Dimensional Topological Insulators Research Articles

Emerging Dirac materials for THz plasmonics

Terahertz (THz) photonics is a key-enabling technology for a wealth of urgently demanding applications and societal challenges like ultrahigh speed communication systems, medical imaging and diagnostics, industrial and food quality control, and security screening. Therefore, making novel THz materials, that are able to effectively interact and manipulate THz radiation, is a challenge in this respect. Dirac materials that are endowed with linearly dispersed electronic bands, are a promising frontier in this framework as they are suited to generate plasmon resonances in the THz regime. Dirac materials include the well-known cases of graphene and three dimensional topological insulators. In perspective they can be extended to new emerging materials including graphene-like Xenes (from silicene to bismuthene) and Weyl/Dirac semimetals. In addition to the materials aspects, in this perspective review we deliberately single out an easy framework where to validate Dirac materials for THz applications. This one includes the optical conductivity deduced by THz spectroscopy as a good figure of merit, and the micro-ribbon pattern as a good plasmonic grating. In the end, we outline future challenges and current bottlenecks in the production and exploitation of Dirac materials in the THz technology.

Spin polarization in nanojunctions of quantum anomalous Hall insulators

We theoretically investigate spin polarized conductance through nanojunctions made by magnetic domains in a thin films of three dimensional ferromagnetic topological insulator (TI) as a quantum anomalous Hall insulator. Writing of magnetic domains is now feasible in recent experiments. Ferromagnetism induced in such materials can control topological phase of the band structure and as consequence, configuration of the states in each band. By means of band analysis, it is demonstrated that in topologically non-trivial bands with non-zero Chern number, there exists a change in spin dominant states among Brillouin zone while spin polarization of trivial bands shows dominant of one spin type. Indeed, there is an interplay between topological invariant of the band spectrum and contribution of the spin states in conductance. We show that in-plane magnetization or structure inversion asymmetry result in a k-dependent parity configuration of surface states in ultrathin film topological insulator. In the conduction and valence bands, a nearly perfect spin polarized conductance is found in a nanojunction composed of anti-parallel magnetic domains which is mediated by a layer under application of in-plane magnetization or perpendicular applied bias. This spin polarized region is extendable with the magnetization. To the sake of completeness, proposed polarization in conductance was also supported by interpretation based on spin and parity local density of states along the interfaces of magnetic domain walls. Analysis of the spin-parity states sheds light to the quantum transport through magnetically doped TI thin-film’s nanojunctions with different mass terms.

Dirac Materials in a MatrixWay

Recent years have been the platform of discovery of a wide range of materials, like d-wave superconductors, graphene, and topological insulators. These materials do indeed share a fundamental similarity in their low-energy spectra namely the fermionic excitations. There carriers behave as massless Dirac particles rather than conventional fermions that obey the usual Schrodinger Hamiltonian. A surprising aspect of most Dirac materials is that many of their physical properties measured in experiments can be understood at the non-interacting level. In spite of the large effective coupling constant in case of graphene, it has been observed that the interactions do not seem to play a major key role. Controlling the electrons at Dirac nodes in the first Brillouin zone needs the interplay of sublattice symmetry, inversion symmetry and the time-reversal symmetry. In this article, we have used explicit fundamental symmetry to understand the basic features of Dirac materials occurring in three diverse systems in a compact 2 × 2 matrix way. Furthermore, the robustness of the Dirac cones has also been explored from the scientific notion of topological physics. In addition, an elementary introduction on the three dimensional (3D) topological insulators and d wave superconductors will shed light in their respective fields. Furthermore, we have also discussed the way to evaluate the effective mass tensor of the carriers in the two dimensional (2D) Dirac materials. This methodology has also been critically extended to three dimensional (3D) topological insulators and d wave superconductors.

