Dirac Dispersion Research Articles

Dirac dispersions and Fermi surface nesting in LaCuSb2

LaCuSb2 is a superconductor with a transition temperature of about Tc = 0.9 K and is a potential platform where Dirac fermions can be experimentally observed. In this paper, we report systematic high-resolution studies of its electronic structure using the angle-resolved photoemission spectroscopy (ARPES) technique supported by the DFT calculation. The Fermi surface consists of four branches, of which the two inner ones are more 3-dimensional and the theoretical calculations reproduce well the experiment. We observe several linear dispersions forming Dirac-like structures. The nodal lines are present in the system along the M–A and X–R and Dirac crossings along the X–R are observed by ARPES. Finally, the nesting between external Fermi surface pockets, which corresponds to charge density wave (CDW) modulation vector is enhanced in LaCuSb2 as compared to LaAgSb2, while CDW appears in the latter system.

Engineering Two-Dimensional Nodal Semimetals in Functionalized Biphenylene by Fluorine Adatoms.

We propose a band engineering scheme on the biphenylene network, a newly synthesized carbon allotrope. We illustrate that the electronic structure of the biphenylene network can be significantly altered by controlling conditions affecting the symmetry and destructive interference of wave functions through periodic fluorination. First, we investigate the mechanism for the appearance of a type-II Dirac fermion in a pristine biphenylene network. We show that the essential ingredients are mirror symmetries and stabilization of the compact localized eigenstates via destructive interference. While the former is used for the band-crossing point along high symmetry lines, the latter induces highly inclined Dirac dispersions. Subsequently, we demonstrate the transformation of the biphenylene network's type-II Dirac semimetal phase into various Dirac phases such as type-I Dirac, gapped type-II Dirac, and nodal line semimetals through the deliberate disruption of mirror symmetry or modulation of destructive interference by varying the concentration of fluorine atoms.

Tunable Colossal Anomalous Hall Conductivity in Half-Metallic Material Induced by d-Wave-Like Spin-Orbit Gap.

The anomalous Hall conductivity (AHC) in magnetic materials, resulting from inverted band topology, has emerged as a key adjustable function in spin-torque devices and advanced magnetic sensors. Among systems with near-half-metallicity and broken time-reversal symmetry, cobalt disulfide (CoS2) has proven to be a material capable of significantly enhancing its AHC. In this study, the AHC of CoS2 is empirically assessed by manipulating the chemical potential through Fe- (hole) and Ni- (electron) doping. The primary mechanism underlying the colossal AHC is identified through the application of density functional theory and tight-binding analyses. The main source of this substantial AHC is traced to four spin-polarized massive Dirac dispersions in the kz = 0 plane of the Brillouin zone, located slightly below the Fermi level. In Co0.95Fe0.05S2, the AHC, which is directly proportional to the momentum-space integral of the Berry curvature (BC), reached a record-breaking value of 2507 Ω-1cm-1. This is because the BCs of the four Dirac dispersions all exhibit the same sign, a consequence of the d-wave-like spin-orbit coupling among spin-polarized egorbitals.

Growth of Bi2Te3 topological insulator ultra-thin layers via molecular beam epitaxy on GaAs (100)

Ultra-thin layers (<8 nm) of a Bi2Te3 topological insulator have been grown on GaAs (100) substrates using molecular beam epitaxy. The growth was performed from a single Bi2Te3 effusion cell and one source of extra tellurium. Optical and structural characterizations were carried out through Raman spectroscopy, x-ray diffraction, atomic force microscopy, and scanning electron microscopy. The topological insulator properties were also investigated by angle-resolved photoelectron spectroscopy. A layer of 5 nm showed Dirac cone-like linear electronic band dispersion, indicating the signature of a topological insulator with the Dirac point having large binding energy relative to the Fermi level as expected for ultra-thin films. Topological insulator properties were also investigated at the initial growth stage where deposition follows an islandlike growth mode. Our results can contribute to the development of practical chalcogenide-based thin-film spintronics devices.

Unique Huygens-Fresnel electromagnetic transportation of chiral Dirac wavelet in topological photonic crystal

Light propagates in various ways depending on environment, including uniform medium, surface/interface and photonic crystals, which appears ubiquitously in daily life and has been exploited for advanced optics technology. We unveiled that a topological photonic crystal exhibits unique electromagnetic (EM) transport properties originating from the Dirac frequency dispersion and multicomponent spinor eigenmodes. Measuring precisely local Poynting vectors in microstrips of honeycomb structure where optics topology emerges upon a band gap opening in the Dirac dispersion and a p-d band inversion induced by a Kekulé-type distortion respecting C6v symmetry, we showed that a chiral wavelet induces a global EM transportation circulating in the direction counter to the source, which is intimately related to the topological band gap specified by a negative Dirac mass. This brand-new Huygens-Fresnel phenomenon can be considered as the counterpart of negative refraction of EM plane waves associated with upwardly convex dispersions of photonic crystals, and our present finding is expected to open a new window for photonic innovations.

