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At least 559 records · Page 31
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DOE OSTI2021

Twisted bilayer graphene. IV. Exact insulator ground states and phase diagram

Here, we derive the exact insulator ground states of the projected Hamiltonian of magic-angle twisted bilayer graphene (TBG) flat bands with Coulomb interactions in various limits, and study the perturbations away from these limits. We define the (first) chiral limit where the AA stacking hopping is zero, and a flat limit with exactly flat bands. In the chiral-flat limit, the TBG Hamiltonian has a U(4) × U(4) symmetry, and we find that the exact ground states at integer filling – 4 ≤ $\textit{ν}$ ≤ 4 relative to charge neutrality are Chern insulators of Chern numbers $ν_C$ = 4 – |$\textit{ν}$ |, 2 – |$\textit{ν}$ |, $\cdots$, |$\textit{ν}$ | – 4, all of which are degenerate. This confirms recent experiments where Chern insulators are found to be competitive low-energy states of TBG. When the chiral-flat limit is reduced to the nonchiral-flat limit which has a U(4) symmetry, we find $\textit{ν}$ = 0 , ± 2 has exact ground states of Chern number 0, while $\textit{ν}$ = ±1, ± 3 has perturbative ground states of Chern number $ν_C$ = ± 1, which are U(4) ferromagnetic. In the chiral-nonflat limit with a different U(4) symmetry, different Chern number states are degenerate up to second-order perturbations. In the realistic nonchiral-nonflat case, we find that the perturbative insulator states with Chern number $ν_C$ = 0 (0 < |$ν_C$| < 4 – |$\textit{ν}$ |) at integer fillings $\textit{ν}$ are fully (partially) intervalley coherent, while the insulator states with Chern number |$ν_C$| = 4 – |$\textit{ν}$ | are valley polarized. However, for 0 < |$ν_C$| ≤ 4 – |$\textit{ν}$ |, the fully intervalley coherent states are highly competitive (0.005 meV/electron higher). At nonzero magnetic field |$\textit{B}$ | > 0, a first-order phase transition for $\textit{ν}$ = ± 1, ± 2 from Chern number $ν_C$ = sgn ($\textit{νB}$)(2 – |$\textit{ν}$ |) to $ν_C$ = sgn ($\textit{νB}$)(4 – |$\textit{ν}$ |) is expected, which agrees with recent experimental observations. Lastly, the TBG Hamiltonian reduces into an extended Hubbard model in the stabilizer code limit.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Twisted bilayer graphene. VI. An exact diagonalization study at nonzero integer filling

Using exact diagonalization, we research the projected Hamiltonian with the Coulomb interaction in the eight flat bands of first magic angle twisted bilayer graphene. Employing the U(4) [U(4) × U(4)] symmetries in the nonchiral (chiral) flat band limit, we reduced the Hilbert space to an extent that allows for study around ν = ±3,±2,±1 fillings. In the first chiral limit w 0 /w 1 = 0, where w 0 (w 1 ) is the A A (AB) stacking hopping, we find that the ground states at these fillings are extremely well-described by Slater determinants in a so-called Chern basis, and the exactly solvable charge ±1 excitations found in Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] are the lowest charge excitations up to system sizes 8 × 8 (for restricted Hilbert space) in the chiral-flat limit. We also find that the flat metric condition (FMC) used by Bernevig et al. [Phys. Rev. B 103, 205411 (2021)], Song et al. [Phys. Rev. B 103, 205412 (2021)], Bernevig et al. [Phys. Rev. B 103, 205413 (2021)], Lian et al. [Phys. Rev. B 103, 205414 (2021)], and Bernevig et al. [Phys. Rev. B 103, 205415 (2021)] for obtaining a series of exact ground states and excitations holds in a large parameter space. For ν = -3, the ground state is the spin and valley polarized Chern insulator with ν C = ±1 at w 0 /w 1 ≲ 0.9 (0.3) with (without) FMC. At ν = -2, we can only numerically access the valley polarized sector, and we find a spin ferromagnetic phase when w 0 /w 1 ≳ 0.5 t where t ϵ [0,1] is the factor of rescaling of the actual TBG bandwidth, and a spin singlet phase otherwise, confirming the perturbative calculation [Lian. et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. The analytic FMC ground state is, however, predicted in the intervalley coherent sector which we cannot access [Lian et al., Phys. Rev. B 103, 205414 (2021), Bultinck et al., Phys. Rev. X 10, 031034 (2020)]. For ν = -3 with/without FMC, when w 0 /w 1 is large, the finite-size gap Δ to the neutral excitations vanishes, leading to phase transitions. Further analysis of the ground state momentum sectors at ν = -3 suggests a competition among (nematic) metal, momentum M M (π) stripe and K M -CDW orders at large w 0 /w 1 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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

