Dirac Fermions Research Articles

Frame potential of Brownian SYK model of Majorana and Dirac fermions

We consider the Brownian SYK, i.e. a system of N Majorana (Dirac) fermions with a white-noise q-body interaction term. We focus on the dynamics of the Frame potentials, a measure of the scrambling and chaos, given by the moments of the overlap between two independent realisations of the model. By means of a Keldysh path-integral formalism, we compute its early and late-time value. We show that, for q > 2, the late time path integral saddle point correctly reproduces the saturation to the value of the Haar frame potential. On the contrary, for q = 2, the model is quadratic and consistently we observe saturation to the Haar value in the restricted space of Gaussian states (Gaussian Haar). The latter is characterised by larger system size corrections that we correctly capture by counting the Goldstone modes of the Keldysh saddle point. Finally, in the case of Dirac fermions, we highlight and resolve the role of the global U(1) symmetry.

Strain-tunable Dirac semimetal phase transition and emergent superconductivity in a borophane

A two-dimensional (2D) Dirac semimetal with concomitant superconductivity has been long sought but rarely reported. It is believed that light-element materials have the potential to realize this goal owing to their intrinsic lightweight and metallicity. Here, based on the recently synthesized β12 hydrogenated borophene, we investigate its counterpart named β12-B5H3. Our first-principles calculations suggest it has good stability. β12-B5H3 is a scarce Dirac semimetal demonstrating a strain-tunable phase transition from three Dirac cones to a single Dirac cone. Additionally, β12-B5H3 is also a superior phonon-mediated superconductor with a superconducting critical temperature of 32.4 K and can be further boosted to 42 K under external strain. The concurrence of Dirac fermions and superconductivity, supplemented with dual tunabilities, reveals β12-B5H3 is an attractive platform to study either quantum phase transition in 2D Dirac semimetal or the superconductivity or the exotic physics brought about by their interplay.

FeynGrav and Recent Progress in Computational Perturbative Quantum Gravity

This article reviews recent progress in computational quantum gravity caused by the framework that efficiently computes Feynman’s rules. The framework is implemented in the FeynGrav package, which extends the functionality of the widely used FeynCalc package. FeynGrav provides all the tools to study quantum gravitational effects within the standard model. We review the framework, provide the theoretical background for the efficient computation of Feynman rules, and present the proof of its completeness. We review the derivation of Feynman rules for general relativity, Horndeski gravity, Dirac fermions, Proca field, electromagnetic field, and SU(N) Yang–Mills model. We conclude with a discussion of the current state of the FeynGrav package and discuss its further development.

Dephasing Dynamics Accessed by High Harmonic Generation: Determination of Electron-Hole Decoherence of Dirac Fermions.

We reveal the critical effect of ultrashort dephasing on the polarization of high harmonic generation in Dirac fermions. As the elliptically polarized laser pulse falls in or slightly beyond the multiphoton regime, the elliptically polarized high harmonic generation is produced and exhibits a characteristic polarimetry of the polarization ellipse, which is found to depend on the decoherence time T2. T2 could then be determined to be a few femtoseconds directly from the experimentally observed polarimetry of high harmonics. This shows a sharp contrast with the semimetal regime of higher pump intensity, where the polarimetry is irrelevant to T2. An access to the dephasing dynamics would extend the prospect of high harmonic generation into the metrology of a femtosecond dynamic process in the coherent quantum control.

Comprehensive investigation of quantum oscillations in semimetal using an ac composite magnetoelectric technique with ultrahigh sensitivity

Quantum oscillation (QO), a physical phenomenon that reflects the characteristics of the Fermi surface and transport fermions, has been extensively observed in metals and semimetals through various approaches, like magnetostriction, magnetization, resistivity, and thermoelectric power. However, only limited oscillation frequencies can be revealed by the aforementioned methods, particularly in semimetals with intricate Fermi pockets and associated magnetic breakdown phenomena. In this paper, we present the application of an ac composite magnetoelectric (ME) technique to measure the QOs of a topological nodal-line semimetal, ZrSiS, which possesses six fundamental QO frequencies. By employing the ME technique with a maximum magnetic field of 13 T and a minimum temperature of 2 K, we are able to capture all the fundamental frequencies and most of the permissible magnetic breakdown frequencies. Remarkably, a series of magnetic breakdown frequencies around 8000 T were revealed even in a magnetic field as low as 7.5 T. These findings highlight the ME technique as an ultrahigh-sensitive tool for studying Dirac Fermions and other topological semimetals with complex Fermi surfaces.

