Gapped Dirac Cones Research Articles

Wafer-Scale Synthesis of Highly Oriented 2D Topological Semimetal PtTe2 via Tellurization.

Platinum ditelluride (1T-PtTe2) is a two-dimensional (2D) topological semimetal with a distinctive band structure and flexibility of van der Waals integration as a promising candidate for future electronics and spintronics. Although the synthesis of large-scale, uniform, and highly crystalline films of 2D semimetals system is a prerequisite for device application, the synthetic methods meeting these criteria are still lacking. Here, we introduce an approach to synthesize highly oriented 2D topological semimetal PtTe2 using a thermally assisted conversion called tellurization, which is a cost-efficient method compared to the other epitaxial deposition methods. We demonstrate that achieving highly crystalline 1T-PtTe2 using tellurization is not dependent on epitaxy but rather relies on two critical factors: (i) the crystallinity of the predeposited platinum (Pt) film and (ii) the surface coverage ratio of the Pt film considering lateral lattice expansion during transformation. By optimizing the surface coverage ratio of the epitaxial Pt film, we successfully obtained 2 in. wafer-scale uniformity without in-plane misalignment between antiparallelly oriented domains. The electronic band structure of 2D topological PtTe2 is clearly resolved in momentum space, and we observed an interesting 6-fold gapped Dirac cone at the Fermi surface. Furthermore, ultrahigh electrical conductivity down to ∼3.8 nm, which is consistent with that of single crystal PtTe2, was observed, proving its ultralow defect density.

Atomic layer molecular beam epitaxy of kagome magnet RMn6Sn6 (R = Er, Tb) thin films

Kagome lattices have garnered substantial interest because their band structure consists of topological flat bands and Dirac cones. The RMn6Sn6 (R = rare earth) compounds are particularly interesting because of the existence of the large intrinsic anomalous Hall effect (AHE), which originates from the gapped Dirac cones near the Fermi level. This makes RMn6Sn6 an outstanding candidate for realizing the high-temperature quantum AHE. The growth of RMn6Sn6 thin films is beneficial for both fundamental research and potential applications. However, most of the studies on RMn6Sn6 have focused on bulk crystals, and the synthesis of RMn6Sn6 thin films has not been reported so far. Here, we report the atomic layer molecular beam epitaxy growth, structural and magnetic characterizations, and transport properties of ErMn6Sn6 and TbMn6Sn6 thin films. It is especially noteworthy that TbMn6Sn6 thin films have out-of-plane magnetic anisotropy, which is important for realizing the quantum AHE. Our work paves the avenue toward the control of the AHE using devices patterned from RMn6Sn6 thin films.

Antiferromagnetic topological insulator with selectively gapped Dirac cones

Antiferromagnetic (AF) topological materials offer a fertile ground to explore a variety of quantum phenomena such as axion magnetoelectric dynamics and chiral Majorana fermions. To realize such intriguing states, it is essential to establish a direct link between electronic states and topology in the AF phase, whereas this has been challenging because of the lack of a suitable materials platform. Here we report the experimental realization of the AF topological-insulator phase in NdBi. By using micro-focused angle-resolved photoemission spectroscopy, we discovered contrasting surface electronic states for two types of AF domains; the surface having the out-of-plane component in the AF-ordering vector displays Dirac-cone states with a gigantic energy gap, whereas the surface parallel to the AF-ordering vector hosts gapless Dirac states despite the time-reversal-symmetry breaking. The present results establish an essential role of combined symmetry to protect massless Dirac fermions under the presence of AF order and widen opportunities to realize exotic phenomena utilizing AF topological materials.

Intrinsic magnetic topological materials

Topological states of matter possess bulk electronic structures categorized by topological invariants and edge/surface states due to the bulk-boundary correspondence. Topological materials hold great potential in the development of dissipationless spintronics, information storage and quantum computation, particularly if combined with magnetic order intrinsically or extrinsically. Here, we review the recent progress in the exploration of intrinsic magnetic topological materials, including but not limited to magnetic topological insulators, magnetic topological metals, and magnetic Weyl semimetals. We pay special attention to their characteristic band features such as the gap of topological surface state, gapped Dirac cone induced by magnetization (either bulk or surface), Weyl nodal point/line and Fermi arc, as well as the exotic transport responses resulting from such band features. We conclude with a brief envision for experimental explorations of new physics or effects by incorporating other orders in intrinsic magnetic topological materials.

