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DOE OSTI2021

Intertwined charge, spin, and pairing orders in doped iron ladders

Motivated by recent experimental progress on iron-based ladder compounds, we study the doped two-orbital Hubbard model for the two-leg ladder BaFe2S3. The model is constructed by using ab initio hopping parameters and the ground state properties are investigated using the density matrix renormalization group method. We show that the (π,0) magnetic ordering at half filling, with ferromagnetic rungs and antiferromagnetic legs, becomes incommensurate upon hole doping. Moreover, depending on the strength of the Hubbard U coupling, other magnetic patterns, such as (0,π), are also stabilized. We found that the binding energy for two holes becomes negative for intermediate Hubbard interaction strength, indicating hole pairing. Due to the crystal-field split among orbitals, the holes primarily reside in one orbital, with the other one remaining half filled. This resembles orbital selective Mott states. The formation of tight hole pairs continues with increasing hole density, as long as the magnetic order remains antiferromagnetic in one direction. The study of pair-pair correlations indicates the dominance of the intraorbital spin-singlet channel, as opposed to other pairing channels. Although in a range of hole doping pairing correlations decay slowly, our results can also be interpreted as corresponding to a charge density wave made of pairs, a precursor of eventual superconductivity after interladder couplings are included. Such a scenario of intertwined orders has been extensively discussed before in the cuprates, and our results suggest a similar physics could exist in ladder iron-based superconductors. Finally, we also show that a robust Hund's coupling is needed for pairing to occur.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Adiabatic construction of hierarchical quantum Hall states

We propose an exact model of anyon ground states including higher Landau levels, and use it to obtain fractionally quantized Hall states at filling fractions ν = p/(p(m - 1) + 1) with m odd, from integer Hall states at ν = p through adiabatic localization of magnetic flux. For appropriately chosen two-body potential interactions, the energy gap remains intact during the process. The construction hence establishes the existence of incompressible states at these fillings.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Optical conductivity of the two-dimensional Hubbard model: Vertex corrections, emergent Galilean invariance, and the accuracy of the single-site dynamical mean field approximation

We compute the frequency-dependent conductivity of the two-dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single-site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the model exhibits an emergent Galilean invariance. The DMFT approximation also becomes qualitatively inaccurate very near half filling if nesting is important.

2-dimensional systems↗
DOE OSTI2022

Theory of a continuous bandwidth-tuned Wigner-Mott transition

Here we develop a theory for a continuous bandwidth-tuned transition at fixed fractional electron filling from a metal with a generic Fermi surface to a “Wigner-Mott” insulator that spontaneously breaks crystalline space-group symmetries. Across the quantum critical point, (i) the entire electronic Fermi surface disappears abruptly upon approaching from the metallic side, and (ii) the insulating charge gap and various order parameters associated with the spontaneously broken space-group symmetries vanish continuously upon approaching from the insulating side. Additionally, the insulating side hosts a Fermi surface of neutral spinons. We present a framework for describing such continuous metal-insulator transitions (MITs) and analyze the example of a bandwidth-tuned transition at a filling, $v$=1/6, for spinful electrons on the triangular lattice. By extending the theory to a certain large-$N$ limit, we provide a concrete example of such a continuous MIT and discuss numerous experimental signatures near the critical point. We place our results in the context of recent experiments in moiré transition metal dichalcogenide materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Metal to Wigner-Mott insulator transition in two-leg ladders

Here we study theoretically the quantum phase transition from a metal to a Wigner-Mott insulator at fractional commensurate filling on a two-leg ladder. We show that a continuous transition out of a symmetry-preserving Luttinger liquid metal is possible where the onset of insulating behavior is accompanied by the breaking of the lattice translation symmetry. At fillings $v$=1/$m$ per spin per unit cell, we find that the spin degrees of freedom also acquire a gap at the Wigner-Mott transition for odd integer $m$. In contrast for even integer $m$, the spin sector remains gapless and the resulting insulator is a ladder analog of the two-dimensional spinon surface state. In both cases, a charge neutral spinless mode remains gapless across the Wigner-Mott transition. We discuss physical properties of these transitions and comment on insights obtained for thinking about continuous Wigner-Mott transitions in two-dimensional systems which are being studied in moire materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Phase diagram of the Su-Schrieffer-Heeger-Hubbard model on a square lattice