Quantum oscillations in nanowires of topological insulator Bi0.83Sb0.17

Three dimensional topological insulators (TIs) are novel materials with a conducting surface covering an insulating bulk interior. We examine the topological properties of nanowires of TI Bi0.83Sb0.17 and observed that they display oscillations of the magnetoresistance (MR) that can be interpreted as topological surface electronic transport. In this work, we study the nanowires at various magnetic field orientations, at low temperatures (1.5 K ≤ T < 5 K), and for field strengths up to 14 T. In the 4 T < B < 10 T range we observe B-periodic, Aharonov–Bohm (AB) oscillations of longitudinal MR with two periods, namely, one flux quantum Φ0 and half of flux quantum Φ0/2 (ΔB1 = Φ0/S, ΔB2 = Φ0/2S, where S is the cross-sectional area of the nanowire). The periods depend on the angle α between the magnetic field and the wire axis according to a cosine law that indicates that the phenomenon is governed by the axial flux enclosed by the nanowire. In additional to the high magnetic field oscillations, in the low magnetic field range, B < 4 T, we observe a conductance maximum for zero magnetic field and the first magnetoresistance maximum for Φ = Φ0/2.

Predicting quantum spin hall effect in graphene/GaSb and normal strain-controlled band structures

Graphene (Gr) has been demonstrated to be a two dimensional (2D) topological insulator (TI) with an opened spin–orbit coupling (SOC) energy gap at Dirac point. The extremely small energy gap, however, makes the predicted quantum spin Hall (QSH) effect difficult to be observed at room temperature. In present work, we propose an effective way to tune the energy gap of Gr by combining with GaSb. The intrinsic bulk gap of Gr reaches up to 125 meV and 116 meV in Gr/(Ga)Sb and Gr/Ga(Sb), respectively, which makes it available in practical applications. Moreover, the energy gap of Gr can be opened and increased to 147 meV in GaSb/Gr/GaSb by hydrogen passivation. The inverted band ordering and gapless edge states further demonstrate that our considered heterostructures possess QSH effect. Normal strain engineering leads to effective control and substantial enhancement of their energy gap and band inversion. Hexagonal boron nitride (h-BN) is also verified to be a suitable substrate to supporting films without destroying their QSH effect. Our results provide feasible platform to design Gr-based spintronics devices.

Quantum spin Hall effect, thermoelectric performance, and optical properties of XBi (X = Sc, Y) monolayers

Abstract The investigations of quantum spin Hall effect and the edge states manipulation of two dimensional topological insulators are very salient for the practical applications and fundamental sciences. The high thermoelectric efficiency of these materials has also been confirmed, recently. So, in this study the first-principles calculations are implemented based on density functional theory in the presence of spin orbit interaction, to evaluate the topological phase transition and thermoelectric performance of XBi (X = Sc, Y) monolayers under in-plane strains. It is found that the compressive in-plane strains and spin orbit interaction, which host considerable effects on the electronic structure, can cause the topologically nontrivial phase and high thermoelectric performance. The topological state of XBi monolayers is confirmed with the Z2 topological invariant calculation. These results provide these monolayers for the novel thermoelectric and nanoelectronics quantum devices and topological phenomena. Also some optical properties of XBi monolayers are calculated and investigated under in-plane strains. The results show the considerable transparency and reflectivity of these monolayers near zero energy.

Thermodynamics of a higher-order topological insulator

We investigate the order of the topological quantum phase transition in a two dimensional quadrupolar topological insulator within a thermodynamic approach. Using numerical methods, we separate the bulk, edge and corner contributions to the grand potential and detect different phase transitions in the topological phase diagram. The transitions from the quadrupolar to the trivial or to the dipolar phases are well captured by the thermodynamic potential. On the other hand, we have to resort to a grand potential based on the Wannier bands to describe the transition from the trivial to the dipolar phase. The critical exponents and the order of the phase transitions are determined and discussed in the light of the Josephson hyperscaling relation.

Chiral Hall effect in the kink states in topological insulators with magnetic domain walls

In this article we consider the chiral Hall effect due to topologically protected kink states formed in topological insulators at boundaries between domains with differing topological invariants. Such systems include the surfaces of three dimensional topological insulators magnetically doped or in proximity with ferromagnets, as well as certain two dimensional topological insulators. We analyze the equilibrium charge current along the domain wall and show that it is equal to the sum of counter-propagating equilibrium currents flowing along external boundaries of the domains. In addition, we also calculate a dissipative current along the domain wall when an external voltage is applied perpendicularly to the wall.

