Dirac Metal Research Articles

Quantum theory of phonon-induced anomalous Hall effect in two-dimensional massive Dirac metals

Quantum theory of phonon-induced anomalous Hall effect in two-dimensional massive Dirac metals

Unconventional Hole Doping of S = ½ Kagome Antiferromagnet CoCu3(OH)6Cl2

AbstractGeometrically perfect S = ½ kagome lattices with frustrated magnetism are typically electrical insulators. Electron or hole doping is predicted to induce an exotic conducting state including superconductivity. Herein, an unconventional strategy of doping an S = ½ kagome lattice CoCu3(OH)6Cl2 is adopted – a structural analogue of a well‐known quantum spin liquid (QSL) candidate herbertsmithite (ZnCu3(OH)6Cl2) – by integrating it with reduced graphene oxide (rGO) via in situ redox chemistry. Such an integration drastically enhances the electrical conductivity, resulting in the transformation of an insulator to a semiconductor, corroborating the respective density of states obtained from the density functional theory calculations. Estimation of the magnetic moments, data on the Hall‐effect measurements, Bader charge analysis, and photoemission signals, altogether provide a bold signature of remote hole doping in CoCu3(OH)6Cl2 by rGO. The remote doping provides an alternative to the site doping approach to impart exotic electronic properties in spin liquid candidates, specifically, the generation of topological states like Dirac metal is envisioned.

A mid-infrared ultra-wideband polarization-independent tunable perfect absorber based on Dirac metal materials

A mid-infrared ultra-wideband tunable terahertz absorber based on bulk Dirac semimetal (BDS) is presented. It has a simple three-layer structure: a top BDS metal layer, a middle dielectric layer, and a bottom reflective metal layer. The BDS layer was designed by creating a square cavity and a long rectangular cavity in the center of the BDS rectangle. The long rectangle was then rotated by 90° to form a centrosymmetric cavity. Using CST Studio Suite software, we numerically simulate the absorption characteristics. The simulation results indicate that the absorber achieves a high absorption (>90 %) of about 47.59 THz in the range of 37.5–90 THz when the Fermi energy level is 70 meV. The average absorption exceeds 95 %. In addition, adjusting the Fermi energy level of the BDS alters the absorption bandwidth. The centrosymmetric design of the structure ensures the absorber exhibits insensitivity to different polarization modes and angles of incidence, as well as excellent absorption stability. The designed shock absorber also exhibits excellent tolerance in manufacturing, reducing fabrication challenges and enabling practical applications. In addition, our design possesses the unique ability to modulate light in the mid-infrared band. These remarkable properties position our findings with significant potential in fields such as spectral analysis, optical biosensing technology, infrared sensing, and related applications.

Deficiency-induced absence of topological insulator behavior in antiperovskite Dirac metal oxide Sr3-x SnO: a DFT study

This study focuses on Sr3SnO (SSO), an antiperovskite Dirac metal-oxide (ADMO), that exhibits improved and enhanced physical properties when decreasing the number of Strontium (Sr) atoms in the crystal structure Sr3-xSnO. Stability and electronic properties calculations were performed using the density functional theory (DFT). Furthermore, transport and thermoelectric properties were determined by solving the Boltzmann transport equation implemented in BoltzTraP code. We report a topological insulator behavior when applying spin–orbit coupling (SOC) to pristine SSO. This behavior became absent when Sr concentration decreased. Moreover, when increasing oxygen concentration (Sr3SnO2), we reveal an improvement in the system’s stability. Electrical conductivity enhanced, for both Sr deficient SSO and for oxygen excess, reaching a value of 1.8×10201/Ω.m.s for x = 1. In addition, we show that Sr3-xSnO possesses both p-type and n-type nature, depending on the value of Sr deficiency concentration x, which makes this compound a suitable candidate for a thermoelectric generator (TEG) module.

A Comparative Study of the Electronic Transport and Gas-Sensitive Properties of Graphene+, T-graphene, Net-graphene, and Biphenylene-Based Two-Dimensional Devices.

