Three-dimensional Dirac Semimetals Research Articles

Observation of superconductivity induced by a point contact on 3D Dirac semimetal Cd3As2 crystals

Three-dimensional (3D) Dirac semimetals, which possess 3D linear dispersion in the electronic structure as a bulk analogue of graphene, have lately generated widespread interest in both materials science and condensed matter physics. Recently, crystalline Cd3As2 has been proposed and proved to be a 3D Dirac semimetal that can survive in the atmosphere. Here, by using point contact spectroscopy measurements, we observe exotic superconductivity around the point contact region on the surface of Cd3As2 crystals. The zero-bias conductance peak (ZBCP) and double conductance peaks (DCPs) symmetric around zero bias suggest p-wave-like unconventional superconductivity. Considering the topological properties of 3D Dirac semimetals, our findings may indicate that Cd3As2 crystals under certain conditions could be topological superconductors, which are predicted to support Majorana zero modes or gapless Majorana edge/surface modes in the boundary depending on the dimensionality of the material.

Phonon-drag thermopower in 3D Dirac semimetals

A theory of low-temperature phonon-drag thermopower Sg in three-dimensional (3D) Dirac semimetals has been developed considering screened electron–phonon deformation potential coupling. Numerical investigations of Sg, in the boundary scattering regime for phonons, are made in 3D Dirac semimetal Cd3As2, as a function of temperature T and electron concentration ne. Sg is found to increase rapidly for about T < 1 K and nearly levels off for higher T. It is also seen that Sg increases (decreases) with decreasing ne at lower (higher) T (<2 K). A screening effect is found to be very significant, strongly affecting T and ne dependence for about <1 K and becoming negligible at higher temperature. In the Bloch–Gruneisen (BG) regime the power laws Sg ~ T8 (T4) and Sg ~ with (without) screening are obtained. These laws with respect to T and ne are, respectively, characteristics of 3D phonons and Dirac 3D electrons. Comparison with diffusion thermopower Sd shows that Sg dominates (and is much greater than) Sd for about T > 0.2 K. Herring’s law Sgμp ~ T −1, relating phonon limited mobility μp and Sg in the BG regime, is shown to be valid in 3D Dirac semimetals. The results obtained here are compared with those in 3D semiconductors, low-dimensional semiconductor heterojunctions and graphene. We conclude that ne-dependent measurements, rather than T-dependent ones, provide a clearer signature of the 3D Dirac semimetal phase.

Topological charges of three-dimensional Dirac semimetals with rotation symmetry

In general, the stability of a band crossing point indicates the presence of a quantized topological number associated with it. In particular, the recent discovery of three-dimensional Dirac semimetals in Na$_{3}$Bi and Cd$_{3}$As$_{2}$ demonstrates that a Dirac point with four-fold degeneracy can be stable as long as certain crystalline symmetries are supplemented in addition to the time-reversal and inversion symmetries. However, the topological charges associated with Na$_{3}$Bi and Cd$_{3}$As$_{2}$ are not clarified yet. In this work, we identify the topological charge of three-dimensional Dirac points. It is found that although the simultaneous presence of the time-reversal and inversion symmetries forces the net chiral charge to vanish, a Dirac point can carry another quantized topological charge when an additional rotation symmetry is considered. Two different classes of Dirac semimetals are identified depending on the nature of the rotation symmetries. First, the conventional symmorphic rotational symmetry which commutes with the inversion gives rise to the class I Dirac semimetals having a pair of Dirac points on the rotation axes. Since the topological charges of each pair of Dirac points have the opposite sign, a pair-creation or a pair-annihilation is required to change the number of Dirac points in the momentum space. On the other hand, the class II Dirac semimetals possess a single isolated Dirac point at a time-reversal invariant momentum, which is protected by a screw rotation. The non-symmorphic nature of screw rotations allows the anti-commutation relation between the rotation and inversion symmetries, which enables to circumvent the doubling of the number of Dirac points and create a single Dirac point at the Brillouin zone boundary.

