Two-Dimensional Quantum Hall Effect and Zero Energy State in Few-Layer ZrTe 5
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2D quantum Hall effect↗
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Zero-energy bound states in the high-temperature superconductors at the two-dimensional limit
Majorana zero modes (MZMs) that obey the non-Abelian statistics have been intensively investigated for potential applications in topological quantum computing. The prevailing signals in tunneling experiments “fingerprinting” the existence of MZMs are the zero-energy bound states (ZEBSs). However, nearly all of the previously reported ZEBSs showing signatures of the MZMs are observed in difficult-to-fabricate heterostructures at very low temperatures and additionally require applied magnetic field. Here, by using in situ scanning tunneling spectroscopy, we detect the ZEBSs upon the interstitial Fe adatoms deposited on two different high-temperature superconducting one-unit-cell iron chalcogenides on SrTiO 3 (001). The spectroscopic results resemble the phenomenological characteristics of the MZMs inside the vortex cores of topological superconductors. Our experimental findings may extend the MZM explorations in connate topological superconductors toward an applicable temperature regime and down to the two-dimensional (2D) limit.
Science & Technology - Other Topics↗
An epitaxial graphene platform for zero-energy edge state nanoelectronics
Graphene’s original promise to succeed silicon faltered due to pervasive edge disorder in lithographically patterned deposited graphene and the lack of a new electronics paradigm. Here we demonstrate that the annealed edges in conventionally patterned graphene epitaxially grown on a silicon carbide substrate (epigraphene) are stabilized by the substrate and support a protected edge state. The edge state has a mean free path that is greater than 50 microns, 5000 times greater than the bulk states and involves a theoretically unexpected Majorana-like zero-energy non-degenerate quasiparticle that does not produce a Hall voltage. In seamless integrated structures, the edge state forms a zero-energy one-dimensional ballistic network with essentially dissipationless nodes at ribbon–ribbon junctions. Seamless device structures offer a variety of switching possibilities including quantum coherent devices at low temperatures. This makes epigraphene a technologically viable graphene nanoelectronics platform that has the potential to succeed silicon nanoelectronics.
42 ENGINEERING↗
Robust topological state against magnetic impurities observed in the superconductor PbTaSe 2
Magnetic impurities deposited on topological superconductor candidate PbTaSe 2 can introduce a nonsplitting zero-energy state inside the superconducting gap, which has been proposed as a field-free platform for topological zero modes. However, it is still unclear how robust the topological state in PbTaSe 2 is against magnetic impurities, which is related to the topological nature of the zero-energy state as well as its potential for quantum computation. In this paper, we use scanning tunneling microscopy to study the topological surface state in the normal state of PbTaSe 2 under the perturbation of magnetic impurities. We visualize the quasiparticle interference (QPI) arising from the topological surface state. We then deposit Fe impurities on the surface to form atomic Fe adatoms. We find that each Fe adatom sits at a unique interstitial position on the surface and features a local state at high energies, both of which are consistent with our first-principles calculation that further reveals its large magnetic moment. Our systematic Fe deposition and subsequent measurements show that the arclike QPI pattern at the Fermi energy is robust with up to 3% Fe coverage where the atomic nature of Fe adatoms still holds. Our results provide evidence that the topological surface state at the Fermi energy in PbTaSe 2 is robust against dilute magnetic impurities.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Pair wave function symmetry in UTe2 from zero-energy surface state visualization
Although nodal spin-triplet topological superconductivity appears probable in uranium ditelluride (UTe 2 ), its superconductive order parameter Δ k remains unestablished. In theory, a distinctive identifier would be the existence of a superconductive topological surface band, which could facilitate zero-energy Andreev tunneling to an s-wave superconductor and also distinguish a chiral from a nonchiral Δ k through enhanced s-wave proximity. In this study, we used s-wave superconductive scan tips and detected intense zero-energy Andreev conductance at the UTe 2 (0-11) termination surface. Imaging revealed subgap quasiparticle scattering interference signatures with a-axis orientation. The observed zero-energy Andreev peak splitting with enhanced s-wave proximity signifies that Δ k of UTe 2 is a nonchiral state: B 1u , B 2u , or B 3u . However, if the quasiparticle scattering along the a axis is internodal, then a nonchiral B 3u state is the most consistent for UTe 2 .