The electronic transport properties of the four carbon isomers: graphene+, T-graphene, net-graphene, and biphenylene, as well as the gas-sensing properties to the nitrogen-based gas molecules including NO2, NO, and NH3 molecules, are systematically studied and comparatively analyzed by combining the density functional theory with the nonequilibrium Green's function. The four carbon isomers are metallic, especially with graphene+ being a Dirac metal due to the two Dirac cones present at the Fermi energy level. The two-dimensional devices based on these four carbon isomers exhibit good conduction properties in the order of biphenylene > T-graphene > graphene+ > net-graphene. More interestingly, net-graphene-based and biphenylene-based devices demonstrate significant anisotropic transport properties. The gas sensors based on the above four structures all have good selectivity and sensitivity to the NO2 molecule, among which T-graphene-based gas sensors are the most prominent with a maximum ΔI value of 39.98 μA, being only three-fifths of the original. In addition, graphene+-based and biphenylene-based gas sensors are also sensitive to the NO molecule with maximum ΔI values of 29.42 and 25.63 μA, respectively. However, the four gas sensors are all physically adsorbed for the NH3 molecule. By the adsorption energy, charge transfer, electron localization functions, and molecular projection of self-consistent Hamiltonian states, the mechanisms behind all properties can be clearly explained. This work shows the potential of graphene+, T-graphene, net-graphene, and biphenylene for the detection of toxic molecules of NO and NO2.

CaPdBi: A Nontrivial Topological Candidate

In the framework of density functional theory, a comprehensive investigation of the mechanical, dynamical, and electronic properties of the compounds CaPdX (X= Sb and Bi) is performed. The investigated systems are both mechanically and dynamically stable. These compounds are claimed to be metallic by the electronic structure properties, with intriguing crossing points in the close proximity of the Fermi level. With spin orbit coupling (SOC) included, a gap appears at particular crossing points. The predicted electronic band structure shows that the d-states of Ca and Pd and the p-states of Bi and Sb dominate at the crossing sites. Inversion and time-reversal symmetry, together with the inclusion of SOC, demonstrate that CaPdBi is a Dirac metal. The calculated Z2 invariants for CaPdSb and CaPdBi are 0 and 1, which infer the trivial and non-trivial strong topological nature, respectively. As a whole, the investigated compound has future scope for its fascinating topological features, one amongst which is the presence of low-energy excitons (Dirac points).

Intrinsic optical absorption in Dirac metals

A Dirac metal is a doped (gated) Dirac material with the Fermi energy (EF) lying either in the conduction or valence bands. In the non-interacting picture, optical absorption in gapless Dirac metals occurs only if the frequency of incident photons (Ω) exceeds the direct (Pauli) frequency threshold, equal to 2EF. In this work, we study, both analytically and numerically, the role of electron–electron (ee) and electron–hole (eh) interactions in optical absorption of two-dimensional (2D) and three-dimensional (3D) Dirac metals in the entire interval of frequencies below 2EF. We show that, for Ω≪EF, the optical conductivity, ℜσ(Ω), arising from the combination of ee and certain eh scattering processes, scales as Ω2lnΩ in 2D and as Ω2 in 3D, respectively, both for short-range (Hubbard) and long-range (screened Coulomb) interactions. Another type of eh processes, similar to Auger–Meitner (AM) processes in atomic physics, starts to contribute for Ω above the direct threshold, equal to EF. Similar to the case of doped semiconductors with parabolic bands studied in prior literature, the AM contribution to ℜσ(Ω) in Dirac metals is manifested by a threshold singularity, ℜσ(Ω)∝(Ω−EF)d+2, where d is the spatial dimensionality and 0<Ω−EF≪EF. In contrast to doped semiconductors, however, the AM contribution in Dirac metals is completely overshadowed by the ee and other eh contributions. Numerically, ℜσ(Ω) happens to be small in almost the entire range of Ω<2EF. This finding may have important consequences for collective modes in Dirac metals lying below 2EF.

