Intertwined Rashba, Dirac, and Weyl Fermions in Hexagonal Hyperferroelectrics

Abstract

By means of density functional theory based calculations, we study the role of spin-orbit coupling in the new family of ABC hyperferroelectrics [Phys. Rev. Lett. 112, 127601 (2014)]. We unveil an extremely rich physics strongly linked to ferroelectric properties, ranging from the electric control of bulk Rashba effect to the existence of a three dimensional topological insulator phase, with concomitant topological surface states even in the ultrathin film limit. Moreover, we predict that the topological transition, as induced by alloying, is followed by a Weyl semi-metal phase of finite concentration extension, which is robust against disorder, putting forward hyperferroelectrics as promising candidates for spin-orbitronic applications. Introduction. Spin-orbit coupling (SOC) is a relativistic interaction that gives rise to a rich variety of interesting phenomena in solid state physics, ranging from topological quantum phases of matter to Rashba/Dresselhaus-like spin splitting effects. In the former case, fully spin-polarized massless Dirac fermions appear at the surface of topological insulators (TIs), showing protected metallic surface states despite their bulk insulating character [1,2]. In the latter case, which is realized at surfaces or interfaces as due to a structural inversion asymmetry of the confinment potential or in non-centrosymmetric materials, spin-splitting effects on the bands of massive fermions appear, which may ultimately give rise to a spin-Hall effect. [3,4] The presence of strong spin-momentum locking in both systems allows, in principle, for an all-electric control of the electron spins, putting forward these material systems as ideal candidates for new spintronic applications.

Two-dimensional ferroelectric topological insulators in functionalized atomically thin bismuth layers

“…Ferroelectricity is an intriguing quantum phenomenon in materials possessing switchable spontaneous polarization. In insulators with strong SOC and inversion asymmetry in the crystal structures, interesting ferroelectric Rashba behaviour can be observed [21][22][23],…”

“…Recent studies of GeTe [22] and tin iodide perovskite (FA)SnI 3 [26] have shown that the combination of ferroelectricity and SOC leads to a giant Rashba effect with a tunable spin texture via ferroelectric switch [27]. These so called ferroelectric Rashba semiconductors (FERSC) [27] have been also found in ABC hyper-ferroelectrics (A=Li, Na, K; B=Be, Mg, Ca; C=Sb, Bi) [21,23,28]. While FERSCs are normal semiconductors, the associated findings raise the intriguing prospects of having SOC induced band inversion to accompany the ferroelectric polarization in some properly constructed materials.…”

Strain-tunable ferroelectricity and its control of Rashba effect in KTaO3

“…9 The similar phenomenon was also reported in other FE materials. [10][11][12][13][14] In this regard, the FE Rashba semiconductors or insulators as a kind of novel multifunctional materials 15 can be used to design new types of devices, such as nonvolatile spin-fieldeffect transistor 9,16 and ferroelectric tunnel junctions. [17][18][19] It would be beneficial to find FE Rashba materials with both large polarization and strong spin-orbit coupling (SOC) for realization of controlling the spin via an electric field.…”

Antiferroelectric Topological Insulators in Orthorhombic AMgBi Compounds ( A=Li , Na, K)

“…These unconventional properties have led to a plethora of proposals for the use of topological materials in fundamental research spanning from magnetic monopoles [4] to Majorana fermions [5], and in applications such as fault-tolerant quantum computers. In this context, an innovative route towards the control of topological order is by means of electric fields [6][7][8][9][10][11][12].A promising direction to control topological order with an electric field is to utilize ferroelectric materials that harbor topological states. Ferroelectrics exhibit two states of opposite polarity (P) that can be controlled by an electric field (E) as shown schematically in Fig.…”

“…The two polarization states in these ferroelectric topological insulators could be used, for example, to create spin-selected collimated electron beams [11] or to control the spin texture around the Dirac cones of the surface states [12]. Several materials have been proposed to exhibit these properties: superlattice combinations of the ferroelectric material GeTe and the topological insulator Sb 2 Te 3 exhibit electric field control of topological order [8]; strained LiZnSb and CsPbI 3 are candidate ferroelectric topological insulators [10,11]; and ferroelectricity and topological order coexist in some ABC hyperferroelectrics, which could be candidates for thin-film applications [12].In this work we explore the possibility of controlling topological order in antiferroelectric materials, which exhibit an antipolar ground state and two polar states that can be accessed using an electric field, as shown schematically in Fig. 1b.…”