States Of Dirac Fermions Research Articles

Bound states of Dirac fermions in the presence of a Fermi velocity modulation

We investigate the effect of a position-dependent Fermi velocity on the electronic properties of two-dimensional Dirac materials. A physical Fermi velocity distribution, which approaches a finite value at infinity and experiences a modulation near x = 0, is considered. Such a position-dependent Fermi velocity could be realized in the curved graphene or by applying strain. It is shown that the bound states are absent in the presence of a pure Fermi velocity modulation without an electrostatic potential well. However, an extra electrostatic potential modulation could produce the bound states. A set of discrete energy level spectrum and the corresponding wave functions are obtained by solving the Dirac equation exactly. Local probes such as scanning tunnel microscopy should be able to observe the predicted bound states in two-dimensional materials.

Spontaneous Spin and Valley Symmetry-Broken States of Interacting Massive Dirac Fermions in a Bilayer Graphene Quantum Dot.

We predict the existence of spontaneous spin and valley symmetry-broken states of interacting massive Dirac Fermions in a gated bilayer graphene quantum dot based on the exact diagonalization of the many-body Hamiltonian. The dot is defined by a vertical electric field and lateral gates, and its single-particle (SP) energies, wave functions, and Coulomb matrix elements are computed by using the atomistic tight-binding model. The effect of the Coulomb interaction is measured by the ratio of Coulomb elements to the SP level spacing. As we increase the interaction strength, we find the electrons in a series of spin and valley symmetry-broken phases with increasing valley and spin polarizations. The phase transitions result from the competition of the SP, exchange, and correlation energy scales. A phase diagram for N = 1-6 electrons is mapped out as a function of the Coulomb interaction strength.

Strain-induced massless Dirac fermion state of the molecular conductor α-(BEDT-TTF)2I3

Uniaxial pressure can dramatically change the properties of low-dimensional systems and induce electronic phase transitions. The first-discovered molecular massless Dirac electron system α-(BEDT-TTF)2I3 has intensively been studied because of its unique features, such as the Fermi energy being very close to the Dirac point, strong electron correlation, and the quantum phase transition from the charge-ordered insulating state. However, the Dirac state is realized only under high pressure of 15 kbar, which limits the measurement of physical properties (e.g., experimental determination of band dispersion and density of states). Here, we demonstrate that the Dirac state of α-(BEDT-TTF)2I3 can be realized by applying uniaxial bending strain without confining it in a pressure cell. Uniaxial strain below 1% completely suppresses the metal–insulator transition observed at ambient pressure. Under strain, a characteristic temperature dependence of magnetoresistance associated with the formation of the n = 0 Landau level is observed, indicating the realization of the massless Dirac state.

Behavior of gapped and ungapped Dirac cones in the antiferromagnetic topological metal SmBi

We studied the behavior of nontrivial Dirac fermion states in the antiferromagnetic metal SmBi using angle-resolved photoemission spectroscopy (ARPES). The experimental results exhibit multiple Fermi pockets around the $\overline{\mathrm{\ensuremath{\Gamma}}}$ and $\overline{M}$ points along with a band inversion in the spectrum along the $\overline{\mathrm{\ensuremath{\Gamma}}}\text{\ensuremath{-}}\overline{M}$ line consistent with the density functional theory results. In addition, ARPES data reveal Dirac cones at the $\overline{\mathrm{\ensuremath{\Gamma}}}$ and $\overline{M}$ points within the energy gap of the bulk bands. The Dirac cone at $\overline{M}$ exhibits a distinct Dirac point and is intense in the high-photon-energy data, while the Dirac cone at $\overline{\mathrm{\ensuremath{\Gamma}}}$ is intense at low photon energies. Employing ultrahigh-resolution ARPES, we discover destruction of a Fermi surface constituted by the surface states across the Ne\'el temperature of 9 K. Interestingly, the Dirac cone at $\overline{\mathrm{\ensuremath{\Gamma}}}$ is found to be gapped at 15 K, and the behavior remains similar across the magnetic transition. These results reveal complex momentum-dependent gap formation and Fermi surface destruction across the magnetic transition in an exotic correlated topological material; the interplay between magnetism and topology in this system calls for ideas beyond the existing theoretical models.