Observation of linear magnetoelectric effect in a Dirac magnon antiferromagnet Cu3TeO6

Cu3TeO6, a three-dimensional antiferromagnet forming a unique spin-web lattice of spin-1/2 Cu2+ ions below the Néel temperature TN ≈ 62 K, has recently been found to exhibit topological Dirac or nodal magnon dispersion. In this study, we report the discovery of the linear magnetoelectric (ME) effects in Cu3TeO6 below TN. Our pyroelectric current measurements at a constant magnetic field (H) reveal a linear increase of electric polarization (P) with H for both P//H and P⊥ H configurations; a maximum P//[110] = 20 µC/m2 is obtained at µ0H//11¯0 = 14 T, corresponding to a linear ME coefficient 1.8 ps/m. Magnetic point group analysis and Monte-Carlo simulations confirm that finite linear ME coefficients are allowed in the off-diagonal and diagonal ME tensor components, consistent with the magnetic point group of 3¯′. As the parity-time symmetry can be broken in the presence of H or electric field E in the linear ME materials, we envisage that Cu3TeO6 should exhibit a H- or E-induced transformation in the topological magnon dispersion from a Dirac point/nodal line type into two Weyl point types.

Topological half-metallic features in alkali metal doped CrCl3 monolayers

Two-dimensional (2D) topological half metals, namely, empowering nontrivial topological states with 100% spin-polarized 2D systems, may find important applications in low-dissipation spintronics. However, exploration of such intriguing materials is still very challenging. The recently discovered 2D magnetic materials provide unprecedented opportunities to realize 2D topological half-metallic state. Using first-principles calculations, we first find that the ferromagnetism of $\mathrm{Cr}{\mathrm{Cl}}_{3}$ monolayer can be well reserved by doping alkali metals, in fact, whose Curie temperature can be enhanced from 23 to 66 K after doping K. Then, we notice that semiconducting to Dirac half-metallic phase transition is achieved via Na and K doping, where the linear Dirac dispersion originates from the honeycomb lattice formed by Cr atoms. Most strikingly, Na- and K doped $\mathrm{Cr}{\mathrm{Cl}}_{3}$ exhibit quantum anomalous Hall effect (QAHE) with Chern number $C=1$, while the Li-doped one harbors high Chern number QAHE with $C=\ensuremath{-}2$. Thus, our work provides a theoretical guideline to realize 2D topological half-metallic state, rendering it as a promising platform for future applications.

Single-crystal growth and physical properties of LaMn0.86Sb2

Single crystals of ${\mathrm{LaMn}}_{0.86}{\mathrm{Sb}}_{2}$ were synthesized via the flux method. Band structure calculation indicates the existence of Dirac dispersion below the Fermi level as expected for the square-net-based materials. Magnetization in combination with neutron diffraction measurements suggests that the magnetic structure below ${T}_{\mathrm{N}}=146 \mathrm{K}$ can be described by a G-type antiferromagnetic structure with a weak spin canting. A spin-flop transition was observed when external magnetic fields were applied parallel to the $c$ axis. Negative magnetoresistance is observed at low temperatures, likely originating from the spin alignment effect. Our results indicate that ${\mathrm{LaMn}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{2}$ has Dirac dispersion and a vacancy tunable magnetism, which could be a potential platform for studying the interplay of magnetism, charge transport, and possible topological band.

Probing photocarrier dynamics of pressurized graphene using time-resolved terahertz spectroscopy

Graphene hosts intriguing photocarrier dynamics such as negative transient terahertz (THz) photoconductivity, high electron temperature, benefiting from the unique linear Dirac dispersion. In this work, the pressure effects of photocarrier dynamics of graphene have been investigated using in situ time-resolved THz spectroscopy in combination with diamond anvil cell exceeding 9 GPa. We find that the negative THz conductivity maintains in our studied pressure range both for monolayer and bilayer graphene. In particular, the amplitude of THz photoconductivity in monolayer graphene manifests an extraordinary dropping with pressure, compared with that from the counterparts such as bulk silicon and bilayer graphene. Concomitantly, the time constant is reduced with increasing pressure, highlighting the pressure-induced hot carrier cooling. The pressure dependence of photocarrier dynamics in monolayer graphene is likely related with the enhancement of the interfacial coupling between diamond surface and sample, allowing for the activity of new electron–phonon scattering. Our work is expected to provide an impetus for the studies of high-pressure THz spectroscopy of two-dimensional materials.

