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DOE OSTI2025

Identification of Prompt Proton Emission in $N = Z - 1$ 61 Ga: Isospin Symmetry at the Limit of Nuclear Binding

Excited states in the proton drip line nucleus 61 Ga were populated via the fusion-evaporation reaction 24 Mg ⁢( 40 Ca, 𝑝⁢2⁢𝑛)⁢ 61 Ga. The experimental setup at Argonne National Laboratory comprised a novel combination of the Gammasphere array with two CD-shaped double-sided Si-strip detectors inside the Microball CsI(Tl) charged-particle detection array, as well as the Neutron-Shell liquid scintillators and the Fragment Mass Analyzer. Owing to the setup’s unprecedented in-beam proton spectroscopy and tracking capabilities, a coincidence between a 957.6(5)-keV 𝛾 ray and a 1.876(24)-MeV proton line was observed, which identifies the quasibound proton 𝜋⁢𝑔 9/2 single-particle state in 61 Ga at 𝐸 𝑥 = 2150⁢(34) keV. This probes isospin symmetry at the limit of nuclear binding by providing a unique challenge for the shell-model interpretation of mirror nuclei beyond doubly magic 56 Ni .

Hrabar, Yuliia [Lund Univ. (Sweden)] (ORCID:000000↗

DOE OSTI2026

Exploration for astromers near 132 Sn with the Canadian Penning Trap

Nuclear isomers can have significant impacts on astrophysical nucleosynthesis processes, with recent efforts demonstrating that the population of isomeric states with different half-lives may require separate treatment in reaction networks to accurately capture the differences in heating or in identifiable electromagnetic signals. Several potential so-called “astromers” in tin and antimony isotopes near doubly magic 132 Sn were identified and direct mass measurements of their ground and isomeric states were performed with the Canadian Penning Trap at Argonne National Laboratory's CARIBU facility, and their impact on astrophysical reaction rates and in reaction networks was calculated. Finally, it was found that 129⁢𝑔,𝑚 Sn , with measured mass excesses of −80593.2⁢(25) and −80557.4⁢(25) keV, respectively, and an excitation energy of 35.8(35) keV, behaves as an astromer during neutron capture in the 𝑖-process and in the 𝑟-process.

isomer decays↗

DOE OSTI2023

Optical telecommunications-band clock based on neutral titanium atoms

Here, we propose an optical clock based on ultranarrow transitions in neutral titanium, which exhibit small blackbody radiation and quadratic Zeeman shifts and have wavelengths in the S-, C-, and L-telecommunications fiber bands, allowing for integration with robust laser technology. We calculate relevant properties using a high-precision relativistic hybrid method that combines configuration interaction and coupled-cluster approaches. To identify magic wavelengths, we have completed the largest-to-date direct dynamical polarizability calculations. Finally, we identify challenges that arise from magnetic dipole-dipole interactions and describe an approach to overcome them. A telecommunications-band atomic frequency standard will aid the deployment of optical clock networks and clock comparisons over long distances.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2019

Self-assembled Ag(111) nanostructures induced by Fermi surface nesting

Scanning tunneling microscopy measurements on Ag(111)/MoS 2 reveal atomically flat preferred, or “magic,” heights occurring at 6, 10, and 14 atomic layers. We note these results are consistent with Ag growth on a variety of semiconducting substrates and correlate with electronic energy savings in electronic structure calculations of freestanding Ag(111) films. Thus, under certain conditions, Ag will spontaneously form quantized structures independent of the substrate. To explain this, we have found Fermi surface nesting vectors in the bulk Ag band structure which account for these results and the fact Ag that is gapped along the surface normal. This model extends to a range of metallic systems which exhibit electronic confinement, epitaxial growth, and minimal strain. As with Au/MoS 2 , the Ag/MoS 2 system exhibits this behavior at unusually high temperatures so that these principles might be used for control over device features at the nanometer scale under standard fabrication conditions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Landau level of fragile topology

Here, we study the Hofstadter butterfly and Landau levels of the twisted bilayer graphene (TBG). We show that the nontrivial fragile topology of the lowest two bands near the charge neutral point makes their Hofstadter butterfly generically connected with higher bands, closing the gap between the first and second conduction (valence) bands at a certain magnetic flux per unit cell. We also develop a momentum space method for calculating the TBG Hofstadter butterfly, from which we identify three phases where the Hofstadter butterflies of the lowest two bands and the higher bands are connected in different ways. We show this leads to a crossing between the $\textit{ν}$ = 4 Landau fan from the charge neutral point and the zero-field band gap at one flux per moiré unit cell, which corresponds to a magnetic field 25$θ^2$ T (twist angle $\textit{θ}$ in degrees). This provides an experimentally testable feature of the fragile topology. In general, we expect it to be a generic feature that the Hofstadter butterfly of the topological bands are connected with the Hofstadter spectra of other bands. We further show the TBG band theory with Zeeman splitting being the most sizable splitting could result in Landau fans at the charge neutral point and half fillings near the magic angle, and we predict their variations under an in-plane magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Spin magnetometry as a probe of stripe superconductivity in twisted bilayer graphene

