Emergence of Nontrivial Low-Energy Dirac Fermions in Antiferromagnetic EuCd 2 As 2
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Chemistry↗
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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↗
Chiral Dirac Fermion in a Collinear Antiferromagnet
In a Dirac semimetal, the massless Dirac fermion has zero chirality, leading to surface states connected adiabatically to a topologically trivial surface state as well as vanishing anomalous Hall effect. Recently, it is predicted that in the nonrelativistic limit of certain collinear antiferromagnets, there exists a type of chiral "Dirac-like" fermion, whose dispersion manifests four-fold degenerate crossing points formed by spin-degenerate linear bands, with topologically protected Fermi arcs. Such an unconventional chiral fermion, protected by a hidden SU(2) symmetry in the hierarchy of an enhanced crystallographic group, namely spin space group, is not experimentally verified yet. Here, by angle-resolved photoemission spectroscopy measurements, we reveal the surface origin of the electron pocket at the Fermi surface in collinear antiferromagnet CoNb 3 S 6 . Combining with neutron diffraction and first-principles calculations, we suggest a multidomain collinear antiferromagnetic configuration, rendering the the existence of the Fermi-arc surface states induced by chiral Dirac-like fermions. Finally, our work provides spectral evidence of the chiral Dirac-like fermion caused by particular spin symmetry in CoNb 3 S 6 , paving an avenue for exploring new emergent phenomena in antiferromagnets with unconventional quasiparticle excitations.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Manipulation of Dirac Fermions in Nanochain-Structured Graphene
Graphene has afforded an ideal 2D platform for investigating a rich and fascinating behavior of Dirac fermions. Here, we develop a theoretical mechanism for manipulating the Dirac fermions in graphene, such as from type-I to type-II and type-III, by a top-down nanopatterning approach. We demonstrate that by selective chemical adsorption to pattern the 2D graphene into coupled 1D armchair chains (ACs), the intrinsic isotropic upright Dirac cone becomes anisotropic and strongly tilted. Based on model analyses and first-principles calculations, we show that both the shape and tilt of Dirac cone can be tuned by the species of chemisorption, e.g., halogen vs hydrogen, which modifies the strength of inter-AC coupling. Furthermore, the topological edge states and transport properties of the engineered Dirac fermions are investigated. Our work sheds lights on understanding the Dirac fermions in a nanopatterned graphene platform, and provides guidance for designing nanostructures with novel functionality.
Physics↗
Antiferromagnetic transitions of Dirac fermions in three dimensions
We use determinant quantum Monte Carlo simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the π-flux model on a cubic lattice. We show that the Hubbard interaction drives the 3D Dirac semimetal to an antiferromagnetic (AF) insulator only above a finite critical interaction strength and the long-range AF order persists up to a finite temperature. We evaluate the critical interaction strength and temperatures using finite-size scaling of the spin structure factor. The critical behaviors are consistent with the (3+1)-dimensional Gross-Neveu universality class for the quantum critical point and 3D Heisenberg universality class for the thermal phase transitions. We further investigate correlation effects in the birefringent Dirac fermion system. It is found that the critical interaction strength U c is decreased by reducing the velocity of the Dirac cone, quantifying the effect of velocity on the critical interaction strength in 3D Dirac fermion systems. Our findings unambiguously uncover correlation effects in 3D Dirac fermions and may be observed using ultracold atoms in an optical lattice.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Criticality of Two-Dimensional Disordered Dirac Fermions in the Unitary Class and Universality of the Integer Quantum Hall Transition
Two-dimensional (2D) Dirac fermions are a central paradigm of modern condensed matter physics, describing low-energy excitations in graphene, in certain classes of superconductors, and on surfaces of 3D topological insulators. At zero energy E=0, Dirac fermions with mass m are band insulators, with the Chern number jumping by unity at m=0. This observation lead Ludwig et al. [Phys. Rev. B 50, 7526 (1994)PRBMDO0163-182910.1103/PhysRevB.50.7526] to conjecture that the transition in 2D disordered Dirac fermions (DDF) and the integer quantum Hall transition (IQHT) are controlled by the same fixed point and possess the same universal critical properties. Given the far-reaching implications for the emerging field of the quantum anomalous Hall effect, modern condensed matter physics, and our general understanding of disordered critical points, it is surprising that this conjecture has never been tested numerically. In this work, we report the results of extensive numerics on the phase diagram and criticality of 2D DDF in the unitary class. We find a critical line at m=0, with an energy-dependent localization length exponent. At large energies, our results for the DDF are consistent with state-of-the-art numerical results ν IQH =2.56-2.62 from models of the IQHT. At E=0, however, we obtain ν 0 =2.30-2.36 incompatible with ν IQH . This result challenges conjectured relations between different models of the IQHT, and several interpretations are discussed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Dirac fermions and possible weak antilocalization in LaCuSb 2