Observation of gapped Dirac cones in a two-dimensional Su-Schrieffer-Heeger lattice

The Su-Schrieffer-Heeger (SSH) model in a two-dimensional rectangular lattice features gapless or gapped Dirac cones with topological edge states along specific peripheries. While such a simple model has been recently realized in photonic/acoustic lattices and electric circuits, its material realization in condensed matter systems is still lacking. Here, we study the atomic and electronic structure of a rectangular Si lattice on Ag(001) by angle-resolved photoemission spectroscopy and theoretical calculations. We demonstrate that the Si lattice hosts gapped Dirac cones at the Brillouin zone corners. Our tight-binding analysis reveals that the Dirac bands can be described by a 2D SSH model with anisotropic polarizations. The gap of the Dirac cone is driven by alternative hopping amplitudes in one direction and staggered potential energies in the other one and hosts topological edge states. Our results establish an ideal platform to explore the rich physical properties of the 2D SSH model.

Predicted Novel Type of Photoinduced Topological Phase Transition Accompanied by Collision and Collapse of Dirac-cone Pair in Organic Salt α-(BEDT-TTF)2I3

Photoinduced topological phase transitions in the Dirac-electron systems have attracted intensive research interest since its theoretical prediction in graphene, where the application of circularly polarized light opens a gap at the Dirac points and renders the system a topologically nontrivial Chern insulator phase through breaking the time-reversal symmetry. However, most of the previously studied phenomena in two-dimensional Dirac systems are basically based on the same physicical mechanism, i.e., the gap opening in the Dirac electron bands with circularly polarized light, and it is lacking in variety of the physics. In this paper, we theoretically predict a novel type of photoinduced topological phase transition accompanied by collision and collapse of gapped Dirac points in the organic salt $\alpha$-(BEDT-TTF)$_2$I$_3$. By constructing the Floquet theory for this compound, we demonstrate that the irradiation of elliptically polarized light causes collision of the Dirac points through the photoinduced band deformation and their collapse, which eventually results in the topological phase transition from a topological semimetal with gapped Dirac cones to a normal insulator when the elliptical axis is oriented at a specfic angle with respect to the crystallographic axes. We argue that this novel photoinduced phase transition can be experimentally detected by the measurement of Hall conductivity. The present work enriches the fundamental physics of photoinduced topological phase transitions and thus contribute to development of this rapidly growing research field.

Colossal in-plane magnetoresistance ratio of graphene sandwiched with Ni nanostructures.

In this study, we present a theoretical study on the in-plane conductance of graphene partially sandwiched between Ni(111) nanostructures with a width of ∼12.08 Å. In the sandwiched part, the gapped Dirac cone of the graphene was controlled using a pseudospin by changing the magnetic alignment of the Ni(111) nanostructures. Upon considering the antiparallel configuration of Ni(111) nanostructures, the transmission probability calculation of the in-plane conductance of graphene shows a gap-like transmission at E − EF = 0.2 and 0.65 eV from the pd-hybridization and controllable Dirac cone of graphene, respectively. In the parallel configuration, the transmission probability calculation showed a profile similar to that of the pristine graphene. High and colossal magnetoresistance ratios of 284% and 3100% were observed at E − EF = 0.65 eV and 0.2 eV, respectively. Furthermore, a magnetoresistance beyond 3100% was expected at E − EF = 0.65 eV when the width of the Ni(111) nanostructures on the nanometer scale was considered.

Moving Morphable Components-based inverse design formulation for quantum valley/spin hall insulators

Supplying topologically protected wave propagation immune to backscattering, design of novel materials analogous to topological insulators is of great interest in different physical systems. Most of the related studies relies on designer’s intuition or pre-knowledge, and is achieved through a trail-and-error process. In order to present a unified and rational design approach applicable to quantum valley/spin Hall insulators (QVHIs/QSHIs), a mathematical programming is proposed by combining the band theory and the Moving Morphable Components (MMC) topology optimization method. The key idea is to directly obtain a pair of unit cells with both reverse-ordered gapped Dirac cones and maximized working bandwidth through the optimization process. This design paradigm can be generalized for the systematic design of optimized 2D/3D topological insulators among different physical systems.

