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DOE OSTI2024

Higgs-confinement transitions in QCD from symmetry protected topological phases

In gauge theories with fundamental matter there is typically no sharp way to distinguish confining and Higgs regimes, e.g. using generalized global symmetries acting on loop order parameters. It is standard lore that these two regimes are continuously connected, as has been explicitly demonstrated in certain lattice and continuum models. We point out that Higgsing and confinement sometimes lead to distinct symmetry protected topological (SPT) phases -- necessarily separated by a phase transition -- for ordinary global symmetries. We present explicit examples in 3+1 dimensions, obtained by adding elementary Higgs fields and Yukawa couplings to QCD while preserving parity P and time reversal T. In a suitable scheme, the confining phases of these theories are trivial SPTs, while their Higgs phases are characterized by non-trivial P- and T-invariant theta-angles θ f , θ g = π for flavor or gravity background gauge fields, i.e. they are topological insulators or superconductors. Finally, we consider conventional three-flavor QCD (without elementary Higgs fields) at finite U(1) B baryon-number chemical potential μ B , which preserves P and T. At very large μ B , three-flavor QCD is known to be a completely Higgsed color superconductor that also spontaneously breaks U(1) B . We argue that this high-density phase is in fact a gapless SPT, with a gravitational theta-angle θ g = π that safely co-exists with the U(1) B Nambu-Goldstone boson. We explain why this SPT motivates unexpected transitions in the QCD phase diagram, as well as anomalous surface modes at the boundary of quark-matter cores inside neutron stars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Realizing symmetry-protected topological phases in a spin-1/2 chain with next-nearest-neighbor hopping on superconducting qubits

Quantum simulation on near-term quantum hardware is a topic of intense interest. The preparation of novel quantum states of matter provides a quantitative assessment of the capabilities of near-term digital quantum computers to implement circuits with structure of relevance to quantum simulation. Here, we conduct a benchmark study by realizing symmetry-protected topological (SPT) phases of a spin-1/2 Hamiltonian with next-nearest-neighbor hopping on up to 11 qubits on a programmable superconducting quantum processor using adiabatic state preparation. Using recompilation techniques to reduce the gate count to around 50 two-qubit gates, we observe clear signatures of the two distinct SPT phases, such as excitations localized to specific edges and finite string-order parameters. Finally, we identify a parasitic phase associated with the two-qubit gate as the dominant imperfection that limits the depth of the circuits, indicating a research topic of interest for future hardware development.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Engineering topologically protected superconducting states

Efforts to develop systems which support non-Abelian excitations are motivated by both scientific curiosity and a practical desire to built a fault tolerant quantum computer to solve problems fundamentally intractable for classical computations. Experimentally, signatures of simplest non-Abelian excitations have been seen in spectroscopic measurements, yet current experiments fall shot of demonstrating non-Abelian exchange statistics. With DOE support we explore several systems where non-Abelian excitations are expected to appear, with special attention paid to the ability to demonstrate braiding. In nanowire semiconductor/superconductor hybrid system we are developing devices where position of Majorana particles, the simplest non-Abelian excitations, can be varied by magnetic field. The system will allow braiding of Majorana fermions and study non-Abelian statistics. In another system we focus on the development of a new platform where higher order non-Abelian excitations - parafermions - can be realized. Recently we demonstrated formation of heliacal channels in the fractional quantum Hall regime, precursors of topological superconductors that support parafermion excitations. Investigation of these channels and induced superconductivity will be an important part of the proposed research. Finally, investigation of induced superconductivity in topological insulators and discovery of highly unharmonic current-phase relation in Josephson junctions is the basis for the proposed realization of a topologically protected qubits with abelian anions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Topologically protected Grover's oracle for the partition problem

The number partitioning problem (NPP) is one of the NP-complete (nondeterministic polynomial-time complete) computational problems. Its definite exact solution generally requires a check of all $N$ solution candidates, which is exponentially large. Here we describe a path to the fast solution of this problem in $\sqrt{N}$ quasi-adiabatic quantum annealing steps. We argue that the errors due to the finite duration of the quantum annealing can be suppressed if the annealing time scales with $N$ only logarithmically. Moreover, our adiabatic oracle is topologically protected, in the sense that it is robust against small uncertainty and slow time dependence of the physical parameters or the choice of the annealing protocol. In conclusion, we also argue that our approach can solve many other famous NP-complete computational problems in $\sqrt{N}$ steps.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Topologically Protected Flatness in Chiral Moiré Heterostructures

