Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators

In the three-dimensional topological insulator (TI), the physics of doped semiconductors exists literally side-by-side with the physics of ultrarelativistic Dirac fermions. This unusual pairing creates a novel playground for studying the interplay between disorder and electronic transport. In this mini-review, we focus on the disorder caused by the three-dimensionally distributed charged impurities that are ubiquitous in TIs, and we outline the effects it has on both the bulk and surface transport in TIs. We present self-consistent theories for Coulomb screening both in the bulk and at the surface, discuss the magnitude of the disorder potential in each case, and present results for the conductivity. In the bulk, where the band gap leads to thermally activated transport, we show how disorder leads to a smaller-than-expected activation energy that gives way to variable-range hopping at low temperatures. We confirm this enhanced conductivity with numerical simulations that also allow us to explore different degrees of impurity compensation. For the surface, where the TI has gapless Dirac modes, we present a theory of disorder and screening of deep impurities, and we calculate the corresponding zero-temperature conductivity. We also comment on the growth of the disorder potential in passing from the surface of the TI into the bulk. Finally, we discuss how the presence of a gap at the Dirac point, introduced by some source of time-reversal symmetry breaking, affects the disorder potential at the surface and the mid-gap density of states.     

Experimental realization of a three-dimensional topological insulator phase in ternary chalcogenide TlBiSe₂

We report the first observation of a topological surface state on the (111) surface of the ternary chalcogenide TlBiSe? by angle-resolved photoemission spectroscopy. By tuning the synchrotron radiation energy we reveal that it features an almost ideal Dirac cone with the Dirac point well isolated from bulk continuum states. This suggests that TlBiSe? is a promising material for realizing quantum topological transport.     

Electronic states and spin-filter effect in three-dimensional topological insulator Bi_2Se_3 nanoribbons

We study the electronic band structure, density distribution, and transport of a Bi_2Se_3 nanoribbon. We find that the density distribution of the surface states is dependent on not only the shape and size of the transverse cross section of the nanoribbon, but also the energy of the electron. We demonstrate that a transverse electric field can eliminate the coupling between surface states on the walls of the nanoribbon, remove the gap of the surface states, and restore the quantum spin Hall effects. In addition, we study the spin-dependent transport property of the surface states transmitting from top and bottom surfaces(x-y plane) to the side surfaces(z-x plane) of a Bi_2Se_3 nanoribbon. We find that transverse electric fields can open two surface channels for spin-up and-down Dirac electrons, and then switch off one channel for the spin-up Dirac electron. Our results may provide a simple way for the design of a spin filter based on topological insulator nanostructures.     

Three-dimensional topological insulator in a magnetic field: chiral side surface states and quantized Hall conductance

Low energy excitation of surface states of a three-dimensional topological insulator (3DTI) can be described by Dirac fermions. By using a tight-binding model, the transport properties of the surface states in a uniform magnetic field are investigated. It is found that chiral surface states parallel to the magnetic field are responsible for the quantized Hall (QH) conductance (2n + 1)e2/h multiplied by the number of Dirac cones. Due to the two-dimensional nature of the surface states, the robustness of the QH conductance against impurity scattering is determined by the oddness and evenness of the Dirac cone number. An experimental setup for transport measurement is proposed.     

Electronic transport in graphene nanoribbons with disorder look at the pseudo-spin polarization: Dirac versus tight-binding model

We have compared results of electronic transport using two different approaches: Dirac vs tight-binding (TB) Hamiltonians to assesses disorder-induced effects in graphene nanoribbons. We apply the proposed Hamiltonians to calculate the density of states, the transmission along the ribbon, and the pseudo-spin polarization (P(E)) in metallic armchair graphene nanoribbons. We clearly show differences between these two approaches in the interference processes, especially in the low-lying energy limit, when the systems are found in the presence of random impurities (disorder). This allows us to find fingerprints associated with each model used. As the disorder increases, more robust electronic transmission (through polarized states in a given sublattice) arises when one is dealing with the Dirac model only. We also find with this model unexpected peaks in the P(E) far from the Dirac point for wider nanoribbons. In the other hand, the model TB show the Dirac limit with disturbances of the hyperboloid subbands for certain potentials of the impurities. In general, our study is indicating that a P(E) spectroscopy (analyzing the line width and intensity) can be used to detect fingerprints of the increase of asymmetry in the scattering processes and the transport limits where hyperboloid subbands are important.     

Charge transport and shot noise on the surface of a topological insulator with a magnetic modulation

In this paper, we investigate the transport features and the Fano factor of Dirac electrons on the surface of a three-dimensional topological insulator with a magnetic modulation. We consider a hard wall bounding condition on the edge of the topological insulator, which implies that a surface state of the topological insulator is insulating. We find that a valley of conductivity at the Dirac point is associated with a Fano factor peak, and more interestingly, this topological metal changes from insulating to metallic by controlling the effective exchange field.     