Gu, Qiangqiang [Cornell Univ., Ithaca, NY (United ↗
Single-electron charge transfer into putative Majorana and trivial modes in individual vortices
Majorana bound states are putative collective excitations in solids that exhibit the self-conjugate property of Majorana fermions—they are their own antiparticles. In iron-based superconductors, zero-energy states in vortices have been reported as potential Majorana bound states, but the evidence remains controversial. Here, we use scanning tunneling noise spectroscopy to study the tunneling process into vortex bound states in the conventional superconductor NbSe 2 , and in the putative Majorana platform FeTe 0.55 Se 0.45 . We find that tunneling into vortex bound states in both cases exhibits charge transfer of a single electron charge. Our data for the zero-energy bound states in FeTe 0.55 Se 0.45 exclude the possibility of Yu–Shiba–Rusinov states and are consistent with both Majorana bound states and trivial vortex bound states. Our results open an avenue for investigating the exotic states in vortex cores and for future Majorana devices, although further theoretical investigations involving charge dynamics and superconducting tips are necessary.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Topological Mott transition in a two band model of spinless fermions with on-site Coulomb repulsion
Highlights: • The effect of the on-site Coulomb repulsion and the spin–orbit Rashba coupling lead to the 2D topological semimetal. • The ground state phase diagram is calculated. • The topological semimetal phase is characterized by the zero energy Majorana states. In the framework of mean field approach, we study topological Mott transition in a two band model of spinless fermions on a square lattice at half filling. We consider the combined effect of the on-site Coulomb repulsion and the spin–orbit Rashba coupling. The ground state phase diagram is calculated as a function of the strength of the spin–orbit Rashba coupling and the Coulomb repulsion. The spin–orbit Rashba coupling leads to a distinct phase of matter, the topological semimetal. We study a new type of phase transition between the non-topological insulator and topological semimetal states. Topological phase state is characterized by the zero energy Majorana states, which there are in defined region of the wave vectors and are localized at the boundaries of the sample. The region of existence of the zero energy Majorana states tends to zero at the point of the Mott phase transition. The zero energy Majorana states are dispersionless (they can be considered as flat bands), the Chern number and Hall conductance are equal to zero (note in two dimensional model).
36 MATERIALS SCIENCE↗
WKB Estimate of Bilayer Graphene’s Magic Twist Angles
We report that graphene bilayers exhibit zero-energy flatbands at a discrete series of magic twist angles. In the absence of intrasublattice interlayer hopping, zero-energy states satisfy a Dirac equation with a non-Abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck’s constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wave functions. We find zero-energy solutions at a discrete set of values of the dimensionless Planck’s constant, which we obtain analytically. Our analytic flatband twist angles correspond closely to those determined numerically in previous work.
36 MATERIALS SCIENCE↗
Quantum scars of bosons with correlated hopping
Abstract Recent experiments on Rydberg atom arrays have found evidence of anomalously slow thermalization and persistent density oscillations, which have been interpreted as a many-body analog of the phenomenon of quantum scars. Periodic dynamics and atypical scarred eigenstates originate from a “hard” kinetic constraint: the neighboring Rydberg atoms cannot be simultaneously excited. Here we propose a realization of quantum many-body scars in a 1D bosonic lattice model with a “soft” constraint in the form of density-assisted hopping. We discuss the relation of this model to the standard Bose-Hubbard model and possible experimental realizations using ultracold atoms. We find that this model exhibits similar phenomenology to the Rydberg atom chain, including weakly entangled eigenstates at high energy densities and the presence of a large number of exact zero energy states, with distinct algebraic structure.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Chiral-Symmetric Higher-Order Topological Phases of Matter
Herein, we introduce novel higher-order topological phases of matter in chiral-symmetric systems (class AIII of the tenfold classification), most of which would be misidentified as trivial by current theories. These phases are protected by “multipole chiral numbers,” bulk integer topological invariants that in 2D and 3D are built from sublattice multipole moment operators, as defined herein. The integer value of a multipole chiral number indicates how many degenerate zero-energy states localize at each corner of a system. These higher-order topological phases of matter are generally boundary-obstructed and robust in the presence of chiral-symmetry-preserving disorder.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Optical vortex manipulation for topological quantum computation
