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DOE OSTI2022

Double echo symmetry-based REDOR and RESPDOR pulse sequences for proton detected measurements of heteronuclear dipolar coupling constants

1 H{X} symmetry-based rotational echo double resonance pulse sequences (S-REDOR) and symmetry-based rotational echo saturation pulse double resonance (S-RESPDOR) solid-state NMR experiments have found widespread application for 1 H detected measurements of difference NMR spectra, dipolar coupling constants, and internuclear distances under conditions of fast magic angle spinning (MAS). In these experiments the supercycled $\text{R4}^2_1 (\text{SR4}^2_1)$ symmetry-based recoupling pulse sequence is typically applied to the 1 H spins to reintroduce heteronuclear dipolar couplings. However, the timing of $\text{SR4}^2_1$ and other symmetry-based pulse sequences must be precisely synchronized with the rotation of the sample, otherwise, the evolution of 1 H CSA and other interactions will not be properly refocused. For this reason, significant distortions are often observed in experimental dipolar dephasing difference curves obtained with S-REDOR or S-RESPDOR pulse sequences. Here we introduce a family of double echo (DE) S-REDOR/S-RESPDOR pulse sequences that function in an analogous manner to the recently introduced $t_1$-noise eliminated (TONE) family of dipolar heteronuclear multiple quantum coherence (D-HMQC) pulse sequences. Through numerical simulations and experiments the DE S-REDOR/S-RESPDOR sequences are shown to provide dephasing difference curves similar to those obtained with S-REDOR/S-RESPDOR. However, the DE sequences are more robust to the deviations of the MAS frequency from the ideal value that occurs during typical solid-state NMR experiments. In this work, the DE sequences are shown to provide more reliable 1 H detected dipolar dephasing difference curves for nuclei such as 15 N (with isotopic labelling), 183 W and 35 Cl. The double echo sequences are therefore recommended to be used in place of conventional S-REDOR/S-RESPDOR sequences for measurement of weak dipolar coupling constants and long-range distances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Magnetic crystalline-symmetry-protected axion electrodynamics and field-tunable unpinned Dirac cones in EuIn 2 As 2

Knowledge of magnetic symmetry is vital for exploiting nontrivial surface states of magnetic topological materials. EuIn 2 As 2 is an excellent example, as it is predicted to have collinear antiferromagnetic order where the magnetic moment direction determines either a topological-crystalline-insulator phase supporting axion electrodynamics or a higher-order-topological-insulator phase with chiral hinge states. Here, we use neutron diffraction, symmetry analysis, and density functional theory results to demonstrate that EuIn 2 As 2 actually exhibits low-symmetry helical antiferromagnetic order which makes it a stoichiometric magnetic topological-crystalline axion insulator protected by the combination of a 180° rotation and time-reversal symmetries: $C_2 × \mathcal{T} =$ 2'. Surfaces protected by 2' are expected to have an exotic gapless Dirac cone which is unpinned to specific crystal momenta. All other surfaces have gapped Dirac cones and exhibit half-integer quantum anomalous Hall conductivity. We predict that the direction of a modest applied magnetic field of $μ_0H ≈$ 1 to 2 T can tune between gapless and gapped surface states.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Visualizing symmetry-breaking electronic orders in epitaxial Kagome magnet FeSn films

Abstract Kagome lattice hosts a plethora of quantum states arising from the interplay of topology, spin-orbit coupling, and electron correlations. Here, we report symmetry-breaking electronic orders tunable by an applied magnetic field in a model Kagome magnet FeSn consisting of alternating stacks of two-dimensional Fe 3 Sn Kagome and Sn 2 honeycomb layers. On the Fe 3 Sn layer terminated FeSn thin films epitaxially grown on SrTiO 3 (111) substrates, we observe trimerization of the Kagome lattice using scanning tunneling microscopy/spectroscopy, breaking its six-fold rotational symmetry while preserving the translational symmetry. Such a trimerized Kagome lattice shows an energy-dependent contrast reversal in dI/dV maps, which is significantly enhanced by bound states induced by Sn vacancy defects. This trimerized Kagome lattice also exhibits stripe modulations that are energy-dependent and tunable by an applied in-plane magnetic field, indicating symmetry-breaking nematicity from the entangled magnetic and charge degrees of freedom in antiferromagnet FeSn.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Approximate symmetries and quantum error correction

Abstract Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin–Knill theorem, which forbids the existence of QEC codes that admit transversal continuous symmetry actions (transformations). Here, we systematically study the competition between continuous symmetries and QEC in a quantitative manner. We first define a series of meaningful measures of approximate symmetries motivated from different perspectives, and then establish a series of trade-off bounds between them and QEC accuracy utilizing multiple different methods. Remarkably, the results allow us to derive general quantitative limitations of transversally implementable logical gates, an important topic in fault-tolerant quantum computation. As concrete examples, we showcase two explicit types of quantum codes, obtained from quantum Reed–Muller codes and thermodynamic codes, respectively, that nearly saturate our bounds. Finally, we discuss several potential applications of our results in physics.