Bonding and Electronic Nature of the Anionic Framework in LaPd3S4

Double Dirac materials are a topological phase of matter in which a non-symmorphic symmetry enforces greater electronic degeneracy than normally expected – up to eightfold. The cubic palladium bronzes NaPd3O4 and LaPd3S4 are built of Pd3X4 (X = O, S) anionic frameworks that are ionically bonded to A cations (A = Na, La). These materials were recently identified computationally as harboring eightfold fermions. Here we report the preparation of single crystals and electronic properties of LaPd3S4. Measurements down to T = 0.45 K and in magnetic fields up to μ0H = 65 T are consistent with normal Fermi liquid physics of a Dirac metal in the presence of dilute magnetic impurities. This interpretation is further confirmed by analysis of specific heat, magnetization measurements and comparison to density functional theory (DFT) calculations. Through a bonding analysis of the DFT electronic structure of NaPd3O4 and LaPd3S4, we identify the origin of the stability of the anionic Pd3X4 framework at higher electron counts for X = S than X = O, and propose chemical tuning strategies to enable shifting the 8-fold fermion points to the Fermi level.

High-field Studies on Layered Magnetic and Polar Dirac Metals: Novel Quantum Transport Phenomena Coupled with Spin-valley Degrees of Freedom

Recently, the interplay between the Dirac/Weyl fermion and various bulk properties, such as magnetism, has attracted considerable attention, since unconventional transport and optical phenomena were discovered. However, the design principles for such materials have not been established well. Here, we propose that the layered material $A$Mn$X_2$ ($A$: alkaline and rare-earth ions, $X$: Sb, Bi) is a promising platform for systematically exploring strongly correlated Dirac metals, which consists of the alternative stack of the $X^-$ square net layer hosting a 2D Dirac fermion and the $A^{2+}$-Mn$^{2+}$-$X^{3-}$ magnetic block layer. In this article, we shall review recent high-field studies on this series of materials to demonstrate that various types of Dirac fermions are realized by designing the block layer. First, we give an overview of the Dirac fermion coupled with the magnetic order in EuMnBi$_2$ ($A$=Eu). This material exhibits large magnetoresistance by the field-induced change in the magnetic order of Eu layers, which is associated with the strong exchange interaction between the Dirac fermion and the local Eu moment. Second, we review the Dirac fermion coupled with the lattice polarization in BaMn$X_2$ ($A$=Ba). There, spin-valley coupling manifests itself owing to the Zeeman-type spin-orbit interaction, which is experimentally evidenced by the bulk quantum Hall effect observed at high fields.

Magnetic freeze-out and anomalous Hall effect in ZrTe5

The ultra-quantum limit is achieved when a magnetic field confines an electron gas in its lowest spin-polarised Landau level. Here we show that in this limit, electron doped ZrTe5 shows a metal-insulator transition followed by a sign change of the Hall and Seebeck effects at low temperature. We attribute this transition to a magnetic freeze-out of charge carriers on the ionized impurities. The reduction of the charge carrier density gives way to an anomalous Hall response of the spin-polarised electrons. This behavior, at odds with the usual magnetic freeze-out scenario, occurs in this Dirac metal because of its tiny Fermi energy, extremely narrow band gap and a large g-factor. We discuss the different possible sources (intrinsic or extrinsic) for this anomalous Hall contribution.

Exploration of trivial and nontrivial electronic phases and of collinear and noncollinear magnetic phases in low-spin d5 perovskites

The $4d$ and $5d$ transition metal oxides have become important members of the emerging quantum materials family due to competition between onsite Coulomb repulsion ($U$) and spin-orbit coupling (SOC). Specifically, the systems with $d^5$ electronic configuration in an octahedral environment are found to be capable of posessing invariant semimetallic state and perturbations can lead to diverse magnetic phases. In this work, by formulating a multi-band Hubbard model and performing SOC tunable DFT+$U$ calculations on a prototype SrIrO$_3$ and extending the analysis to other iso-structural and isovalent compounds, we present eight possible electronic and magnetic configurations in the $U$-SOC phase diagram that can be observed in the family of low-spin $d^5$ perovskites. They include the protected Dirac semimetal state, metal and insulator regimes, collinear and noncollinear spin ordering. The latter is explained through connecting hopping interactions to the rotation and tilting of the octahedra as observed in GdFeO$_3$. Presence of several soft phase boundaries makes the family of $d^5$ perovskites an ideal platform to study electronic and magnetic phase transitions under external stimuli.