Quantum critical exponents for a disordered three-dimensional Weyl node

Three-dimensional Dirac and Weyl semimetals exhibit a disorder-induced quantum phase transition between a semimetallic phase at weak disorder and a diffusive-metallic phase at strong disorder. Despite considerable effort, both numerically and analytically, the critical exponents $\nu$ and $z$ of this phase transition are not known precisely. Here we report a numerical calculation of the critical exponent $\nu=1.47\pm0.03$ using a minimal single-Weyl node model and a finite-size scaling analysis of conductance. Our high-precision numerical value for $\nu$ is incompatible with previous numerical studies on tight-binding models and with one- and two-loop calculations in an $\epsilon$-expansion scheme. We further obtain $z=1.49\pm0.02$ from the scaling of the conductivity with chemical potential.

Magnetic catalysis and axionic charge density wave in Weyl semimetals

Three-dimensional Weyl and Dirac semimetals can support a chiral-symmetry-breaking, fully gapped, charge-density-wave order even for sufficiently weak repulsive electron-electron interactions, when placed in strong magnetic fields. In the former systems, due to the natural momentum space separation of Weyl nodes the ordered phase lacks the translational symmetry and represents an axionic phase of matter, while that in a Dirac semimetal (neglecting the Zeeman coupling) is only a trivial insulator. We present the scaling of this spectral gap for a wide range of subcritical (weak) interactions as well as that of the diamagnetic susceptibility with the magnetic field. A similar mechanism for charge-density-wave ordering at weak coupling is shown to be operative in double and triple-Weyl semimetals, where the dispersion is linear (quadratic and cubic, respectively) for the z (planar) component(s) of the momentum. We here also address the competition between the charge-density-wave and a spin-density-wave orders, both of which breaks the chiral symmetry and leads to gapped spectrum, and show that at least in the weak coupling regime the former is energetically favored. The anomalous surface Hall conductivity, role of topological defects such as axion strings, existence of one-dimensional gapless dispersive modes along the core of such defects, and anomaly cancellation through the Callan-Harvey mechanism are discussed.

Anisotropic Fermi Surface and Quantum Limit Transport in High Mobility Three-Dimensional Dirac SemimetalCd3As2

The three-dimensional (3D) topological Dirac semimetal is a new topological phase of matter, viewed as the 3D analogy of graphene with a linear dispersion in the 3D momentum space. Here, we report the angular dependent magnetotransport in Cd3As2 single crystal and clearly show how the Fermi surface evolves when tilting the magnetic field. Remarkably, when the magnetic field lies in [112] and [44-1] axis, only single oscillation period features present, however, the system shows double period oscillations when the field is applied along [1-10] direction. Moreover, tilting the magnetic field at certain direction also gives double period oscillations. We attribute the anomalous oscillation behavior to the sophisticated geometry of Fermi surface and illustrate a complete 3D Fermi surfaces with two nested anisotropic ellipsoids around the Dirac point. Additionally, a sub-millimeter mean free path at 6 K is observed in Cd3As2 crystal, indicating a large ballistic transport region in this material. Tracking the magnetoresistance oscillations to 60 T, we reach the quantum limit (n = 1 Landau Level) at about 43 T. These results improve the knowledge of the Dirac semimetal material Cd3As2, and also pave the way for proposing new electronic applications based on 3D Dirac materials.

Semimetal-semiconductor transition and giant linear magnetoresistances in three-dimensional Dirac semimetal Bi0.96Sb0.04 single crystals

Three-dimensional (3D) Dirac semimetals are new quantum materials and can be viewed as 3D analogues of graphene. Many fascinating electronic properties have been proposed and realized in 3D Dirac semimetals, which demonstrate their potential applications in next generation quantum devices. Bismuth-antimony Bi1−xSbx can be tuned from a topological insulator to a band insulator through a quantum critical point at x ≈ 4%, where 3D Dirac fermions appear. Here, we report on a magnetotransport study of Bi1−xSbx at such a quantum critical point. An unusual magnetic-field induced semimetal-semiconductor phase transition was observed in the Bi0.96Sb0.04 single crystals. In a magnetic field of 8 T, Bi0.96Sb0.04 single crystals show giant magnetoresistances of up to 6000% at low-temperature, 5 K, and 300% at room-temperature, 300 K. The observed magnetoresistances keep linear down to approximate zero-field when the temperature is below 200 K. Our experimental results are not only interesting for the fundamental physics of 3D Dirac semimetals but also for potential applications of 3D Dirac semimetals in magnetoelectronic devices.

