution functions show that the amplitudes of local atomic displacements are temperature independent below the transition and persist to well above the transition, a signature of order-disorder behavior. The implications for the associated electronic transitions are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene

In conventional superconductors, Cooper pairing occurs between electrons of opposite spin. We observe spin-polarized superconductivity in Bernal bilayer graphene when doped to a saddle-point van Hove singularity generated by a large applied perpendicular electric field. We observe a cascade of electrostatic gate-tuned transitions between electronic phases distinguished by their polarization within the isospin space defined by the combination of the spin and momentum-space valley degrees of freedom. Although all of these phases are metallic at zero magnetic field, we observe a transition to a superconducting state at finite magnetic field B ∥ ≈ 150 milliteslas applied parallel to the two-dimensional sheet. Superconductivity occurs near a symmetry-breaking transition and exists exclusively above the B ∥ limit expected of a paramagnetic superconductor with the observed transition critical temperature T C ≈ 30 millikelvins, consistent with a spin-triplet order parameter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Disorder-dependent slopes of the upper critical field in nodal and nodeless superconductors

In this work we study the slopes of the upper critical field S = ∂H c2 /∂T at the superconducting transition temperature T c in anisotropic superconductors with transport (nonmagnetic) scattering employing the Ginzburg-Landau theory, developed for this case by Pokrovsky and Pokrovsky [Phys. Rev. B 54, 13275 (1996)]. We find unexpected behavior of the slopes for a d -wave superconductor and, in a more general case, of materials with line nodes in the order parameter. Specifically, the presence of line nodes causes S to decrease with increasing nonmagnetic scattering parameter P = ℏ/2πT c0 τ (T c0 is for the clean limit, τ is the scattering time), unlike the nodeless case where the slope increases. In a pure d -wave case, the slope changes from decreasing to increasing when the scattering parameter approaches P ≈ 0.91 P crit , where P crit ≈ 0.28, at which T c → 0, which implies the existence of a “gapless” state in d -wave superconductors with transport scattering in the interval, 0.91 P crit < P < P crit . Furthermore, we consider the mixed (s + d)-wave order parameter with four nodes on a cylindrical Fermi surface when the d part is dominant, or no nodes at all when the s-wave phase dominates. We find that the presence of nodes causes the slope S(P) to decrease initially with increasing P, whereas in the nodeless state, S(P) monotonically increases. Therefore, relatively straightforward measurements of the disorder dependence of the slope of H c2 at T c can help distinguish between nodal and nodeless order parameters, which is particularly useful for quickly assessing newly discovered superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Observation of broken inversion and chiral symmetries in the pseudogap phase in single- and double-layer bismuth-based cuprates

We deduce the symmetry of the pseudogap phase in the single- and double-layer bismuth-based cuprate superconductors, where charge and pseudogap order onset concurrently, by measuring and analyzing their circular and linear photogalvanic responses, which are related linearly to the chirality and inversion breaking, respectively, of the order parameter. After separating out the trivial contribution arising from the surface where inversion symmetry is already broken, we show that both responses start below the pseudogap temperature T* and grow below it to a sizable magnitude, revealing the broken symmetries in the bulk of the crystal. Through a detailed analysis of the dependence of the signals on the angle of incidence, the polarization of the light, and the orientation of the crystal, we are able to discover that the point group symmetry below T* is limited to mm2 or mm21– groups. Here, taking into account formation of domains and previous measurements, our results narrow down the possible symmetries of the microscopic origin of the phase transition(s) at T*, which leads to the conclusion that while charge order may affect the observed symmetry it is not the main cause of the pseudogap order parameter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Detecting thermodynamic phase transition via explainable machine learning of photoemission spectroscopy

Identifying thermodynamic signatures of electronic phases, such as superconductivity, is challenging in low-dimensional materials due to strong fluctuations and low probing volume. Spectroscopic methods are often used to identify new bulk phases, but their main measurable quantity—electronic energy gaps—is no longer an effective order parameter in low-dimensional and fluctuating systems. Combining angle-resolved photoemission with a domain-adversarial neural network, we report a data-driven method to identify thermodynamic phase transitions solely based on single-particle spectra. We demonstrate 97.6% accuracy in cuprate superconductor Bi 2 Sr 2 CaCu 2 O 8+δ with strong superconducting fluctuations. This model notably compensates for the scarcity of experimental data by leveraging virtually inexhaustible simulated data. Further, its explainability reveals the crucial role of in-gap spectral weight in detecting phase fluctuations and thermodynamic transitions. Our work pinpoints the spectroscopic signatures of fluctuating orders and enables using spectroscopy for machine-learning-assisted material discovery for low-dimensional and strong coupling systems.