Magnetic skyrmion crystal at a topological insulator surface

We consider a magnetic skyrmion crystal formed at the surface of a topological insulator. Incorporating the exchange interaction between the helical Dirac surface states and the periodic N\'eel or Bloch skyrmion texture, we obtain the resulting electronic band structure and discuss the constraints that symmetries impose on the energies and Berry curvature. We find substantive qualitative differences between the N\'eel and Bloch cases, with the latter generically permitting a multiband low energy tight-binding representation whose parameters are tightly constrained by symmetries. We explicitly compute the associated Wannier orbitals, which resemble the ringlike chiral bound states of helical Dirac fermions coupled to a single skyrmion in a ferromagnetic background. We construct a two-band tight-binding model with real nearest-neighbor hoppings which captures the salient topological features of the low-energy bands. Our results are relevant to magnetic topological insulators (TIs), as well as to TI-magnetic thin film heterostructures, in which skyrmion crystals may be stabilized.

Controllable spin filtering and half-metallicity in β12 -borophene nanoribbons

The experimental observation of the Dirac fermion states in $\beta_{12}$-borophene sheets and the discovery of their novel topological properties properties have made them a promising candidate for spintronic applications. Here, by combining non-equilibrium Green's function (NEGF) and tight-binding (TB) approximation, we study the charge and spin transport properties through a $\beta_{12}$-borophene nanoribbon (BNR) with the different edge shapes. We show when a BNR exposed to a nonlocal exchange magnetic field, the spin filtering occurs for both spin-up and spin-down so that the spin direction of transmitted electrons could be controlled by adjusting the energy of incoming electrons with the help of an external backgate voltage. It is found that an armchair BNR (ABNR) in the simultaneous presence of a transverse electric field and a nonlocal exchange field indicates a half-metallic nature which is electrically controllable. Moreover, the influence of local exchange field fields is evaluated by exposing the edges of ABNR to ferromagnetic strips with parallel and antiparallel configurations. Our findings show that the edge manipulations in ABNRs lead to the emergence of a giant magnetoresistance and a perfect spin filter. Finally, we studied the effects of edge vacancies and Anderson disorder on the spin-dependent conductance of an ABNR and find that the perfect spin polarization is not destroyed in the presence of Anderson disorder and various single vacancies. Our results reveal the outstanding spin transport properties of ABNRs for future spintronic devices.

Anomalies in the temperature evolution of Dirac states in the topological crystalline insulator SnTe

Discovery of topologically protected surface states, believed to be immune to weak disorder and thermal effects, opened up a new avenue to reveal exotic fundamental science and advanced technology. While time-reversal symmetry plays the key role in most such materials, the bulk crystalline symmetries such as mirror symmetry preserve the topological properties of topological crystalline insulators (TCIs). It is apparent that any structural change may alter the topological properties of TCIs. To investigate this relatively unexplored landscape, we study the temperature evolution of the Dirac fermion states in an archetypical mirror-symmetry protected TCI, SnTe employing high-resolution angle-resolved photoemission spectroscopy and density functional theory studies. Experimental results reveal a perplexing scenario; the bulk bands observed at 22 K move nearer to the Fermi level at 60 K and again shift back to higher binding energies at 120 K. The slope of the surface Dirac bands at 22 K becomes smaller at 60 K and changes back to a larger value at 120 K. Our results from the first-principles calculations suggest that these anomalies can be attributed to the evolution of the hybridization physics with complex structural changes induced by temperature. In addition, we discover drastically reduced intensity of the Dirac states at the Fermi level at high temperatures may be due to complex evolution of anharmonicity, strain, etc. These results address robustness of the topologically protected surface states due to thermal effects and emphasize importance of covalency and anharmonicity in the topological properties of such emerging quantum materials.

Detecting topological phase transitions in cadmium arsenide films via the transverse magnetoresistance

Topological protection against localization causes electrical transport phenomena in disordered topological materials to differ from those in topologically trivial systems. For example, a transition between a regime of weak localization to one of weak antilocalization can occur in systems such as topological insulators and topological semimetals when an external potential is applied across the system. Here, we report on the transverse magnetoresistance of thin films of cadmium arsenide, a topologically nontrivial, as we tune the electronic states and the Fermi level. We show that the appearance of weak localization and weak antilocalization sensitively reflects the relative contributions of multiple transport channels involving both gapless (massless) and gapped (massive) Dirac fermion states present in these films. The data are consistent with expectations of the different topological states of these films. Weak (anti-)localization phenomena can, therefore, serve as a probe of the types of Dirac fermions present in topological semimetals.