The Hubbard and Su-Schrieffer-Heeger (SSH) Hamiltonians are iconic models for understanding the qualitative effects of electron-electron and electron-phonon interactions, respectively. In the two-dimensional square lattice Hubbard model at half filling, the on-site Coulomb repulsion U between up and down electrons induces antiferromagnetic (AFM) order and a Mott insulating phase. On the other hand, for the SSH model, there is an AFM phase when the electron-phonon coupling λ is less than a critical value λ c and a bond order wave when λ > λ c . In this Letter, we perform numerical studies on the square lattice optical Su-Schrieffer-Heeger-Hubbard Hamiltonian, which combines both interactions. We use the determinant quantum Monte Carlo method which does not suffer from the fermionic sign problem at half filling. We map out the phase diagram and find that it exhibits a direct first-order transition between an antiferromagnetic phase and a bond-ordered wave as λ increases. Here, the AFM phase is characterized by two different regions. At smaller λ the behavior is similar to that of the pure Hubbard model; the other region, while maintaining long-range AFM order, exhibits larger kinetic energies and double occupancy, i.e., larger quantum fluctuations, similar to the AFM phase found in the pure SSH model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Integer quantum Hall effect and enhanced g factor in quantum-confined Cd 3 As 2 films

Here, we investigate the integer quantum Hall effect in Cd 3 ⁢As 2 thin films under conditions of strong to moderate quantum confinement (thicknesses of 10, 12, and 15 nm). In all the films, we observe the integer quantum Hall effect in the spin-polarized lowest Landau level (filling factor v = 1) and at spin-degenerate higher index Landau levels with even filling factors (v = 2,4,6). With increasing quantum confinement, we also observe a lifting of the Landau-level spin degeneracy at v = 3, manifest as the emergence of an anomaly in the longitudinal and Hall resistivities. Tight-binding calculations show that the enhanced g factor likely arises from a combination of quantum confinement and corrections from nearby subbands.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Superconductivity and magnetic and transport properties of single-crystalline CaK ( Fe 1 – x Cr x ) 4 As 4

Members of the CaK (Fe 1–x Cr x ) 4 As 4 series have been synthesized by high-temperature solution growth in single-crystalline form and characterized by x-ray diffraction, elemental analysis, and magnetic and transport measurements. The effects of Cr substitution on the superconducting and magnetic ground states of CaKFe 4 As 4 (T c = 35 K) have been studied. These measurements show that the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K as x is increased from 0 to 0.038. For x-values greater than 0.012, signatures of a magnetic transition can be detected in magnetic measurements with the associated features in the transport measurements becoming detectable for x ≥ 0.038. The magnetic transition temperature increases in a roughly linear manner as Cr substitution increases. A temperature-composition (T – x) phase diagram is constructed, revealing a half-dome of superconductivity with the magnetic transition temperature, T*, appearing near 22 K for x ~ 0.017 and rising slowly up to 60 K for x ~ 0.077. The T – x phase diagrams for CaK (Fe 1–x T x ) 4 As 4 for T = Cr and Mn are essentially the same despite the nominally different band filling; this is in marked contrast to T = Co and Ni series for which the T – x diagrams scale by a factor of 2, consistent with the different changes in band filling Co and Ni would produce when replacing Fe. Superconductivity of CaK (Fe 1–x Cr x ) 4 As 4 is also studied as a function of magnetic field. A clear change in $H^{'}_{c2}$ (T)/T c , where $H^{'}_{c2}$ (T) is dH c2 (T)/dT, at x ~ 0.012 is observed and probably is related to a change of the Fermi surface due to magnetic order. Further, coherence length and the London penetration depths are also calculated based on H c1 and H c2 data. Both of them as a function of x show changes near x = 0.012, again consistent with Fermi surface changes associated with the magnetic ordering seen for higher x-values.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Magic-angle twisted symmetric trilayer graphene as a topological heavy-fermion problem