The discovery of alternating superconducting and insulating ground states in magic angle graphene has suggested an intriguing analogy with cuprate high-T c materials. In this paper we argue that the network states of small angle twisted bilayer graphene (TBG) afford a further perspective on the cuprates by emulating their stripe-ordered phases, as in La 1.875 Ba 0.125 CuO 4 . We show that the spin and valley quantum numbers of stripes in TBG graphene fractionalize, developing characteristic signatures in the tunneling density of states and the magnetic noise spectrum of impurity spins. By examining the coupling between the charge rivers we determine the superconducting transition temperature. Our study suggests that twisted bilayer graphene can be used for a controlled emulation of stripe superconductivity and quantum sensing experiments of emergent anyonic excitations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

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. V. Exact analytic many-body excitations in Coulomb Hamiltonians: Charge gap, Goldstone modes, and absence of Cooper pairing

We find exact analytic expressions for the energies and wave functions of the charged and neutral excitations above the exact ground states (at rational filling per unit cell) of projected Coulomb Hamiltonians in twisted bilayer graphene. Our exact expressions are valid for any form of the Coulomb interaction and any form of A A and A B / B A tunneling. The single charge excitation energy is a convolution of the Coulomb potential with a quantum geometric tensor of the TBG bands. The neutral excitations are (high-symmetry group) magnons, and their dispersion is analytically calculated in terms of the form factors of the active bands in TBG. The two-charge excitation energy and wave functions are also obtained, and a sufficient condition on the graphene eigenstates for obtaining a Cooper pair from Coulomb interactions is obtained. For the actual TBG bands at the first magic angle, we can analytically show that the Cooper pair binding energy is zero in all such projected Coulomb models, implying that either phonons and/or nonzero kinetic energy are needed for superconductivity. Since Vafek and Kang [Phys. Rev. Lett. 125, 257602 (2020)] showed that the kinetic energy bounds on the superexchange energy are less 10 -3 in Coulomb units, the phonon mechanism becomes then very likely. If nonetheless the superconductivity is due to kinetic terms which render the bands nonflat, one prediction of our theory is that the highest T c would not occur at the highest DOS.

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

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

Reentrant superconductivity through a quantum Lifshitz transition in twisted trilayer graphene

A series of recent experiments has demonstrated robust superconductivity in magic-angle twisted trilayer graphene (TTG). In particular, a recent work by Cao et al. [Nature (London) 595, 526 (2021)] studies the behavior of the superconductor in an in-plane magnetic field and an out-of-plane displacement field, finding that the superconductor is unlikely to have purely spin-singlet pairing. Herein, this work also finds that at high magnetic fields and a smaller range of dopings and displacement fields, the superconductor undergoes a transition to a distinct field-induced superconducting state. Inspired by these results, we develop an understanding of the superconductivity in TTG using a combination of phenomenological reasoning and microscopic theory. We describe the role that an in-plane field plays in TTG, and we use this understanding to argue that the reentrant transition may be associated with a quantum Lifshitz phase transition, with the high-field phase possessing finite-momentum pairing. We argue that the superconductor is likely to involve a superposition of singlet and triplet pairing, and we describe the structure of the normal state. We also draw lessons for twisted bilayer graphene (TBG), and we explain the differences in the phenomenology with TTG despite their close microscopic relationship. We propose that a singlet-triplet superposition is realized in the TBG superconductor as well, and that the ν = –2 correlated insulator may be a time-reversal protected Z 2 topological insulator obtained through spontaneous spin symmetry breaking.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Interfacial electron-phonon coupling and quantum confinement in ultrathin Yb films on graphite

Interfacial electron-phonon coupling in ultrathin films has attracted much interest recently. Here, by combining angle-resolved photoemission spectroscopy and scanning tunneling microscopy, we report quantized electronic states and strong interfacial electron-phonon coupling in ultrathin Yb films on graphite. We observed clear kinks in the energy-momentum dispersion of quantum well states, and the kink positions agree well with the energies of optical phonons of graphite. The extracted coupling strength λ is largest for the thinnest film with a preferred (“magic”) thickness of four monolayers and exhibits a strong band dependence, which can be qualitatively accounted for by a simple model. The interfacial electron-phonon coupling also gives rise to characteristic steplike structures in the $dI/dV$ spectra, implying dominant coupling with the phonons with zero in-plane momentum. A Lifshitz transition occurs at higher coverage, where quantum well states derived mainly from 5d electrons dominate near the Fermi level and possess large effective mass (up to ~ 19 m e ). Here our results highlight the potentially important role of interfacial electron-phonon interaction for ultrathin films and provide spectroscopic insight to understand this cross-interface fermion-boson interaction.