Modular Hamiltonian in the semi infinite line. Part II. Dimensional reduction of Dirac fermions in spherically symmetric regions

In this article, we extend our study on a new class of modular Hamiltonians on an interval attached to the origin on the semi-infinite line, introduced in a recent work dedicated to scalar fields. Here, we shift our attention to fermions and similarly to the scalar case, we investigate the modular Hamiltonians of theories which are obtained through dimensional reduction, this time, of a free massless Dirac field in d dimensions. By following the same methodology, we perform dimensional reduction on both the physical and modular Hamiltonians. This process enables us to establish a correspondence: we identify the modular Hamiltonian in an interval connected to the origin to the one obtained from the reduction of the modular Hamiltonian pertaining to the conformal parent theory on a sphere. Intriguingly, although the resulting one-dimensional theories lack conformal symmetry due to the presence of a term proportional to 1/r, the corresponding modular Hamiltonians are local functions in the energy density. This phenomenon mirrors the well known behaviour observed in the conformal case and indicates the existence of a residual symmetry, characterized by a subset of the original conformal group.Furthermore, through an analysis of the spectrum of the modular Hamiltonians, we derive an analytic expression for the associated entanglement entropy. Our findings also enable us to successfully recover the conformal anomaly coefficient from the universal piece of the entropy in even dimensions, as well as the universal constant F term in d = 3, by extending the radial regularization scheme originally introduced by Srednicki to perform the sum over angular modes.

Renormalization of a Standard Model extension with a Dark Abelian Sector and predictions for the W-boson mass

The described Dark Abelian Sector Model (DASM) extends the Standard Model (SM) by a “dark” sector containing a spontaneously broken U(1)d gauge group. Keeping this dark sector quite generic we only add one additional Higgs boson, one Dirac fermion, and right-handed SM-like neutrinos to the SM. Using the only two singlet operators of the SM with dimension less than 4 (the U(1)Y field-strength tensor and the SM Higgs mass operator |Φ|2) as well as the right-handed neutrino fields we open up three portals to the dark sector. Dark sectors, such as the one of the DASM, that introduce an additional Higgs boson H as well as an additional Z′ gauge boson can have a large influence on the predictions for electroweak precision observables and even accommodate possible dark matter candidates. We consider one of the two Higgs bosons to be the known 125 GeV Higgs boson and parameterize the extension of the scalar sector by the mass of the second Higgs boson, the Higgs mixing angle, and a Higgs self-coupling. We do not assume any mass hierarchy in the gauge sector and use the mass of the additional Z′ boson and a corresponding gauge-boson mixing angle to parameterize the extension of the gauge sector. The fermion sector is parameterized by the mass of the additional fermion and a fermion mixing angle. We describe an on-shell as well as an MS¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ extrm{MS}} $$\\end{document} renormalization scheme for the DASM sectors and give explicit results for the renormalization constants at the 1-loop level, and, thus, prepare the ground for full NLO predictions for collider observables in the DASM. As a first example, we provide the DASM prediction for the W-boson mass derived from muon decay.

Multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals

We study multi-charged moments and symmetry-resolved Rényi entropy of free compact boson for multiple disjoint intervals. The Rényi entropy evaluation involves computing the partition function of the theory on Riemann surfaces with genus g > 1. This makes Rényi entropy sensitive to the local conformal algebra of the theory. The free compact boson possesses a global U(1) symmetry with respect to which we resolve Rényi entropy. The multi-charged moments are obtained by studying the correlation function of flux-generating vertex operators on the associated Riemann surface. Symmetry-resolved Rényi entropy is then obtained from the Fourier transforms of the charged moments. Rényi entropy is shown to have the familiar equipartition into local charge sectors upto the leading order. The multi-charged moments are also essential in studying the symmetry resolution of mutual information. The multi-charged moments of the self-dual compact boson and massless Dirac fermion are also shown to match for the cases when the associated reduced density moments are known to be the same. Finally, we numerically check our results against the tight-binding model.

Generalized Ginsparg-Wilson relations

We give a general derivation of Ginsparg-Wilson relations for both Dirac and Majorana fermions in any dimension. These relations encode continuous and discrete chiral, parity and time-reversal anomalies and will apply to the various classes of free-fermion topological insulators and superconductors (in the framework of a relativistic quantum field theory in Euclidean spacetime). We show how to formulate the exact symmetries of the lattice action and the relevant index theorems for the anomalies. Published by the American Physical Society 2024

Coexistence of topological node surface and Dirac fermions in phonon-mediated superconductor YB2C2.

