Massive Dirac Fermions Research Articles

2D Ladder Polyborane: An Ideal Dirac Semimetal with a Multi-Field-Tunable Band Gap.

Hydrogen, a simple and magic element, has attracted increasing attention for its effective incorporation within solids and powerful manipulation of electronic states. Here, we show that hydrogenation tackles common problems in two-dimensional borophene, e.g., stability and applicability. As a prominent example, a ladder-like boron hydride sheet, named as 2D ladder polyborane, achieves the desired outcome, enjoying the cleanest scenario with an anisotropic and tilted Dirac cone, that can be fully depicted by a minimal two-band tight-binding model. Introducing external fields, such as an electric field or a circularly polarized light field, can effectively induce distinctive massive Dirac fermions, whereupon four types of multi-field-driven topological domain walls hosting tunable chirality and valley indexes are further established. Moreover, the 2D ladder polyborane is thermodynamically stable at room temperature and supports highly switchable Dirac fermions, providing an ideal platform for realizing and exploring the various multi-field-tunable electronic states.

Recent progress of transport theory in Dirac quantum materials

Dirac quantum materials comprise a broad category of condensed matter systems characterized by low-energy excitations described by the Dirac equation. These excitations, which can manifest as either collective states or band structure effects, have been identified in a wide range of systems, from exotic quantum fluids to crystalline materials. Over the past several decades, they have sparked extensive experimental and theoretical investigations in various materials, such as topological insulators and topological semimetals. The study of Dirac quantum materials has also opened up new possibilities for topological quantum computing, giving rise to a burgeoning field of physics and offering a novel platform for realizing rich topological phases, including various quantum Hall effects and topological superconducting phases. Furthermore, the topologically non-trivial band structures of Dirac quantum materials give rise to plentiful intriguing transport phenomena, including longitudinal negative magnetoresistance, quantum interference effects, helical magnetic effects, and others. Currently, numerous transport phenomena in Dirac quantum materials remain poorly understood from a theoretical standpoint, such as linear magnetoresistance in weak fields, anomalous Hall effects in nonmagnetic materials, and three-dimensional quantum Hall effects. Studying these transport properties will not only deepen our understanding of Dirac quantum materials, but also provide important insights for their potential applications in spintronics and quantum computing. In this paper, quantum transport theory and quantum anomaly effects related to the Dirac equation are summarized, with emphasis on massive Dirac fermions and quantum anomalous semimetals. Additionally, the realization of parity anomaly and half-quantized quantum Hall effects in semi-magnetic topological insulators are also put forward. Finally, the key scientific issues of interest in the field of quantum transport theory are reviewed and discussed.

Topological Hall Effect Anisotropy in Kagome Bilayer Metal Fe_{3}Sn_{2}.

Kagome lattice materials have attracted growing interest for their topological properties and flatbands in electronic structure. We present a comprehensive study on the anisotropy and out-of-plane electric transport in Fe_{3}Sn_{2}, a metal with bilayer of Fe kagome planes and with massive Dirac fermions that features high-temperature noncollinear magnetic structure and magnetic skyrmions. For the electrical current path along the c axis, in micron-size crystals, we found a large topological Hall effect over a wide temperature range down to spin-glass state. Twofold and fourfold angular magnetoresistance are observed for different magnetic phases, reflecting the competition of magnetic interactions and magnetic anisotropy in kagome lattice that preserve robust topological Hall effect for inter-kagome bilayer currents. This provides new insight into the anisotropy in Fe_{3}Sn_{2}, of interest in skyrmionic-bubble application-related micron-size devices.

The role of Pryce’s spin and coordinate operators in the theory of massive Dirac fermions

It is shown that the components of Pryce’s spin operator of Dirac’s theory are SU(2) generators of a representation carried by the space of Pauli’s spinors determining the polarization of the plane wave solutions of Dirac’s equation. These operators are conserved via Noether’s theorem such that new conserved polarization operators can be defined for various polarizations. The corresponding one-particle operators of quantum theory are derived showing how these are related to the isometry generators of the massive Dirac fermions of any polarization, including momentum-dependent ones. In this manner, the problem of separating conserved spin and orbital angular momentum operators is solved naturally. Moreover, the operator proposed by Pryce as a mass-center coordinate is studied, showing that after quantization, this becomes in fact the dipole one-particle operator. As an example, the quantities determining the principal one-particle operators are derived for the first time in a momentum-helicity basis.