Magnetism-induced topological transition in EuAs3

The nature of the interaction between magnetism and topology in magnetic topological semimetals remains mysterious, but may be expected to lead to a variety of novel physics. We systematically studied the magnetic semimetal EuAs3, demonstrating a magnetism-induced topological transition from a topological nodal-line semimetal in the paramagnetic or the spin-polarized state to a topological massive Dirac metal in the antiferromagnetic ground state at low temperature. The topological nature in the antiferromagnetic state and the spin-polarized state has been verified by electrical transport measurements. An unsaturated and extremely large magnetoresistance of ~2 × 105% at 1.8 K and 28.3 T is observed. In the paramagnetic states, the topological nodal-line structure at the Y point is proven by angle-resolved photoemission spectroscopy. Moreover, a temperature-induced Lifshitz transition accompanied by the emergence of a new band below 3 K is revealed. These results indicate that magnetic EuAs3 provides a rich platform to explore exotic physics arising from the interaction of magnetism with topology.

Temperature dependence of quantum oscillations from non-parabolic dispersions

The phase offset of quantum oscillations is commonly used to experimentally diagnose topologically nontrivial Fermi surfaces. This methodology, however, is inconclusive for spin-orbit-coupled metals where π-phase-shifts can also arise from non-topological origins. Here, we show that the linear dispersion in topological metals leads to a T2-temperature correction to the oscillation frequency that is absent for parabolic dispersions. We confirm this effect experimentally in the Dirac semi-metal Cd3As2 and the multiband Dirac metal LaRhIn5. Both materials match a tuning-parameter-free theoretical prediction, emphasizing their unified origin. For topologically trivial Bi2O2Se, no frequency shift associated to linear bands is observed as expected. However, the π-phase shift in Bi2O2Se would lead to a false positive in a Landau-fan plot analysis. Our frequency-focused methodology does not require any input from ab-initio calculations, and hence is promising for identifying correlated topological materials.

Pressure dependent structural phase transition and observation of Dirac-like dispersions in CaTe and SrTe

At ambient pressure both CaTe and SrTe are known to exist in NaCl type structure (B1 phase) and undergo structural transition at high pressure to CsCl type structure (B2 phase). Most theoretical studies presented regarding the structural transition from B1 to B2 phase are based upon enthalpy comparisons. In this paper, we have computed elastic constants C11, C12, and C44 for both phases at various pressures and used Born stability conditions to compare the relative mechanical stability of both phases with pressure. The dynamical stability of these structures has been investigated using phonon dispersion calculations at different pressures. Our study finds that phonon dispersion calculations match well with enthalpy based predictions for the transition from B1 to B2 phase. Moreover, the Born stability conditions are necessary but not sufficient conditions to predict the structural stability of a crystal. Both CaTe and SrTe are 3D Dirac metals in the B2 phase and exhibit linear dispersions of electronic states near the Fermi level.

Pseudo Landau levels, negative strain resistivity, and enhanced thermopower in twisted graphene nanoribbons

As a canonical response to the applied magnetic field, the electronic states of a metal are fundamentally reorganized into Landau levels. In Dirac metals, Landau levels can be expected without magnetic fields, provided that an inhomogeneous strain is applied to spatially modulate electron hoppings in a way similar to the Aharonov-Bohm phase. We here predict that a twisted zigzag nanoribbon of graphene exhibits strain-induced pseudo Landau levels of unexplored but analytically solvable dispersions at low energies. The presence of such dispersive pseudo Landau levels results in a negative strain resistivity characterizing the ($1+1$)-dimensional chiral anomaly if partially filled and can greatly enhance the thermopower when fully filled.