Layered heavy-metal square-lattice compounds have recently emerged as potential Dirac fermion materials due to bonding within those sublattices. We report quantum transport and spectroscopic data on the layered Sb square-lattice material LaCuSb 2 . Linearly dispersing band crossings, necessary to generate Dirac fermions, are experimentally observed in the electronic band structure observed using angle-resolved photoemission spectroscopy, along with a quasi-two-dimensional Fermi surface. Weak antilocalization that arises from two-dimensional transport is observed in the magnetoresistance, as well as regions of linear dependence, both of which are indicative of topologically nontrivial effects. Measurements of the Shubnikov–de Haas quantum oscillations show low effective mass electrons on the order of 0.065m e , further confirming the presence of Dirac fermions in this material.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Observation of dimension-crossover of a tunable 1D Dirac fermion in topological semimetal NbSi x Te 2
Condensed matter systems in low dimensions exhibit emergent physics that does not exist in three dimensions. When electrons are confined to one dimension (1D), some significant electronic states appear, such as charge density wave, spin-charge separations, and Su-Schrieffer-Heeger (SSH) topological state. However, a clear understanding of how the 1D electronic properties connects with topology is currently lacking. Here we systematically investigated the characteristic 1D Dirac fermion electronic structure originated from the metallic NbTe 2 chains on the surface of the composition-tunable layered compound NbSi x Te 2 (x = 0.40 and 0.43) using angle-resolved photoemission spectroscopy. We found the Dirac fermion forms a Dirac nodal line structure protected by the combined $\widetilde {M_y}$ and time-reversal symmetry T and proves the NbSi x Te2 system as a topological semimetal, in consistent with the ab-initio calculations. As x decreases, the interaction between adjacent NbTe 2 chains increases and Dirac fermion goes through a dimension-crossover from 1D to 2D, as evidenced by the variation of its Fermi surface and Fermi velocity across the Brillouin zone in consistence with a Dirac SSH model. Our findings demonstrate a tunable 1D Dirac electron system, which offers a versatile platform for the exploration of intriguing 1D physics and device applications.
36 MATERIALS SCIENCE↗
Dirac fermions and flat bands in the ideal kagome metal FeSn
A kagome lattice of 3d transition metal ions is a versatile platform for correlated topological phases hosting symmetry-protected electronic excitations and magnetic ground states. However, the paradigmatic states of the idealized two-dimensional kagome lattice-Dirac fermions and flat bands-have not been simultaneously observed. Here, we use angle-resolved photoemission spectroscopy and de Haas-van Alphen quantum oscillations to reveal coexisting surface and bulk Dirac fermions as well as flat bands in the antiferromagnetic kagome metal FeSn, which has spatially decoupled kagome planes. Our band structure calculations and matrix element simulations demonstrate that the bulk Dirac bands arise from in-plane localized Fe-3d orbitals, and evidence that the coexisting Dirac surface state realizes a rare example of fully spin-polarized two-dimensional Dirac fermions due to spin-layer locking in FeSn. Finally, the prospect to harness these prototypical excitations in a kagome lattice is a frontier of great promise at the confluence of topology, magnetism and strongly correlated physics.
36 MATERIALS SCIENCE↗
Signatures of coupling between spin waves and Dirac fermions in YbMnBi 2
Here, we present inelastic neutron scattering measurements of magnetic excitations in YbMnBi 2 , which reveal features consistent with a direct coupling of magnetic excitations to Dirac fermions. In contrast with the large broadening of magnetic spectra observed in antiferromagnetic metals such as the iron pnictides, here the spin waves exhibit a small but resolvable intrinsic width, consistent with our theoretical analysis. The subtle manifestation of spin-fermion coupling is a consequence of the Dirac nature of the conduction electrons, including the vanishing density of states near the Dirac points. Accounting for the Dirac fermion dispersion specific to YbMnBi 2 leads to particular signatures, such as the nearly wave-vector-independent damping observed in the experiment.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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)↗
Topological obstructed atomic limit insulators by annihilating Dirac fermions
We show that annihilating a pair of Dirac fermions implies a topological transition from the critical semimetallic phase to an obstructed atomic limit insulator phase instead of a trivial insulator. This is shown to happen because of branch cuts in the phase of the wave functions, leading to nontrivial Zak phase along certain directions. To this end, we study their ${\mathbb{Z}}_{2}$ invariant and also study the phase transition using entanglement entropy. We use low-energy Hamiltonians and numerical result from model systems to show this effect. These transitions are observed in realistic materials, including strained graphene and buckled honeycomb group V (Sb/As).