The interaction between nontrivial topology and superconductivity in condensed matter physics has attracted tremendous research interest as it could give rise to exotic phenomena. Herein, based on first-principles calculations, we investigate the electronic structures, mechanical properties, topological properties, dynamic stability, electron-phonon coupling (EPC), and superconducting properties of the synthesized real material YB2C2. It is a tetragonal structure with P4/mbm symmetry and exhibits excellent stability. The calculated electronic band structures reveal that a zero-dimension (0D) Dirac point and two-dimensional (2D) nodal surface coexist near the Fermi level. A spin-orbit coupling (SOC) Dirac point with the topological Fermi arc is observed on the (001) surface. These nodal surfaces are protected by a two-fold screw axis and time-reversal symmetry. Based on the Bardeen-Cooper-Schrieffer theory, the superconducting transition temperature (Tc) in the range 1.25-4.45 K with different Coulomb repulsion constant μ* for YB2C2 is estimated to be consistent with previous experimental results. In addition, the EPC is mainly from the coupling between the dx2-y2 and dz2 orbitals of the Y atom and low-energy phonon modes. The presence of superconductivity and nontrivial topological surface state in YB2C2 suggests that it may be a candidate material for topological superconductors.

Anomalies in the Dirac bands in the proximity of correlated electrons.

Dirac fermions, particles with zero rest mass, are observed in topological materials and are believed to play a key role in the exotic phenomena in fundamental science and the advancement of quantum technology. Most of the topological systems studied so far are weakly correlated systems and the study of their properties in the presence of electron correlation is an interesting emerging area of research, where the electron correlation is expected to enhance the effective mass of the particles. Here, we studied the properties of Dirac bands in a non-symmorphic layered Kondo lattice system, CeAgSb2, employing high-resolution angle-resolved photoemission spectroscopy and first-principles calculations. In addition to the Dirac cones due to non-symmorphic symmetry, this material hosts Dirac fermions in the squarenet layer in the proximity of a strongly correlated Ce layer exhibiting Kondo behavior. Experimental results reveal crossings of the highly dispersive linear bands at the Brillouin zone boundary due to non-symmorphic symmetry. In addition, there are anisotropic Dirac cones constituted by the squarenet Sb 5p states forming a diamond-shaped nodal line. These Dirac bands are linear in a wide energy range with an unusually high slope. Interestingly, near the local Ce 4f bands, these bands exhibit a change in the slope akin to the formation of a 'kink' observed in other materials due to electron-phonon coupling. The emergence of such exotic properties in proximity to strongly correlated electronic states has significant implications in the study of complex quantum materials including unconventional superconductors.

Nearly three-dimensional Dirac fermions in an organic crystalline material unveiled by electron spin resonance

Original analysis methods of the electron spin resonance revealed that nearly three-dimensional Dirac fermions coexistent with standard fermions in an organic charge-transfer complex with each temperature-dependence and rotation symmetry.

Ferromagnetic Dirac half-metallicity in edge-modified zigzag boron nitride nanoribbons

Fully spin polarized Dirac fermions, with tunable gaps and room temperature ferromagnetism are discovered, by passivating single and both edges of ZBNNRs.

Influcence of external electric field and B/N doping on the band gap of stanene

Stanene possesses excellent properties, including an extremely high charge carrier density, massless Dirac fermions, and high thermal conductivity. Moreover, it exhibits band inversion phenomena, being made a candidate for a topological insulator. Topological insulators can generate dissipationless electric currents under certain conditions, showing great application potentials. However, the presence of a Dirac cone in the band structure of stanene at the high-symmetry point <i>K</i> in the Brillouin zone, resulting in a zero band gap, significantly limits its applications in the semiconductor field. This study adopts the method of doping B/N elements in stanene and applying an electric field perpendicular to the stanene to open the band gap at the <i>K</i> point. The effects of doping and the intensity of the applied electric field on the structural and electronic properties of stanene are investigated. The results reveal that both doping B elements and applying a vertical electric field can open the band gap at the <i>K</i> point while preserving the topological properties of stanene. Additionally, there is a positive correlation between the applied vertical electric field intensity and the band gap at the <i>K</i> point. Simultaneously doping B elements and applying a vertical electric field can increase the band gap at the <i>K</i> point, reaching 0.092 eV when the electric field intensity is 0.5 V/Å. After doping N elements, stanene is transformed into an indirect band gap semiconductor with a band gap of 0.183 eV. Applying a vertical electric field cannot change the structure of N-doped stanene, and the intensity of the applied vertical electric field is negatively correlated with the band gap at the <i>K</i> point. When the electric field intensity is 0.5 V/Å, the band gap at the <i>K</i> point decreases to 0.153 eV.

Chiral Anomalies in Organic Dirac Semimetals

A three-dimensional massless Dirac fermion system exhibiting broken chiral symmetry was successfully realized in organic conductor α-(BEDT-TTF)2I3 under high pressures. Our study detected the chiral anomaly-induced negative magnetoresistance and planar Hall effects and opened new avenues for further advancements in the field.

