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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Clifford transformations for fermionic quantum systems: From Pauli and Majorana operators to Dirac fermions

Clifford gates and transformations, which map products of elementary Pauli or Majorana operators to other such products, are foundational in quantum computing, underpinning the stabilizer formalism, error-correcting codes, magic state distillation, quantum communication and cryptography, and qubit tapering. Moreover, circuits composed entirely of Clifford gates are classically simulatable, highlighting their computational significance. In this article we extend the concept of Clifford transformations to Dirac fermions. We demonstrate that discrete Clifford transformations are generated by half-body and pair operators while continuous Clifford transformations are generated by number operators, providing a systematic framework for their characterization. Additionally, we establish connections with fermionic mean-field theories and applications in qubit tapering, offering insights into their broader implications in quantum computing.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Semi-Dirac Fermions in a Topological Metal

Topological semimetals with massless Dirac and Weyl fermions represent the forefront of quantum materials research. In two dimensions, a peculiar class of fermions that are massless in one direction and massive in the perpendicular direction was predicted 16 years ago. These highly exotic quasiparticles—the semi-Dirac fermions—ignited intense theoretical and experimental interest but remain undetected. Using magneto-optical spectroscopy, we demonstrate the defining feature of semi-Dirac fermions— B 2 / 3 scaling of Landau levels—in a prototypical nodal-line metal ZrSiS. In topological metals, including ZrSiS, nodal lines extend the band degeneracies from isolated points to lines, loops, or even chains in the momentum space. With calculations and theoretical modeling, we pinpoint the observed semi-Dirac spectrum to the crossing points of nodal lines in ZrSiS. Crossing nodal lines exhibit a continuum absorption spectrum but with singularities that scale as B 2 / 3 at the crossing. Our work sheds light on the hidden quasiparticles emerging from the intricate topology of crossing nodal lines and highlights the potential to explore quantum geometry with linear optical responses. Published by the American Physical Society 2024

Shao, Yinming (ORCID:0000000228910028)↗
DOE OSTI2025

Emergence of Moiré Dirac Fermions at the Interface of Topological and 2D Magnetic Insulators

Dirac Fermions on the surface of the topological insulator are spin-momentum locked and topologically protected, making them interesting for spintronics and quantum computing applications. When in proximity to magnetism and superconductivity, these electronic states could result in quantum anomalous Hall effect and Majorana Fermions, respectively. An even more dramatic enrichment of the topological insulators’ physics is expected for moiré superlattices, where, analogously to the twisted graphene layers, electronic correlations could be strongly enhanced, a task previously notoriously difficult to achieve in topological matter. Until now, the experimental confirmation of such moiré properties has remained elusive. Here, we grow the two-dimensional van der Waals magnetic insulators FeX 2 (where X = Cl or Br) on top of the topological insulator Bi 2 Se 3 and establish a moiré superlattice formation at the interface. By means of scanning tunneling microscopy and angle-resolved photoemission spectroscopy, we investigate the electronic properties of the formed moiré superlattice and demonstrate its tunability via the film choice. We reveal replicated Dirac cones and focus on their intersections, which, in the case of FeBr 2 /Bi 2 Se 3 , occur below the Fermi level. We identify the signatures of small gaps at the intersections around the M̅ i points that we attribute to the moiré interaction. These findings point to the specific type of magnetic moiré potential that breaks the time-reversal symmetry at these points but not at the $\barΓ$ point. Our observations provide an intriguing scenario of correlated topological phases induced by moiré superlattice that may result in topological superconductivity, high Chern number phases, and exotic noncollinear magnetic textures.