Magnetic crystalline-symmetry-protected axion electrodynamics and field-tunable unpinned Dirac cones in EuIn2As2

Knowledge of magnetic symmetry is vital for exploiting nontrivial surface states of magnetic topological materials. EuIn2As2 is an excellent example, as it is predicted to have collinear antiferromagnetic order where the magnetic moment direction determines either a topological-crystalline-insulator phase supporting axion electrodynamics or a higher-order-topological-insulator phase with chiral hinge states. Here, we use neutron diffraction, symmetry analysis, and density functional theory results to demonstrate that EuIn2As2 actually exhibits low-symmetry helical antiferromagnetic order which makes it a stoichiometric magnetic topological-crystalline axion insulator protected by the combination of a 180∘ rotation and time-reversal symmetries: {C}_{2}times {mathcal{T}}={2}^{prime}. Surfaces protected by {2}^{prime} are expected to have an exotic gapless Dirac cone which is unpinned to specific crystal momenta. All other surfaces have gapped Dirac cones and exhibit half-integer quantum anomalous Hall conductivity. We predict that the direction of a modest applied magnetic field of μ0H ≈ 1 to 2 T can tune between gapless and gapped surface states.

Hybrid topological guiding mechanisms for photonic crystal fibers.

We create hybrid topological-photonic localisation of light by introducing concepts from the field of topological matter to that of photonic crystal fiber arrays. S-polarized obliquely propagating electromagnetic waves are guided by hexagonal, and square, lattice topological systems along an array of infinitely conducting fibers. The theory utilises perfectly periodic arrays that, in frequency space, have gapped Dirac cones producing band gaps demarcated by pronounced valleys locally imbued with a nonzero local topological quantity. These broken symmetry-induced stop-bands allow for localised guidance of electromagnetic edge-waves along the crystal fiber axis. Finite element simulations, complemented by asymptotic techniques, demonstrate the effectiveness of the proposed designs for localising energy in finite arrays in a robust manner.

Chiral channel network from magnetization textures in two-dimensional MnBi2Te4

When atomically thin van der Waals (vdW) magnet forms long-period moir\'e pattern with a magnetic substrate, the sensitive dependence of interlayer magnetic coupling on the atomic registries can lead to moir\'e defined magnetization textures in the two-dimensional (2D) magnets. The recent discovery of 2D magnetic topological insulators such as MnBi2Te4 leads to the interesting possibility to explore the interplay of such magnetization textures with the topological surface states, which we explore here with a minimal model established for 2D MnBi2Te4. The sign flip of the exchange gap across a magnetization domain wall gives rise to a single in-gap chiral channel on each surface. In the periodic magnetization textures, such chiral spin channels at the domain walls couple to form a network and superlattice minibands emerge. We find that in magnetization textures with closed domain wall geometries, the formed superlattice miniband is a gapped Dirac cone featuring orbital magnetization from the current circulation in the close loops of chiral channels, while in magnetization textures with open domain wall geometries, gapless mini-Dirac cone is found instead. The miniband Bloch states feature a spatial texture of spin and local current density, which are clear manifestation of the spin-momentum locked chiral channels at the domain walls. The results suggest a new platform to engineer spin and current flows through the manipulation of magnetization domains for spintronic devices.

Intrinsic axion insulating behavior in antiferromagnetic MnBi6Te10

A striking feature of time reversal symmetry (TRS) protected topological insulators (TIs) is that they are characterized by a half integer quantum Hall effect on the boundary when the surface states are gapped by time reversal breaking perturbations. While time reversal symmetry (TRS) protected TIs have become increasingly under control, magnetic analogs are still largely unexplored territories with novel rich structures. In particular, topological magnetic insulators can also host a quantized axion term in the presence of lattice symmetries. Since these symmetries are naturally broken on the boundary, the surface states can develop a gap without external manipulation. In this work, we combine theoretical analysis, density functional calculations and experimental evidence to reveal intrinsic axion insulating behavior in MnBi6Te10. The quantized axion term arises from the simplest possible mechanism in the antiferromagnetic regime where it is protected by inversion symmetry and a fractional translation symmetry. The anticipated gapping of the Dirac surface state at the edge is subsequently experimentally established using Angle Resolved Spectroscopy. As a result, this system provides the magnetic analogue of the simplest TRS protected TI with a single, gapped Dirac cone at the surface.