A High-Throughput Screening toward Efficient Nitrogen Fixation: Transition Metal Single-Atom Catalysts Anchored on an Emerging π-π Conjugated Graphitic Carbon Nitride (g-C10N3) Substrate with Dirac Dispersion.

TM-Nx is becoming a comforting catalytic center for sustainable and green ammonia synthesis under ambient conditions, resulting in increasing interest in single-atom catalysts (SACs) for the electrochemical nitrogen reduction reaction (NRR). However, given the poor activity and unsatisfactory selectivity of existing catalysts, it remains a long-standing challenge to design efficient catalysts for nitrogen fixation. Currently, the two-dimensional (2D) graphitic carbon-nitride substrate provides abundant and evenly distributed holes for stably supporting transition-metal atoms, which presents a fascinating prospect for overcoming this challenge and promoting single-atom NRR. An emerging holey graphitic carbon-nitride skeleton with a C10N3 stoichiometric ratio (g-C10N3) from a supercell of graphene is constructed, which provides outstanding electric conductivity for achieving high-efficiency NRR due to the Dirac band dispersion. Herein, a high-throughput first-principles calculation is carried out to evaluate the feasibility of π-d conjugated SACs resulting from a single TM atom anchored on g-C10N3 (TM = Sc-Au) for NRR. We find that W metal embedded in g-C10N3 (W@g-C10N3) can compromise the ability to adsorb the key target reaction species (N2H and NH2), hence acquiring an optimal NRR behavior among 27 TM-candidates. Our calculations demonstrate that W@g-C10N3 shows a well-suppressed HER ability and, impressively, a low energy cost of -0.46 V. Additionally, all-around descriptors are proposed to uncover the fundamental mechanism of NRR activity, among which a 3D volcano plot (limiting potential, screening strategy, and electron origin) uncovers the NRR activity trend, achieving a quick and high-efficiency prescreening for numerous candidates. Overall, the strategy of the structure- and activity-based TM-Nx-containing unit design will offer useful insight for further theoretical and experimental attempts.

Giant Density of States Enhancement Driven by a Zero-Mode Landau Level in Semimetallic Black Phosphorus under Pressure.

Dirac fermion systems form a unique Landau level at the Fermi level-the so-called zero mode-whose observation itself will provide strong evidence of the presence of Dirac dispersions. Here, we report the study of semimetallic black phosphorus under pressure by ^{31}P-nuclear magnetic resonance measurements in a wide range of magnetic field up to 24.0T. We have found a field-induced giant enhancement of 1/T_{1}T, where 1/T_{1} is the nuclear spin lattice relaxation rate: 1/T_{1}T at 24.0T reaches more than 20 times larger than that at 2.0T. The increase in 1/T_{1}T above 6.5T is approximately proportional to the squared field, implying a linear relationship between the density of states and the field. We also found that, while 1/T_{1}T at a constant field is independent of temperature in the low-temperature region, it steeply increases with temperature above 100K. All these phenomena are well explained by considering the effect of Landau quantization on three-dimensional Dirac fermions. The present study demonstrates that 1/T_{1} is an excellent quantity to probe the zero-mode Landau level and to identify the dimensionality of the Dirac fermion system.

Enhanced Anomalous Nernst Effect by Tuning the Chemical Potential in the Topological Kagome Ferromagnet Fe3Sn2

Large anomalous Nernst effect (ANE) in magnetic topological materials (MTMs) has attracted various attentions because of its potential thermoelectric applications. Recently, MTMs with the kagome lattice have become a focus of research to investigate enhanced ANE. In this work, the ANE (${S}_{yx}^{A}$) at room temperature in a kagome ferromagnet ${\mathrm{Fe}}_{3}{\mathrm{Sn}}_{2}$ with massive Dirac bands is greatly enhanced to $5.44\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}{\mathrm{VK}}^{\ensuremath{-}1}$ when its Fermi level is gradually tuned to Dirac nodal points. Then the intrinsic contributions to the enhanced ${S}_{yx}^{A}$ is further investigated. The anomalous transverse Peltier conductivity ${\ensuremath{\alpha}}_{yx}^{A}$ shows the linear temperature-dependent behavior, which is consistent with Berry-curvature-contributed ${\ensuremath{\alpha}}_{yx}^{A}$, and this behavior is different from temperature-dependent variation of magnetization. Combined with theoretic calculations, the ${\ensuremath{\alpha}}_{yx}^{A}$ and $|{\ensuremath{\alpha}}_{yx}^{A}/{\ensuremath{\sigma}}_{xy}^{A}|$ ratio increases significantly when approaching the massive Dirac cone, indicating that the massive Dirac dispersion and intrinsic contributions play a role in enhanced ANE instead of the side-jump mechanism. Our work demonstrates an effective universal approach to enhance ANE in such MTMs.