Quantum Size Effects, Multiple Dirac Cones, and Edge States in Ultrathin Bi(110) Films

The presence of inherently strong spin-orbit coupling in bismuth, its unique layer-dependent band topology and high carrier mobility make it an interesting system for both fundamental studies and applications. Theoretically, it has been suggested that strong quantum size effects should be present in the Bi(110) films, with the possibility of Dirac Fermion states in the odd-bilayer (BL) films, originating from dangling pz orbitals and quantum-spin hall (QSH) states in the even-bilayer films. However, the experimental verification of these claims has been lacking. Here, we study the electronic structure of Bi(110) films grown on a high-Tc superconductor, Bi2Sr2CaCu2O8+δ (Bi2212) using angle-resolved photoemission spectroscopy (ARPES). We observe an oscillatory behavior of electronic structure with the film thickness and identify the Dirac-states in the odd-bilayer films, consistent with the theoretical predictions. In the even-bilayer films, we find another Dirac state that was predicted to play a crucial role in the QSH effect. In the low thickness limit, we observe several extremely one-dimensional states, probably originating from the edge-states of Bi(110) islands. Our results provide a much needed experimental insight into the electronic and structural properties of Bi(110) films.

Topological Thermoelectric Materials Based on Bismuth Telluride

The main directions of experimental studies of topological insulators based on bismuth and antimony chalcogenides, which are related to the possibility of using the properties of the surface states of Dirac fermions in thermoelectricity, have been considered. The results of studies of the Van der Waals interlayer surface (0001) in single-crystal layered films of solid solutions of n- and p-type conductivity with substitutions of atoms in Bi and Te sublattices performed by micro-Raman spectroscopy, scanning tunneling microscopy, and scanning tunneling spectroscopy have been discussed. The oscillations of galvanomagnetic effects in strong magnetic fields and thermoelectric properties measured under normal conditions and at high pressures have been analyzed. The compositions of solid solutions in which the contribution of the surface states of Dirac fermions increases because of an increase in the surface concentration of fermions and the Fermi velocity depending on the energy of the Dirac point, the value of the Seebeck coefficient, and the power parameter have been determined.

Nonequilibrium states in quantum materials under time-period driving

The topology of quantum materials is the frontier research in condensed matter physics. In contrast with the conventional classification of materials by using the local symmetry breaking criterion, the states of quantum systems are classified according to the topology of wave functions. The potential applications of topological states may lead the traditional microelectronics to break through and accelerate the significant improvement in topological electronics. Most of the recent studies focus on the topological states of quantum systems under equilibrium conditions without external perturbations. The topological states of quantum systems far from the equilibrium under time-periodic driving have attracted wide attention. Here we first introduce the framework of Floquet engineering under the frame of the Floquet theorem. The nonequilibrium topological states of massless and massive Dirac fermions are discussed including the mechanism of phase transition. Light field driven electronic transition term in the quantum material gains extra time-dependent phase. Thereby the manipulation of effective transition term of the electron is realized to regulate the non-equilibrium topological states. We also mention how the photoinduced coherent phonon affects the nonequilibrium topological states of quantum systems from the perspective of atom manufacturing. Furthermore, research outlook on the nonequilibrium topological states is given. This review provides some clues to the design of physical properties and transport behaviors of quantum materials out of equilibrium.

Дифференциальная туннельная проводимость в многокомпонентных твердых растворах Bi-=SUB=-2-x-=/SUB=-Sb-=SUB=-x-=/SUB=-Te-=SUB=-3-y-z-=/SUB=-Se-=SUB=-y-=/SUB=-S-=SUB=-z-=/SUB=-

Differential tunnel conductance of the interlayer van der Waals surface (0001) was investigated in n-Bi2-xSbxTe3-y-zSeySz multicomponent solid solutions at x = 0.2, y = z = 0.09, optimized for near room temperatures with a high power factor, and at x = 0.4, y = 0, z = 0.06 with optimal thermoelectric properties for low temperatures and a high Seebek coefficient. It is shown that the intensity of the fluctuations of the Dirac point energy, a shift the top of the valence band and presence of surface levels in the energy gap formed by impurity defects is determined with composition and thermoelectric properties of solid solutions. The contribution of the surface states of Dirac fermions increases in n-Bi1.8Sb0.2Te2.82Se0.09S0.09 solid solution with a high power factor due to significant decrease of the surface concentration near the charge neutrality point and the growth of fermion mobility.

