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At least 37 records · Page 2
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DOE OSTI2024

Quantum transport response of topological hinge modes

Electronic topological phases are typified by the conducting surface states that exist on the boundary of an insulating three-dimensional bulk. While the transport response of the two-dimensional surface states has been studied, the quantum response of the one-dimensional hinge modes has not been demonstrated. Here we provide evidence for quantum transport in gapless topological hinge states existing within the insulating bulk and surface energy gaps in the intrinsic topological insulator α-Bi 4 Br 4 . Our magnetoresistance measurements reveal pronounced Aharonov–Bohm oscillations that are periodic in h/e (where h denotes Planck’s constant and e is the electron charge). The observed periodicity evinces quantum interference of electrons circumnavigating around the hinges. We also demonstrate that the h/e oscillations evolve as a function of magnetic field orientation, following the interference paths along the hinge modes that are allowed by topology and symmetry. Furthermore, our findings reveal the quantum transport response of topological hinge modes with both topological nature and quantum coherence, which can eventually be applied to the development of efficient topological electronic devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A hybrid topological quantum state in an elemental solid

Topology and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three important research directions: (1) the competition between distinct interactions, as in several intertwined phases, (2) the interplay between interactions and topology that drives the phenomena in twisted layered materials and topological magnets, and (3) the coalescence of several topological orders to generate distinct novel phases. The first two examples have grown into major areas of research, although the last example remains mostly unexplored, mainly because of the lack of a material platform for experimental studies. Here, using tunnelling microscopy, photoemission spectroscopy and a theoretical analysis, we unveil a ‘hybrid’ topological phase of matter in the simple elemental-solid arsenic. Through a unique bulk-surface-edge correspondence, we uncover that arsenic features a conjoined strong and higher-order topology that stabilizes a hybrid topological phase. Although momentum-space spectroscopy measurements show signs of topological surface states, real-space microscopy measurements unravel a unique geometry of topologically induced step-edge conduction channels revealed on various natural nanostructures on the surface. Using theoretical models, we show that the existence of gapless step-edge states in arsenic relies on the simultaneous presence of both a non-trivial strong Z 2 invariant and a non-trivial higher-order topological invariant, which provide experimental evidence for hybrid topology. Finally, our study highlights pathways for exploring the interplay of different band topologies and harnessing the associated topological conduction channels in engineered quantum or nano-devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Higher-order nodal hinge states in doped superconducting topological insulator

Doped strong topological insulators are one of the most promising candidates to realize a fully gapped three-dimensional topological superconductor (TSC). In this Letter, we revisit this system and reveal a possibility for higher-order topology which was previously missed. We find that over a finite range of doping, the Fu-Berg superconducting pairing can give rise to both Majorana surface states and nodal hinge states. Interestingly, we observe the coexistence of surface and hinge modes in the superconducting state only when there are both bulk and surface Fermi surfaces in the normal state. Furthermore, we find that the hinge modes can appear for normal states consisting of doped strong or weak topological insulators. In summary, this work may allow for the discovery of superconducting hinge modes in a well explored class of materials, i.e., doped strong or weak topological insulators.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Higher-order topological corner and bond-localized modes in magnonic insulators

We theoretically investigate a two-dimensional decorated honeycomb lattice framework to realize a second-order topological magnon insulator (SOTMI) phase featuring distinct corner-localized modes. Here, our study emphasizes the pivotal role of spin-magnon mapping in characterizing bosonic topological properties, which exhibit differences from their fermionic counterparts. We employ a symmetry indicator topological invariant to identify and characterize this SOTMI phase, particularly for systems respecting time-reversal and rotational symmetry. Using a spin model defined on a honeycomb lattice geometry, we demonstrate that introducing “kekulé” type distortions yields a topological phase. In contrast, “antikekulé” distortions result in a nontopological magnonic phase. The presence of kekulé distortions manifests in two distinct topologically protected bosonic corner modes—an intrinsic and a pseudo, based on the specific edge terminations. On the other hand, antikekulé distortions give rise to Tamm/Shockley type bond-localized boundary modes, which are nontopological and reliant on particular edge termination. We further investigate the effects of random out-of-plane exchange anisotropy disorder on the robustness of these bosonic corner modes. The distinction between SOTMIs and their fermionic counterparts arises due to the system-specific magnonic onsite energies, a crucial feature often overlooked in prior literature. Our study unveils exciting prospects for engineering higher-order topological phases in magnon systems and enhances our understanding of their unique behavior within decorated honeycomb lattices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Third-order Hall effect in the surface states of a topological insulator