36 MATERIALS SCIENCE↗
Dirac Fermion Cloning, Moiré Flat Bands, and Magic Lattice Constants in Epitaxial Monolayer Graphene
Tuning interactions between Dirac states in graphene has attracted enormous interest because it can modify the electronic spectrum of the 2D material, enhance electron correlations, and give rise to novel condensed-matter phases such as superconductors, Mott insulators, Wigner crystals, and quantum anomalous Hall insulators. Previous works predominantly focus on the flat band dispersion of coupled Dirac states from different twisted graphene layers. Here in this work, a new route to realizing flat band physics in monolayer graphene under a periodic modulation from substrates is proposed. Graphene/SiC heterostructure is taken as a prototypical example and it is demonstrated experimentally that the substrate modulation leads to Dirac fermion cloning and, consequently, the proximity of the two Dirac cones of monolayer graphene in momentum space. Theoretical modeling captures the cloning mechanism of the Dirac states and indicates that moiré flat bands can emerge at certain magic lattice constants of the substrate, specifically when the period of modulation becomes nearly commensurate with the ($\sqrt{3}$ x $\sqrt{3}$) R30° supercell of graphene. Our results show that epitaxial single monolayer graphene on suitable substrates is a promising platform for exploring exotic many-body quantum phases arising from interactions between Dirac electrons.
36 MATERIALS SCIENCE↗
Coupling of magnetism and Dirac fermions in YbMnSb 2
Here, we report inelastic neutron scattering measurements of magnetic excitations in YbMnSb 2 , a low-carrier-density Dirac semimetal in which the antiferromagnetic Mn layers are interleaved with Sb layers that host Dirac fermions. We observe a measurable broadening of spin waves, which is consistent with substantial spin-fermion coupling. The spin-wave damping γ in YbMnSb 2 is roughly twice larger compared to that in a sister material, YbMnBi 2 , where an indication of a small damping consistent with a theoretical analysis of the spin-fermion coupling was reported. The interplane interaction between the Mn layers in YbMnSb 2 is also much stronger, suggesting that the interaction mechanism is rooted in the same spin-fermion coupling. Our results establish the systematics of spin-fermion interactions in layered magnetic Dirac materials.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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↗
Lattice regularization of reduced Kähler-Dirac fermions and connections to chiral fermions
We show how a path integral for reduced Kähler-Dirac fermions suffers from a phase ambiguity associated with the fermion measure that is an analog of the measure problem seen for chiral fermions. However, unlike the case of chiral symmetry, a doubler free lattice action exists which is invariant under the corresponding onsite symmetry. This allows for a clear diagnosis and solution to the problem using mirror fermions resulting in a unique gauge invariant measure. By introducing an appropriate set of Yukawa interactions which are consistent with ’t Hooft anomaly cancellation we conjecture the mirrors can be decoupled from low energy physics. Moreover, the minimal such Kähler-Dirac mirror model yields a light sector which corresponds, in the flat space continuum limit, to the Pati-Salam GUT model.
Physics↗
Coexistence of Dirac fermion and charge density wave in the square-net-based semimetal LaAuSb 2
Here, we report a comprehensive study of magnetotransport properties, angle-resolved photoemission spectroscopy (ARPES), and density functional theory (DFT) calculations on self-flux grown LaAuSb 2 single crystals. Resistivity and Hall measurements reveal a charge density wave (CDW) transition at 77 K. MR and de Haas-Van Alphen (dHvA) measurements indicate that the transport properties of LaAuSb 2 are dominated by Dirac fermions that arise from Sb square nets. ARPES measurements and DFT calculations reveal an electronic structure with a common feature of the square-net-based topological semimetals, which is in good agreement with the magnetotransport properties. Our results indicate the coexistence of CDW and Dirac fermion in LaAuSb 2 , both of which are linked to the bands arising from the Sb-square net, suggesting that the square net could serve as a structural motif to explore various electronic orders.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Fermi-crossing Type-II Dirac fermions and topological surface states in NiTe 2
Transition-metal dichalcogenides (TMDs) offer an ideal platform to experimentally realize Dirac fermions. However, typically these exotic quasiparticles are located far away from the Fermi level, limiting the contribution of Dirac-like carriers to the transport properties. Here we show that NiTe 2 hosts both bulk Type-II Dirac points and topological surface states. The underlying mechanism is shared with other TMDs and based on the generic topological character of the Te p-orbital manifold. However, unique to NiTe 2 , a significant contribution of Ni d orbital states shifts the energy of the Type-II Dirac point close to the Fermi level. In addition, one of the topological surface states intersects the Fermi energy and exhibits a remarkably large spin splitting of 120 meV. Our results establish NiTe 2 as an exciting candidate for next-generation spintronics devices.
36 MATERIALS SCIENCE↗