Plethora of tunable Weyl fermions in kagome magnet Fe3Sn2 thin films

Interplay of magnetism and electronic band topology in unconventional magnets enables the creation and fine control of novel electronic phenomena. In this work, we use scanning tunneling microscopy and spectroscopy to study thin films of a prototypical kagome magnet Fe3Sn2. Our experiments reveal an unusually large number of densely-spaced spectroscopic features straddling the Fermi level. These are consistent with signatures of low-energy Weyl fermions and associated topological Fermi arc surface states predicted by theory. By measuring their response as a function of magnetic field, we discover a pronounced evolution in energy tied to the magnetization direction. Electron scattering and interference imaging further demonstrates the tunable nature of a subset of related electronic states. Our experiments provide a direct visualization of how in-situ spin reorientation drives changes in the electronic density of states of the Weyl fermion band structure. Combined with previous reports of massive Dirac fermions, flat bands, and electronic nematicity, our work establishes Fe3Sn2 as an interesting platform that harbors an extraordinarily wide array of topological and correlated electron phenomena.

Spin-valley polarized transport in a field-controllable bilayer silicene superlattice

We have theoretically investigated the spin-valley asymmetric transport of massive Dirac fermions in the field-controllable bilayer silicene superlattices. The spin-valley dependent ballistic transmission, conductance, and polarization have been systematically calculated by formulating the scattering matrix method for the completed four-band low-energy effective Hamiltonian. Our results uncover that for a single valley transport, near-perfect spin polarization and its perfect switching could be efficiently modulated by the gate field engineering. Under the one-dimensional periodic field modulation, two types of flat bands with less dispersion and, importantly, the perfect contrast in the spin-dependent subbands are observed for the bilayer silicene superlattice. Together with its larger spin-orbit coupling and better stability, these spin-valley asymmetric characteristics engineered by the gate field indicate that the field-controllable bilayer silicene could be a potential component candidate to achieve a fully spin-valley polarized beam for quantum logic applications.

Nanoscale View of Engineered Massive Dirac Quasiparticles in Lithographic Superstructures

Massive Dirac fermions are low-energy electronic excitations characterized by a hyperbolic band dispersion. They play a central role in several emerging physical phenomena such as topological phase transitions, anomalous Hall effects, and superconductivity. This work demonstrates that massive Dirac fermions can be controllably induced by lithographically patterning superstructures of nanoscale holes in a graphene device. Their band dispersion is systematically visualized using angle-resolved photoemission spectroscopy with nanoscale spatial resolution. A linear scaling of effective mass with feature sizes is reported, underlining the Dirac nature of the superstructures. In situ electrostatic doping dramatically enhances the effective hole mass and leads to the direct observation of an electronic band gap that results in a peak-to-peak band separation of 0.64 ± 0.03 eV, which is shown via first-principles calculations to be strongly renormalized by carrier-induced screening. The methodology demonstrates band structure engineering guided by directly viewing structurally and electrically tunable massive Dirac quasiparticles in lithographic superstructures at the nanoscale.

Freeze-In of radiative keV-scale neutrino dark matter from a new U(1)B-L

We extend the Dirac Scotogenic model with the aim of realizing neutrino masses together with the mass of a keV-scale dark matter (DM) candidate via the same one-loop topology. Two of the Standard Model (SM) neutrinos become massive Dirac fermions while the third one remains massless. Our particle content is motivated by an anomaly free U(1)B-L gauge symmetry with exotic irrational charges and we need to enforce an additional mathcal{Z} 5 symmetry. The dark matter candidate does not mix with the active neutrinos and does not have any decay modes to SM particles. DM is produced together with dark radiation in the form of right handed neutrinos via out of equilibrium annihilations of the SM fermions mediated by the heavy B-L gauge boson. In order to avoid DM over-production from Higgs decays and to comply with Lyman-α bounds we work in a low temperature reheating scenario with 4 MeV ≲ TRH ≲ 5 GeV. Our setup predicts a contribution to ∆Neff. that decreases for larger DM masses and is below the sensitivity of upcoming precision measurements such as CMB-S4. A future observation of a signal with ∆Neff. ≳ 0.012 would exclude our scenario. We further sketch how inflation, reheating and Affleck-Dine baryogenesis can also be potentially realized in this unified framework.

Massive Dirac fermions in moiré superlattices: A route towards topological flat minibands and correlated topological insulators

We demonstrate a generic mechanism to realize topological flat minibands by confining massive Dirac fermions in a periodic moir\'e potential, which can be achieved in a heterobilayer of transition metal dichalcogenides. We show that the topological phase can be protected by the symmetry of moir\'e potential and survive to arbitrarily large Dirac band gap. We take the MoTe$_2$/WSe$_2$ heterobilayer as an example and find that the topological phase can be driven by a vertical electric field. By projecting the Coulomb interaction onto the topological fat minibands, we identify a correlated Chern insulator at half filling and a quantum valley-spin Hall insulator at full filling which explains the topological states observed in the MoTe$_2$/WSe$_2$ in experiment. Our work clarifies the importance of Dirac structure for the topological minibands and unveils a general strategy to design topological moir\'e materials.