Topological quantum computation based on Majorana bound states may enable new paths to fault-tolerant quantum computing. Several recent experiments have suggested that the vortex cores of topological superconductors, such as iron-based superconductors, may host Majorana bound states at zero energy. However, quantum computation with these zero-energy vortex bound states requires precise and fast manipulation of individual vortices, which is difficult to do in a scalable manner. To address this issue, in this study we propose a control scheme based on local heating via, for example, scanning optical microscopy to braid vortex-bound Majorana zero modes in a two-dimensional topological superconductor. First, we derive the conditions required for transporting a single vortex between two defects in the superconducting material by trapping it with a hot spot generated by local optical heating. Equipped with critical conditions for the vortex motion, we then establish the ideal material properties for vortex braiding and describe how transition errors resulting from finite speed and/or temperature can be minimized. Our work paves the way toward optical or microscopic control of zero-energy vortex bound states in two-dimensional topological superconductors.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Transition to the Haldane phase driven by electron-electron correlations
One of the most famous quantum systems with topological properties, the spin S = 1 antiferromagnetic Heisenberg chain, is well-known to display exotic S = 1/2 edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons – the two orbital Hubbard model—with increasing repulsion strength U and Hund interaction J H . We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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↗
A New State of the Art: Zero Energy Modular Multifamily Construction
In 2020, the U.S. Department of Energy's Building Technologies Office (BTO) launched the Advanced Building Construction (ABC) Initiative. This initiative aimed to integrate energy efficiency into high-production construction practices. One focus area of the initiative is off-site construction, an approach that may achieve scalable, efficient, and high-performing construction buildings through process standardization. This report presents the findings and recommendations from our ABC Initiative project: A New State of the Art: Zero-Energy Modular Multifamily Construction System. The objectives of the BTO-funded project are to: 1) Achieve energy performance 50% better than the 2018 International Energy Conservation Code (IECC). 2) Achieve this level of energy performance at no additional cost VEIC worked with Louisiana State University (LSU), National Renewal Energy Lab (NREL), [the project team], and industry partners at the Mod Coach, KBS, and Solar Home Factory to identify and analyze multifamily business designs and modular construction practices. These designs and processes hold the promise of achieving the goals set out by the DOE.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Exact Ground State of Interacting Electrons in Magic Angle Graphene
One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene systems with equal twist angles. We identify symmetries of the chiral limit of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi-θ$${\theta }$$ and Weierstrass-℘$${\wp }$$ functions.
Becker, Simon↗
Chirality reversal at finite magnetic impurity strength and local signatures of a topological phase transition
Here, we study the honeycomb lattice with a single magnetic impurity modeled by adding imaginary next-nearest-neighbor hopping 𝑖ℎ on a single hexagon. This Haldane defect gives a topological mass term to the gapless Dirac cones and generates chirality. For a small density of defects, Neehus et al. [Phys. Rev. Lett. 135, 126604 (2025)] found that the system's chirality reverses at a critical ℎ 𝑐 ≈ 0.95 associated with an unexpected tricritical point of Dirac fermions at zero defect density. We investigate this zero-density limit by analyzing a single defect and computing two experimentally relevant measures of chirality: (1) orbital magnetization via local Chern marker, a bulk probe of all occupied states; and (2) electronic currents of low-energy states. Both probes show a chirality reversal at a critical ℎ 𝑐 ≈ 0.9–1.0. Motivated by this consistency, we propose a defect-scale toy model whose low-energy states reverse their chirality at ℎ$^{'}_{c}$ ≈ 0.87. Remarkably, the same pair of zero-energy bound states also generates the critical point ℎ 𝑐 in the full impurity projected T-matrix. Our results show how the chirality reversal produced by an impurity can be observed either in local probes or in the global topology, and suggest a possible role of the microscopic defect structure at the critical point.
Chern insulators↗
On the contribution of intramolecular zero point energy to the equation of state of solid H2
Experimental evidence shows that the internal zero-point energy of the H2 molecule exhibits a relatively strong pressure dependence in the solid as well as changing considerably upon condensation. It is shown that these effects contribute about 6% to the total sublimation energy and to the pressure in the solid state. Methods to modify the ab initio isolated pair potential to account for these environmental effects are discussed.
Chandrasekharan, V.↗