3D Dirac Semimetals Research Articles

Observation of symmetry-protected Dirac states in nonsymmorphic α -antimonene

Two-dimensional (2D) Dirac states with linear band dispersion have attracted enormous interest since the discovery of graphene. However, to date, 2D Dirac semimetals are still very rare due to the fact that 2D Dirac states are generally fragile against perturbations such as spin-orbit couplings. Nonsymmorphic crystal symmetries can enforce the formation of Dirac nodes, providing a new route to establishing symmetry-protected Dirac states in 2D materials. Here we report the symmetry-protected Dirac states in nonsymmorphic alpha-antimonene. The antimonene was synthesized by the method of molecular beam epitaxy. Two Dirac cones with large anisotropy were observed by angle-resolved photoemission spectroscopy. The Dirac state in alpha-antimonene is of spin-orbit type in contrast to the spinless Dirac states in graphene. The result extends the 'graphene' physics into a new family of 2D materials where spin-orbit coupling is present.

Maximal terahertz emission in high harmonic generation from 3D Dirac semimetals

Unlike conventional semiconductor platforms, 3D Dirac semimetals (DSMs) require relatively low input laser intensities for efficient terahertz (THz) high harmonic generation (HHG), making them promising materials for developing compact THz light sources. Here, we show that 3D DSMs’ high nonlinearity opens up a regime of nonlinear optics where extreme subwavelength current density features develop within nanoscale propagation distances of the driving field. Our results reveal orders-of-magnitude enhancement in HHG intensity with thicker 3D DSM films, and show that these subwavelength features fundamentally limit HHG enhancement beyond an optimal film thickness. This decrease in HHG intensity beyond the optimal thickness constitutes an effective propagation-induced dephasing. Our findings highlight the importance of propagation dynamics in nanofilms of extreme optical nonlinearity.

Strong suppression of electron convection in Dirac and Weyl semimetals

It is shown that the convective instability in electron fluids in three- and two-dimensional (3D and 2D) Dirac and Weyl semimetals is strongly inhibited. The major obstacles for electron convection are the effects of the Coulomb forces and the momentum relaxation related to the interaction with impurities and phonons. The effect of the Coulomb forces is less pronounced in 2D materials, such as graphene. However, momentum relaxation still noticeably inhibits convection making it very difficult to achieve in practice.

Dirac Semimetals in Homogeneous Holey Carbon Nitride Monolayers

In this work, we propose four novel holey carbon nitride monolayer C7N3, C10N3, C13N3, and C19N3 stoichiometries intriguingly behaving as ideal 2D Dirac semimetals whose Dirac cones are rightly loc...

Features of the Behavior of Mn2+ Ions in the 3D Dirac Semimetal α-Cd3As2 from EPR Data

Features of the Behavior of Mn2+ Ions in the 3D Dirac Semimetal α-Cd3As2 from EPR Data

Efficient generation of extreme terahertz harmonics in three-dimensional Dirac semimetals

Frequency multiplication of terahertz signals on a solid state platform is highly sought-after for the next generation of high-speed electronics and the creation of frequency combs. Solutions to efficiently generate extreme harmonics (up to the $31^{\rm{st}}$ harmonic and beyond) of a terahertz signal with modest input intensities, however, remain elusive. Using fully nonperturbative simulations and complementary analytical theory, we show that 3D Dirac semimetals (DSMs) have enormous potential as compact sources of extreme terahertz harmonics, achieving energy conversion efficiencies beyond $10^{-5}$ at the $31^{\rm{st}}$ harmonic with input intensities on the order of $10$ MW/cm$^2$, over $10^5$ times lower than in conventional THz high harmonic generation systems. Our theory also reveals a fundamental feature in the nonlinear optics of 3D DSMs: a distinctive regime where higher-order optical nonlinearity vanishes, arising as a direct result of the extra dimensionality in 3D DSMs compared to 2D DSMs. Our findings should pave the way to the development of efficient platforms for high-frequency terahertz light sources and optoelectronics based on 3D DSMs.