Phase diagram of the anisotropic triangular lattice Hubbard model

In a recent study [Phys. Rev. X 10, 021042 (2020)], we showed using large-scale density matrix renormalization group (DMRG) simulations on infinite cylinders that the triangular lattice Hubbard model has a chiral spin liquid phase. In this work, we introduce hopping anisotropy in the model, making one of the three distinct bonds on the lattice stronger or weaker compared with the other two. We implement the anisotropy in two inequivalent ways, one which respects the mirror symmetry of the cylinder and one which breaks this symmetry. In the full range of anisotropy, from the square lattice to weakly coupled one-dimensional chains, we find a variety of phases. Near the isotropic limit we find the three phases identified in our previous work: metal, chiral spin liquid, and 120$^\circ$ spiral order; we note that a recent paper suggests the apparently metallic phase may actually be a Luther-Emery liquid, which would also be in agreement with our results. Furthermore, when one bond is weakened by a relatively small amount, the ground state quickly becomes the square lattice N\'{e}el order. When one bond is strengthened, the story is much less clear, with the phases that we find depending on the orientation of the anisotropy and on the cylinder circumference. While our work is to our knowledge the first DMRG study of the anisotropic triangular lattice Hubbard model, the overall phase diagram we find is broadly consistent with that found previously using other methods, such as variational Monte Carlo and dynamical mean field theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Numerically exact generalized Green's function cluster expansions for electron-phonon problems

We generalize the family of approximate momentum average methods to formulate a numerically exact, convergent hierarchy of equations whose solution provides an efficient algorithm to compute the Green's function of a particle dressed by bosons suitable in the entire parameter regime. We use this approach to extract ground-state properties and spectral functions. Our approximation-free framework, dubbed the generalized Green's function cluster expansion (GGCE), allows access to exact numerical results in the extreme adiabatic limit, where many standard methods struggle or completely fail. We showcase the performance of the method, specializing three important models of charge-boson coupling in solids and molecular complexes: the molecular Holstein model, which describes coupling between charge density and local distortions, the Peierls model, which describes modulation of charge hopping due to intersite distortions, and a more complex Holstein + Peierls system with couplings to two different phonon modes, paradigmatic of charge-lattice interactions in organic crystals. Furthermore, the GGCE serves as an efficient approach that can be systematically extended to different physical scenarios, thus providing a tool to model the frequency dependence of dressed particles in realistic settings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Twisted symmetric trilayer graphene. II. Projected Hartree-Fock study

The Hamiltonian of the magic-angle twisted symmetric trilayer graphene (TSTG) can be decomposed into a twisted-bilayer-graphene- (TBG-) like flat band Hamiltonian and a high-velocity Dirac fermion Hamiltonian. We use Hartree-Fock mean field approach to study the projected Coulomb interacting Hamiltonian of TSTG developed in Calugaru et al. [Phys. Rev. B 103, 195411 (2021)] at integer fillings ν = -3, -2, -1, and 0 measured from charge neutrality. We study the phase diagram with w 0 /w 1 , the ratio of AA and AB interlayer hoppings, and the displacement field, which introduces an interlayer potential U and hybridizes the TBG-like bands with the Dirac bands. At small U, we find the ground states at all fillings ν are in the same phases as the tensor products of a Dirac semimetal with the filling ν TBG insulator ground states, which are spin-valley polarized at ν = -3, and fully (partially) intervalley coherent at ν = -2, 0(ν = -1) in the flat bands. An exception is ν = -3 with w 0 /w 1 ≳ 0.7 , which possibly becomes a metal with competing orders at small U due to charge transfers between the Dirac and flat bands. At strong U where the bandwidths exceed interactions, all the fillings ν enter a metal phase with small or zero valley polarization and intervalley coherence. Lastly, at intermediate U, semimetal or insulator phases with zero intervalley coherence may arise for ν = -2, -1, 0. Finally, our results provide a simple picture for the electron interactions in TSTG systems, and reveal the connection between the TSTG and TBG ground states.