STM and STS studies of topological n-type (Bi, In)2(Te, Se, S)3 thermoelectrics

In topological n-type thermoelectrics based on Bi2Te3 with atomic substitutions Bi → In, Te → Se, S, the morphology and the surface states of Dirac fermions on the interlayer (0001) surface of van der Waals were studied by scanning tunneling microscopy and spectroscopy (STM/STS) techniques. By the STM method, the dark and light spots on the surface were found, which intensities depend on the composition and thermoelectric properties of solid solutions such as the Seebeck coefficient and thermoelectric power factor. The observed surface morphology features in the solid solutions are explained by distortions of surface electronic states originated from atomic substitutions, the influence of doping impurity, and formation mainly of substitutional impurity defects in thermoelectrics. The dips associated with substitutional impurities and antisite defects were found from the analysis of the height profiles obtained on the (0001) surface. Fast Fourier transform of the morphology STM images of the (0001) surface were used to obtain the interference patterns of the quasiparticles excitation caused by surface electrons scattering by defects. The Dirac point energy and its fluctuations, peak energies of surface defects, the positions of the valence and conduction band edges, and the energy gap were determined from an analysis of tunneling spectra. A correlation between the parameters of surface states of Dirac fermions and thermoelectric properties was found. Thus, a contribution of the fermions surface states increases with rise of the surface concentration in solid solutions with high power factor, and the largest concentration value was observed in the Bi1.98In0.02Te2.85Se0.15 composition. The dependences of Fermi energy on the wave vector for different solid solutions are described by a set of Dirac cone sections located within the limits of the fluctuations of the Dirac point energy that explained by weak changes of the Fermi velocity for studied atomic substitutions in sublattices of bismuth telluride.

Generation and control of photo-excited thermal currents in triple degenerate topological semimetal MoP with circularly polarized ultrafast light pulses

Ultrafast spectroscopy is a powerful method to generate and control topological phase transitions and spin-polarized electrical currents in topological quantum materials. These light-induced novel physical properties originate from the topologically nontrivial states of Dirac and Weyl fermions. The topological semimetal molybdenum phosphide (MoP) exhibits double and triple degenerate points in the momentum space. We present the preliminary results of spin-polarized electrical currents and optical response investigations of MoP. We design and construct an experimental setup to perform the photocurrent generation and control by circularly polarized light in topological insulator Bi<sub>2</sub>Se<sub>3</sub>. The results compare well with those reported, which confirms the validity and reliability of our experimental setup. Further, we conduct the photocurrent experiment on MoP by using 400 nm laser pulses for excitation and successfully detect the current signals at different sample positions. We attribute the observed currents to photo-induced thermal currents (not the photo current associated with the triple degenerate topological properties), which facilitates generating and controlling photocurrents in MoP in the future investigation. Our thermal current investigations are of essence for further exploring the photocurrents in various types of topological quantum materials.

Topological Surface States of Multicomponent Thermoelectrics Based on Bismuth Telluride

The surface states of Dirac fermions in p-Bi2Te3, p-Bi2 –xSbxTe3 –ySey, and p-Bi2 –x–ySnxGeyTe3 thermoelectrics were studied and its topological characteristics were obtained by scanning tunneling techniques in dependence on compositions. It was shown that the thermoelectric power factor and the material parameter enhance with the shift of the Dirac point to the top of the valence band with the increasing of atomic substitution in these thermoelectrics. A growth contribution of the surface states is determined by an increase of the Fermi velocity for large atomic substitutions of Bi at x > 1.5 and small substitutions in the Te sublattice (y = 0.06). In compositions with smaller substitutions at x = 1–1.3 and y = 0.06–0.09, similar effect of the surface states is determined due to raising the surface concentration of charge carriers.

Topological crystalline insulator state with type-II Dirac fermions in transition metal dipnictides

The interplay between topology and crystalline symmetries in materials can lead to a variety of topological crystalline insulator (TCI) states. Despite significant effort towards their experimental realization, so far only Pb$_{1-x}$Sn$_x$Te has been confirmed as a mirror-symmetry protected TCI. Here, based on first-principles calculations combined with a symmetry analysis, we identify a rotational-symmetry protected TCI state in the transition-metal dipnictide RX$_2$ family, where R = Ta or Nb and X = P, As, or Sb. Taking TaAs$_2$ as an exemplar system, we show that its low-energy band structure consists of two types of bulk nodal lines in the absence of spin-orbit coupling (SOC) effects. Turning on the SOC opens a continuous bandgap in the energy spectrum and drives the system into a $C_2T$-symmetry-protected TCI state. On the (010) surface, we show the presence of rotational-symmetry-protected nontrivial Dirac cone states within a local bulk energy gap of $\sim$ 300 meV. Interestingly, the Dirac cones have tilted energy dispersion, realizing a type-II Dirac fermion state in a topological crystalline insulator. Our results thus indicate that the TaAs$_2$ materials family provides an ideal setting for exploring the unique physics associated with type-II Dirac fermions in rotational-symmetry-protected TCIs.