One-­loop correction contributions in the decoupling limit of generalized Yukawa model

We consider the generalized Yukawa model consisting of two Dirac fermions and two scalar fields. One of the scalars is assumed to be much heavier than the other particles, so it decouples at low energies. Low­energy effective Lagrangian (EL) of the model is derived. It describes the contributions of the heavy scalar into observables in the limit when this particle is decoupled. We consider the cross­sections of s­- and t­-channel processes, obtained within the complete model and its low-­energy approximation. The contributions of theone­loop corrections in the cross-­sections coming from light particles are analyzed. These are corrections to the parameters of the heavy boson and the contributions of the one­-loop mixing of light and heavy scalars. We identify the ranges of Yukawa’s couplings where the corrections are significant. We find that if the interaction between fermions and either light or heavy scalar is strong enough, the derived EL could not be applied for the description of the analyzed cross-­sections even if the heavy scalar decouples. Implications of our results in searching for new particles beyond the Standard model are discussed.

Probing Pauli susceptibility of [formula omitted]-borophene in the presence of gas molecules

Monolayer β12-borophene hosts two different Dirac and triplet fermions. Due to the large number of atoms in its unit cell, a description of their perturbed models leads to interesting phenomena. In this paper, we focus on an analytical tight-binding framework to describe the effect of adsorbed gas molecules on the magnetic properties of β12-borophene. We employ the Green’s function approach to calculate the Pauli spin paramagnetic susceptibility of the system. With this, we explain the peculiar characteristics of magnetic responses of the system depending on the position of gas molecules on the host boron atoms. From a wider perspective, these results can be useful for practical applications based on low-dimensional gas sensors.

Dirac fermions in monolayer blue phosphorus: A multi-orbital tight-binding investigation

This work is a theoretical investigation of the energy dispersion bands of blue phosphorus (buk-P) system within the multi-orbital tight-binding (MOTB) approach. The aim is to corroborate the presence of Dirac fermions, as observed in a recent experimental study. The existence of the Dirac cone at the high-symmetry K point primarily arises from the contributions of elemental phosphorus (P) s, px, and py atomic orbitals. Note that the Fermi velocity of the monolayer buk-P system (vf≈ 2.2 × 106 m s−1) is approximately 3 times higher than that of graphene (G). This discovery classifies monolayer buk-P as a novel and scarce two-dimensional Dirac material. Furthermore, it has been reported that these Dirac fermions exhibit remarkable adaptability along the Γ–K region while preserving their degeneracy intact.Here, we quantitatively improve the overall tight-binding (TB) picture of the monolayer buk-P throughout the Brillouin zone (BZ) by engaging more neighboring interacting sites up to the fifth intra-layer nearest-neighbors (5NN). However, our models reproduce the computations based on the DFT approach and the experimental findings quite accurately.To the best of our knowledge, this work is the first to systematically investigate the presence of Dirac cone in monolayer buk-P system within the MOTB model. This rigorous analytical approach, along with the experimental observations and DFT computations, holds significant promise for exploring the intrinsic characteristics of Dirac materials beyond buk-P. Moreover, the observed electronic properties and high Fermi velocity make this material a highly promising candidate for future high-performance nano-electronic devices.

The Anomalous Photo‐Nernst Effect of Massive Dirac Fermions In HfTe5

AbstractThe quantum geometric Berry curvature results in an anomalous correction to the band velocity of crystal electrons with a corresponding transverse (thermo)electric conductivity. However, time‐reversal symmetry typically constrains the direct observation and exploitation of anomalous transport to magnetic compounds. Here, it is demonstrated the anomalous Hall and Nernst conductivities are essential for describing the optoelectronic transport in thin films of the non‐magnetic, weakly gapped semimetal HfTe5 subject to an external magnetic field. A focused photoexcitation adresses the symmetries of the local Nernst conductivity, which unveils a hitherto hidden, anomalous photo‐Nernst effect of three‐dimensional (3D) massive Dirac fermions. The experimental temperature and density dependencies are compared with a semiclassical Boltzmann transport model. For HfTe5 thin films with the Fermi level close to the gap, the model suggests that the anomalous photo‐Nernst currents originate from an intrinsic Berry curvature mechanism, where the Zeeman interaction effectively breaks time‐reversal symmetry of the massive Dirac fermions already at moderate external magnetic fields.

Spin splitting and disorder of Landau levels in HgTe-based Dirac fermions

Spin splitting and disorder of Landau levels in HgTe-based Dirac fermions