Anisotropic magnetoresistance and electronic features of the candidate topological compound praseodymium monobismuthide.

PrBi, a sister member of the rare-earth monopnictide family, is an excellent candidate for studying extreme magnetoresistance and nontrivial topological electronic states. In this study, we perform angular magnetoresistance measurements as well as bulk and surface band structure calculations on this compound. PrBi's magnetoresistance is revealed to be significantly angle-dependent and shows a fourfold symmetry as always observed in the nonmagnetic isostructural counterparts, including LaSb, LaBi, and LuBi. Its angular magnetoresistance can be reproduced well using the semiclassical two-band model. The deduced parameters suggest that PrBi hosts an elongated electron pocket with a mobility anisotropy of ∼3.13 and is slightly uncompensated in its carrier concentration. Our bulk and surface band structure calculations confirm the anisotropic electronic features. Moreover, we reveal that a nodal-line-shaped surface state appears at the X̄ point, and is associated with the quadratic dispersion along the -X̄ direction, and the linear type-I Dirac dispersion along the X̄-M̄ direction. Owing to the type-I Dirac dispersion feature, PrBi could serve as a promising material platform for studying many unexpected physical properties, such as the highly anisotropic transport and valley polarization of electrons.

Application of the real space decimation method in determining intricate electronic phases of matter: a review.

The real space decimation method has been successfully applied over the years to understand the critical phenomena as well as the nature of single particle excitations in periodic, quasiperiodic, fractal, and decorated lattices in one dimension and beyond. The power of the method is specially revealed through its application in lattice models, leading to an elegant understanding of the nature of the single-particle states and the corresponding transport properties. In this review, we discuss, using a variety of decorated lattices, how the realm of this method is extended to unravel diverse electronic phases of matter, such as the Dirac systems, or lattices exhibiting flat bands and topological phase transitions.

Type-II corner modes in topolectrical circuits

We study the rich properties of a topolectrical (TE) circuit array consisting of lossless basic electrical components, such as capacitors and inductors, which can be designed to exhibit higher-order topological phases (HOTP). The HOTP of the circuit exhibits the characteristics of higher-order topology, i.e., unconventional bulk-boundary correspondence with strongly localized corner modes, and higher winding numbers. More interestingly, a type-II corner mode emerges in the presence of long-range interaction, which is realized in the TE circuit by the introduction of next-nearest neighbor (NNN) coupling capacitances. Unlike the usual (i.e., ``type-I'') corner modes that are localized at a particular sublattice node due to the chiral symmetry, the type-II corner modes possess a spatial extent with an exponential decay length. We analytically derive this decay length as a function of the circuit parameters. The NNN coupling is also associated with the tilt parameter in the admittance spectrum of the circuit. The admittance spectrum is reminiscent of that of Dirac fermions. Changing the tilt parameter can lead to a transition from the type-I to the overtilted type-II Dirac dispersion. This overtilting results in a hybridization of the bulk and corner modes in which the distinct corner modes disappear. Furthermore, the type-I and type-II corner modes can be distinguished by their impedance readout. By virtue of their flexibility, the TE circuits provide an ideal platform to demonstrate unusual features of HOTPs arising from long-range interactions, and to engineer different types of robust topological corner modes.

Synergetic Ferroelectricity and Superconductivity in Zero-Density Dirac Semimetals near Quantum Criticality.

We study superconductivity in a three-dimensional zero-density Dirac semimetal in proximity to a ferroelectric quantum critical point. We find that the interplay of criticality, inversion-symmetry breaking, and Dirac dispersion gives rise to a robust superconducting state at the charge-neutrality point, where no Fermi surface is present. Using Eliashberg theory, we show that the ferroelectric quantum critical point is unstable against the formation of a ferroelectric density wave (FDW), whose fluctuations, in turn, lead to a first-order superconducting transition. Surprisingly, long-range superconducting and FDW orders are found to cooperate with each other, in contrast to the more usual scenario of phase competition. Therefore, we suggest that driving charge neutral Dirac materials, e.g., Pb_{x}Sn_{1-x}Te, through a ferroelectric quantum critical point may lead to superconductivity intertwined with FDW order.