Recently, Song and Bernevig [Phys. Rev. Lett. 129, 047601 (2022)] reformulated magic-angle twisted bilayer graphene as a topological heavy fermion problem, and used this reformulation to provide a deeper understanding for the correlated phases at integer fillings. Here, in this work, we generalize this heavy-fermion paradigm to magic-angle twisted symmetric trilayer graphene, and propose a low-energy f–c–d model that reformulates magic-angle twisted symmetric trilayer graphene as heavy localized f modes coupled to itinerant topological semimetalic c modes and itinerant Dirac d modes. Our f–c–d model well reproduces the single-particle band structure of magic-angle twisted symmetric trilayer graphene at low energies for displacement field $\mathcal{E}$ ϵ [0,300]⁢ meV. By performing Hartree-Fock calculations with the f–c–d model for v = 0,–1,–2 electrons per Moiré unit cell, we reproduce all the correlated ground states obtained from the previous numerical Hartree-Fock calculations with the Bistritzer-MacDonald-type model, and we find additional new correlated ground states at high displacement field. Based on the numerical results, we propose a simple rule for the ground states at high displacement fields by using the f–c–d model, and provide analytical derivation for the rule at charge neutrality. We also provide analytical symmetry arguments for the (nearly) degenerate energies of the high-$\mathcal{E}$ ground states at all the integer fillings of interest, and make experimental predictions of which charge-neutral states are stabilized in magnetic fields. Our f–c–d model provides a new perspective for understanding the correlated phenomena in magic-angle twisted symmetric trilayer graphene, suggesting that the heavy fermion paradigm of Song and Bernevig [Phys. Rev. Lett. 129, 047601 (2022)] should be the generic underpinning of correlated physics in multilayer moire graphene structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Collective dynamics and defect generation for Wigner crystal ratchets

Here we consider a two-dimensional Wigner crystal coupled to a quasi-one-dimensional asymmetric potential under ac or dc driving. As a function of electron density, substrate strength, and ac amplitude, we find that the system exhibits ordered and disordered pinned and dynamical states. Ratchet effects can appear under an applied ac drive and can be associated with pronounced structural changes from a disordered state to a one-dimensional smecticlike state. We observe a pinned phase, a diodelike ratchet where motion only occurs along the easy direction of the substrate asymmetry, a plastic ratchet where motion occurs in both directions but there is only a net drift in the easy direction, and an elastic ratchet where the system forms a crystal without plastic deformation that can still undergo ratcheting. At high filling, we find that there can be a ratchet reversal in which the net drift is along the hard direction of the substrate asymmetry. For weak disorder, there is an Aubry transition to a floating phase where the ratchet effects are lost. We map out the different dynamical phases as a function of substrate strength, filling, ac amplitude, and ac frequency. The ratchet effect on strong substrates is enhanced by thermal fluctuations, but is destroyed when the fluctuations become too large. Based on our results, we suggest other ways to detect Wigner crystals as well as methods for creating different types of devices to control disordered charge flow.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Comparative determinant quantum Monte Carlo study of the acoustic and optical variants of the Su-Schrieffer-Heeger model

We compare the acoustic Su–Schrieffer–Heeger (SSH) model with two of its optical variants where the phonons are defined on either on the sites or bonds of the system. First, we discuss how to make fair comparisons between these models in any dimension by ensuring their dimensionless coupling λ and relevant phonon energies are the same. We then use determinant quantum Monte Carlo to perform nonperturbative and sign-problem-free simulations of all three models on one-dimensional chains at and away from half-filling. By comparing the results obtained from each model, we demonstrate that the optical and acoustic models produce near identical results within error bars for suitably chosen phonon energies and λ at half-filling. In contrast, the bond model has quantitatively different behavior due to its coupling to the q = 0 phonon mode. These differences also manifest in the total length of the chain, which shrinks for the bond model but not for the acoustic and optical models when λ ≠ 0. Furthermore, our results have important implications for quantum Monte Carlo modeling of SSH-like interactions, where these models are sometimes regarded as being interchangeable.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Charge order and superconductivity in a two-band model for infinite-layer nickelates