Giant photoinduced anomalous Hall effect of the topological surface states in three dimensional topological insulators Bi2Te3

Topological insulators (TIs) are considered as ideal spintronic materials due to the spin-momentum-locked Dirac surface states. The photoinduced anomalous Hall effect (PAHE) is a powerful tool to investigate the spin Hall effect of topological insulators even at room temperature. In this Letter, the PAHE has been observed in three dimensional topological insulator Bi2Te3 thin films grown on Si substrates at room temperature. As the thickness of the Bi2Te3 films increases from 3 to 20 quintuple layer (QL), the PAHE first increases and then decreases, and it reaches a maximum at 7 QL. The sign reversal of the PAHE of the 3 QL sample after oxidation reveals that the PAHE of the Bi2Te3 thin films is dominated by the top surface states, which is further confirmed by the circular photogalvanic effect under front and back illuminations. The photoinduced anomalous Hall conductivity excited by 1064 nm light is as large as 5.28 nA V−1 W−1 cm2 in the 7 QL sample, much larger than that observed in InGaAs/AlGaAs quantum wells (0.445 nA V−1 W−1 cm2) and GaN/AlGaN heterostructures (0.143 nA V−1 W−1 cm2). By comparing the PAHE current excited by 1064 nm with that excited by 1342 nm, we reveal that the tremendous PAHE excited by 1064 nm light is due to the modulation effect of spin injection from Si substrates. The giant PAHE value observed in TI Bi2Te3 may offer spintronic applications of TIs such as high-efficient light-polarization-state detectors.

High thermoelectric efficiency of LaX (X = Sb, Bi) two dimensional topological insulators

Topological insulators with novel surfaces or edge states are the topological nature sequel of bulk electronic wave functions of these materials. The observed signatures in the electronic structure of topological insulators can make them excellent candidates for thermoelectric materials. Low dimensional materials such as phosphorene and Bi2Te3 nanowire have been confirmed to be desirable for the design of devices with high thermoelectric performance. So in this work, the phonon modes, formation energy and cohesive energy of LaX (X = Sb, Bi) monolayers are first calculated and investigated. Then the band order of these monolayers is investigated by the band structure calculations and the topological phase of these monolayers is proved by using the calculation of Z2 topological invariant. The energy band gap and the band inversion strength of these monolayers are evaluated under in-plane strains. Also, the effect of different temperatures and in-plane strains on the thermoelectric performance of LaX monolayers is studied. The results show the high thermoelectric efficiency and d-p topological band inversion of these monolayers under compressive strains.

Fermionic tensor networks for higher-order topological insulators from charge pumping

We apply the charge pumping argument to fermionic tensor network representations of d-dimensional topological insulators (TIs) to obtain tensor network states for (d+1)-dimensional TIs. We exemplify the method by constructing a two-dimensional projected entangled pair states (PEPS)for a Chern insulator starting from a matrix product state (MPS) in d=1 describing pumping in the Su-Schrieffer-Heeger (SSH) model. In extending the argument to second-order TIs, we build a three-dimensional TNS for a chiral hinge TI from a PEPS in d=2 for the obstructed atomic insulator (OAI) of the quadrupole model. The (d+1)-dimensional TNSs obtained in this way have a constant bond dimension inherited from the d-dimensional TNSs in all but one spatial direction, making them candidates for numerical applications. From the d-dimensional models, we identify gapped next-nearest neighbour Hamiltonians interpolating between the trivial and OAI phases of the fully dimerized SSH and quadrupole models, whose ground states are given by an MPS and a PEPS with a constant bond dimension equal to 2, respectively.

Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators

This paper establishes a general proof of bulk-hinge correspondence in inversion-symmetric insulators. By continuously introducing a cut to a three dimensional second order topological insulator, the resulting spectral flow reflects parities of the bulk eigenstates, necessarily leading to band inversions through this cutting procedure. As a result, it is shown that a two dimensional slab of a three dimensional second-order topological insulator is always a two-dimensional Chern insulator.