Physics↗

DOE OSTI2022

Nonsymmorphic symmetry-protected band crossings in a square-net metal PtPb 4

Topological semimetals with symmetry-protected band crossings have emerged as a rich landscape to explore intriguing electronic phenomena. Nonsymmorphic symmetries in particular have been shown to play an important role in protecting the crossings along a line (rather than a point) in momentum space. Here we report experimental and theoretical evidence for Dirac nodal line crossings along the Brillouin zone boundaries in PtPb 4 , arising from the nonsymmorphic symmetry of its crystal structure. Interestingly, while the nodal lines would remain gapless in the absence of spin–orbit coupling (SOC), the SOC, in this case, plays a detrimental role to topology by lifting the band degeneracy everywhere except at a set of isolated points. Nevertheless, the nodal line is observed to have a bandwidth much smaller than that found in density functional theory (DFT). Our findings reveal PtPb 4 to be a material system with narrow crossings approximately protected by nonsymmorphic crystalline symmetries.

36 MATERIALS SCIENCE↗

DOE OSTI2021

A light-induced phononic symmetry switch and giant dissipationless topological photocurrent in ZrTe 5

Dissipationless currents from topologically protected states are promising for disorder-tolerant electronics and quantum computation. In this work, we photogenerate giant anisotropic terahertz nonlinear currents with vanishing scattering, driven by laser-induced coherent phonons of broken inversion symmetry in a centrosymmetric Dirac material ZrTe 5 . Our work suggests that this phononic terahertz symmetry switching leads to formation of Weyl points, whose chirality manifests in a transverse, helicity-dependent current, orthogonal to the dynamical inversion symmetry breaking axis, via circular photogalvanic effect. The temperature-dependent topological photocurrent exhibits several distinct features: Berry curvature dominance, particle–hole reversal near conical points and chirality protection that is responsible for an exceptional ballistic transport length of ~10 μm. These results, together with first-principles modelling, indicate two pairs of Weyl points dynamically created by B 1u phonons of broken inversion symmetry. Such phononic terahertz control breaks ground for coherent manipulation of Weyl nodes and robust quantum transport without application of static electric or magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Spectroscopic signatures of time-reversal symmetry breaking superconductivity

The collective mode spectrum of a symmetry-breaking state, such as a superconductor, provides crucial insight into the nature of the order parameter. In this work, we study two collective modes which are unique to unconventional superconductors that spontaneously break time reversal symmetry. We show that these modes are coherent and underdamped for a wide variety of time-reversal symmetry breaking superconducting states. By further demonstrating that these modes can be detected using a number of existing experimental techniques, we propose that our work can be leveraged as a form of “collective mode spectroscopy” that drastically expands the number of experimental probes capable of detecting time-reversal symmetry breaking in unconventional superconductors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Prediction of chlorine and fluorine crystal structures at high pressure using symmetry driven structure search with geometric constraints

The high-pressure properties of fluorine and chlorine are not yet well understood because both are highly reactive and volatile elements, which have made conducting diamond anvil cell and x-ray diffraction experiments a challenge. Here, we use ab initio methods to search for stable crystal structures of both elements at megabar pressures. We demonstrate how symmetry and geometric constraints can be combined to efficiently generate crystal structures that are composed of diatomic molecules. Furthermore, our algorithm extends the symmetry driven structure search method by adding constraints for the bond length and the number of atoms in a molecule while still maintaining generality. As a method of validation, we have tested our approach for dense hydrogen and reproduced the known molecular structures of Cmca-12 and Cmca-4. We apply our algorithm to study chlorine and fluorine in the pressure range of 10 GPa–4000 GPa while considering crystal structures with up to 40 atoms per unit cell. We predict chlorine to follow the same series of phase transformations as elemental iodine from Cmca to Immm to Fm3¯m, but at substantially higher pressures. We predict fluorine to transition from a C2/c to Cmca structure at 70 GPa, to a novel orthorhombic and metallic structure with P42/mmc symmetry at 2500 GPa, and finally to its cubic analog form with Pm3¯n symmetry at 3000 GPa.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Beyond Graphene: Low-Symmetry and Anisotropic 2D Materials