The recent discovery of superconductivity in infinite-layer nickelates has drawn considerable attention; however, a consensus on the fundamental building blocks and common ingredients necessary to understand and describe their ground states and emergent properties is lacking. A series of experimental and theoretical studies have suggested that an effective two-band Hubbard model with Ni 3d x 2 -y 2 and rare-earth (R) 5d character may describe the low-energy physics. In this report we study the ground state properties of this two-band model on four-leg cylinders using the density-matrix renormalization group (DMRG) technique to better grasp whether such a simple model can embody the essential physics. A key difference compared to single-band Hubbard materials is that the system is self-doped: even at overall half-filling, the R-band acts as an electron reservoir, hole-doping the Ni-layer and fundamentally altering the physics expected from an undoped antiferromagnet. On the four-leg cylinder, the ground state is consistent with a Luttinger liquid, with anti-phase modulations of the charge density in the Ni- and R-layers having corresponding wavevectors that lock together. Light hole doping away from 1/2 filling releases the locking between the Ni and the R charge modulations, as the electron density in the R-band decreases and eventually becomes exhausted at a hole doping concentration that depends sensitively on the effective splitting between the Ni and the R orbitals. The ground state of the doped system is consistent with a Luther-Emery liquid, possessing quasi-long-range superconducting correlations in the Ni layer, similar to the single-band Hubbard model. Our results are consistent with experimental observations and may help to reveal the microscopic mechanism for pairing and other emergent properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Breakdown of order fractionalization in the CPT model

Here, we present an analysis of the half-filled CPT model, an analytically tractable Kondo lattice model with Yao-Lee spin-spin interactions on a 3D hyperoctagon lattice, proposed by Coleman, Panigrahi, and Tsvelik. Previous studies have established that the CPT model exhibits odd-frequency triplet superconductivity and order fractionalization. Through asymptotic analyses in the small- and large- Kondo coupling limits, we identify a quantum critical point at , marking a transition from a superconductor to a Kondo insulator. By estimating the vison gap energy to account for thermal gauge fluctuations, we determine the energy scales governing the thermal breakdown of order fractionalization. Moreover, at large the Kondo insulator undergoes orbital decoupling, leading to the formation of a decoupled Kitaev orbital liquid. These findings and analogies with the -gauged model lead us to propose a tentative phase diagram for the CPT model at half-filling.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Particle-hole asymmetric phases in doped twisted bilayer graphene

Twisted bilayer graphene (TBG) has emerged as a paradigmatic platform for exploring the interplay between strong interactions in a multi-band system with nearly flat bands, while offering unprecedented control over the filling fraction of electron/hole carriers. Despite much theoretical work, developing a comprehensive ab initio model for this system has proven challenging due to the inherent trade-off between accurately describing the band structure and incorporating the interactions within the Hamiltonian. Here, we constructed an extended multi-orbital Hubbard model, and performed Hartree-Fock (HF) calculations to explore its phase diagram across commensurate fillings. We found several nearly-degenerate insulating states at charge neutrality, all of which exhibit orbital orders. We also observed that most of the Hartree–Fock ground states exhibit a generalized valley Hund’s-like rule, resulting in valley polarization. Importantly, we show that the incorporation of the intra-valley and inter-valley exchange interactions is crucial to properly stabilize the ordered symmetry-broken states. In agreement with experiments, we find significant particle-hole asymmetry, which underscores the importance of using particle-hole asymmetric models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Neutron-proton pairing correction in the extended isovector and isoscalar pairing model