Transport in two-dimensional Rashba electron systems doped with interacting magnetic impurities

We study the transport properties of two dimensional electron systems with strong Rashba spin-orbit coupling (SOC) doped with interacting magnetic impurities. Interactions between magnetic impurities cause the formation of magnetic clusters with temperature dependent mean sizes (CMSs) distributed randomly on the surface of the system. Treating magnetic clusters as scattering centers, by employing a generalized relaxation time approximation we obtain the non-equilibrium distribution functions of Rashba electrons in both regimes of above and below the band-crossing point (BCP) and present the explicit forms of the conductivity in terms of effective relaxation times. We demonstrate that the combined effects of SOC and magnetic clusters cause the system to be anisotropic and the magneto-resistance strongly depends on both the clusters' mean size and spin, the strengths of SOC and the location of Fermi energy with respect to the BCP. Our results show that there are many contrasts between the transport properties of the system in the two regimes of above and below the BCP. By comparing the anisotropic magneto-resistance (AMR) of the two dimensional Rashba systems with the surface AMR of three dimensional magnetic topological insulators, we also point out the differences between these systems.

Ultrahigh Stability 3D TI Bi2Se3/MoO3 Thin Film Heterojunction Infrared Photodetector at Optical Communication Waveband

AbstractInfrared (IR) detection at 1300–1650 nm (optical communication waveband) is of great significance due to its wide range of applications in commerce and military. Three dimensional (3D) topological insulator (TI) Bi2Se3 is considered a promising candidate toward high‐performance IR applications. Nevertheless, the IR devices based on Bi2Se3 thin films are rarely reported. Here, a 3D TI Bi2Se3/MoO3 thin film heterojunction photodetector is shown that possesses ultrahigh responsivity (Ri), external quantum efficiency (EQE), and detectivity (D*) in the broadband spectrum (405–1550 nm). The highest on–off ratio of the optimized device can reach up to 5.32 × 104. Ri, D*, and the EQE can reach 1.6 × 104 A W−1, 5.79 × 1011 cm2 Hz1/2 W−1, and 4.9 × 104% (@ 405 nm), respectively. Surprisingly, the Ri can achieve 2.61 × 103 A W−1 at an optical communication wavelength (@ 1310 nm) with a fast response time (63 µs), which is two orders of magnitude faster than that of other TIs‐based devices. In addition, the device demonstrates brilliant long‐term (&gt;100 days) environmental stability under environmental conditions without any protective measures. Excellent device photoelectric properties illustrate that the 3D TI/inorganic heterojunction is an appropriate way for manufacturing high‐performance photodetectors in the optical communication, military, and imaging fields.

Quasiperiodic dynamical quantum phase transitions in multiband topological insulators and connections with entanglement entropy and fidelity susceptibility

We investigate the Loschmidt amplitude and dynamical quantum phase transitions in multiband one dimensional topological insulators. For this purpose we introduce a new solvable multiband model based on the Su-Schrieffer-Heeger model, generalized to unit cells containing many atoms but with the same symmetry properties. Such models have a richer structure of dynamical quantum phase transitions than the simple two-band topological insulator models typically considered previously, with both quasiperiodic and aperiodic dynamical quantum phase transitions present. Moreover the aperiodic transitions can still occur for quenches within a single topological phase. We also investigate the boundary contributions from the presence of the topologically protected edge states of this model. Plateaus in the boundary return rate are related to the topology of the time evolving Hamiltonian, and hence to a dynamical bulk-boundary correspondence. We go on to consider the dynamics of the entanglement entropy generated after a quench, and its potential relation to the critical times of the dynamical quantum phase transitions. Finally, we investigate the fidelity susceptibility as an indicator of the topological phase transitions, and find a simple scaling law as a function of the number of bands of our multiband model which is found to be the same for both bulk and boundary fidelity susceptibilities.

Topological phase transition and tunable electronic properties of hydrogenated bismuthene: from single-layer to double-layer

Planar bismuthene grown on SiC substrate provides a promising candidate to engineer van der Waals double-layer (DL) made of two dimensional (2D) topological insulators. We perform systematical calculations in DL hydrogenated bismuthene (H-Bi) that can be used to simulate the experimentally grown planar bismuthene to explore realizable 2D topological insulator van der Waals DL. Two possible geometry configurations of AA- and AB-stacked DL H-Bi are investigated. Due to pseudo Jahn-Teller effect, AB-stacked DL H-Bi has a strong interlayer coupling interaction and shows buckled lattice. Particularly, both AA- and AB-stacked DL H-Bi are topologically trivial rather than topologically nontrivial. The physical origin of the trivial topology is clarified by analyzing orbital composition. We discuss how the electronic properties are modified by interlayer coupling, external strain, and metal atom intercalation. It is also found that, for AB-stacked DL H-Bi, metal atom intercalation gives rise to novel multiple Rashba splitting near the valence band top, which is expected to manipulate the same spin in different planar bismuthene layers. Our results present various and tunable electronic properties of van der Waals DL H-Bi and allow for probing into multiple Rashba effect in 2D inversion-asymmetric topological insulators.