2D magnets↗
DOE OSTI2026

Dirac Fermions and Flat Bands in Phosphorus Carbide Nanotubes: Structural and Quantum Phase Transitions in a Quasi-One-Dimensional Material

Chemically realistic quasi-one-dimensional (1D) materials in which Dirac Fermions and highly degenerate flat bands coexist intrinsically at the Fermi level are exceedingly rare, while representing a highly desirable platform for correlated and topological quantum phenomena. Here, in this work, using specialized symmetry-adapted first-principles calculations we predict a new class of nanomaterials─phosphorus carbide nanotubes (P 2 C 3 NTs)─obtained by rolling monolayer P 2 C 3 , a two-dimensional material shown in a previous letter to host “double Kagome bands”. Both armchair and zigzag P 2 C 3 NTs are stable at room temperature and feature the rare coexistence of Dirac crossings and multiple flat bands at the Fermi level inherited from the underlying honeycomb–Kagome lattice, with the flat bands resilient to elastic deformations. Under large strain, the structure transforms from honeycomb–Kagome to “brick-wall”, accompanied by multiple coupled structural and quantum phase transitions. We also uncover localized edge states, spin splitting from vacancies and dopants, and strain-tunable magnetism. Together, these results establish P 2 C 3 NTs as a chemically specific and mechanically tunable 1D material platform with potential applications in quantum hardware and spintronics.

carbon nanotubes↗
DOE OSTI2025

Terahertz Landau level spectroscopy of Dirac fermions in millimeter-scale twisted bilayer graphene

Exotic electronic physics including correlated insulating states and fractional Chern insulators have been observed in twisted bilayer graphene in a magnetic field when the Fermi velocity vanishes; however, a question remains as to the stability of these states, which is controlled by the gap to the first excited state. Free-space terahertz magneto-optics can directly probe the gap to charge excitations, which bounds the stability of electronic states, but this measurement has thus far been inaccessible due to the micron size of twisted bilayer graphene samples, while the wavelength of terahertz light is up to 1 mm. Here we leverage advances in fabrication to create twisted bilayer graphene samples over 5×5 mm in size with a uniform twist angle and study the magnetic field dependence of the cyclotron resonance by a complex Faraday rotation experiment in 𝑝-doped large angle twisted bilayer graphene. These measurements directly probe charge excitations in inter-Landau level transitions and determine the Fermi velocity as a function of twist angle.

Mead, Benjamin [University of Pennsylvania]↗
DOE OSTI2025

Terahertz Landau level spectroscopy of Dirac fermions in millimeter-scale twisted bilayer graphene

Exotic electronic physics including correlated insulating states and fractional Chern insulators have been observed in twisted bilayer graphene in a magnetic field when the Fermi velocity vanishes, however a question remains as to the stability of these states which is controlled by the gap to the first excited state. Free-space terahertz magneto-optics can directly probe the gap to charge excitations which bounds the stability of electronic states, but this measurement has thus-far been inaccessible due to the micron size of twisted bilayer graphene samples, while the wavelength of terahertz light is up to a millimeter. Here we leverage advances in fabrication to create twisted bilayer graphene samples over 5 mm x 5 mm in size with a uniform twist angle and study the magnetic field dependence of the cyclotron resonance by a complex Faraday rotation experiment in p-doped large angle twisted bilayer graphene. These measurements directly probe charge excitations in inter-Landau level transitions and determine the Fermi velocity as a function of twist angle.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Generalized Ginsparg-Wilson relations: Fermionic anomalies on the lattice

The Ginsparg-Wilson (GW) relation elegantly captures how the anomalous chiral symmetry of a Dirac fermion manifests on the lattice. In this talk, we discuss how the GW relation and its closed-form solution, the overlap operator, can be generalized to Majorana or Dirac fermions in any dimension for finite symmetry transformations (continuous or discrete). We find an exact symmetry which reproduces both perturbative and global anomalies on the lattice. These generalized GW fermions are boundary theories of various bulk symmetry-protected topological phases and thus provide an explicit lattice realization of the fermionic bulk-boundary correspondence central to recent proposals for chiral gauge theories on the lattice.