Phase diagram of the quantum electrodynamics of two-dimensional and three-dimensional Dirac semimetals

We study the quantum electrodynamics of two-dimensional (2D) and three-dimensional (3D) Dirac semimetals by means of a self-consistent resolution of the Schwinger-Dyson equations, aiming to obtain the respective phase diagrams in terms of the relative strength of the Coulomb interaction and the number $N$ of Dirac fermions. In this framework, 2D Dirac semimetals have just a strong-coupling instability characterized by exciton condensation (and dynamical generation of mass) that we find at a critical coupling well above previous theoretical estimates, thus explaining the absence of that instability in free-standing graphene samples. On the other hand, we show that 3D Dirac semimetals have a richer phase diagram, with a strong-coupling instability leading to dynamical mass generation up to $N\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}4$ and a line of critical points for larger values of $N$ characterized by the vanishing of the electron quasiparticle weight in the low-energy limit. Such a critical behavior signals the transition to a strongly correlated liquid, characterized by noninteger scaling dimensions that imply the absence of a pole in the electron propagator and are the signature of non-Fermi-liquid behavior with no stable electron quasiparticles.

Magnetotransport Properties of Cd3As2 Nanostructures.

Three-dimensional (3D) topological Dirac semimetal has a linear energy dispersion in 3D momentum space, and it can be viewed as an analogue of graphene. Extensive efforts have been devoted to the understanding of bulk materials, but yet it remains a challenge to explore the intriguing physics in low-dimensional Dirac semimetals. Here, we report on the synthesis of Cd3As2 nanowires and nanobelts and a systematic investigation of their magnetotransport properties. Temperature-dependent ambipolar behavior is evidently demonstrated, suggesting the presence of finite-size of bandgap in nanowires. Cd3As2 nanobelts, however, exhibit metallic characteristics with a high carrier mobility exceeding 32,000 cm(2) V(-1) s(-1) and pronounced anomalous double-period Shubnikov-de Haas (SdH) oscillations. Unlike the bulk counterpart, the Cd3As2 nanobelts reveal the possibility of unusual change of the Fermi sphere owing to the suppression of the dimensionality. More importantly, their SdH oscillations can be effectively tuned by the gate voltage. The successful synthesis of Cd3As2 nanostructures and their rich physics open up exciting nanoelectronic applications of 3D Dirac semimetals.

Collective modes, ac response, and magnetic properties of the three-dimensional Dirac semimetal in the triplet superconducting state

It was recently shown that conventional phonon-electron interactions may induce a triplet pairing state in time-reversal invariant three-dimensional Dirac semimetals. Starting from the microscopic model of the isotropic Dirac semimetal, the Ginzburg-Landau equations for the vector order parameter is derived using the Gor'kov technique. The collective modes including gapless Goldstone modes and gapped Higgs modes of various polarizations are identified. They are somewhat analogous to the modes in the B phase of ${\text{He}}^{3}$, although in the present case quantitatively there is a pronounced difference between longitudinal and transverse components. The difference is caused by the vector nature of the order parameter leading to two different coherence lengths or penetration depths. The system is predicted to be highly dissipative due to the Goldstone modes. The time-dependent Ginzburg-Landau model in the presence of external fields is used to investigate some optical and magnetic properties of such superconductors. The ac conductivity of a clean sample depends on the orientation of the order parameter. It is demonstrated that the difference between the penetration depths results in rotation of the polarization vector of microwave passing a slab made of this material. The upper critical magnetic field ${H}_{c2}$ was found. It turns out that at fields close to ${H}_{c2}$ the order parameter orients itself perpendicular to the field direction. In certain range of parameters the triplet superconducting phase persists at arbitrarily high magnetic field like in some $p$-wave superconductors.