In-plane transport and enhanced thermoelectric performance in thin films of the topological insulators Bi₂Te₃ and Bi₂Se₃

Several small-band-gap semiconductors are now known to protect metallic surface states as a consequence of the topology of the bulk electron wave functions. The known "topological insulators" with this behavior include the important thermoelectric materials Bi?Te? and Bi?Se?, whose surfaces are observed in photoemission experiments to have an unusual electronic structure with a single Dirac cone. We study in-plane (i.e., horizontal) transport in thin films made of these materials. The surface states from top and bottom surfaces hybridize, and conventional diffusive transport predicts that the tunable hybridization-induced band gap leads to increased thermoelectric performance at low temperatures. Beyond simple diffusive transport, the conductivity shows a crossover from the spin-orbit-induced antilocalization at a single surface to ordinary localization.     

Electronic structure,Dirac points and Fermi arc surface states in three-dimensional Dirac semimetal Na_3Bi from angle-resolved photoemission spectroscopy

The three-dimensional(3D) Dirac semimetals have linearly dispersive 3D Dirac nodes where the conduction band and valence band are connected. They have isolated 3D Dirac nodes in the whole Brillouin zone and can be viewed as a 3D counterpart of graphene. Recent theoretical calculations and experimental results indicate that the 3D Dirac semimetal state can be realized in a simple stoichiometric compound A_3Bi(A = Na, K, Rb). Here we report comprehensive high-resolution angle-resolved photoemission(ARPES) measurements on the two cleaved surfaces,(001) and(100), of Na_3Bi. On the(001) surface, by comparison with theoretical calculations, we provide a proper assignment of the observed bands, and in particular, pinpoint the band that is responsible for the formation of the three-dimensional Dirac cones. We observe clear evidence of 3D Dirac cones in the three-dimensional momentum space by directly measuring on the k_x–k_y plane and by varying the photon energy to get access to different out-of-plane k_zs. In addition, we reveal new features around the Brillouin zone corners that may be related with surface reconstruction. On the(100) surface, our ARPES measurements over a large momentum space raise an issue on the selection of the basic Brillouin zone in the(100) plane. We directly observe two isolated 3D Dirac nodes on the(100) surface. We observe the signature of the Fermi-arc surface states connecting the two 3D Dirac nodes that extend to a binding energy of ~150 me V before merging into the bulk band. Our observations constitute strong evidence on the existence of the Dirac semimetal state in Na_3Bi that are consistent with previous theoretical and experimental work. In addition, our results provide new information to clarify on the nature of the band that forms the3 D Dirac cones, on the possible formation of surface reconstruction of the(001) surface, and on the issue of basic Brillouin zone selection for the(100) surface.     

Non-Monotonic Evolution of Carrier Density and Mobility under Thermal Cycling Treatments in Dirac Semimetal Cd_3As_2 Microbelts

Tunable carrier density plays a key role in the investigation of novel transport properties in three-dimensional topological semimetals.We demonstrate that the carrier density,as well as the mobility,of Dirac semimetal Cd_3As_2 nanoplates can be effectively tuned via in situ thermal treatment at 350 K for one hour,resulting in non-monotonic evolution by virtue of the thermal cycling treatments.The upward shift of Fermi level relative to the Dirac nodes blurs the surface Fermi-arc states,accompanied by an anomalous phase shift in the oscillations of bulk states,due to a change in the topology of the electrons.Meanwhile,the oscillation peaks of bulk longitudinal magnetoresistivity shift at high fields,due to their coupling to the oscillations of the surface Fermi-arc states.Our work provides a thermal control mechanism for the manipulation of quantum states in Dirac semimetal Cd_3As_2 at high temperatures,via their carrier density.     

Tunable multiple layered Dirac cones in optical lattices

We show that multiple layered Dirac cones can emerge in the band structure of properly addressed multicomponent cold fermionic gases in optical lattices. The layered Dirac cones contain multiple copies of massless spin-1/2 Dirac fermions at the same location in momentum space, whose different Fermi velocity can be tuned at will. On-site microwave Raman transitions can further be used to mix the different Dirac species, resulting in either splitting of or preserving the Dirac point (depending on the symmetry of the on-site term). The tunability of the multiple layered Dirac cones allows us to simulate a number of fundamental phenomena in modern physics, such as neutrino oscillations and exotic particle dispersions with E~p(N) for arbitrary integer N.     

Electrically controllable surface magnetism on the surface of topological insulators

We study theoretically the RKKY interaction between magnetic impurities on the surface of three-dimensional topological insulators, mediated by the helical Dirac electrons. Exact analytical expression shows that the RKKY interaction consists of the Heisenberg-like, Ising-like, and Dzyaloshinskii-Moriya (DM)-like terms. It provides us a new way to control surface magnetism electrically. The gap opened by doped magnetic ions can lead to a short-range Bloembergen-Rowland interaction. The competition among the Heisenberg, Ising, and DM terms leads to rich spin configurations and an anomalous Hall effect on different lattices.     