Time reversal and inversion symmetric materials fail to yield linear and nonlinear responses since they possess net zero Berry curvature. However, higher-order Hall response can be generated in these systems upon constraining the crystalline symmetries. Motivated by the recently discovered third-order Hall (TOH) response mediated by Berry connection polarizability, namely, the variation of the Berry connection with respect to an applied electric field, here, we investigate the existence of such a Hall effect in the surface states of hexagonal warped topological insulators (e.g., Bi 2 Te 3 ) under the application of only electric field. Using the semiclassical Boltzmann formalism, we investigate the effect of tilt and hexagonal warping on the Berry connection polarizability tensor and, consequently, the TOH effect, provided the Dirac cone remains gapless. We find that the magnitude of the response increases significantly with increasing tilt strength and warping, and therefore, they can provide the tunability of this effect. In addition, we also explore the effect of chemical doping on the TOH response in this system. Interestingly, we show, based on the symmetry analysis, that the TOH can be the leading-order response in this system, which can directly be verified in experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Gate-Tunable Transport in Quasi-One-Dimensional α-Bi 4 I 4 Field Effect Transistors

Bi 4 I 4 belongs to a novel family of quasi-one-dimensional (1D) topological insulators (TIs). While its β phase was demonstrated to be a prototypical weak TI, the α phase, long thought to be a trivial insulator, was recently predicted to be a rare higher order TI. Here, we report the first gate tunable transport together with evidence for unconventional band topology in exfoliated α-Bi 4 I 4 field effect transistors. We observe a Dirac-like longitudinal resistance peak and a sign change in the Hall resistance; their temperature dependences suggest competing transport mechanisms: a hole-doped insulating bulk and one or more gate-tunable ambipolar boundary channels. Our combined transport, photoemission, and theoretical results indicate that the gate-tunable channels likely arise from novel gapped side surface states, two-dimensional (2D) TI in the bottommost layer, and/or helical hinge states of the upper layers. Markedly, a gate-tunable supercurrent is observed in an α-Bi 4 I 4 Josephson junction, underscoring the potential of these boundary channels to mediate topological superconductivity.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Spin-resolved topology and partial axion angles in three-dimensional insulators

Abstract Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ( $${{{{{{{\mathcal{T}}}}}}}}$$ T -) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), “spin-Weyl” semimetals, and $${{{{{{{\mathcal{T}}}}}}}}$$ T -doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that β -MoTe 2 realizes a spin-Weyl state and that α -BiBr hosts both 3D QSHI and T-DAXI regimes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Electromagnetic response and emergent topological orders in transition metal dichalcogenide MoTe 2 bilayers

Twisted bilayer transition metal dichalcogenides, such as MoTe 2 , provide a versatile platform for exploring correlated topological phases. This work investigates the interplay between perpendicular magnetic and electric fields in tuning the electronic structure and emergent topological orders of twisted bilayer MoTe 2 (t-MoTe 2 ) across two distinct regimes: a low-twist-angle phase (θ ≈ 2.1°) hosting multiple Chern bands of identical Chern numbers per valley, and a higher-angle phase (θ ≈ 3.89°) featuring Haldane-like bands with opposite Chern numbers. Using a continuum model incorporating moiré potentials up to second harmonics, we compute the Hofstadter fractal spectra under applied fields, revealing Landau fan structures and magnetic-flux-dependent band topology. These fractal spectra are useful in studying emergent topological orders in terms of the composite fermion picture, where the statistical Chern-Simons flux is approximated as a uniform gauge field. We demonstrate that the system hosts both Jain-sequence fractional Chern insulators (FCIs) and non-Jain fractal FCIs with higher Chern numbers. As a result, the electric field suppresses composite fermion gaps and induces topological quantum phase transitions. Furthermore, our analysis extends to valley-contrasting flux attachment, proposing pathways to describe fractional quantum spin Hall states.

Anyons↗
DOE OSTI2023

Thermally driven phase transitions in freestanding low-buckled silicene, germanene, and stanene