Singh, Hersh [Fermilab] (ORCID:0000000220026959)↗
DOE OSTI2026

Symmetry-engineered chiral magnetotransport in the correlated oxide SrNbO 3

Chiral transport in topological materials, arising from the interplay between topology and chirality, holds significant potential for energy-efficient spintronics and quantum information technologies through dissipationless, coherent charge flow. However, the emergence of chiral transport by tuning the electronic states of novel chiral materials is largely unexplored. Here, we report chiral transport driven by correlated Dirac fermions in SrNbO 3 epitaxial thin films, where strain-induced nonsymmorphic symmetry of oxygen octahedra tunes the material from metallic to Dirac states. Such symmetry-driven Dirac fermions feature a remarkable enhancement of electron mobility and magnetoresistance. Signatures of chiral transport induced by the chiral anomaly, including negative longitudinal magnetoresistance and twofold planar Hall oscillation, are observed in the Dirac semimetallic state, whereas they are absent in the metallic state of SrNbO 3 thin films. This work highlights a crucial role of symmetry engineering in generating chiral charge transport in oxide Dirac semimetals, opening an avenue to novel oxide-based topological and quantum devices.

Materials science↗
DOE OSTI2024

Uniform Diffusion of Cooper Pairing Mediated by Hole Carriers in Topological Sb 2 Te 3 /Nb

Spin-helical Dirac Fermions at a doped topological insulator’s boundaries can support Majorana quasiparticles when coupled with s-wave superconductors, but in n-doped systems, the requisite induced Cooper pairing in topological states is often buried at heterointerfaces or complicated by degenerate coupling with bulk conduction carriers. Rarely probed are p-doped topological structures with nondegenerate Dirac and bulk valence bands at the Fermi level, which may foster long-range superconductivity without sacrificing Majorana physics. Using ultrahigh-resolution photoemission, we report proximity pairing with a large decay length in p-doped topological Sb 2 Te 3 on superconducting Nb. Despite no momentum-space degeneracy, the topological and bulk states of Sb 2 Te 3 /Nb exhibit the same isotropic superconducting gaps at low temperatures. Furthermore, our results unify principles for realizing accessible pairing in Dirac Fermions relevant to topological superconductivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Protected fermionic zero modes in periodic gauge fields

It is well known that macroscopically normalizable zero-energy wave functions of spin-$\frac{1}{2}$ particles in a two-dimensional inhomogeneous magnetic field are spin-polarized and exactly calculable with degeneracy equaling the number of flux quanta linking the whole system. Here, extending this argument to massless Dirac fermions subjected to magnetic fields that have zero net flux but are doubly periodic in real space, we show that there exist only two Bloch-normalizable zero-energy eigenstates, one for each spin flavor. This result is immediately relevant to graphene multilayer systems subjected to doubly periodic strain fields, which at low energies enter the Hamiltonian as periodic pseudogauge vector potentials. Furthermore, we explore various related settings including nonlinearly dispersing band structure models and systems with singly periodic magnetic fields.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Cascading from $\mathscr{N}$ = 2 supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD

We argue that adjoint QCD in 3 + 1 dimensions, with any SU(N) gauge group and two Weyl fermion flavors (i.e. one adjoint Dirac fermion), confines and spontaneously breaks its chiral symmetries via the condensation of a fermion bilinear. We flow to this theory from pure $\mathscr{N}$ = 2 SUSY Yang–Mills theory with the same gauge group, by giving a SUSY-breaking mass M to the scalars in the $\mathscr{N}$ = 2 vector multiplet. This flow can be analyzed rigorously at small M, where it leads to a deconfined vacuum at the origin of the $\mathscr{N}$ = 2 Coulomb branch. The analysis can be extended to all M using an Abelian dual description that arises from the N multi-monopole points of the $\mathscr{N}$ = 2 theory. At each such point, there are N −1 hypermultiplet Higgs fields h$^{i=1,2}_m$, which are SU(2) R doublets. We provide a detailed study of the phase diagram as a function of M, by analyzing the semi-classical phases of the dual using a combination of analytic and numerical techniques. The result is a cascade of first-order phase transitions, along which the Higgs fields h i m successively turn on, and which interpolates between the Coulomb branch at small M, where all h$^{i}_m$ = 0, and a maximal Higgs branch, where all h$^{i}_m$ ≠ 0, at sufficiently large M. We show that this maximal Higgs branch precisely matches the confining and chiral symmetry breaking phase of two-flavor adjoint QCD, including its broken and unbroken symmetries, its massless spectrum, and the expected large-N scaling of various observables. The spontaneous breaking pattern SU(2) R → U(1) R , consistent with the Vafa–Witten theorem, is ensured by an intricate alignment mechanism for the h$^{i}_m$ in the dual, and leads to a CP 1 sigma model of increasing radius along the cascade.