Non-adiabatic Hall effect at Berry curvature hot spot

Hot spot of Berry curvature is usually found at Bloch band anti-crossings, where the Hall effect due to the Berry phase can be most pronounced. With small gaps there, the adiabatic limit for the existing formulations of Hall current can be exceeded in a moderate electric field. Here we present a theory of non-adiabatic Hall effect, capturing non-perturbatively the across gap electron-hole excitations by the electric field. We find a general connection between the field induced electron-hole coherence and intrinsic Hall velocity. In coherent evolution, the electron-hole coherence can manifest as a sizeable ac Hall velocity. When environmental noise is taken into account, its joint action with the electric field favors a form of electron-hole coherence that is function of wavevector and field only, leading to a dc non-linear Hall effect. The Hall current has all odd order terms in field, and still retains the intrinsic role of the Berry curvature. The quantitative demonstration uses the example of gapped Dirac cones, and our theory can be used to describe the bulk pseudospin Hall current in insulators with gapped edge such as graphene and 2D MnBi2Te4.

Gapped Dirac cones and spin texture in thin film topological insulator

The protected surface states of topological insulators (TIs) form gapless Dirac cones corresponding non-degenerate eigenstates with helical spin polarisation. The presence of a warping term deforms the isotropic cone of the most simple model into snowflake Fermi surfaces as in Bi2Se3 and Bi2Te3. Their features have been identified in STM quasiparticle interference (QPI) experiments on isolated surfaces. Here we investigate the QPI spectrum for the TI thin-film geometry with finite tunnelling between the surface states. This leads to a dramatic change of spectrum due to gapping and a change in spin texture that should leave distinct signatures in the QPI pattern. We consider both normal and magnetic exchange scattering from the surface impurities and obtain the scattering t-matrix in Born approximation as well as the general closed solution. We show the expected systematic variation of QPI snowflake intensity features by varying film thickness and study, in particular, the influence on backscattering processes. We predict the variation of the QPI spectrum for Bi2Se3 thin films using the observed gap dependence from ARPES results.

Chemical Aspects of the Candidate Antiferromagnetic Topological Insulator MnBi2Te4

Crystal growth of MnBi$_{2}$Te$_{4}$ has delivered the first experimental corroboration of the 3D antiferromagnetic topological insulator state. Our present results confirm that the synthesis of MnBi$_{2}$Te$_{4}$ can be scaled-up and strengthen it as a promising experimental platform for studies of a crossover between magnetic ordering and non-trivial topology. High-quality single crystals of MnBi$_{2}$Te$_{4}$ are grown by slow cooling within a narrow range between the melting points of Bi$_{2}$Te$_{3}$ (586 {\deg}C) and MnBi$_{2}$Te$_{4}$ (600 {\deg}C). Single crystal X-ray diffraction and electron microscopy reveal ubiquitous antisite defects in both cation sites and, possibly, Mn vacancies. Powders of MnBi$_{2}$Te$_{4}$ can be obtained at subsolidus temperatures, and a complementary thermochemical study establishes a limited high-temperature range of phase stability. Nevertheless, quenched powders are stable at room temperature and exhibit long-range antiferromagnetic ordering below 24 K. The expected Mn(II) out-of-plane magnetic state is confirmed by the magnetization, X-ray photoemission, X-ray absorption and linear dichroism data. MnBi$_{2}$Te$_{4}$ exhibits a metallic type of resistivity in the range 4.5-300 K. The compound is an n-type conductor that reaches a thermoelectric figure of merit up to ZT = 0.17. Angle-resolved photoemission experiments provide evidence for a surface state forming a gapped Dirac cone.