Two-Dimensional Dirac Semimetals without Inversion Symmetry.

Realizing stable two-dimensional (2D) Dirac points against spin-orbit coupling (SOC) has attracted much attention because it provides a platform to study the unique transport properties. In previous work, Young and Kane [Phys. Rev. Lett. 115, 126803 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.126803 proposed stable 2D Dirac points with SOC, in which the Berry curvature and edge states vanish due to the coexistence of inversion and time-reversal symmetries. Herein, using the tight-binding model and k·p effective Hamiltonian, we present that 2D Dirac points can survive in the presence of SOC without inversion symmetry. Such 2D Dirac semimetals possess nonzero Berry curvature near the crossing nodes, and two edge states are terminated at one pair of Dirac points. In addition, according to symmetry arguments and high-throughput first-principles calculations, we identify a family of ideal 2D Dirac semimetals, which has nonzero Berry curvature in the vicinity of Dirac points and visible edge states, thus facilitating the experimental observations. Our work shows that 2D Dirac points can emerge without inversion symmetry, which not only enriches the classification of 2D topological semimetals but also provides a promising avenue to observe exotic transport phenomena beyond graphene, e.g., nonlinear Hall effect.

Effective magnetic field induced by inhomogeneous Fermi velocity in strained honeycomb structures

In addition to the known pseudomagnetic field, nonuniform strains independently induce a position-dependent Fermi velocity (PDFV) in graphene. Here we demonstrate that, due to the presence of a PDFV, the Dirac fermions on a nonuniform (strained) honeycomb lattice may experiment a sort of magnetic effect, which is linearly proportional to the momentum of the quasiparticle. As a consequence, the quasiparticles have a sublinear dispersion relation. Moreover, we analyze the general consequence of a PDFV on the Klein tunneling of electrons through pseudomagnetic barriers. In particular, we report an anomalous (Klein) tunneling for an electron passing across velocity barriers with magnetic features. Our findings about the effects induced by a PDFV on Dirac fermions in (2D) strained honeycomb lattice could be extended to (3D) Dirac and Weyl semimetals and/or its analogous artificial systems.

Fermion–fermion duality in 3+1 dimensions

Dualities play a central role in both quantum field theories and condensed matter systems. Recently, a web of dualities has been discovered in 2+1 dimensions. Here, we propose in particular a generalization of the Son’s fermion–fermion duality to 3+1 dimensions. We show that the action of charged Dirac fermions coupled to an external electromagnetic field is dual to an action of neutral fermions minimally coupled to an emergent vector gauge field. This dual action contains also a further tensor (Kalb–Ramond) gauge field coupled to the emergent and electromagnetic vector potentials. We firstly demonstrate the duality in the massive case. We then show the duality in the case of massless fermions starting from a lattice model and employing the slave-rotor approach already used in the 2+1-dimensional duality [Burkov (2019)]. We finally apply this result to 3D Dirac semimetals in the low-energy regime. Besides the implications in topological phases of matter, our results shed light on the possible existence of a novel web of dualities in 3+1-dimensional (non-supersymmetric) quantum field theories.

Broadband strong optical dichroism in topological Dirac semimetals with Fermi velocity anisotropy**Project supported by Singapore Ministry of Education (MOE) Tier 2 Grant No. (2018-T2-1-007) and USA ONRG Grant No. (N62909-19-1-2047). JL is supported by MOE PhD RSS. KJAO acknowledges the funding support of Xiamen University Malaysia Research Fund, Grant Nos. XMUMRF/2019-C3/IECE/0003 and XMUMRF/2020-C5/IENG/0025, and the Ministry of Higher Education Malaysia