THz photodetector using sideband-modulated transport through surface states of a 3D topological insulator

The transport properties of the surface charge carriers of a three dimensional topological insulator under a terahertz (THz) field along with a resonant double barrier structure is theoretically analyzed within the framework of Floquet theory to explore the possibility of using such a device for photodetection purposes. We show that due to the contribution of elastic and inelastic scattering processes in the resulting transmission, side-bands are formed in the conductance spectrum. This side band formation is similar to the side-bands formation in cavity transmission spectra in an optical cavity and this information can be used to detect the frequency of unknown THz radiation. The dependence of the conductance on the bias voltage, the effect of THz radiation on resonances and the influence of zero energy points on the transmission spectrum are also discussed.

Unconventional Josephson junctions with topological Kondo insulator weak links

Proximity-induced superconductivity in three dimensional (3D) topological insulators forms a new quantum phase of matter and accommodates exotic quasiparticles such as Majorana bound states. One of the biggest drawbacks of the commonly studied 3D topological insulators is the presence of conducting bulk that obscures both surface states and low energy bound states. Introducing superconductivity in topological Kondo insulators such as SmB$_6$, however, is promising due to their true insulating bulk at low temperatures. In this work, we develop an unconventional Josephson junction by coupling superconducting Nb leads to the surface states of a SmB$_6$ crystal. We observe a robust critical current at low temperatures that responds to the application of an out-of-plane magnetic field with significant deviations from usual Fraunhofer patterns. The appearance of Shaphiro steps under microwave radiation gives further evidence of a Josephson effect. Moreover, we explore the effects of Kondo breakdown in our devices, such as ferromagnetism at the surface and anomalous temperature dependence of supercurrent. Particularly, the magnetic diffraction patterns show an anomalous hysteresis with the field sweep direction suggesting the coexistence of magnetism with superconductivity at the SmB$_6$ surface. The experimental work will advance the current understanding of topologically nontrivial superconductors and emergent states associated with such unconventional superconducting phases.

Temperature and excitation wavelength dependence of circular and linear photogalvanic effect in a three dimensional topological insulator Bi2Se3

The circular (CPGE) and linear photogalvanic effect (LPGE) of a three-dimensional topological insulator Bi2Se3 thin film of seven quintuple layers excited by near-infrared (1064 nm) and mid-infrared (10.6 m) radiations have been investigated. The comparison of the CPGE current measured parallel and perpendicular to the incident plane, together with the comparison of the CPGE current under front and back illuminations, indicates that the CPGE under front illumination of 1064 nm light is dominated by the top surface states of the Bi2Se3 thin film. The CPGE current excited by 10.6 m light is about one order larger than that excited by 1064 nm light, which may be attributed to the smaller cancelation effect of the CPGE generated in the two-dimensional electron gas when excited by 10.6 m light. Under the excitation of 1064 nm light, the LPGE current is dominated by the component which shows an even parity of incident angles, while the LPGE current excited by 10.6 m light is mainly contributed by the component which is an odd parity of incident angles. Both of the CPGE and LPGE currents excited by 1064 nm decrease with increasing temperature, which may be owing to the decrease of the momentum relaxation time and the stronger electron–electron scattering with increasing temperature, respectively.

Topological vortex phase transitions in iron-based superconductors

We study topological vortex phases in iron-based superconductors. Besides the previously known vortex end Majorana zero modes (MZMs) phase stemming from the existence of a three dimensional (3D) strong topological insulator state, we show that there is another topologically nontrivial phase as iron-based superconductors can be doped superconducting 3D weak topological insulators (WTIs). The vortex bound states in a superconducting 3D WTI exhibit two different types of quantum states, a robust nodal superconducting phase with pairs of bulk MZMs and a full-gap topologically nontrivial superconducting phase which has single vortex end MZM in a certain range of doping level. Moreover, we predict and summarize various topological phases in iron-based superconductors, and find that carrier doping and interlayer coupling can drive systems to have phase transitions between these different topological phases.