Low-buckled silicene, germanene, and stanene are group-IV graphene allotropes. They form a honeycomb lattice out of two interpenetrating (A and B) triangular sublattices that are vertically separated by a small distance Δ z . The atomic numbers Z of silicon, germanium, and tin are larger than that of carbon (Z C = 6), making them the first experimentally viable two-dimensional topological insulators. Those materials have a twice-energy-degenerate atomistic structure characterized by the buckling direction of the B sublattice with respect to the A sublattice [whereby the B atom either protrudes above (Δ z > 0) or below (Δ z < 0) the A atoms], and the consequences of that energy degeneracy on their elastic and electronic properties have not been reported thus far. Here, we uncover ferroelastic, bistable behavior on silicene, which turns into an average planar structure at about 600 K. Furthermore, the creation of electron and hole puddles obfuscates the zero-temperature spin-orbit coupling (SOC)-induced band gaps at temperatures as low as 200 K, which may discard silicene as a viable two-dimensional topological insulator for room-temperature applications. Germanene, on the other hand, never undergoes a low-buckled-to-planar two-dimensional transformation, becoming amorphous at around 675 K instead, and preserving its SOC-induced band gap despite band broadening. Stanene undergoes a transition onto a crystalline three-dimensional structure at about 300 K, preserving its SOC-induced electronic band gap up to that temperature. Unlike what is observed in silicene and germanene, stanene readily develops a higher-coordinated structure with a high degree of structural order. Furthermore, the structural phenomena are shown to have far-reaching consequences for the electronic and vibrational properties of those two-dimensional topological insulators.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Engineering Corner States from Two-Dimensional Topological Insulators

We theoretically demonstrate that the second-order topological insulator with robust corner states can be realized in two-dimensional $\mathbb{Z}_2$ topological insulators by applying an in-plane Zeeman field. The Zeeman field breaks the time-reversal symmetry and thus destroys the $\mathbb{Z}_2$ topological phase. Nevertheless, it respects some crystalline symmetries and thus can protect the higher-order topological phase. By taking the Kane-Mele model as a concrete example, we find that spin-helical edge states along zigzag boundaries are gapped out by the Zeeman field whereas the in-gap corner state at the intersection between two zigzag edges arises, which is independent of the field orientation. In this work, we further show that the corner states are robust against the out-of-plane Zeeman field, staggered sublattice potentials, Rashba spin-orbit coupling, and the buckling of honeycomb lattices, making them experimentally feasible. Similar behaviors can also be found in the well-known Bernevig-Hughes-Zhang model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Dynamical symmetry indicators for Floquet crystals

Various exotic topological phases of Floquet systems have been shown to arise from crystalline symmetries. Yet, a general theory for Floquet topology that is applicable to all crystalline symmetry groups is still in need. In this work, we propose such a theory for (effectively) non-interacting Floquet crystals. We first introduce quotient winding data to classify the dynamics of the Floquet crystals with equivalent symmetry data, and then construct dynamical symmetry indicators (DSIs) to sufficiently indicate the inherently dynamical Floquet crystals. The DSI and quotient winding data, as well as the symmetry data, are all computationally efficient since they only involve a small number of Bloch momenta. We demonstrate the high efficiency by computing all elementary DSI sets for all spinless and spinful plane groups using the mathematical theory of monoid, and find a large number of different nontrivial classifications, which contain both first-order and higher-order 2+1D anomalous Floquet topological phases. Using the framework, we further find a new 3+1D anomalous Floquet second-order topological insulator (AFSOTI) phase with anomalous chiral hinge modes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Hofstadter Topology: Noncrystalline Topological Materials at High Flux

he Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding ~10 4 T magnetic fields to a trivial band structure. In this work, we show that when a magnetic field is added to an initially topological band structure, a wealth of possible phases emerges. Remarkably, we find topological phases that cannot be realized in any crystalline insulators. We prove that threading magnetic flux through a Hamiltonian with a nonzero Chern number or mirror Chern number enforces a phase transition at fixed filling and that a 2D Hamiltonian with a nontrivial Kane–Mele invariant can be classified as a 3D topological insulator (TI) or 3D weak TI phase in periodic flux. We then study fragile topology protected by the product of twofold rotation and time reversal and show that there exists a higher order TI phase where corner modes are pumped by flux. We show that a model of twisted bilayer graphene realizes this phase. Our results rely primarily on the magnetic translation group that exists at rational values of the flux. The advent of Moiré lattices renders our work relevant experimentally. Due to the enlarged Moiré unit cell, it is possible for laboratory-strength fields to reach one flux per plaquette and allow access to our proposed Hofstadter topological phase.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Imaging the Breakdown and Restoration of Topological Protection in Magnetic Topological Insulator MnBi 2 Te 4