Prototypical three-dimensional (3D) topological Dirac semimetals (DSMs), such as Cd3As2 and Na3Bi, contain electrons that obey a linear momentum–energy dispersion with different Fermi velocities along the three orthogonal momentum dimensions. Despite being extensively studied in recent years, the inherent Fermi velocity anisotropy has often been neglected in the theoretical and numerical studies of 3D DSMs. Although this omission does not qualitatively alter the physics of light-driven massless quasiparticles in 3D DSMs, it does quantitatively change the optical coefficients which can lead to nontrivial implications in terms of nanophotonics and plasmonics applications. Here we study the linear optical response of 3D DSMs for general Fermi velocity values along each direction. Although the signature conductivity-frequency scaling, σ(ω) ∝ ω, of 3D Dirac fermion is well-protected from the Fermi velocity anisotropy, the linear optical response exhibits strong linear dichroism as captured by the universal extinction ratio scaling law, Λij = (vi/vj)2 (where i ≠ j denotes the three spatial coordinates x,y,z, and vi is the i-direction Fermi velocity), which is independent of frequency, temperature, doping, and carrier scattering lifetime. For Cd3As2 and Na3Bi3, an exceptionally strong extinction ratio larger than 15 and covering a broad terahertz window is revealed. Our findings shed new light on the role of Fermi velocity anisotropy in the optical response of Dirac semimetals and open up novel polarization-sensitive functionalities, such as photodetection and light modulation.

Reducing Electronic Transport Dimension to Topological Hinge States by Increasing Geometry Size of Dirac Semimetal Josephson Junctions.

The notion of topological phases has been extended to higher-order and has been generalized to different dimensions. As a paradigm, Cd_{3}As_{2} is predicted to be a higher-order topological semimetal, possessing three-dimensional bulk Dirac fermions, two-dimensional Fermi arcs, and one-dimensional hinge states. These topological states have different characteristic length scales in electronic transport, allowing one to distinguish their properties when changing sample size. Here, we report an anomalous dimensional reduction of supercurrent transport by increasing the size of Dirac semimetal Cd_{3}As_{2}-based Josephson junctions. An evolution of the supercurrent quantum interferences from a standard Fraunhofer pattern to a superconducting quantum interference device (SQUID)-like one is observed when the junction channel length is increased. The SQUID-like interference pattern indicates the supercurrent flowing through the 1D hinges. The identification of 1D hinge states should be valuable for deeper understanding of the higher-order topological phase in a 3D Dirac semimetal.

The de Haas-van Alphen quantum oscillations in a three-dimensional Dirac semimetal TiSb2

Characterization of the Fermi surface of high-quality crystalline TiSb2 by de Haas-van Alphen measurement reveals nontrivial topological properties. Moreover, our analysis of the quantum oscillation frequencies associated with nonzero Berry phase when the magnetic field is parallel to both the ab-plane and c-axis of TiSb2 finds that the Fermi surface topology has a three-dimensional feature. The results are supported by first-principle calculations which reveal a symmetry-protected Dirac point along the Γ-Z high symmetry line near the Fermi level. On the (001) surface, the bulk Dirac points are found to project onto the Γ¯ point with nontrivial surface states. Our finding will substantially enrich the family of 3D Dirac semimetals which are useful for topological applications.

Structural and electronic properties of the pure and stable elemental 3D topological Dirac semimetal α-Sn

In-plane compressively strained α-Sn films have been theoretically predicted and experimentally proven to possess non-trivial electronic states of a 3D topological Dirac semimetal. The robustness of these states typically strongly depends on purity, homogeneity, and stability of the grown material itself. By developing a reliable fabrication process, we were able to grow pure strained α-Sn films on InSb(100), without heating the substrate during growth nor using any dopants. The α-Sn films were grown by molecular beam epitaxy, followed by experimental verification of the achieved chemical purity and structural properties of the film’s surface. Local insight into the surface morphology was provided by scanning tunneling microscopy. We detected the existence of compressive strain using Mössbauer spectroscopy, and we observed a remarkable robustness of the grown samples against ambient conditions. The topological character of the samples was confirmed by angle-resolved photoemission spectroscopy, revealing the Dirac cone of the topological surface state. Scanning tunneling spectroscopy, moreover, allowed us to obtain an improved insight into the electronic structure of the 3D topological Dirac semimetal α-Sn above the Fermi level.