2-dimensional systems↗
DOE OSTI2021

Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered interacting quantum spin chain

Here, we consider the random-field Heisenberg model, a paradigmatic model for many-body localization (MBL) and add a Markovian dephasing bath coupled to the Anderson orbitals of the model's noninteracting limit. We map this system to a classical facilitated hopping model that is computationally tractable for large system sizes and investigate its dynamics. The classical model exhibits a robust crossover between an ergodic (thermal) phase and a frozen (localized) phase. The frozen phase is destabilized by thermal subregions (bubbles), which thermalize surrounding sites by providing a fluctuating interaction energy and so enable off-resonance particle transport. Investigating steady-state transport, we observe that the interplay between thermal and frozen bubbles leads to a clear transition between diffusive and subdiffusive regimes. This phenomenology both describes the MBL system coupled to a bath and provides a classical analog for the MBL transition in the corresponding quantum model, in that the classical model displays long local memory times. It also highlights the importance of the details of the bath coupling in studies of MBL systems coupled to thermal environments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Multitude of topological phase transitions in bipartite dice and Lieb lattices with interacting electrons and Rashba coupling

We report the results of a Hartree-Fock study applied to interacting electrons moving in two different bipartite lattices: the dice and the Lieb lattices, at half-filling. Both lattices develop ferrimagnetic order in the phase diagram U-λ, where U is the Hubbard on-site repulsion and λ is the Rashba spin-orbit coupling strength. Our main result is the observation of an unexpected multitude of topological phases for both lattices. All these phases are ferrimagnetic, but they differ among themselves in their set of six Chern numbers (six numbers because the unit cells have three atoms). Here, the Chern numbers |C| observed in our study range from 0 to 3, showing that large Chern numbers can be obtained by the effect of electronic correlations, adding to the recently discussed methodologies to increase |C| based on extending the hopping range in tight-binding models, using sudden quenches, or photonic crystals, all without including electronic interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Superconductivity in the bilayer Hubbard model: Two Fermi surfaces are better than one

Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping t⊥, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Lifshitz transition and even when it becomes incipient. Here we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust s± pairing correlations in the large t⊥ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased Tc. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Enhanced hybridization in the electronic ground state of the intercalated honeycomb iridate Ag 3 LiIr 2 O 6

In this work, we use x-ray spectroscopy at the Ir L 3 /L 2 absorption edge to study powder samples of the intercalated honeycomb magnet Ag 3 LiIr 2 O 6 . Based on x-ray absorption and resonant inelastic x-ray scattering measurements, and exact diagonalization calculations including nearest-neighbor Ir-Ir electron hopping integrals, we argue that the intercalation of Ag atoms results in a delocalized electronic structure with enhanced Ir-O hybridization, departing from the local relativistic j eff =1/2 state. We find that the relative orbital contribution to the magnetic moment is increased and the magnetization density is spatially extended and asymmetric in this hybridized state. Our results confirm the importance of metal-ligand hybridization in the magnetism of transition metal oxides and provide empirical guidance for understanding the collective magnetism in intercalated honeycomb iridates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Bond-Peierls polaron: Moderate mass enhancement and current-carrying ground state

We study polarons in the one-dimensional Bond-Peierls electron-phonon model in which phonons on bonds of a lattice modulate the hopping of electrons between lattice sites and contrast the results to those known for the breathing-mode Peierls problem. By inspecting the atomic limit, we show that polaronic dressing and mass enhancement of Bond-Peierls polarons depend on the momentum dependence of the phonons. For dispersionless phonons, Bond-Peierls polarons are perfectly localized in the atomic limit, unlike their breathing-mode counter-parts because the carrier creates a string of phonon excitations that can only be annihilated via processes that retrace the carrier to its original site. Furthermore, inclusion of phonon dispersion leads to a nondivergent polaron mass even in the atomic limit and depending on the form of the phonon dispersion may lead to a transition to a non-zero-momentum ground state akin to that found in the breathing-mode Peierls model.