D’Hoker, Eric [Univ. of California, Los Angeles, C↗
DOE OSTI2026

Pairing around a single Dirac point: A unifying view of Kohn-Luttinger superconductivity in Chern bands, quarter metals, and topological surface states

Superconductivity of a single two-dimensional Dirac fermion offers a natural route to topological superconductivity. While usually considered extrinsic—arising from proximity to a conventional superconductor—we investigate when a doped Dirac cone can develop superconductivity from a short-range repulsive interaction 𝑈 via the Kohn–Luttinger mechanism. We show that an ideal, linear Dirac cone is immune to pairing at leading order in 𝑈 2 . Superconductivity instead emerges only through higher-order in 𝑘 corrections to the dispersion, which are unavoidable in any lattice realization and crucially dictate the pairing symmetry. The form of the pairing thus reflects how the well-known obstruction to realizing a single Dirac cone on a lattice is circumvented. When a Dirac cone arises from broken time-reversal symmetry—for instance, at a transition between Chern insulators or in a valley-polarized phase—we find a topological 𝑝−𝑖⁢𝑝 state whose chirality is opposite to that of the parent chiral metal above 𝑇 𝑐 . By contrast, for a surface Dirac cone of a 3D topological insulator, superconductivity is stabilized by anisotropies in the dispersion. For 𝐶 3⁢𝑣 -symmetric warping, as in , pairing is strongest when the Fermi surface becomes hexagonal, leading to order in the (𝑑±𝑖⁢𝑑)×(𝑝+𝑖⁢𝑝) channel with accidental near-nodes. In the highly anisotropic limit 𝑣 𝑥 ≫𝑣 𝑦 , relevant to side surfaces of layered materials, the Fermi surface splits into two branches, and nesting favors a pairing symmetry 𝛥∼s⁢g⁡n⁢(𝑘 𝑥 )⁢cos⁡(𝑘 𝑦 ) reminiscent of organic superconductors.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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 OSTI2026

Exact chiral symmetry with quantum signal processing

We give a quantum signal processing (QSP) algorithm for the overlap fermion Hamiltonian which preserves the Ginsparg-Wilson relation up to a controllable error $ε_e$. Quantum simulations of Dirac fermions with exact chiral symmetry are thus nearly free: applying the overlap Hamiltonian costs only a factor logarithmic in $ε_e$ more than the Wilson-Dirac Hamiltonian. Comparing to domain-wall fermions, a mild overhead is found in circuit complexity while reducing qubit costs. We show how QSP effectively constructs an extra dimension when simulating the overlap operator, illustrating that the scaling of quantum algorithms reflects the deeper physics of overlap fermions arising at the boundary of domain-wall fermions.