Quantum anomalous Hall (QAH) insulators transport charge without resistance along topologically protected chiral 1D edge states. Yet, in magnetic topological insulators to date, topological protection is far from robust, with zero-magnetic field QAH effect only realized at temperatures an order of magnitude below the Néel temperature T N , though small magnetic fields can stabilize QAH effect. Understanding why topological protection breaks down is therefore essential to realizing QAH effect at higher temperatures. Here a scanning tunneling microscope is used to directly map the size of exchange gap (E g,ex ) and its spatial fluctuation in the QAH insulator 5-layer MnBi 2 Te 4 . Long-range fluctuations of E g,ex are observed, with values ranging between 0 (gapless) and 70 meV, appearing to be uncorrelated to individual surface point defects. The breakdown of topological protection is directly imaged, showing that the gapless edge state, the hallmark signature of a QAH insulator, hybridizes with extended gapless regions in the bulk. Finally, it is unambiguously demonstrated that the gapless regions originate from magnetic disorder, by demonstrating that a small magnetic field restores E g,ex in these regions, explaining the recovery of topological protection in magnetic fields. The results indicate that overcoming magnetic disorder is the key to exploiting the unique properties of QAH insulators.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Higher Chern numbers in multilayer Lieb lattices ( N ≥ 2 ): Topological transitions and quadratic band crossing lines

In this work, we consider a hitherto unexplored setting of a stacked multilayer (N) Lieb lattice which undergoes an unusual topological transition in the presence of intralayer spin-orbit coupling (SOC). The specific stacking configuration induces an effective nonsymmorphic two-dimensional lattice structure, even though the constituent monolayer Lieb lattice is characterized by a symmorphic space group. This emergent nonsymmorphicity leads to multiple doubly degenerate bands extending over the edge of the Brillouin zone (i.e., quadratic band crossing lines). In the presence of intralayer SOC, these doubly degenerate bands typically form three N-band subspaces, mutually separated by two band gaps. We analyze the topological properties of these multiband subspaces, using specially devised Wilson loop operators to compute non-Abelian Berry phases in order to show that they carry a higher Chern number N.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Increased Defect Resistance and Ordering in MnBi 2 (Se 1– x Te x ) 4 via Accurate Diffusion Monte Carlo

Stabilizing materials and controlling defect formation remain key challenges in materials science, particularly for theory, where small energy differences must be resolved for accurate predictions. Here, we applied state-of-the-art theoretical methods to topological materials, focusing on MnBi 2 Te 4 (MBT), which is a promising intrinsic magnetic topological insulator. Antisite defects in MBT alter its electronic structure and magnetism, degrading topological properties and causing experimental inconsistencies. Using diffusion Monte Carlo and density functional theory, we investigated the thermodynamic stability and defect formation in MBT, MnBi 2 Se 4 (MBS), and MnBi 2 (Se 1–x Te x ) 4 . We found that MnBi 2 Se 2 Te 2 can be stable at finite temperatures, with higher defect formation energies due to stronger Mn–Se bonding and reduced internal strain. Se preferentially substitutes Te near Mn instead of Te in the outer layer, encouraging long-range ordering when incorporated. For MnBi 2 (Se 1–x Te x ) 4 , cluster expansion phase diagrams revealed solid solution behavior when x <0.5 and phase separation for larger x. MBT and MBS are topological insulators; therefore, the MnBi 2 (Se 1–x Te x ) 4 family could offer tunable topological behavior and improved stability.

MnBi2Te4↗
DOE OSTI2021

Topological Charge Pumping in Excitonic Insulators

Here, we show that in excitonic insulators with s-wave electron-hole pairing, an applied electric field (either pulsed or static) can induce a p-wave component to the order parameter, and further drive it to rotate in the s + ip plane, realizing a Thouless charge pump. In one dimension, each cycle of rotation pumps exactly two electrons across the sample. Higher dimensional systems can be viewed as a stack of one-dimensional chains in momentum space in which each chain crossing the Fermi surface contributes a channel of charge pumping. Physics beyond the adiabatic limit, including in particular dissipative effects is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

Abstract Dirac and Weyl semimetals both exhibit arc-like surface states. However, whereas the surface Fermi arcs in Weyl semimetals are topological consequences of the Weyl points themselves, the surface Fermi arcs in Dirac semimetals are not directly related to the bulk Dirac points, raising the question of whether there exists a topological bulk-boundary correspondence for Dirac semimetals. In this work, we discover that strong and fragile topological Dirac semimetals exhibit one-dimensional (1D) higher-order hinge Fermi arcs (HOFAs) as universal, direct consequences of their bulk 3D Dirac points. To predict HOFAs coexisting with topological surface states in solid-state Dirac semimetals, we introduce and layer a spinful model of an s – d -hybridized quadrupole insulator (QI). We develop a rigorous nested Jackiw–Rebbi formulation of QIs and HOFA states. Employing ab initio calculations, we demonstrate HOFAs in both the room- ( α ) and intermediate-temperature ( α ″ ) phases of Cd 3 As 2 , KMgBi, and rutile-structure ( $$ \beta ^{\prime} $$ β ′ -) PtO 2 .

Science & Technology - Other Topics↗