Quantum spin mixing in Dirac materials

The spin of the electron is nowadays replacing the charge as basic carrier of information not only in spintronics applications, but also in the emerging field of quantum information. Topological quantum materials, where spin-momentum locking is believed to lead to particularly long spin lifetimes, are regarded as a promising platform for such applications. However, spin-orbit coupling, that is essential to all topological matter, at the same time gives rise to spin mixing and decoherence as a major obstacle for quantum computing. Here, we give experimental evidence that hot-spots of spin-mixing and spin-conserving contributions of the spin-orbit operator coexist in an archetypal topological Dirac metal, and that these hot spots can have a strongly anisotropic distribution of their respective wave vectors with respect to the spin quantization direction. Our results can be understood within a theory that takes into account the decomposition of the spin-orbit Hamiltonian into spin-conserving and spin-flip terms, contributing to a better understanding of quantum decoherence in topological materials, in general.

Tunable spin-valley coupling in layered polar Dirac metals

In non-centrosymmetric metals, spin-orbit coupling induces momentum-dependent spin polarization at the Fermi surfaces. This is exemplified by the valley-contrasting spin polarization in monolayer transition metal dichalcogenides with in-plane inversion asymmetry. However, the valley configuration of massive Dirac fermions in transition metal dichalcogenides is fixed by the graphene-like structure, which limits the variety of spin-valley coupling. Here, we show that the layered polar metal BaMnX2 (X = Bi, Sb) hosts tunable spin-valley-coupled Dirac fermions, which originate from the distorted X square net with in-plane lattice polarization. We found that BaMnBi2 has approximately one-tenth the lattice distortion of BaMnSb2, from which a different configuration of spin-polarized Dirac valleys is theoretically predicted. This was experimentally observed as a clear difference in the Shubnikov-de Haas oscillation at high fields between the two materials. The chemically tunable spin-valley coupling in BaMnX2 makes it a promising material for various spin-valleytronic devices.

Second harmonic generation in the tilted type-I Dirac metals under terahertz frequency regime

Abstract In this work, we theoretically demonstrate that the second order response can survive in a two-dimensional (2D) tilted type-I Dirac metal due to the time reversal symmetry (TRS) breaking. We find that, in the terahertz regime, the second harmonic generation (SHG) is appreciably strong and is widely depending on the tilting parameter, temperature, excitation frequency and the applied electric field, respectively. By comparing with the first and third order optical response, we also note that each of the three modes of optical response dominates in different frequency intervals in accordance with the strength of the applied electric field. With the help of the ω − E c diagram (with ω and E c being the excitation frequency and the critical electric field, respectively), we are able to engineer the desired nonlinear response by varying the excitation frequency and the strength of the applied electric field. Finally, we briefly discuss on the influences of relaxation time on SHG by considering four types of k-dependent scattering mechanisms.

Semiconductor Bloch-equations formalism: Derivation and application to high-harmonic generation from Dirac fermions

We rederive the semiconductor Bloch equations emphasizing the close link to the Berry connection. Our rigorous derivation reveals the existence of two further contributions to the current, in addition to the frequently considered intraband and polarization-related interband terms. The extra contributions become sizable in situations with strong dephasing or when the dipole-matrix elements are strongly wave-number dependent. We apply the formalism to high-harmonic generation for a Dirac metal. The extra terms add to the frequency-dependent emission intensity (high-harmonic spectrum) significantly at certain frequencies changing the total signal up to a factor of 10.

Multiple insulating states due to the interplay of strong correlations and lattice geometry in a single-orbital Hubbard model

We report 10 ground states arising from strong correlations in the single-orbital Hubbard model on the decorated honeycomb lattice, including Dirac metals, flat-band ferromagnets, real-space Mott insulators, dimer and trimer Mott insulators, and a spin-1 Mott insulator. The rich phase diagram arises from structures within the unit cell. Hence, such states are absent on simpler lattices. We argue that such insulating phases are prevalent on decorated lattices. These are found in many materials and common in coordination polymers, providing a playground to explore this physics.