Simple Chemical Rules for Predicting Band Structures of Kagome Materials

Compounds featuring a kagome lattice are studied for a wide range of properties, from localized magnetism to massless and massive Dirac Fermions. These properties come from the symmetry of the kagome lattice, which gives rise to Dirac cones and flat bands. However, not all compounds with a kagome sublattice show properties related to it. We derive chemical rules predicting if the low-energy physics of a material is determined by the kagome sublattice and bands arising from it. After sorting out all known crystals with the kagome lattice into four groups, we use chemical heuristics and local symmetry to explain additional conditions that need to be met to have kagome bands near the Fermi level.

Half-quantized Hall effect and power law decay of edge-current distribution

The half-quantized Hall conductance is characteristic of quantum systems with parity anomaly. Here we investigate topological and transport properties of a class of parity anomalous semimetals, in which massive Dirac fermions coexist with massless Dirac fermions in momentum space or real space, and uncovered a distinct bulk-edge correspondence that the half-quantized Hall effect is realized via the bulk massless Dirac fermions while the nontrivial Berry curvature is provided by the massive Dirac fermions. The spatial distribution of the edge current decays away from the boundary in a power law instead of an exponential law in integer quantum Hall effect. We further address physical relevance of parity anomalous semimetal to three-dimensional semi-magnetic topological insulators and two-dimensional photonic crystals.

Inhomogeneous quantum quenches in the sine-Gordon theory

We study inhomogeneous quantum quenches in the attractive regime of the sine--Gordon model. In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sine--Gordon Hamiltonian. Varying either the interaction strength of the sine--Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein--Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sine--Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial. Nevertheless, their interplay is expected to influence the sine--Gordon dynamics in arbitrary inhomogeneous settings.

Andreev reflection of massive pseudospin-1 fermions

We theoretically investigate the Andreev reflection of the massive pseudospin-1 Dirac fermions including the +U-type, the −U-type, and the S z -type mass terms, corresponding to the flat band locating at the top, the bottom, and the center of the band gap, respectively. For the ±U-type fermions, it is found that the Andreev reflection probability at the oblique incidence can be even larger than that at the normal incidence. For the retro-reflection, such an oblique enhancement occurs in the n-doped +U-type (p-doped −U-type) massive fermion systems. While for the specular reflection, the enhancement occurs in the n-doped −U-type (p-doped +U-type) systems. For the S z -type massive fermions, an ideal Andreev reflection with all-angle unit efficiency is predicted in an undoped junction with the incident energy equal to the superconducting gap.

Large Magnetic Gap in a Designer Ferromagnet-Topological Insulator-Ferromagnet Heterostructure.

Combining magnetism and nontrivial band topology gives rise to quantum anomalous Hall (QAH) insulators and exotic quantum phases such as the QAH effect where current flows without dissipation along quantized edge states. Inducing magnetic order in topological insulators via proximity to a magnetic material offers a promising pathway toward achieving the QAH effect at a high temperature for lossless transport applications. One promising architecture involves a sandwich structure comprising two single-septuple layers (1SL) of MnBi2 Te4 (a 2D ferromagnetic insulator) with ultrathin few quintuple layer (QL) Bi2 Te3 in the middle, and it is predicted to yield a robust QAH insulator phase with a large bandgap greater than 50 meV. Here, the growth of a 1SL MnBi2 Te4 /4QL Bi2 Te3 /1SL MnBi2 Te4 heterostructure via molecular beam epitaxy is demonstrated and the electronic structure probed using angle-resolved photoelectron spectroscopy. Strong hexagonally warped massive Dirac fermions and a bandgap of 75 ± 15 meV are observed. The magnetic origin of the gap is confirmed by the observation of the exchange-Rashba effect, as well as the vanishing bandgap above the Curie temperature, in agreement with density functional theory calculations. These findings provide insights into magnetic proximity effects in topological insulators and reveal a promising platform for realizing the QAH effect at elevated temperatures.

Generalized Hamiltonian for Kekulé graphene and the emergence of valley-cooperative Klein tunneling

We introduce a generalized Hamiltonian describing not only all topological phases observed experimentally in Kekul\'e graphene (KekGr) but predicting also new ones. These phases show features like a quadratic band crossing point, valley splitting, or the crossing of conduction bands, typically induced by Rashba spin-orbit interactions or Zeeman fields. The electrons in KekGr behave as Dirac fermions and follow pseudorelativistic dispersion relations with Fermi velocities, rest masses, and valley-dependent self-gating. Transitions between the topological phases can be induced by tuning these parameters. The model is applied to study the current flow in KekGr $pn$ junctions evidencing a cooperative transport phenomenon, where Klein tunneling goes along with a valley flip. These junctions act as perfect filters and polarizers of massive Dirac fermions, which are the essential devices for valleytronics. The plethora of different topological phases in KekGr may also help to establish phenomena from spintronics.