Electronic structure and transport on the surface of topological insulator attached to an electromagnetic superlattice

We study the electronic structure and transport for Dirac electron on the surface of a three-dimensional (3D) topological insulator attached to an electromagnetic superlattice. It is found that, by means of the transfer-matrix method, the number of electronic tunneling channels for magnetic barriers in antiparallel alignment is larger than that in parallel alignment, which stems to the energy band structures. Interestingly, a remarkable semiconducting transport behavior appears in this system with a strong magnetic barrier due to low energy band nearly paralleling to the Fermi level. Consequently, there is only small incident angle transport in the higher energy region when the system is modulated mainly by the higher electric barriers. We further find that the spatial distribution of the spin polarization oscillates periodically in the incoming region, but it is almost in-plane with a fixed direction in the transmitting region. The results may provide a further understanding of the nature of 3D TI surface states, and may be useful in the design of topological insulator-based electronic devices such as collimating electron beam.     

A special triple point in non-centrosymmetric materials Zn3In2Se6 and In2Se3

We predict that the non-centrosymmetric materials Zn₃In₂Se₆ and In₂Se₃ are the symmetry protected topological critical triple point metals based on first principles calculation. The dispersion along the Γ-Z line almost vanishes because of the particular crystal structure, and the strain along the c direction maybe drives accidental Dirac point to triple point. An effective theory is developed to describe accidental Dirac points and triple points, by which we calculate the surface states. These materials provide us a new platform to discuss the relation between the triple points and Dirac points.     

Electron transport of step-shaped graphene nanoribbon

In this work, we report a theoretical study of the electronic transport through a step-shaped graphene nanoribbon by the tight-binding method. We found that the conductance suppression near the Dirac point is pervasive, and the top boundary configuration is irrelevant; this arises from the antiresonance effect associated with an edge state localized at the transition edge of the top layer of graphene nanoribbon. In addition, the conductance can be easily tuned from zero to unity by a gate bias in the bilayer graphene nanoribbon, this feature will help us to realize the electric nanoswitch.     

拓扑绝缘体的普适电导涨落

拓扑绝缘体因其无能量耗散的拓扑表面输运而备受关注, 揭示拓扑表面态因其 的贝利相位而产生的拓扑输运现象, 将有助于拓扑绝缘体相关器件的应用开发. 本文回顾了普适电导涨落(UCF) 揭示拓扑绝缘体奇异输运性质的研究进展. 通过调控温度、角度、门电压、垂直磁场和平行磁场等外部参量, 实现了对拓扑绝缘体的UCF 效应的系统研究, 证实了拓扑绝缘体中二维UCF 的输运现象, 并通过尺寸标度规律获得了UCF 的拓扑起源的实验证据, 讨论了拓扑表面态的UCF 的统计对称规律. 从而实现了对拓扑绝缘体UCF 效应的较为完整的理解.     

Ferromagnetic-insulators-modulated transport properties on the surface of a topological insulator

Transport properties on the surface of a topological insulator （TI） under the modulation of a two-dimensional （2D） ferromagnet/ferromagnet junction are investigated by the method of wave function matching. The single ferromagnetic barrier modulated transmission probability is expected to be a periodic function of the polarization angle and the planar rotation angle, that decreases with the strength of the magnetic proximity exchange increasing. However, the transmission probability for the double ferromagnetic insulators modulated n-n junction and n-p junction is not a periodic function of polarization angle nor planar rotation angle, owing to the combined effects of the double ferromagnetic insulators and the barrier potential. Since the energy gap between the conduction band and the valence band is narrowed and widened respectively in ranges of 0 ≤ 0 〈π/2 and r/2 〈 0 ≤ π, the transmission probability of the n-n junction first increases rapidly and then decreases slowly with the increase of the magnetic proximity exchange strength. While the transmission probability for the n-p junction demonstrates an opposite trend on the strength of the magnetic proximity exchange because the band gaps contrarily vary. The obtained results may lead to the possible realization of a magnetic/electric switch based on TIs and be useful in further understanding the surface states of TIs.     

The Egorov theorem for transverse Dirac-type operators on foliated manifolds

Egorov’s theorem for transversally elliptic operators, acting on sections of a vector bundle over a compact foliated manifold, is proved. This theorem relates the quantum evolution of transverse pseudodifferential operators determined by a first-order transversally elliptic operator with the (classical) evolution of its symbols determined by the parallel transport along the orbits of the associated transverse bicharacteristic flow. For a particular case of a transverse Dirac operator, the transverse bicharacteristic flow is shown to be given by the transverse geodesic flow and the parallel transport by the parallel transport determined by the transverse Levi-Civita connection. These results allow us to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations.