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Register a new userA Two-dimensional Dirac fermion microscope
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Peter B{\\o}ggild Peter B{\\o}ggild
Publication date
2017
fields
Physics
and research's language is
English
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The electron microscope has been a powerful, highly versatile workhorse in the fields of material and surface science, micro and nanotechnology, biology and geology, for nearly 80 years. The advent of two-dimensional materials opens new possibilities for realising an analogy to electron microscopy in the solid state. Here we provide a perspective view on how a two-dimensional (2D) Dirac fermion-based microscope can be realistically implemented and operated, using graphene as a vacuum chamber for ballistic electrons. We use semiclassical simulations to propose concrete architectures and design rules of 2D electron guns, deflectors, tunable lenses and various detectors. The simulations show how simple objects can be imaged with well-controlled and collimated in-plane beams consisting of relativistic charge carriers. Finally, we discuss the potential of such microscopes for investigating edges, terminations and defects, as well as interfaces, including external nanoscale structures such as adsorbed molecules, nanoparticles or quantum dots.
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Scanning tunneling microscopy and spectroscopy have been used to investigate the femtosecond dynamics of Dirac fermions in the topological insulator Bi$_2$Se$_3$ ultrathin films. At two-dimensional limit, bulk electrons becomes quantized and the quantization can be controlled by film thickness at single quintuple layer level. By studying the spatial decay of standing waves (quasiparticle interference patterns) off steps, we measure directly the energy and film thickness dependence of phase relaxation length $l_{phi}$ and inelastic scattering lifetime $tau$ of topological surface-state electrons. We find that $tau$ exhibits a remarkable $(E-E_F)^{-2}$ energy dependence and increases with film thickness. We show that the features revealed are typical for electron-electron scattering between surface and bulk states.
We obtain exact solutions to the two-dimensional (2D) Dirac equation for the one-dimensional Poschl-Teller potential which contains an asymmetry term. The eigenfunctions are expressed in terms of Heun confluent functions, while the eigenvalues are determined via the solutions of a simple transcendental equation. For the symmetric case, the eigenfunctions of the supercritical states are expressed as spheroidal wave functions, and approximate analytical expressions are obtained for the corresponding eigenvalues. A universal condition for any square integrable symmetric potential is obtained for the minimum strength of the potential required to hold a bound state of zero energy. Applications for smooth electron waveguides in 2D Dirac-Weyl systems are discussed.
Three dimensional (3D) Dirac semimetals which can be seen as 3D analogues of graphene have attracted enormous interests in research recently. In order to apply these ultrahigh-mobility materials in future electronic/optoelectronic devices, it is crucial to understand the relaxation dynamics of photoexcited carriers and their coupling with lattice. In this work, we report ultrafast transient reflection measurements of the photoexcited carrier dynamics in cadmium arsenide (Cd3As2), which is one of the most stable Dirac semimetals that have been confirmed experimentally. By using low energy probe photon of 0.3 eV, we probed the dynamics of the photoexcited carriers that are Dirac-Fermi-like approaching the Dirac point. We systematically studied the transient reflection on bulk and nanoplate samples that have different doping intensities by tuning the probe wavelength, pump power and lattice temperature, and find that the dynamical evolution of carrier distributions can be retrieved qualitatively by using a two-temperature model. This result is very similar to that of graphene, but the carrier cooling through the optical phonon couplings is slower and lasts over larger electron temperature range because the optical phonon energies in Cd3As2 are much lower than those in graphene.
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. textbf{115}, 126803 (2015)] 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$cdot$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.
Two-dimensional Dirac semimetals have attracted much attention because of their linear energy dispersion and non-trivial Berry phase. Graphene-like 2D Dirac materials are gapless only within certain approximations, e.g., if spin-orbit coupling (SOC) is neglected. It has recently been reported that materials with nonsymmorphic crystal lattice possess symmetry-enforced Dirac-like band dispersion around certain high-symmetry momenta even in the presence of SOC. Here we calculate the optical absorption coefficient of nonsymmorphic semimetals, such as $alpha$-bismuthene, which hosts two anisotropic Dirac cones with different Fermi velocities along $x$ and $y$ directions.We find that the optical absorption coefficient depends strongly on the anisotropy factor and the photon polarization. When a magnetic field is applied perpendicular to the plane of the material, the absorption coefficient also depends on an internal parameter we termed the mixing angle of the band structure. We further find that an in-plane magnetic field, while leaving the system gapless, can induce a Van-Hove singularity in the joint density of states: this causes a significant enhancement of the optical absorption at the frequency of the singularity for one direction of polarization but not for the orthogonal one, making the optical properties even more strongly dependent on polarization. Due to the anisotropy present in our model, the Dirac cones at two high-symmetry momenta in the Brillouin zone contribute very differently to the optical absorbance. Consequently, it might be possible to preferentially populate one valley or the other by varying photon polarization and frequency. These results suggest that nonsymmorphic 2D Dirac semimetals are excellent candidate materials for tunable magneto-optic devices.
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