Quantum phase transition and criticality in quasi-one-dimensional spinless Dirac fermions

We study quantum criticality of spinless fermions on the quasi one dimensional $\pi$-flux square lattice in cylinder geometry, by using the infinite density matrix renormalization group and abelian bosonization. For a series of the cylinder circumferences $L_y=4n+2=2, 6, \cdots$ with the periodic boundary condition, there are quantum phase transitions from gapped Dirac fermion states to charge density wave (CDW) states. We find that the quantum phase transitions for such circumferences are continuous and belong to the (1+1)-dimensional Ising universality class. On the other hand, when $L_y=4n=4, 8, \cdots$, there are gapless Dirac fermions at the non-interacting point and the phase transition to the CDW state is Gaussian. Both of these two criticalities are described in a unified way by the bosonization. We clarify their intimate relationship and demonstrate that a central charge $c=1/2$ Ising transition line arises as a critical state of an emergent Majorana fermion from the $c=2$ Gaussian transition point.

Thermoelectric and Galvanomagnetic Properties of Layered n-Bi2 –xSbxTe3 –ySey Films

The thermoelectric properties in the temperature range 4.2–300 K and magnetoresistance oscillations in strong magnetic fields at low temperatures are studied in nanostructured layered films of topological thermoelectric materials n-Bi2 –xSbxTe3 –ySey. It is shown that the thermoelectric figure of merit in layered n-Bi2 –xSbxTe3 –ySey films is larger than that in the bulk material due both to an increase in the Seebeck coefficient below room temperature and to a decrease in the thermal conductivity and its weaker temperature dependence. Analysis of the magnetoresistance oscillations is used to determine the parameters of the topological surface states of Dirac fermions and estimate their influence on the thermoelectric properties.

Topological Surface States of Dirac Fermions in n-Bi2Te3 –ySey Thermoelectrics

In n-Bi2Te3 and n-Bi2Te3 –ySey thermoelectrics, the surface states of Dirac fermions of the interlayer Van der Waals surface (0001) are studied by scanning tunneling microscopy and spectroscopy. The surface morphology and modulated line profiles of the tunneling microscopy images are determined by local distortions of the surface density of electronic states and depend on the composition. The Dirac point ED in the studied compositions is localized in the band gap and shifts to the top of the valence band with increasing Se content in n-Bi2Te3 –ySey alloys. The dependence between the parameters of the surface states of Dirac fermions (Dirac-point position, Fermi velocity, surface fermion concentration) and thermoelectric properties (Seebeck coefficient and power parameter) in the thermoelectrics under study is determined.

Two-dimensional honeycomb-kagome Ta2S3: a promising single-spin Dirac fermion and quantum anomalous hall insulator with half-metallic edge states.

Recent experimental success in the realization of two-dimensional (2D) magnetism has invigorated the search for new 2D magnetic materials with a large magnetocrystalline anisotropy, high Curie temperature, and high carrier mobility. Using first-principles calculations, here we predict a novel class of single-spin Dirac fermion states in a 2D Ta2S3 monolayer, characterized by a band structure with a large gap in one spin channel and a Dirac cone in the other with carrier mobility comparable to that of graphene. Ta2S3 is dynamically and thermodynamically stable under ambient conditions, and possesses a large out-of-plane magnetic anisotropy energy and a high Curie temperature (TC = 445 K) predicted from the spin-wave theory. When the spin and orbital degrees of freedom are allowed to couple, the Ta2S3 monolayer becomes a Chern insulator with a fully spin-polarized half-metallic edge state. An effective four-band tight-binding model is constructed to clarify the origin of a semi-Dirac cone in a spin-up channel and nontrivial band topology, which can be well maintained on a semiconducting substrate. The combination of these unique single-spin Dirac fermion and quantum anomalous Hall states renders the 2D Ta2S3 lattice a promising platform for applications in topologically high fidelity data storage and energy-efficient spintronic devices.