The observation of delicate correlated phases in twisted heterostructures of graphene and transition metal dichalcogenides suggests that moiré flat bands are intrinsically resilient against certain types of disorder. Here, we investigate the robustness of moiré flat bands in the chiral limit of the Bistritzer-MacDonald model—applicable to both platforms in certain limits—and demonstrate drastic differences between the first magic angle and higher magic angles in response to chiral symmetric disorder that arise, for instance, from lattice relaxation. We understand these differences using a hidden constant of motion that permits the decomposition of the non-Abelian gauge field induced by interlayer tunnelings into two decoupled Abelian ones. At all magic angles, the resulting effective magnetic field splits into an anomalous contribution and a fluctuating part. The anomalous field maps the moiré flat bands onto a zeroth Dirac Landau level, whose flatness withstands any chiral symmetric perturbation such as nonuniform magnetic fields due to a topological index theorem—thereby underscoring a topological mechanism for band flatness. Only the first magic angle can fully harness this topological protection due to its weak fluctuating magnetic field. In higher magic angles, the amplitude of fluctuations largely exceeds the anomalous contribution, which we find results in a physically meaningless chiral operator and an extremely large sensitivity to microscopic details and an exponential collapse of the single-particle gap. Through numerical simulations, we further study various types of disorder and identify the scattering processes that are enhanced or suppressed in the chiral limit. Interestingly, we find that the topological suppression of disorder broadening persists away from the chiral limit and is further accentuated by isolating a single sublattice polarized flat band in energy. Our analysis suggests the Berry curvature hot spot at the top of the K and K ′ valence band in the transition metal dichalcogenide monolayers is essential for the stability of its moiré flat bands and their correlated states. Published by the American Physical Society 2025

Crépel, Valentin (ORCID:0000000302403412)↗
DOE OSTI2023

Breakdown of helical edge state topologically protected conductance in time-reversal-breaking excitonic insulators

Gapless helical edge modes are a hallmark of the quantum spin Hall effect. Protected by time-reversal symmetry, each edge contributes a quantized zero-temperature conductance quantum G 0 ≡ e 2 /h. However, the experimentally observed conductance in WT e2 decreases below G 0 per edge already at edge lengths around 100 nm, even in the absence of explicit time-reversal breaking due to an external field or magnetic impurities. Here we show how a time-reversal breaking excitonic condensate with a spin-spiral order that can form in WT e2 leads to the breakdown of conductance quantization. We perform Hartree-Fock calculations to compare time-reversal breaking and preserving excitonic insulators. Using these mean-field models we demonstrate via quantum transport simulations that weak nonmagnetic disorder reproduces the edge length scaling of resistance observed in the experiments. We complement this by analysis in the Luttinger liquid picture, shedding additional light on the mechanism behind the quantization breakdown.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Symmetry-protected topological polarons

Emergent quasiparticles in solids often exhibit unique topological properties as a result of the complex interplay between charge, orbital, spin, and lattice degrees of freedom. Among these quasiparticles, the polaron occupies a special place as the first known manifestation of the interaction between a fermion and a boson field. While polarons have been investigated for almost a century, whether these quasiparticles exhibit topological properties and why remain open questions. Here, we establish the universal symmetry principles governing the topology of polar textures in large polarons. Using a group-theoretic analysis, we identify four distinct classes of polar textures in time-reversal-invariant systems, and we show that they carry integer topological charges. We validate this classification by performing state-of-the-art first-principles calculations of materials representative of each class. For these materials, we compute the fingerprints of polaron topology in Huang diffuse scattering and propose ultrafast electron and X-ray scattering experiments to detect these quasiparticles.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Two-atom-thin topological crystalline insulators lacking out of plane inversion symmetry