Floquet dynamics in two-dimensional semi-Dirac semimetals and three-dimensional Dirac semimetals

We study the photoresponse of two-dimensional semi-Dirac semimetals and three-dimensional Dirac semimetals to off-resonant circularly polarized light. For two-dimensional semi-Dirac semimetals we find that incident light does not open a gap in the spectrum, in contrast to the case of purely linear dispersion. For the three-dimensional case we find that applying a circularly polarized light, one can tune from a trivial insulator to three-dimensional Dirac semimetal with an inverted gap. We propose and show that application of light leads to an intriguing platform for generation, motion and merging of three-dimensional Dirac points.

Three-dimensional Dirac semimetals: Design principles and predictions of new materials

Design principles and novel predictions of new 3D Dirac semimetals are presented, along with the context of currently known materials. Current materials include those based on a topological to trivial phase transition, such as in TlBiSe$_{2-x}$S$_x$ and Hg$_{1-x}$Cd$_x$Te, Bi$_{1-x}$Sb$_x$, Bi$_{2-x}$In$_x$Se$_3$, and Pb$_{1-x}$Sn$_x$Se. Some more recently revealed materials, Na$_3$Bi and Cd$_3$As$_2$, are 3D Dirac semimetals in their native composition. The different design principles presented each yield novel predictions for new candidates. For Case I, 3D Dirac semimetals based on charge balanced compounds, BaAgBi, SrAgBi, YbAuSb, PtBi$_2$ and SrSn$_2$As$_2$ are identified as candidates. For Case II, 3D Dirac semi-metals in analogy to graphene, BaGa$_2$ is identified as a candidate, and BaPt and Li$_2$Pt are discussed. For Case III, 3D Dirac semi-metals based on glide planes and screw axes, TlMo$_3$Te$_3$ and the AMo$_3$X$_3$ family in general (A=K, Na, In, Tl, X=Se,Te) as well as the Group IVb trihalides such as HfI$_3$ are identified as candidates. Finally we discuss conventional intermetallic compounds with Dirac cones, and identify Cr$_2$B as a potentially interesting material.

Spin texture of the surface state of three-dimensional Dirac material Ca3PbO

The bulk and surface electronic structures of a candidate three-dimensional Dirac material Ca3PbO and its family are discussed especially focusing on the spin texture on the surface states. We first explain the basic features of the bulk band structure of Ca3PbO, such as emergence of Dirac fermions near the Fermi energy, and compare it with the other known three-dimensional Dirac semimetals. Then, the surface bands and spin-texture on them are investigated in detail. It is shown that the surface bands exhibit strong momentum-spin locking, which may be useful in some application for spin manipulation, induced by a combination of the inversion symmetry breaking at the surface and the strong spin-orbit coupling of Pb atoms. The surface band structure and the spin-textures are sensitive to the surface types.

Carrier screening, transport, and relaxation in three-dimensional Dirac semimetals

A theory is developed for the density and temperature-dependent carrier conductivity in doped three-dimensional (3D) Dirac materials focusing on resistive scattering from screened Coulomb disorder due to random charged impurities (e.g., dopant ions and unintentional background impurities). The theory applies both in the undoped intrinsic (``high-temperature,'' $T\ensuremath{\gg}{T}_{F})$ and the doped extrinsic (``low-temperature,'' $T\ensuremath{\ll}{T}_{F})$ limit with analytical scaling properties for the carrier conductivity obtained in both regimes, where ${T}_{F}$ is the Fermi temperature corresponding to the doped free carrier density (electrons or holes). The scaling properties describing how the conductivity depends on the density and temperature can be used to establish the Dirac nature of 3D systems through transport measurements. We also consider the temperature-dependent conductivity limited by the acoustic phonon scattering in 3D Dirac materials. In addition, we theoretically calculate and compare the single-particle relaxation time ${\ensuremath{\tau}}_{s}$, defining the quantum level broadening, and the transport scattering time ${\ensuremath{\tau}}_{t}$, defining the conductivity, in the presence of screened charged impurity scattering. A critical quantitative analysis of the ${\ensuremath{\tau}}_{t}/{\ensuremath{\tau}}_{s}$ results for 3D Dirac materials in the presence of long-range screened Coulomb disorder is provided.