Tuning the many-body interactions in a helical Luttinger liquid

In one-dimensional (1D) systems, electronic interactions lead to a breakdown of Fermi liquid theory and the formation of a Tomonaga-Luttinger Liquid (TLL). The strength of its many-body correlations can be quantified by a single dimensionless parameter, the Luttinger parameter K, characterising the competition between the electrons’ kinetic and electrostatic energies. Recently, signatures of a TLL have been reported for the topological edge states of quantum spin Hall (QSH) insulators, strictly 1D electronic structures with linear (Dirac) dispersion and spin-momentum locking. Here we show that the many-body interactions in such helical Luttinger Liquid can be effectively controlled by the edge state’s dielectric environment. This is reflected in a tunability of the Luttinger parameter K, distinct on different edges of the crystal, and extracted to high accuracy from the statistics of tunnelling spectra at tens of tunnelling points. The interplay of topology and many-body correlations in 1D helical systems has been suggested as a potential avenue towards realising non-Abelian parafermions.

Moiré exciton condensate: Nonlinear Dirac point, broken-symmetry Bloch waves, and unusual optical selection rules

Moir\'e exciton features tunable Dirac dispersion and spatially dependent optical selection rules. With the long lifetime due to its interlayer nature, it is promising to realize a Bose-Einstein condensation of moir\'e excitons. Here we study the properties of moir\'e exciton condensate within the mean-field theory, with special focus on exciton-exciton interaction effect on the nonlinear Bloch band and Bloch waves of exciton condensate in moir\'e potential. We find the nonlinear dispersion of the moir\'e exciton condensate exhibits complex loop structure induced by exciton-exciton interaction. A nonlinear Dirac cone emerges at $\boldsymbol{\Gamma}$ point of the Bloch band, with a three-fold degenerate nonlinear Dirac point. Each degenerate Bloch wave at nonlinear Dirac point spontaneously breaks $C3$ rotational symmetry of the moir\'e potential, and themselves differ by $C3$ rotations. Since they reside in the light cone, these nontrivial Bloch band structure and broken-symmetry Bloch waves can be experimentally detected by examining light emission from those states. Symmetry breaking of Bloch states implies unusual optical selection rules compared with single exciton case: moir\'e exciton condensate at $\boldsymbol{\Gamma}$ point emits light with all three components of polarization instead of only left or right circular polarization. We further propose that, by applying in-plane electric field on one layer to drive an initially optically dark exciton condensate towards light cone, the light polarization of final states as well as their dependence on field direction serves as the smoking gun for experimental observation.

Observation of Coexisting Dirac Bands and Moiré Flat Bands in Magic-Angle Twisted Trilayer Graphene.

Moiré superlattices that consist of two or more layers of 2D materials stacked together with a small twist angle have emerged as a tunable platform to realize various correlated and topological phases, such as Mott insulators, unconventional superconductivity, and quantum anomalous Hall effect. Recently, magic-angle twisted trilayer graphene (MATTG) has shown both robust superconductivity similar to magic-angle twisted bilayer graphene and other unique properties, including the Pauli-limit violating and re-entrant superconductivity. These rich properties are deeply rooted in its electronic structure under the influence of distinct moiré potential and mirror symmetry. Here, combining nanometer-scale spatially resolved angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy, the as-yet unexplored band structure of MATTG near charge neutrality is systematically measured. These measurements reveal the coexistence of the distinct dispersive Dirac band with the emergent moiré flat band, showing nice agreement with the theoretical calculations. These results serve as a stepstone for further understanding of the unconventional superconductivity in MATTG.

Observation of anisotropic Dirac cones in the topological material Ti2Te2P

Anisotropic bulk Dirac (or Weyl) cones in three-dimensional systems have recently gained intense research interest as they are examples of materials with tilted Dirac (or Weyl) cones indicating the violation of Lorentz invariance. In contrast, the studies on anisotropic surface Dirac cones in topological materials which contribute to anisotropic carrier mobility have been limited. By employing angle-resolved photoemission spectroscopy and first-principles calculations, we reveal the anisotropic surface Dirac dispersion in a tetradymite material ${\mathrm{Ti}}_{2}{\mathrm{Te}}_{2}\mathrm{P}$ on the (001) plane of the Brillouin zone. We observe quasielliptical Fermi pockets at the $\overline{M}$ point of the Brillouin zone forming the anisotropic surface Dirac cones. Our calculations of the ${\mathbb{Z}}_{2}$ indices confirm that the system is topologically nontrivial with multiple topological phases in the same material. In addition, the observed nodal-line-like feature formed by bulk bands makes this system topologically rich.