The study of topological insulators has generally involved search of materials that have this property as an innate quality, distinct from normal insulators. Here we focus on the possibility of converting a normal insulator into a topological one by application of an external electric field that shifts different bands by different energies and induces a specific band inversion, which leads to a topological state. Phosphorene is a two-dimensional (2D) material that can be isolated through mechanical exfoliation from layered black phosphorus, but unlike graphene and silicene, single-layer phosphorene has a large band gap (1.5-2.2 eV). Thus, it was unsuspected to exhibit band inversion and the ensuing topological insulator behavior. Using first-principles calculations with applied perpendicular electric field F⊥ on few-layer phosphorene we predict a continuous transition from the normal insulator to a topological insulator and eventually to a metal as a function of F⊥. The tuning of topological behavior with electric field would lead to spin-separated, gapless edge states, that is, quantum spin Hall effect. This finding opens the possibility of converting normal insulating materials into topological ones via electric field and making a multifunctional "field effect topological transistor" that could manipulate simultaneously both spin and charge carrier. We use our results to formulate some design principles for looking for other 2D materials that could have such an electrical-induced topological transition.

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We proposed that the simultaneous presence of both Rashba and band inversion can lead to a Rashba-like spin-splitting formed by two bands with the same in-plane helical spin texture. Because of this unconventional spin texture, the backscattering is forbidden in edge and bulk conductivity channels. We propose a new non-centrosymmetric honeycomb-lattice quantum spin Hall (QSH) insulator family formed by the IV, V, and VII elements with this property. The system formed by Bi, Pb and I atoms is mechanically stable and has both a large Rashba spin-splitting of 60 meV and a large nontrivial band gap of 0.14 eV. Since the edge and the bulk states are protected by the TR symmetry, contrary to what happens in most doped QSH insulators, the bulk states do not contribute to the backscattering in the electronic transport, allowing the construction of a spintronic device with less energy loss. The main objective of spintronics is to understand the mechanisms by which it is possible to achieve efficient control of both spin configurations and spin currents [1,2]. In the last decade, the way to achieve this objective has experienced a breakthrough due to i ) the discovery and understanding of mechanisms to generate spin currents in conductors with magnetic order and in paramagnetic conductors/semiconductors [3][4][5], ii ) the experimental observation of theoretically proposed spin injector systems [6][7][8], and iii ) the synthesis of 2D materials with long spin relaxation time [1,9]. The generation of spin currents, spin injections and spin conservation are mediated by the spin-orbit coupling (SOC) mainly via Rashba effect and/or nontrivial topological phases [10][11][12][13], such as the quantum spin Hall (QSH) effect [14]. Therefore, the search for systems experiencing these properties is a primary concern for the development of spintronics.QSH insulators support helical metallic edge states, forming topological Dirac fermions protected by the timereversal (TR) symmetry on an insulating bulk [6,7]. The topological transition from trivial insulating to topological insulators is evidenced as a band inversion at the TR invariant k-point mediated by the SOC. The topological band dispersion has been experimentally characterized via angle-resolved photoemission spectroscopy (ARPES) and local scanning tunneling microscopy (STM) in 3D topological insulators [6], and via transport measurements in HgTe/CdTe quantum wells [15,16]. On the other hand, the Rashba effect, arising from the lack of inversion symmetry, leads to parallel spin-polarized band dispersion curves with opposite in-plane chiral spin texture [17], allowing the control of the spin direction through an electric field [10,12,13]. These dispersion curves and Fermi contours have been characterized by spectroscopic measurements for many surfaces and interfaces [18][19][20][21]. Large Rashba spin-splitting are found in materials formed by heavy elements with strong intrinsic SOC such as Bi, Pb, W, among others [21][22][23][24][25]. In this work, we look at the consequence...

Stable oxide topological insulators (TIs) have been sought for years, but none have been found; whereas heavier (selenides, tellurides) chalcogenides can be TIs. The basic contradiction between topological insulation and thermo dynamic stability is pointed out, offering a narrow window of opportunity. The electronic motif is first identified and can achieve topological band inversion in ABO 3 as a lonepair, electronrich B atom (e.g., Te, I, Bi) at the octahedral site. Then, twelve ABO 3 compounds are designed in the assumed cubic perovskite structure, which satisfy this electronic motif and are indeed found by density function theory calculations to be TIs. Next, it is illustrated that poorly screened ionic oxides with large inversion energies undergo energy lowering atomic distortions that destabilize the cubic TI phase and remove band inversion. The coexistence windows of topological band inversion and structure stability can nevertheless be expanded under moderate pressures (15 and 35 GPa, respectively, for BaTeO 3 and RbIO 3 ). This study traces the principles needed to design stable oxide topological insulators at ambient pressures as a) a search for oxides with small inversion energies; b) design of large inversionenergy oxide TIs that can be stabilized by pressure; and c) a search for covalent oxides where TIremoving atomic displacements can be effectively screened out.