Magnetic Topological Insulator Heterostructures: A Review

Abstract

Chern number corresponds to the occupancy of discrete Landau levels, which can be varied by tuning the Fermi energy via a gate voltage. It further corresponds to the number of dissipationless conduction channels in the gapless edge state of the quantum Hall insulator that is insulating in the bulk in high magnetic fields.After observing the quantum version of the Hall effect, the natural question to ask is if there is also a quantized version of the anomalous Hall effect (AHE), commonly observed in ferromagnets. This quantum anomalous Hall effect (QAHE) would then be observable in the absence of external fields. The QAHE was initially proposed to arise in 2D honeycomb or kagome lattices, such as monolayer graphene, that host a non-zero out-of-plane magnetic flux density, but zero net flux in each unit cell. [8,9] Later, it was also proposed that the QAHE may be found in Hg 1−y Mn y Te quantum wells without an external magnetic field, in which the effect arises purely due to the spin polarization of the Mn atoms. [10] However, the experimental realization of the QAHE was not reported until 2013, when transport in 3D topological insulators (TIs) doped with magnetic impurities was studied. TIs refer to a class of materials that is insulating in the bulk, but which possess topologically protected conducting surface states. Right from the start, the field was (see refs. [6,11-17]), and continues to be (see refs. [18-20]), to a large degree driven by theory. Common examples of 3D TIs are rhombohedral Bi 2 Se 3 , Bi 2 Te 3 , and Sb 2 Te 3 . [15] The surface state of a TI consists of two linearly dispersing states connecting the bulk conduction and valence bands. The two states cross at one point in reciprocal space, the Dirac point (Figure 1a). The charge carriers in this band structure are massless fermions, which are described by the relativistic Dirac equation. [15] Due to the strong spin-orbit coupling (SOC) in these materials, surface electron spins are locked to their momentum, forming dissipationless, counter-propagating conduction channels in the surface state.By introducing magnetism to a TI, either by impurity doping with magnetic elements, by proximity coupling to a magnetic insulators (MIs), or other magnetic layers, time-reversal symmetry (TRS) can be broken. TRS breaking can induce a bandgap in the surface states, leading to the realization of the QAHE which is characterized by 1D chiral edge conduction in zerofield at remanence, as shown in Figure 1. The Chern number, here being +1 or -1, corresponds to the direction of the spinmomentum locked edge current that can be flipped by a (small) external field. Using first-principles calculations, Sb 2 Te 3 , Bi 2 Te 3 , Topological insulators (TIs) provide intriguing prospects for the future of spintronics due to their large spin-orbit coupling and dissipationless, counterpropagating conduction channels in the surface state. The combination of topological properties and magnetic order can lead to new quantum states including the quantum anomalous Hall effect th...

Low Power In-Memory Computation with Reciprocal Ferromagnet/Topological Insulator Heterostructures

“…In the 3D atomistic grid { i , j , k }, the Hamiltonian looks like − .25ex2ex H = H 3 DTI + H Z + H V H 3 DTI = ∑ i j k c i , j , k † ε 3 DTI c i , j , k + false( c i , j , k † T x c i + 1 , j , k + c i , j , k † T y c i , j + 1 , k + c i , j , k † T z c i , j , k + 1 + h.c. false) H Z = ∑ i j k …”

“…In the 3D atomistic grid { i , j , k }, the Hamiltonian looks like − where the onsite energies ε 3DTI = ( C 0 + 2 C 1 + 4 C 2 ) I 4×4 + ( M + 2 M 1 + 4 M 2 ) I 2×2 ⊗ τ z and the hopping terms T x , y = − M 2 I 2×2 ⊗ τ z – C 2 I 4×4 + (i A 0 /2)­σ x , y ⊗ τ x and T z = − M 1 I 2×2 ⊗ τ z + C 1 I 4×4 + (i B 0 /2)­σ z ⊗ τ x . For Bi 2 Se 3 , we use M = −0.28 eV, A 0 = 0.8 eV, B 0 = 0.32 eV, C 1 = 0.024 eV, C 2 = 1.77 eV, M 1 = 0.216 eV, M 2 = 2.6 eV, and C 0 = −0.0083 eV.…”

Monolayer and bilayer PtCl$_3$: Energetics, magnetism, and band topology

“…The merging point of the two trends, namely, the study of 2D magnetic materials with nontrivial topology, clearly attracts a lot of interest [15]. On the fundamental level, there are topological states unique to such systems.…”

MnBi2Se4-Based Magnetic Modulated Heterostructures

“…However, there is an alternative way to combine magnetism with TI which provides even more magnetic homogeneity than magnetic modulated doping, that is, the formation of van der Waals heterostructures based on magnetic and topological insulators. Van der Waals materials offer a platform that allows the creation of heterostructures (including those composed of topological and magnetic materials) with a variety of properties [17][18][19][20][21]. The magnetic topological van der Waals heterostructure was experimentally realized for the first time by self-organized incorporation of an MnSe bilayer inside Bi 2 Se 3 , resulting in the formation of an MnBi 2 Se 4 /Bi 2 Se 3 heterostructure [22].…”