2D materials↗

DOE OSTI2021

Octahedral rotations in Ruddlesden-Popper layered oxides under pressure from first principles

The combination of reduced dimensionality and tunable structural distortions in layered perovskite oxides makes these materials ideal platforms for designing novel properties and functionalities. One example is hybrid improper ferroelectricity in n = 2 Ruddlesden-Popper oxides, where the combination of a layered crystal structure and rotations of the metal-oxide octahedra break symmetry and induce a polarization. Precisely controlling the octahedral rotation distortions, for example by the application of hydrostatic pressure, provides a pathway to tune and optimize the properties of these materials. Here we combine group theoretic methods, density functional theory calculations, and Landau theory analysis to investigate how octahedral rotations respond to pressure in the hybrid improper ferroelectrics Sr 3 Zr 2 O 7 , Ca 3 Ti 2 O 7 , and Sr 3 Sn 2 O 7 . We find that factors that are known to control the pressure response of ABO 3 perovskites—the formal charge of the A- and B-site cations, tolerance factor, and B-site chemistry—also impact the pressure response of these layered perovskites. We also show that coupling between the octahedral rotation and strain order parameters plays a key role in determining the overall pressure response. Despite some similarities, we find that these layered perovskites display a distinct pressure response compared to their ABO 3 perovskite analogs. By identifying trends and underlying mechanisms that control octahedral rotations in Ruddlesden-Popper oxides under pressure, this work lays the foundation for tailoring the structure and properties of these materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1972

One-dimensional periodic superconducting weak-link systems.

The solution of the one-dimensional Ginzburg-Landau equation is presented for the case of a linear, periodic, superconducting weak-link system. With respect to currents below a critical value, four solutions for the spatially dependent order parameter are obtained.

Blackburn, J. A.↗

DOE OSTI2025

Cooper-pair density modulation state in an iron-based superconductor

Superconducting (SC) states that break space-group symmetries of the underlying crystal can exhibit nontrivial spatial modulation of the order parameter. Previously, such states were intimately associated with the breaking of translational symmetry, resulting in the density-wave orders, with wavelengths spanning several unit cells. However, a related basic concept has long been overlooked: when only intra-unit-cell symmetries of the space group are broken, the SC states can show a distinct type of nontrivial modulation preserving long-range lattice translation. Here, in this study, we refer to this new concept as the pair density modulation (PDM) and report the first observation of a PDM state in exfoliated thin flakes of the iron-based superconductor FeTe 0.55 Se 0.45 . Using scanning tunnelling microscopy (STM), we discover robust SC gap modulation with the wavelength corresponding to the lattice periodicity and the amplitude exceeding 30% of the gap average. Notably, we find that the observed modulation originates from the large difference in SC gaps on the two nominally equivalent iron sublattices. The experimental findings, backed up by model calculations, suggest that, in contrast to the density-wave orders, the PDM state is driven by the interplay of sublattice symmetry breaking and a peculiar nematic distortion specific to the thin flakes. Our results establish new frontiers for exploring the intertwined orders in strong-correlated electronic systems and open a new chapter for iron-based superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Unconventional self-similar Hofstadter superconductivity from repulsive interactions

Abstract Fractal Hofstadter bands have become widely accessible with the advent of moiré superlattices, opening the door to studies of the effect of interactions in these systems. In this work we employ a renormalization group (RG) analysis to demonstrate that the combination of repulsive interactions with the presence of a tunable manifold of Van Hove singularities provides a new mechanism for driving unconventional superconductivity in Hofstadter bands. Specifically, the number of Van Hove singularities at the Fermi energy can be controlled by varying the flux per unit cell and the electronic filling, leading to instabilities toward nodal superconductivity and chiral topological superconductivity with Chern number $${{{{{{{\mathcal{C}}}}}}}}=\pm 6$$ C = ± 6 . The latter is characterized by a self-similar fixed trajectory of the RG flow and an emerging self-similarity symmetry of the order parameter. Our results establish Hofstadter quantum materials such as moiré heterostructures as promising platforms for realizing novel reentrant Hofstadter superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Order-parameter evolution in the Fulde-Ferrell-Larkin-Ovchinnikov phase

Here, we report on the temperature dependence of the spatially modulated spin-polarization amplitude ΔK spin , which is a hallmark of the superconducting Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. For that, we use 13 C nuclear magnetic resonance (NMR) spectroscopy performed on the organic conductor β" -(ET) 2 SF 5 CH 2 CF 2 SO 3 . From a comparison of our experimental results to a comprehensive modeling of the 13 C NMR spectra, we determine the evolution of ΔK spin upon condensation of the FFLO state. Further, the modeling of the spectra in the superconducting phase allows to quantify the decrease of the average spin susceptibility, stemming from the spin-singlet coupling of the superconducting electron pairs in the FFLO state of β" -(ET) 2 SF 5 CH 2 CF 2 SO 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Cluster Variation Method Analysis of Correlations and Entropy in BCC Solid Solutions

Solid solutions occur when multiple chemical species share sites of a common crystal lattice. Although the single site occupation is random, chemical interaction preferences bias the occupation probabilities of neighboring sites, and this bias reduced the entropy of mixing below its ideal value. Sufficiently strong bias leads to symmetry-breaking phase transitions. Here, we apply the cluster variation method to explore solid solutions on body centered cubic lattices in the context of two specific compounds that exhibit opposite ordering trends. Employing density functional theory to model the energetics, we show that CuZn exhibits an order-disorder transition to the CsCl prototype structure, while AlLi instead takes the NaTl prototype structure, and we evaluate their temperature-dependent order parameters, correlations and entropies.

36 MATERIALS SCIENCE↗