Magnetic-field-induced topological phase transition in Fe-doped (Bi,Sb)2Se3 heterostructures

Abstract

Three-dimensional topological insulators (3D-TIs) possess a specific topological order of electronic bands, resulting in gapless surface states via bulk-edge correspondence.Exotic phenomena have been realized in ferromagnetic TIs, such as the quantum anomalous Hall (QAH) effect with a chiral edge conduction and a quantized value of the Hall resistance Ryx. Here, we report on the emergence of distinct topological phases in paramagnetic Fe-doped (Bi,Sb)2Se3 heterostructures with varying structure architecture, doping, and magnetic and electric fields. Starting from a 3D-TI, a two-dimensional insulator appears at layer thicknesses below a critical value, which turns into an Anderson insulator for Fe concentrations sufficiently large to produce localization by magnetic disorder. With applying a magnetic field, a topological transition from the Anderson insulator to the QAH state occurs, which is driven by the formation of an exchange gap owing to a giant Zeeman splitting and reduced magnetic disorder. Topological phase diagram of (Bi,Sb)2Se3 allows exploration of intricate interplay of topological protection, magnetic disorder, and exchange splitting.The Zeeman exceeding hy forms a non-trivial exchange gap with one-dimensional chiraledge channel as shown in Figs. 1(e) and 1(f), with gap size proportional to the magnetic field. In Fig. 1(f), red (blue) thick curve shows the chiral edge mode at one (the other) edge. With a minor contribution of the ordinary Hall effect under magnetic field owing to Fermi energy (EF) locating in the gap, the magnetic-field-induced anomalous Hall effect plays a critical role for the quantization of the Hall conductivity. This study demonstrates the presence of TPTs between 3D-TI, a two-dimensional (2D) insulator, and QAH phases in paramagnetic Fe-doped Bi2Se3-based heterostructures by controlling Fe doping and layer thickness and by application of external magnetic and electric fields. The tetradymite compound Bi2Se3 is a representative 3D-TI, in which a large bulk band gap (approximately 300 meV) hosts gapless surface states [35]. Using angleresolved photoemission spectroscopy (ARPES) of surface states, 50 meV gap formation was detected in paramagnetic Fe-doped bulk Bi2Se3; it was assigned to breakage of the time-reversal symmetry by exchange interactions [36]. Effects of magnetic impurities upon topological surface states were also studied by in-situ deposition of Fe atoms [37-39]. It was found that Fe acts as donor [37,38] if deposited at room temperature but as an acceptor if deposited at 8 K [38]. A question on whether the presence of a Fe surface layer 6 opens a gap or not in the topological states was also examined experimentally and theoretically [37-39].According to one theoretical proposal, Fe-doped Bi2Se3-based heterostructures are a preferred platform for observing the emergence of QAH phase [17]. Nevertheless, no QAH effect has yet been observed in magnetically doped Bi2Se3-based films, probably because of the absence or weakness of the ferromagnetic ordering, and associat...

Superexchange dominates in magnetic topological insulators

“…We find that the superexchange dominates not only in (Cd,Mn)Te [23,24], but also in topological (Hg,Mn)Te. We also show that the conclusion about the predominant role of the superexchange substantiates experimental results on (Cd,Hg,Mn)Te [25,26] and explains hitherto challenging chemical trends in magnetic properties of V, Cr, Mn, and Fe-doped tetradymite topological insulators observed experimentally [9,10,27] and found in ab initio studies [28][29][30].…”

“…Nevertheless, a series of arguments allows extending the conclusion about the dominance of the superexchange to topological tetradymite chalcogenides doped by substitutional V, Cr, or Fe ions, whose magnetism has so far been merely attributed to the Van Vleck mechanism [9,10]. (i) These impurities appear isoelectronic [9,10,27], which means that d orbitals remain fully occupied or empty. Moreover, as in other DMSs, correlations, together with the Jahn-Teller effect and dilution, enhance the d orbital localization further on.…”

Anisotropic scaling in 3D topological models: fromWeyl semimetal to Hopf insulator

“…(30) and Eq. (31), for open-boundary condition along the z direction, we propose ψ(z, k x , k y ) = χ η,zo e − z ξ + − e − z ξ − e i(k x x+k y y) . (33) Evaluating the Schrödinger equation for this wave-function at Dirichlet boundary conditions, i.e., H(k)ψ(z, k y , k z ) | z±∞ = 0 where k z = −i∂ z , we have…”

“…This research topic is closely related to applications since the discovery of new materials can lead to the development of new devices. Nowadays, there are many technological proposals based on topological materials [29][30][31] . The most prominent applications for TIs rely on their properties of carrying an electric current only at the edges or surfaces in two (2D) and three-dimensional (3D) case respectively, while the bulk remains an insulator 2,4 .…”

Realization of the Chern insulator and Axion insulator phases in antiferromagnetic $MnTe$-$Bi_2(Se, Te)_3$-$MnTe$ heterostructures

“…Introducing magnetic order in TIs breaks TRS, an exchange energy gap opens up at the Dirac point (DP) of the topological surface states, and different topological phases emerge when the chemical potential is tuned inside the gap [6,7]. Magnetism in TIs can be achieved either by doping with magnetic impurities [7][8][9][10][11][12] or through proximity with magnetic layers [13][14][15][16][17]. Recently, intrinsic magnetic TIs such as the van der Waals layered M nBi 2 T e 4 -family [18][19][20] have also been discovered [21].…”