Lamm, Henry [Fermilab] (ORCID:0000000330330791)↗
DOE OSTI2024

Nodal fermions in the strongly spin-orbit coupled pyrochlore-lattice compound RbBi2

We explore the topological electronic band structure of the pyrochlore lattice in the strong spin-orbit coupling regime. Using angle-resolved photoemission spectroscopy, first-principles calculations, and symmetry analysis, we have investigated the bulk electronic structure of RbBi2, which has a Bi pyrochlore network. We observe the presence of 3D massless Dirac fermions enforced by nonsymmorphic symmetry, as well as a 3D quadratic band crossing protected by cubic crystalline symmetry. Furthermore, we identify an additional 3D linear Dirac dispersion associated with band inversion protected by threefold rotation symmetry. These observations reveal the rich band topology of itinerant pyrochlore lattice systems in the strong SOC limit and serve as a starting point to explore correlated topological phases in geometrically frustrated lattices.

Oh, Dongjin↗
DOE OSTI2025

$2+1$ dimensional Floquet systems and lattice fermions: Exact bulk spectral equivalence

A connection has recently been proposed between periodically driven systems known as Floquet insulators in continuous time and static fermion theories in discrete time. This connection has been established in a (1+1) ( 1 + 1 ) -dimensional free theory, where an explicit mapping between the spectra of a Floquet insulator and a discrete-time Dirac fermion theory has been formulated. Here we investigate the potential of static discrete-time theories to capture Floquet physics in higher dimensions, where so-called anomalous Floquet topological insulators can emerge that feature chiral edge states despite having bulk bands with zero Chern number. Starting from a particular model of an anomalous Floquet system, we provide an example of a static discrete-time theory whose bulk spectrum is an exact analytic match for the Floquet spectrum. The spectra with open boundary conditions in a particular strip geometry also match up to finite-size corrections. However, the models differ in several important respects. The discrete-time theory is spatially anisotropic, so that the spectra do not agree for all lattice terminations, e.g. other strip geometries or on half spaces. This difference can be attributed to the fact that the static discrete-time model is quasi-one-dimensional in nature and therefore has a different bulk-boundary correspondence than the Floquet model.

Iadecola, Thomas (ORCID:0000000251456441)↗
DOE OSTI2026

Dirac Node Pinning from Dzyaloshinskii-Moriya Interactions in a Kagome Spin Liquid

Recent experiments on the Kagome spin liquid candidate material YCu 3 ⁢(OH) 6 ⁢Br 2 ⁢[Br 1−𝑦 ⁢(OH) 𝑦 ] suggest the presence of Dirac fermionic spinons near the magnetization plateau at 1/9. Theories suggest that the spinons are charge neutral spin-1/2 excitations, in a 2⁢𝜋/3 flux, which triples the unit cell. Generally a gap is expected, and there is no symmetry protection for the Dirac nodes in this system. The question arises as to what causes the nodes and stabilizes them. In this work, we propose a node-creation and node-pinning mechanism driven by Dzyaloshinskii-Moriya (DM) interactions. Employing Gutzwiller-projected variational Monte Carlo calculations, we demonstrate that DM interactions induce a band closing phase transition in the spinon spectrum. There is a change in the Chern number when the bands are inverted. Together with the DM-generated internal gauge flux, the coupling to the spinon orbital magnetization counteracts the band reopening. Furthermore, this interplay energetically pins the Dirac nodes over a range of parameters, resulting in a pinning mechanism distinct from the usual one from symmetry protection.

Kagome lattice↗
DOE OSTI2025

Fermionic sub-GeV dark matter from evaporating primordial black holes at DarkSide-50

We present a search for boosted dark matter from primordial black hole (PBH) evaporation using the DarkSide-50 ionization-signal-only dataset corresponding to the experiment’s ( 12202 ± 180 ) kg d exposure. We focus on evaporation of PBHs with masses in the range [ 10 14 , 10 16 ] g producing Dirac fermionic dark matter particles with sub-GeV kinetic energy. These relativistic particles, with energies up to hundreds of MeV, can generate detectable signals for masses below O ( 100 ) MeV . The absence of a signal enables setting complementary limits to those derived from cosmological observations and direct detection searches for cosmic-ray-boosted dark matter.

Agnes, P. [Gran Sasso; GSSI, Aquila]↗