1-dimensional systems↗
DOE OSTI2022

Constructing Hubbard models for the hydrogen chain using sliced-basis density matrix renormalization group

Sliced-basis DMRG(sb-DMRG) is used to simulate a chain of hydrogen atoms and to construct low-energy effective Hubbard-like models. The downfolding procedure first involves a change of basis to a set of atom-centered Wannier functions constructed from the natural orbitals of the exact DMRG one-particle density matrix. The Wannier function model is then reduced to a fewer-parameter Hubbard-like model, whose parameters are determined by minimizing the expectation value of the Wannier Hamiltonian in the ground state of the Hubbard Hamiltonian. This indirect variational procedure not only yields compact and simple models for the hydrogen chain, but also allows us to explore the importance of constraints in the effective Hamiltonian, such as the restricting the range of the single-particle hopping and two-particle interactions, and to assess the reliability of more conventional downfolding. The entanglement entropy for a model's ground state, cut in the middle, is an important property determining the ability of DMRG and tensor networks to simulate the model, and here we study its variation with the range of the interactions. Counterintuitively, we find that shorter ranged interactions often have larger entanglement.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Coupled Hubbard ladders at weak coupling: Pairing and spin excitations

The Hubbard model provides a simple framework in which one can study how certain aspects of the electronic structure of strongly interacting systems can be tuned to optimize the superconducting pairing correlations and how these changes affect the mechanisms giving rise to them. Here we use a weak-coupling random phase approximation to study a two-dimensional Hubbard model with a unidirectional modulation of the hopping amplitudes as the system evolves from the uniform square lattice to an array of weakly coupled two-leg ladders. We find that the pairing correlations retain their dominant d x 2 - y 2- wavelike structure and that they are significantly enhanced for a slightly modulated lattice. This enhancement is traced backed to an increase in the strength of the spin-fluctuation pairing interaction due to favorable Fermi surface nesting in the modulated system. We then use a random-phase approximation BCS framework to examine the evolution of the neutron resonance in the superconducting state. We find that it changes only weakly for moderate modulations, but breaks up into two distinct resonances at incommensurate wave vectors in the limit of weakly coupled ladders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Multiband superconductivity in strongly hybridized 1 T ' - WTe 2 / NbSe 2 heterostructures

The interplay of topology and superconductivity has become a subject of intense research in condensed-matter physics for the pursuit of topologically nontrivial forms of superconducting pairing. An intrinsically normal-conducting material can inherit superconductivity via electrical contact to a parent superconductor via the proximity effect, usually understood as Andreev reflection at the interface between the distinct electronic structures of two separate conductors. However, at high interface transparency, strong coupling inevitably leads to changes in the band structure, locally, owing to hybridization of electronic states. Here, we investigate such strongly proximity-coupled heterostructures of monolayer $1T$' - $\mathrm{WTe_2}$ grown on NbSe 2 by van der Waals epitaxy. The superconducting local density of states, resolved in scanning tunneling spectroscopy down to 500 mK, reflects a hybrid electronic structure well described by a multiband framework based on the McMillan equations which captures the multiband superconductivity inherent to the NbSe 2 substrate and that is induced by proximity to $\mathrm{WTe_2}$ self-consistently. Our material-specific tight-binding model captures the hybridized heterostructure quantitatively and confirms that strong interlayer hopping gives rise to a semimetallic density of states in the two-dimensional $\mathrm{WTe_2}$ bulk, even for nominally band-insulating crystals. The model further accurately predicts the measured order parameter Δ ≅ 0.6 meV induced in the $\mathrm{WTe_2}$ monolayer bulk, stable beyond a 2 T magnetic field. So we believe that our detailed multiband analysis of the hybrid electronic structure provides a useful tool for sensitive spatial mapping of induced order parameters in proximitized atomically thin topological materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Interpreting angle-dependent magnetoresistance in layered materials: Application to cuprates