Balanced electron-hole transport in spin-orbit semimetal SrIrO3 heterostructures

Relating the band structure of correlated semimetals to their transport properties is a complex and often open issue. The partial occupation of numerous electron and hole bands can result in properties that are seemingly in contrast with one another, complicating the extraction of the transport coefficients of different bands. The 5d oxide SrIrO3 hosts parabolic bands of heavy holes and light electrons in gapped Dirac cones due to the interplay between electron-electron interactions and spin-orbit coupling. We present a multifold approach relying on different experimental techniques and theoretical calculations to disentangle its complex electronic properties. By combining magnetotransport and thermoelectric measurements in a field-effect geometry with first-principles calculations, we quantitatively determine the transport coefficients of different conduction channels. Despite their different dispersion relationships, electrons and holes are found to have strikingly similar transport coefficients, yielding a holelike response under field-effect and thermoelectric measurements and a linear, electronlike Hall effect up to 33 T.

Chern Insulator Phase in a Lattice of an Organic Dirac Semimetal with Intracellular Potential and Magnetic Modulations

We demonstrate that a Chern insulator could be realized on a real two-dimensional lattice of an organic Dirac semimetal {\alpha}-(BEDT-TTF)2I3 by introducing potential and magnetic modulations in a unit cell. It is a topologically-nontrivial insulator which shows the quantum Hall effect even at zero magnetic field. We assumed a pattern of site potential and staggered plaquette magnetic flux on the lattice so as to imitate the observed stripe charge ordering pattern. When the magnetic modulation is sufficiently large, the system becomes a Chern insulator, where Berry curvatures around two gapped Dirac cones have the same sign on each band, and one chiral edge state connects the conduction and valence bands at each crystal edge. The present model is an organic version of Haldane's model, which discussed the Chern insulator on the honeycomb lattice with second nearest neighbor couplings.

Topological states at the (001) surface of SrTiO3

Defect-free SrTiO3 (STO) is a band insulator but Angle Resolved Photoemission Spectroscopy (ARPES) experiments have demonstrated the existence of a nanometer thin two-dimensional electron liquid (2DEG) at the (001) oriented surface of this compound. The bulk is a trivial insulator, but our theoretical study reveals that the parity of electronic wavefunctions in this 2DEG is inverted in the vicinity of special points in reciprocal space where the low-energy dispersion consists of four gapped Dirac cones with a tilted and anisotropic shape. This gives rise to linearly dispersing topological edge states at the one-dimensional boundary. We propose to probe these modes by measuring the Josephson radiation from gapless bound Andreev states in STO based junctions, as it is predicted that they display distinctive signatures of topology.

Designing substrates for silicene and germanene: First-principles calculations

We propose a guideline for exploring substrates that stabilize the monolayer honeycomb structure of silicene and germanene while simultaneously preserve the Dirac states: in addition to have a strong binding energy to the monolayer, a suitable substrate should be a large-gap semiconductor with a proper workfunction such that the Dirac point lies in the gap and far from the substrate states when their bands align. We illustrate our idea by performing first-principles calculations for silicene and germanene on the Al-terminated (0001) surface of Al2O3 . The overlaid monolayers on Al-terminated Al2O3(0001) retain the main structural profile of the low-buckled honeycomb structure via a binding energy comparable to the one between silicene and Ag(111). Unfolded band structure derived from the k-projection method reveals that gapped Dirac cone is formed at the K point due to the structural distortion and the interaction with the substrate. The gaps of 0.4 eV and 0.3 eV respectively for the supported silicene and germanene suggest that they may have potential applications in nanoelectronics.

The induced nontrivial Z2 topological phase in graphene sandwiched by pnictogen bilayers

By performing first-principles calculations, we find that graphene with nearly zero spin orbit coupling can be turned into a topological insulator after being sandwiched between pnictogen bilayers. It is found that a dipole field is induced between graphene and pnictogen bilayers, which will significantly pull down the Dirac point of graphene. Depending on the initial position of the Dirac point of graphene with respect to the energy gap of the pnictogen bilayers, Bi/graphene/Bi is found to be a metallic system while Sb/graphene/Sb a topological insulator. In Sb/graphene/Sb, a sizable gap is opened at the Dirac point of graphene. The strong spin–orbit coupling in Sb bilayers leads to a band inversion in the gapped Dirac cones of graphene via the proximity effect and the calculated Z2 topological index further confirms that a nontrivial topological phase is induced in graphene. By applying longitudinal or lateral strains to Sb/graphene/Sb, topological phase transition occurs based on the change of the thickness of the Sb bilayer instead of the change of the separation between graphene and Sb bilayers.