An extended O ST (8) model with multi j-orbits is constructed based on the angular momentum decomposition with “pseudo”-spin S for valence nucleons in a j-orbit. It is shown that the isovector S = 0 and T=1 pairs are exactly the J=0 and T=1 pairs in a given j-orbit, while the isoscalar S = 1 pairs are linear combinations of J=odd pairs, with which the pairing Hamiltonian can be used to estimate isovector and isoscalar pairing interactions. As an example of the model application, some low-lying J = 0 + level energies of even-even and odd-odd A=18 – 28 nuclei up to the half-filling in the ds-shell above the 16 O core are fit by the model and compared with the fitting results of the same Hamiltonian in the O LST (8) form. It has been verified from the fitting of both the models that the isoscalar pairing interaction can be neglected in the lower energy part of the spectra of these ds-shell nuclei as far as binding energies and a few J=0 + excited levels of these nuclei are concerned. With the mean-field plus isovector pairing interaction only, neutron-neutron, proton-proton, and neutron-proton pairing contributions at the ground or the lowest J=0 + state of these nuclei are estimated. It is shown that the isovector np-pairing contribution to the binding in the odd-odd N=Z nuclei is systematically larger than that in the even-even nuclei. Furthermore, the isoscalar np-pair content at the lowest J=0+ state of these nuclei is also estimated. In both the O ST (8) and O LST (8) models, it is clearly shown that the isoscalar-pair content in the lowest J=0 + state of the N=Z and N=Z±2 nuclei increases with increasing of the valence nucleons, especially in those even-even nuclei, which indicates the isoscalar pairing correlation to be of importance at low-lying states of N=Z and N=Z±2 nuclei, especially in those even-even nuclei with more valence nucleons up to the half-filling, even though the isoscalar pairing interaction is negligible.

20 ≤ A ≤ 38↗
DOE OSTI2023

Quarkyonic mean field theory

We discuss mean field theory of quarkyonic matter at zero temperature. We treat the nucleons with contact interactions in mean field approximation, discussing both vector and scalar mean field interactions. We treat the quarks without mean field vector interactions, but allow mass terms to be generated consistently from a scalar mean field consistent with the additive quark model for quark masses. Quarkyonic matter is composed of a shell of nucleons that under-occupy the total available phase space associated with the underlying quark degrees of freedom. Here, the fully occupied Fermi sphere beneath this shell of nucleons at high densities is thought of as quarks, but when this fully occupied distribution of states first appears, although the phase space is filled, the matter is at low density. For the transition between this low density and high density saturated matter, we advocate a dual description of the fully filled Fermi sea in terms of hadrons, and make a phenomenological hypothesis for the equation of state of this matter. We then proceed to an example where the mean field interactions are all vector and only associated with the nucleons, ignoring the effects of mass change associated with the scalar interactions. Except for the effects of Pauli blocking, the nucleons and quarks do not interact. To get a reasonable transition to quarkyonic matter the interaction of the quarks among themselves are assumed to be nonperturbative, and a simple phenomenological relation between quark Fermi energy and density is introduced.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Isomers and hindrances in No254: A touchstone for theories of superheavy nuclei

We report on a new spectroscopic study of the decay of high-K isomers in No152102254, a touchstone nucleus for testing models to understand the structure of superheavy nuclei. The experiment, performed using the Argonne gas-filled analyzer (AGFA), was geared toward resolving long-standing ambiguities in spin-parity and configuration assignments for the two- and four-quasiparticle (qp) intrinsic excitations identified in this nucleus. The isomer decay schemes are firmly established with the help of the highest-statistics γ-γ coincidence data collected to date, providing anchor points for competing theories. A newly measured half-life in the nanosecond range establishes a second 2-qp isomer in No254. The preferred decay pathways for the 2- and 4-qp isomers are discussed, providing new insights into the underlying hindrance mechanisms at play in these heavy nuclei. With firm configuration assignments, the intrinsic excitations in this deformed mass region provide stringent constraints and challenge the different theoretical approaches at play in understanding the structure of superheavy nuclei.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Novel transition dynamics of topological solitons

Continuous phase transitions can be classified into ones characterized by local-order parameters and others that need additional topological constraints. The critical dynamics near the former transitions have been extensively studied, but the latter is less understood. We fill this gap in knowledge by studying the transition dynamics to a parity-breaking topological ground state called the chiral soliton lattice in quantum chromodynamics at finite temperature, baryon chemical potential, and an external magnetic field. We find a slowing down of the soliton’s translational motion as the critical magnetic field approaches, while the local relaxation rate to the solitonic state remains finite. The time required to converge to the stationary state strongly depends on the symmetry of the initial configuration, determining whether translational motion occurs during the dynamic process. Published by the American Physical Society 2024

Nishimura, Kentaro↗