The evolution of the low-temperature electronic structure of the cuprate metals from the overdoped to the underdoped side has recently been addressed through angle-dependant magnetoresistance (ADMR) experiments in La 1.6-x Nd 0.4 Sr x CuO 4 . Here the results show a striking difference between hole dopings p = 0.24 and p = 0.21, which lie on either side of a putative quantum critical point at intermediate p. Motivated by this, we here study the theory of ADMR in correlated layered materials, paying special attention to the role of angle-dependent quasiparticle weights Z k . Such a Z k is expected to characterize a number of popular models of the cuprate materials, particularly when underdoped. Further, in the limit of weak interlayer hopping the quasiparticle weight will affect the c-axis transport measured in ADMR experiments. We show that proper inclusion of the quasiparticle weight does not support an interpretation of the data in terms of a (π,π) spin density wave ordered state, in agreement with the lack of direct evidence for such order. We show that a simple model of Fermi surface reconfiguring across a van Hove point captures many of the striking differences seen between p = 0.21 and p = 0.24. We comment on why such a model may be appropriate for interpreting the ADMR data, despite having a large Fermi surface at p = 0.21, seemingly in contradiction with other evidence for a small Fermi surface at that doping level.

36 MATERIALS SCIENCE↗
DOE OSTI2022

$O(N)$ ab initio calculation scheme for large-scale moiré structures

Here we present a two-step method specifically tailored for band structure calculation of the small-angle moiré-pattern materials which contain tens of thousands of atoms in a unit cell. In the first step, the self-consistent field calculation for the ground state is performed with the O(N) Krylov subspace method implemented in openmx. Second, the crystal momentum-dependent Bloch Hamiltonian and overlap matrix are constructed from the results obtained in the first step and only a small number of eigenvalues near the Fermi energy are solved with shift-invert and Lanczos techniques. By systematically tuning two key parameters, the cutoff radius for electron hopping interaction and the dimension of the Krylov subspace, we obtained the band structures for both rigid and corrugated twisted bilayer graphene structures down to the first magic angle (θ = 1.08°) with high enough accuracy at affordable costs. The band structures are in good agreement with those from tight-binding models, continuum models, plane-wave pseudopotential based ab initio calculations, and experimental observations. This method is also shown to be efficient in twisted double-bilayer graphene and bilayer WSe 2 . We think this two-step method can play a crucial role in other twisted two-dimensional materials, especially those with much more complex band structure and where the effective model is hard to construct.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Enhancing T c in a composite superconductor/metal bilayer system: A dynamical cluster approximation study

It has been proposed that the superconducting transition temperature T c of an unconventional superconductor with a large pairing scale but strong phase fluctuations can be enhanced by coupling it to a metal. However, the general efficacy of this approach across different parameter regimes remains an open question. Using the dynamical cluster approximation, we study this question in a system composed of an attractive Hubbard layer in the intermediate coupling regime, where the magnitude of the attractive Coulomb interaction |U| is slightly larger than the bandwidth W, hybridized with a noninteracting metallic layer. We find that while the superconducting transition becomes more mean-field-like with increasing interlayer hopping, the superconducting transition temperature T c exhibits a nonmonotonic dependence on the strength of the hybridization t ⊥ . Furthermore, this behavior arises from a reduction of the effective pairing interaction in the correlated layer that outcompetes the growth in the intrinsic pair-field susceptibility induced by the coupling to the metallic layer. We find that the largest T c inferred here for the composite system is comparable to the maximum value currently estimated for the isolated negative-U Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Acoustic plasmons and conducting carriers in hole-doped cuprate superconductors

The layered crystal structures of cuprates enable collective charge excitations fundamentally different from those of three-dimensional metals. Acoustic plasmons have been observed in electron-doped cuprates by resonant inelastic X-ray scattering (RIXS); in contrast, whether acoustic plasmons exist in hole-doped cuprates is under debate, despite extensive measurements. This contrast led us to investigate the charge excitations of hole-doped cuprate La 2-x Sr x CuO 4 . Here we present incidentenergy-dependent RIXS measurements and calculations of collective charge response via the loss function to reconcile the aforementioned issues. Our results provide evidence for the acoustic plasmons of Zhang-Rice singlet (ZRS), which has a character of the Cu 3d x 2 -y 2 strongly hybridised with the O 2p orbitals; the metallic behaviour is implied to result from the movement of ZRS rather than the simple hopping of O 2p holes.

36 MATERIALS SCIENCE↗