Nailing down the topology of a semimetal

Topological Matter Topological insulators are exotic materials that have a conducting surface state that can withstand certain types of material imperfection. Theoreticians have predicted a different kind of surface state in related three-dimensional topological Dirac semimetals, which do not have

Observation of Fermi arc surface states in a topological metal

The topology of the electronic structure of a crystal is manifested in its surface states. Recently, a distinct topological state has been proposed in metals or semimetals whose spin-orbit band structure features three-dimensional Dirac quasiparticles. We used angle-resolved photoemission spectroscopy to experimentally observe a pair of spin-polarized Fermi arc surface states on the surface of the Dirac semimetal Na3Bi at its native chemical potential. Our systematic results collectively identify a topological phase in a gapless material. The observed Fermi arc surface states open research frontiers in fundamental physics and possibly in spintronics.

Topological tuning in three-dimensional dirac semimetals.

We study with first-principles methods the interplay between bulk and surface Dirac fermions in three dimensional Dirac semimetals. By combining density functional theory with the coherent potential approximation, we reveal a topological phase transition in Na_{3}Bi_{1-x}Sb_{x} and Cd_{3}[As_{1-x}P_{x}]_{2} alloys, where the material goes from a Dirac semimetal to a trivial insulator upon changing Sb or P concentrations. Tuning the composition allows us to engineer the position of the bulk Dirac points in reciprocal space. Interestingly, the phase transition coincides with the reversal of the band ordering between the conduction and valence bands.

Marginal Fermi liquid versus excitonic instability in three-dimensional Dirac semimetals

We study the different phases in the Quantum Electrodynamics of three-dimensional Dirac semimetals depending on the number $N$ of Dirac fermions, using renormalization group methods and the self-consistent resolution of the Schwinger-Dyson equation. We find that, for $N&lt;4$, a phase with dynamical generation of mass prevails at sufficiently strong coupling, sharing the same physics of the excitonic instability in two-dimensional Dirac semimetals. For $N\ensuremath{\ge}4$, we show that the phase diagram has instead a line of critical points characterized by the suppression of the quasiparticle weight at low energies, making the system fall into the class of marginal Fermi liquids. Such a boundary marks the transition to a kind of strange metal which can still be defined in terms of electron quasiparticles, but with parameters that have large imaginary parts implying an increasing deviation from the conventional Fermi liquid picture.

Classification of stable three-dimensional Dirac semimetals with nontrivial topology.

A three-dimensional (3D) Dirac semimetal (SM) is the 3D analogue of graphene having linear energy dispersion around Fermi points. Owing to the nontrivial topology of electronic wave functions, the 3D Dirac SM shows nontrivial physical properties and hosts various exotic quantum states such as Weyl SMs and topological insulators under proper external conditions. There are several kinds of Dirac SMs proposed theoretically and partly confirmed experimentally, but its unified picture is still missing. Here we propose a general framework to classify stable 3D Dirac SMs in systems having the time-reversal, inversion and uniaxial rotational symmetries. We show that there are two distinct classes of 3D Dirac SMs. In one class, the Dirac SM possesses a single Dirac point (DP) at a time-reversal invariant momentum on the rotation axis. Whereas the other class of Dirac SMs have a pair of DPs created by band inversion, and carry a quantized topological invariant.

Experimental realization of a three-dimensional Dirac semimetal.

We report the direct observation of the three-dimensional (3D) Dirac semimetal phase in cadmium arsenide (Cd(3)As(2)) by means of angle-resolved photoemission spectroscopy. We identify two momentum regions where electronic states that strongly disperse in all directions form narrow conelike structures, and thus prove the existence of the long sought 3D Dirac points. This electronic structure naturally explains why Cd(3)As(2) has one of the highest known bulk electron mobilities. This realization of a 3D Dirac semimetal in Cd(3)As(2) not only opens a direct path to a wide spectrum of applications, but also offers a robust platform for engineering topologically nontrivial phases including Weyl semimetals and quantum spin Hall systems.