Widely Tunable Optical and Thermal Properties of Dirac Semimetal Cd3As2

AbstractIn this paper, a detailed analysis of the temperature‐dependent optical properties of epitaxially grown cadmium arsenide (Cd3As2), a newly discovered 3D Dirac semimetal is reported. Fermi level tuning—instigated from Pauli‐blocking in the linear Dirac cone—and varying Drude response, generate large variations in the mid‐ and far‐infrared optical properties. Thermo‐optic shifts larger than those of traditional III–V semiconductors are demonstrated. Electron scattering rate, plasma frequency edge, Fermi level shift, optical conductivity, and electron effective mass analysis of Cd3As2 thin‐films are quantified and discussed in detail. The ab initio density functional study and experimental analysis of epitaxially grown Cd3As2 promise applications for nanophotonic and nanoelectronic devices, such as reconfigurable metamaterials and metasurfaces, nanoscale thermal emitters, and on‐chip directional antennas.

Fermion-induced quantum critical point in Dirac semimetals: A sign-problem-free quantum Monte Carlo study

According to Landau criterion, a phase transition should be first order when cubic terms of order parameters are allowed in its effective Ginzburg-Landau free energy. Recently, it was shown by renormalization group (RG) analysis that continuous transition can happen at putatively first-order $Z_3$ transitions in 2D Dirac semimetals and such non-Landau phase transitions were dubbed "fermion-induced quantum critical points" (FIQCP) [Li et al., Nature Communications 8, 314 (2017)]. The RG analysis, controlled by the 1/$N$ expansion with $N$ the number of flavors of four-component Dirac fermions, shows that FIQCP occurs for $N\geq N_c$. Previous QMC simulations of a microscopic model of SU($N$) fermions on the honeycomb lattice showed that FIQCP occurs at the transition between Dirac semimetals and Kekule-VBS for $N\geq 2$. However, precise value of the lower bound $N_c$ has not been established. Especially, the case of $N=1$ has not been explored by studying microscopic models so far. Here, by introducing a generalized SU($N$) fermion model with $N=1$ (namely spinless fermions on the honeycomb lattice), we perform large-scale sign-problem-free Majorana quantum Monte Carlo simulations and find convincing evidence of FIQCP for $N=1$. Consequently, our results suggest that FIQCP can occur in 2D Dirac semimetals for all positive integers $N\geq 1$.

PT -symmetry-protected Dirac states in strain-induced hidden MoS2 monolayer

Two-dimensional (2D) materials have recently attracted significant interest in condensed-matter physics and materials science due to rich intriguing physics and potential applications. Here, by first-principles calculations, we discover a phase of transition-metal dichalcogenides (MoS2 and its family) named the 1H′ phase. We demonstrate that 1H′MoS2 monolayer has multiple topological phase transitions from a topologically trivial insulator state to a 2D type-II Dirac semimetal state, and then to a 2D ideal type-I semimetal state under a moderate tensile strain. The Dirac points are protected by the coexistence of space-inversion (P) and time-reversal (T) symmetry. Our results highlight a family of nonhoneycomb 2D Dirac semimetals with potential application in nanoelectronics.

Theoretical and experimental evidence for the intrinsic three-dimensional Dirac state in Cu2HgSnSe4