Low-symmetry 2D materials—such as ReS 2 and ReSe 2 monolayers, black phosphorus monolayers, group-IV monochalcogenide monolayers, borophene, among others—have more complex atomistic structures than the honeycomb lattices of graphene, hexagonal boron nitride, and transition metal dichalcogenides. The reduced symmetries of these emerging materials give rise to inhomogeneous electron, optical, valley, and spin responses, as well as entirely new properties such as ferroelasticity, ferroelectricity, magnetism, spin-wave phenomena, large nonlinear optical properties, photogalvanic effects, and superconductivity. Novel electronic topological properties, nonlinear elastic properties, and structural phase transformations can also take place due to low symmetry. Lastly, the “Beyond Graphene: Low-Symmetry and Anisotropic 2D Materials” Special Topic was assembled to highlight recent experimental and theoretical research on these emerging materials.

2D materials↗

DOE OSTI2024

Symmetry breaking and self-interaction correction in the chromium atom and dimer

Density functional approximations to the exchange–correlation energy can often identify strongly correlated systems and estimate their energetics through energy-minimizing symmetry-breaking. In particular, the binding energy curve of the strongly correlated chromium dimer is described qualitatively by the local spin density approximation (LSDA) and almost quantitatively by the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA), where the symmetry breaking is antiferromagnetic for both. Here, we show that a full Perdew–Zunger self-interaction-correction (SIC) to LSDA seems to go too far by creating an unphysical symmetry-broken state, with effectively zero magnetic moment but non-zero spin density on each atom, which lies ~4 eV below the antiferromagnetic solution. A similar symmetry-breaking, observed in the atom, better corresponds to the 3d↑↑4s↑3d↓↓4s↓ configuration than to the standard 3d↑↑↑↑↑4s↑. For this new solution, the total energy of the dimer at its observed bond length is higher than that of the separated atoms. In conclusion, these results can be regarded as qualitative evidence that the SIC needs to be scaled down in many-electron regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Diagnosing hot-spot symmetry in surrogate ignition experiments via secondary DT-neutron spectroscopy at the NIF

The directional energy spectrum of neutrons generated from the in-flight fusion reaction of 1-MeV tritons contains information about the hot-spot symmetry. The National Ignition Facility (NIF) fields Symmetry Capsule (Symcap) implosions, which have historically measured the symmetry of the radiation, drive by measuring the hot-spot shape via x-ray self-emission. Symcaps are used to tune the hot-spot symmetry for ignition experiments at the NIF. This work shows the relationship between directional secondary DT-n spectra and x-ray imaging data for a large database of Symcap implosions. A correlation is observed between the relative widths of the DT-n spectra measured with nTOFs and the shape measured with x-ray imaging. A Monte Carlo model, which computes the directional secondary DT-n spectrum, is used to interpret the results. A comparison of the x-ray and secondary DT-n data with the Monte Carlo model indicates that 56% of the variance between the two datasets is explained by a P2 asymmetry. More advanced simulations using HYDRA suggest that the unaccounted variance is due to P1 and P4 asymmetries present in the hot spot. The comparison of secondary DT-n data and x-ray imaging data to the modeling shows the DT-n data contain important information that supplements current P2 measurements and contain new information about the P1 asymmetry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Aspects of symmetry and topology in the charge density wave phase of 1T–TiSe 2

Abstract The charge density wave (CDW) in 1 T –TiSe 2 harbors a nontrivial symmetry configuration. It is important to understand this underlying symmetry both for gaining a handle on the mechanism of CDW formation and for probing the CDW experimentally. Here, based on first-principles computations within the framework of the density functional theory, we unravel the connection between the symmetries of the normal and CDW states and the electronic structure of 1 T –TiSe 2 . Our analysis highlights the key role of irreducible representations of the electronic states and the occurrence of band gaps in the system in driving the CDW. By showing how symmetry-related topology can be obtained directly from the electronic structure, our study provides a practical pathway in search of topological CDW insulators.

Physics↗

DOE OSTI2026

Profusion of symmetry-protected qubits from stable ergodicity breaking

We show how combining a discrete symmetry with topological Hilbert space fragmentation can give rise to exponentially many topologically stable qubits protected by a single discrete symmetry. We illustrate this explicitly with the example of the CZ𝑝 model, where the encoded qubits are prethermally stable to arbitrary symmetry-respecting perturbations for parametrically long times, substantially enhancing the robustness of a recently proposed construction based on nontopological fragmentation. In this model, the encoded qubits naturally come in pairs for which a universal set of transversal logical gates can be performed, ruling out (by the Eastin-Knill theorem) the possibility of using them for quantum error correction. We also comment on the combination of symmetry enrichment and topological fragmentation more generally, and the implications for use of systems exhibiting Hilbert space fragmentation as quantum memories.