A two-dimensional topological crystalline insulator (TCI) with a single unit cell (u.c.) thickness is demonstrated here. To that end, one first shows that tetragonal (C 4 in-plane) symmetry is not a necessary condition for the creation of zero-energy metallic surface states on TCI slabs of finite-thicknesses, because zero-energy states persist even as all the in-plane rotational symmetries—furnishing topological protection—are completely removed. In other words, zero-energy levels on the model are not due to (nor are they protected by) topology. Furthermore, effective two-fold energy degeneracies taking place at few discrete k-points away from zero energy in the bulk Hamiltonian—that are topologically protected—persist at the u.c. thickness limit. Here, the chiral nature of the bulk TCI Hamiltonian permits creating a $2\times 2$ square Hamiltonian, whose topological properties remarkably hold invariant at both the bulk and at the single u.c. thickness limits. The identical topological characterization for bulk and u.c.-thick phases is further guaranteed by a calculation involving Pfaffians. This way, a two-atom-thick TCI is deployed hereby, in a demonstration of a topological phase that holds both in the bulk, and in two dimensions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Floquet dynamics of disordered bands with isolated critical energies

We investigate localization properties of driven models which exhibit a subextensive number of extended states in the static setting. We consider instances where the extended modes are or are not protected by topological considerations. To this end, we contrast the strongly driven, disordered, lowest Landau level, which we refer to as the random Landau model (RLM), with the random dimer model (RDM); the RDM also has a subextensive set of delocalized modes in the middle of the spectrum whose origin is not topological. We map the driven models on to a higher-dimensional effective model and numerically compute the localization length as a function of disorder strength, drive amplitude, and frequency using the recursive Green's function method. Our numerical results indicate that, in the presence of a strong drive (low frequency and/or large drive amplitude), the topologically protected RLM continues to exhibit a spectrum with both localized and delocalized (or critical) modes, but the spectral range of delocalized modes is enhanced by the driving. This occurs due to an admixture of the localized modes with extended modes arising due to the topologically protected critical energy in the middle of the spectrum. On the other hand, in the RDM, a weak drive immediately localizes the entire spectrum. This occurs in contrast to the naive expectation from perturbation theory that mixing between localized and delocalized modes generically enhances the delocalization of all modes. Our work highlights the importance of the origin of the delocalized modes in the localization properties of the corresponding Floquet model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Gapless Floquet topology

Symmetry-protected topological (SPT) phases in insulators and superconductors are known for their robust edge modes, linked to bulk invariants through the bulk-boundary correspondence. While this principle traditionally applies to gapped phases, recent advances have extended it to gapless systems, where topological edge-states persist even in the absence of a bulk gap. We extend this framework to periodically driven chains with chiral symmetry, revealing the existence of topological edge zero and π modes despite the lack of bulk gaps in the quasienergy spectrum. By examining the half-period decomposition of chiral evolutions, we construct topological invariants that circumvent the need to define the Floquet Hamiltonian, making them more suitable for generalization to the gapless regime. We provide explicit examples, including generalizations of the Kitaev chain and related spin models, where localized π modes emerge even when the bulk is gapless at the same quasienergy as the edge modes. Here, we numerically study the effect of interactions, which give a finite lifetime to the edge modes in the thermodynamic limit with the decay rate consistent with Fermi's golden rule.

1-dimensional systems↗
DOE OSTI2023

Quantum spin helices more stable than the ground state: Onset of helical protection

Topological magnetic structures are promising candidates for resilient information storage. An elementary example is spin helices in one-dimensional easy-plane quantum magnets. To quantify their stability, we numerically implement the stochastic Schrödinger equation and time-dependent perturbation theory for spin chains with fluctuating local magnetic fields. Here, we find two classes of quantum spin helices that can reach and even exceed ground-state stability: spin-current-maximizing helices and, for fine-tuned boundary conditions, the recently discovered “phantom helices.” Beyond that, we show that the helicity itself (left or right rotating) is even more stable. We explain these findings by separated helical sectors and connect them to topological sectors in continuous spin systems. The resulting helical protection mechanism is a promising phenomenon for stabilizing helical quantum structures, e.g., in ultracold atoms and solid-state systems. We also identify a third type of phantom helix in the system.

1-dimensional spin chains↗