Photovoltage oscillations in encapsulated graphene

We theoretically analyze the rise of photovoltage oscillations in hexagonal boron-nitride (h-BN) encapsulated monolayer graphene (h-BN/graphene/h-BN) when irradiated with terahertz radiation. We use an extension of the radiation-driven electron orbit model, successfully applied to study the oscillations obtained in irradiated magnetotransport of GaAs/AlGaAs heterostructures. The extension takes mainly into account that now the carriers are massive Dirac fermions. Our simulations reveal that the photovoltage in these graphene systems presents important oscillations similar to the ones of irradiated magnetoresistance in semiconductor platforms but in the terahertz range. We also obtain that these oscillations are clearly affected by the voltages applied to the sandwiched graphene: a vertical gate voltage between the two hBN layers and an external positive voltage applied to one of the sample sides. The former steers the carrier effective mass and the latter the photovoltage intensity and the oscillations amplitude. The frequency dependence of the photo-oscillations is also investigated.

Quantum Criticality of Antiferromagnetism and Superconductivity with Relativity.

We study a quantum phase transition from a massless to massive Dirac fermion phase in a new two-dimensional bipartite lattice model of electrons that is amenable to sign-free quantum MonteCarlo simulations. Importantly, interactions in our model are not only invariant under SU(2) symmetries of spin and charge like the Hubbard model, but they also preserve an Ising-like electron spin-charge flip symmetry. From unbiased fermion bag MonteCarlo simulations with up to 2304 sites, we show that the massive fermion phase spontaneously breaks this Ising symmetry, picking either antiferromagnetism or superconductivity, and that the transition at which both orders are simultaneously quantum critical belongs to a new "chiral spin-charge symmetric" universality class. We explain our observations using effective potential and renormalization group calculations within the framework of a continuum field theory.

One-pot synthesis of vertical graphene/h-BN heterostructure utilizing the passivation role of hydrogen

Graphene/hexagonal boron nitride (h-BN) heterostructures have attracted a lot of research interests due to their superior electronic properties in field effect transistor devices and the novel physical properties such as fractional fractal quantum hall effect and massive Dirac fermions. Chemical vapor deposition (CVD) is the most common method to synthesize h-BN and graphene, however, the directly growth of graphene/h-BN heterostructures remains challenging. Here we report the crucial impact of hydrogen on the nucleation density, growth rate and etching rate in the h-BN CVD growth. It is found that the nucleation density increases monotonically, whereas the growth rate and etching rate first increases and then decreases with the increasing hydrogen partial pressure. Benefitting from the understanding of the crucial role of hydrogen, we successfully grow the graphene/h-BN vertical heterostructures by low pressure CVD in one-pot through the modulation of hydrogen partial pressure. The field effect transistor (FET) fabricated using graphene/h-BN heterostructure shows better performance with higher carrier mobility and lower level of doping than the one without h-BN. Our direct synthesis approach paves a new pathway for large-scale production of graphene/h-BN heterostructures and could be applied for the synthesis of other van der Waals heterostructures.

TEORÍA DE CAMPOS NO RELATIVISTAS: DINÁMICA E IRREVERSIBILIDAD

We study aspects of quantum field theory at finite density using techniques and concepts from quantum information theory. We focus on massive Dirac fermions with chemical potential in 1+1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. This c-function is not monotonous,and incorporates the long-range entanglement from the Fermi surface. Motivated by previous works on lattice models,we next compute the Renyi entropies numerically, and find Friedel-type oscillations. Next, we analyze the mutual in-formation as a measure of correlation functions between different regions. Using a long-distance expansion developed by Cardy, we show how the mutual information detects the Fermi surface correlations already at leading order in the expansion. Finally, we analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge. We find that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy.

Interlayer exchange interaction driven topological phase transition in antiferromagnetic electride Gd2O

Based on first-principles calculations, we discover a two-dimensional layered antiferromagnetic (AFM) electride Gd$_2$O, where anionic excess electrons exist in the interstitial spaces between positively charged cationic layers. It is revealed that each cationic layer composed of three-atom-thick Gd$-$O$-$Gd stacks has in-plane ferromagnetic and out-of-plane AFM superexchange interactions between the localized Gd 4$f$ spins through O 2$p$ orbitals. Furthermore, the interlayer superexchange mediated by the hybridized Gd-5$d$ and interstitial-$s$-like states involves intimate couplings between the spin, lattice, and charge degrees of freedom, thereby inducing simultaneous magnetic, structural, and electronic phase transitions. The resulting ground state with the simple hexagonal lattice hosts massless Dirac fermions protected by nonsymmorphic magnetic symmetry, as well as massive Dirac fermions. We thus demonstrate that the anionic excess electrons in Gd$_2$O play a crucial role in the emergence of magnetic Dirac semimetal states, therefore offering an intriguing interplay between 2D magnetic electrides and topological physics.