kinetically constrained models↗

DOE OSTI2020

Bosonic crystalline symmetry protected topological phases beyond the group cohomology proposal

It is demonstrated by explicit construction that three-dimensional bosonic crystalline symmetry protected topological (cSPT) phases are classified by $H^5_\phi(G; \mathbb{Z})⊕H^1_\phi(G; \mathbb{Z})$ for all 230 space groups $\textit{G}$, where $H^n_\phi(G; \mathbb{Z})$ denotes the $\textit{n}$th twisted group cohomology of $\textit{G}$ with $\mathbb{Z}$ coefficients, and $\phi$ indicates that $\textit{g ε G}$ acts nontrivially on coefficients by sending them to their inverses if $\textit{g}$ reverses space-time orientation and acts trivially otherwise. The previously known summand $H^5_\phi(G;\mathbb{Z})$ corresponds only to crystalline phases built without the $E_8$ state or its multiples on 2-cells of space. It is the crystalline analog of the “group cohomology proposal” for classifying bosonic symmetry protected topological (SPT) phases, which takes the form $H^{d + 2}_\phi(G; \mathbb{Z}) ≅ H^{d + 1}_\phi(G; \text{U}(1))$ for finite internal symmetry groups in d spatial dimensions. The new summand $H^1_\phi(G; \mathbb{Z})$ classifies possible configurations of $E_8$ states on 2-cells that can be used to build crystalline phases beyond the group cohomology proposal. The completeness of our classification and the physical meaning of $H^1_\phi(G; \mathbb{Z})$ are established through a combination of dimensional reduction, surface topological order, and explicit cellular construction. The value of $H^1_\phi(G; \mathbb{Z})$ can be easily read off from the international symbol for $\textit{G}$. In this work, our classification agrees with the prediction of the “generalized cohomology hypothesis,” which concerns the general structure of the classification of SPT phases, and therefore provides strong evidence for the validity of the said hypothesis in the realm of crystalline symmetries.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Tunable chiral symmetry breaking in symmetric Weyl materials

Asymmetric Weyl semimetals, which possess an inherently chiral structure, have different energies and dispersion relations for left- and right-handed fermions. They exhibit certain effects not found in symmetric Weyl semimetals, such as the quantized circular photogalvanic effect and the helical magnetic effect. In this work, we derive the conditions required for breaking chiral symmetry by applying an external field in symmetric Weyl semimetals. Here, we explicitly demonstrate that in certain materials with the T d point group, magnetic fields along low symmetry directions break the symmetry between left- and right-handed fermions; the symmetry breaking can be tuned by changing the direction and magnitude of the magnetic field. In some cases, we find an imbalance between the number of type I left- and right-handed Weyl cones (which is compensated by the number of type II cones of each chirality).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Emergent 1-form symmetries

We explore the necessary conditions for 1-form symmetries to emerge in the long-distance limit when they are explicitly broken at short distances. A minimal requirement is that there exist operators which become topological at long distances and that these operators have nontrivial correlation functions. These criteria are obeyed when the would-be emergent symmetry is spontaneously broken, or is involved in ’t Hooft anomalies. On the other hand, confinement, i.e. a phase with unbroken 1-form symmetry, is nearly incompatible with the emergence of 1-form symmetries. We comment on some implications of our results for QCD as well as the idea of Higgs-confinement continuity. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2024

Gauging staggered fermion shift symmetries

Staggered fermion shift symmetries correspond to translations of the fermion field within the unit cell of a hypercubic lattice. They satisfy an algebra and in four Euclidean dimensions can be related to a discrete subgroup of an S U ( 4 ) flavor symmetry which plays a crucial role in showing that staggered fermions lead to a theory of four degenerate Dirac fermions in the continuum limit. They are associated with the appearance of certain Z 2 valued global parameters. We propose a strategy to try to partially gauge these translation symmetries by allowing these parameters to vary locally in the lattice. To maintain invariance of the action requires the addition of Z 2 valued higher form lattice gauge fields. An analogous procedure can be carried out for reduced staggered fermions where the shifts correspond to a discrete subgroup of an S O ( 4 ) flavor symmetry. Published by the American Physical Society 2024

Catterall, Simon (ORCID:0000000327352682)↗

DOE OSTI2020

Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry

In this work, we introduce the notion of combinatorial gauge symmetry—a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states)—that preserve the commutation and anticommutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated with the automorphism of these matrices with respect to monomial transformations. Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions. In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits.

36 MATERIALS SCIENCE↗