Three-dimensional (3D) Dirac and Weyl semimetals are quantum states that have emerged in physics recently. But their intrinsic transport properties are quite elusive because of either the coexistence of Schr\odinger fermions or the deviation of linear dispersion at Fermi level in previously proposed Dirac and Weyl semimetals. Here, we provide the theoretical and experimental evidences of an intrinsic Dirac state in the quaternary chalcogenide $\mathrm{C}{\mathrm{u}}_{2}\mathrm{HgSnS}{\mathrm{e}}_{4}$ that has bared linear dispersions in conduction bands. Scanning tunneling spectroscopy reveals the quadratic energy-dependent density of states within an extremely large energy range $(\ensuremath{\sim}400\phantom{\rule{0.16em}{0ex}}\mathrm{meV})$ on conduction bands of $\mathrm{C}{\mathrm{u}}_{2}\mathrm{HgSnS}{\mathrm{e}}_{4}$, which is self-consistent with linear dispersion detected by angle-resolved photoemission spectroscopy. In electron-doped $\mathrm{C}{\mathrm{u}}_{2}\mathrm{HgSnS}{\mathrm{e}}_{4}$, positive magnetoresistance at low magnetic field $B(l2.5\phantom{\rule{0.16em}{0ex}}\mathrm{T})$ and negative magnetoresistance under high $B$ are observed, which is attributed to the chiral anomaly effect. However, conventional negative magnetoresistance is observed in hole-doped $\mathrm{C}{\mathrm{u}}_{2}\mathrm{HgSnS}{\mathrm{e}}_{4}$, which is attributed to weak localization broken by $B$. Remarkably, the carrier mobility has a ${10}^{5}$-fold decrease when the Fermi level is adjusted from conduction to valence bands. Our results suggest that $\mathrm{C}{\mathrm{u}}_{2}\mathrm{HgSnS}{\mathrm{e}}_{4}$ not only provides a playground for exploring intrinsic properties of 3D Dirac fermions but also is promising for developing high-speed, low-dissipation electronic devices.

Quasi-1D Topological Nodal Vortex Line Phase in Doped Superconducting 3D Dirac Semimetals.

We study vortex bound states in three-dimensional (3D) superconducting Dirac semimetals with time reversal symmetry. We find that there exist robust gapless vortex bound states propagating along the vortex line in the s-wave superconducting state. We refer to this newly found phase as the quasi-1D nodal vortex line phase. According to the Altland-Zirnbauer classification, the phase is characterized by a topological index (ν;N) at k_{z}=0 and k_{z}=π, where ν is the Z_{2} topological invariant for a 0D class-D system and N is the Z topological invariant for a 0D class-A system. Furthermore, we show that the vortex end Majorana zero mode can coexist with the quasi-1D nodal phase in certain types of Dirac semimetals. The possible experimental observations and material realization of such nodal vortex line states are discussed.

In situ compensation method for high-precision and high-sensitivity integral magnetometry

The ongoing process of the miniaturization of spintronics and magnetic-films-based devices, as well as a growing necessity for basic material research place stringent requirements on sensitive and accurate magnetometric measurements of minute magnetic constituents deposited on large magnetically responsive carriers. However, the ever so popular commercial integral magnetometers based on superconducting quantum interference device sensor are not object-selective probes. Therefore, the sought signal is usually buried in the magnetic response of the carrier, contaminated by signals from the sample support, system instabilities and additionally degraded by inadequate data reduction. In this report a comprehensive method based on in situ magnetic compensation by sample abutting long strips made of matching material is shown to provide means for mitigating all these weak elements of integral magnetometry. Practical solutions and proper expressions to calculate the absolute values of the investigated moments are given. Their universal form allows one to employ the suggested design in investigations of a broad range of specimens of different sizes, shapes and compositions. The method does not require any extensive numerical modeling, relying only on the data provided by the magnetometer. The solution can be straightforwardly implemented in every field where magnetic investigations are of a prime importance, including the emerging new fields of topological insulators, 3D-Dirac semimetals and 2D-materials.

Asymmetric magneto-transport in a Dirac semimetal heterostructure

A three-dimensional (3D) Dirac semimetal is known as a 3D analog of graphene; its Fermi-arc-like surface states are attractive for spintronic applications and can potentially modulate graphene via interface engineering. Here, we report the asymmetric magnetotransport in graphene/Cd3As2 heterostructure devices. The electron transfer occurring at the graphene/Cd3As2 interface results in a strong n-type doping of graphene. The interfacial coupling between graphene and Cd3As2 also enables us to selectively pin the chemical potential of graphene. The asymmetrical magnetotransport near the zero Landau level in graphene suggests that the interfacial coupling between Cd3As2 and graphene can be modulated by the magnetic field.