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

Trions in twisted bilayer graphene

The strong-coupling phase diagram of magic-angle twisted bilayer graphene (TBG) predicts a series of exact one-particle charge ±1 gapped excitations on top of the integer-filled ferromagnetic ground states. Finite-size exact diagonalization studies showed that these are the lowest charge ±1 excitations in the system (for 10 nm screening length), with the exception of charge +1 at filling -1 in the chiral limit. In the current paper we show that this “trion bound state,” a 3-particle, charge 1 excitation of the insulating ferromagnetic ground state of the projected Hamiltonian of TBG, is the lowest charge +1 overall excitation at ν =-1, and also for some large (≈20 nm) screening lengths at ν =-2 in the chiral limit and with very small binding energy. At other fillings, we show that trion bound states do exist, but only for momentum ranges that do not cover the entire moiré Brillouin zone. The trion bound states (at different momenta) exist for finite parameter range w 0 /w 1 but they all disappear in the continuum far below the realistic values of w 0 /w 1 = 0.8. Thus we find the conditions for the existence of the trion bound state, a good variational wave function for it, and investigate its behavior for different screening lengths, at all integer fillings, on both the electron and hole sides.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Skyrmion superconductivity: DMRG evidence for a topological route to superconductivity

It was recently suggested that the topology of magic-angle twisted bilayer graphene's (MATBG) flat bands could provide a novel mechanism for superconductivity distinct from both weakly coupled BCS theory and the d-wave phenomenology of the high-T c cuprates. In this work, we examine this possibility using a density matrix renormalization group (DMRG) study of a model which captures the essential features of MATBG's symmetry and topology. Here, using large-scale cylinder-DMRG calculations to obtain the ground state and its excitations as a function of the electron doping, we find clear evidence for superconductivity driven by the binding of electrons into charge-2e skyrmions. Remarkably, this binding is observed even in the regime where the unscreened Coulomb repulsion is by far the largest energy scale, demonstrating the robustness of this topological, all-electronic pairing mechanism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Time-reversal invariant topological moiré flat band: A platform for the fractional quantum spin Hall effect

Motivated by recent observation of the quantum spin Hall effect in monolayer germanene and twisted bilayer transition-metal-dichalcogenides (TMDs), we study the topological phases of moir twisted bilayers with time-reversal symmetry and spin sz conservation. By using a continuum model description which can be applied to both germanene and TMD bilayers, we show that at small twist angles the emergent moir flat bands can be topologically nontrivial due to inversion symmetry breaking. Each of these flat bands admits a lowest-Landau-level description for each spin projection in the chiral limit and at magic twist angle. Furthermore, this allows for the construction of a many-body Laughlin state with time-reversal symmetry which can be stabilized by a short-range pseudopotential, and therefore serves as an ideal platform for realizing the so-far elusive fractional quantum spin Hall effect with emergent spin-1/2 U(1) symmetry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Doped moiré magnets: Renormalized flat bands and excitonic phases

Here, we explore the phase diagram of a twisted bilayer of strongly interacting electrons on a honeycomb lattice close to half filling using the slave-boson mean-field theory. Our analysis indicates that a variety of new phases can be realized as a function of chemical doping and twist angle. In particular, we find a nonmagnetic excitonic insulating phase that breaks the translational symmetry of the underlying moiré pattern. This phase results from the interplay of strong Coulomb interactions and the twist angle. In addition, we show that the features of the renormalized dispersion, such as the magic angles, depend significantly on the interactions. Our results highlight the rich physics arising in doped moiré superlattices of Mott insulators.

flat bands↗

DOE OSTI2019

Experimental identification of the T = 1 , J π = 6 + state of Co 54 and isospin symmetry in A = 54 studied via one-nucleon knockout reactions

In this paper, new experimental data obtained from γ-ray tagged one-neutron and one-proton knockout from 55 Co are presented. A candidate for the sought-after T = 1, T z = 0, J π = 6 + state in 54 Co is proposed based on a comparison to the new data on 54 Fe, the corresponding observables predicted by large-scale-shell-model (LSSM) calculations in the full fp-model space employing charge-dependent contributions, and isospin-symmetry arguments. Furthermore, possible isospin-symmetry breaking in the A = 54, T = 1 triplet is studied by calculating the experimental c coefficients of the isobaric mass multiplet equation (IMME) up to the maximum possible spin J = 6 expected for the (1f 7/2 ) -2 two-hole configuration relative to the doubly magic nucleus 56 Ni. Lastly, the experimental quantities are compared to the theoretically predicted c coefficients from LSSM calculations using two-body matrix elements obtained from a realistic chiral effective field theory potential at next-to-next-to-next-to-leading order (N 3 LO).

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