JP6161147B2 - Electric field tunable topological insulator using perovskite structure - Google Patents

Description

  The present invention relates to an electric field adjustable topological insulator using a perovskite structure.

  The discovery of the quantum Hall effect (QHE) by von critching has opened a new chapter in condensate physics. It has been clarified that the integer coefficient of the Hall conductivity is nothing but the churn number representing the topological characteristics of the electron wave function (Non-patent Documents 1 and 2). Since then, one of the main driving forces in condensate physics research has been to investigate possible topological states (Non-Patent Documents 3-10).

  Topology called Quantum Spin Hall Effect (QSHE) insulator by Kane and Mele causing electrons on graphene (two-dimensional honeycomb lattice of carbon atoms) to open a gap due to spin-orbit interaction (SOC) When it was clarified that an unobvious state was achieved, a breakthrough development occurred (Non-Patent Document 4). It was also found that graphene cannot be detected because graphene has a very low specific SOC. And QSHE in the HgTe quantum well which has strong SOC was predicted theoretically (nonpatent literature 5), and was realized experimentally (nonpatent literature 6).

  As a base common to both the Kane-Mele model (Non-patent Document 4) and the spinless Haldane model (Non-patent Document 3), the honeycomb lattice is used to understand the topological characteristics of electronic systems. Play a special role. Summarizing the electronic structure with attention to the Berry curvature shape is helpful for explanation (Non-Patent Document 11). There are two sites in the unit cell of the honeycomb structure. Nearest neighbor hopping causes the valance band and conduction band of electrons to be in linear contact, thus creating a Dirac cone at the two non-equivalent k points, K and K ', at the corner of the Brillouin zone. The Bloch wave function shows opposite chiral features around K and K ′, which has the feature that the belly curvature is opposite, which establishes a special position of the honeycomb lattice when examining the topological state It is important to confirm that.

  Due to the time-reversal symmetry, the belly curvatures of the spin-up channel and the spin-down channel overlap as shown in FIG. By introducing the intrinsic SOC, the gap between the two Dirac cones is opened, and the Berry curvature is inverted between the spin-up channel K and the spin-down channel K ′, and the time-reversal symmetry is preserved. As a result, the QSHE state is changed. The belly curvature shape of FIG. 1B to be characterized is obtained (Non-Patent Document 4). Furthermore, an electric field conjugated to a valley degree of freedom such as polarization reverses the belly curvature at K in both the spin-up channel and the spin-down channel, and a configuration diagram (c) is obtained (topologically obvious state) ( Non-patent documents 12 to 15). With a staggered electric field that can be realized by applying a uniform electric field to silicene with a buckled honeycomb lattice (Non-Patent Document 16), Ezawa can invert the belly curvature with K only in one spin channel. As a result, the charge churn number and the spin churn number simultaneously became non-zero in FIG. Band engineering is based on full control of spin, valley, and sublattice degrees of freedom using intrinsic SOC. By the way, the belly curvature shape of FIG.1 (d) is corresponded to a quantum anomalous Hall effect (QAHE) (nonpatent literature 18-23).

  Most recently, Non-Patent Document 24 was proposed, which proposed an electric field adjustable topological insulator in which a staggered magnetic field was generated by two ferromagnets on both sides of a silicene layer. However, the materials proposed by this document only work in the temperature range, for example about -200 ° C., well below room temperature, and therefore devices using this material require refrigeration equipment to operate properly. And

  It is an object of the present invention to provide an electric field tunable topological insulator that utilizes a perovskite structure that functions at room temperature and higher.

  According to one embodiment of the present invention, a topological insulator capable of adjusting an electric field using a perovskite structure is provided, a perovskite G-type antiferromagnetic insulator is grown in a [111] direction, and a magnetic element is a single atomic layer. Is replaced with a non-magnetic element, where d electrons hop on the buckled honeycomb lattice.

  According to the present invention, there is provided an electric field adjustable topological insulator in which the periphery of the sample has metallic properties while the bulk is an insulator. In addition, the edge state is never scattered by defects (whether magnetic or non-magnetic) and thus has a completely spin-polarized quantized current with no dissipation, ie no current loss. Thus, as long as an electric field is applied to the material surface, the current continues to circulate along its edges. This state lasts to a temperature significantly above room temperature, for example up to about 300 ° C. The material of the present invention provides a spin-polarized quantized edge current that is robust to both non-magnetic and magnetic defects, and is ideal for spintronic applications because the spin polarization can be adjusted by reversing the electric field. is there. The material (or condition) also provides a non-dissipative current, which limits power loss and thus helps current transport within the grid.

FIG. 4 is a diagram of the configuration of Berry curvature and Chern number for the insulation state on the honeycomb lattice, (a) simple honeycomb lattice, (b) QSHE, (c) self-evident state with broken time reversal symmetry, (d) QAHE, (E) A topological state in which the charge and the spin churn number are simultaneously non-zero. (A) State diagram of staggered potential V and antiferromagnetic field M when it is assumed that the intrinsic SOC is positive (λ> 0). (B) and (c) are schematic diagrams of energy levels that intersect when adjusting the electric field when M <λ and M> λ. (D) Band structure of N = 100 zigzag ribbon of honeycomb lattice when V = 0.25, M = 0.2 and λ = 0.1. (A) It is the schematic which shows the three-dimensional structure of 6 layer ABB'X perovskite by which one layer of B (dark color) was replaced by B '(light color). (B) and (c) Schematic showing side and top views of a buckled honeycomb lattice composed of B ′ cations. (D) is a diagram showing a tight-binding band structure with no interaction e _g system, each band is represented by a corresponding electronic structure when it is occupied. Illustrations shows two e _g orbitals of B '. [111] is a view showing a super unit cell _{(A 2 B '2 O 6} ) / (A 2 B 2 O 6) band structure in accordance with first principles calculations on LaCrAgO and LaCrAuO having ₅ along the direction. FIG. 6 is a schematic diagram showing a device of “synthetic QSHE” insulator constructed by two copies of a new topological state.

  Electrons on the honeycomb lattice based on band engineering with staggered potential and antiferromagnetic exchange magnetic field in the presence of intrinsic spin-orbit interaction can have topological states in which the churn number and spin churn number are both nonzero. According to first-principles calculations, this is realized by replacing one atomic layer magnetic element with a non-magnetic element in a perovskite G-type antiferromagnetic insulator grown along the [111] direction, where It has been confirmed that the d-electron system hops on the buckled honeycomb lattice.

  In the present invention, it was found that the staggered magnetic field plays a role similar to that provided by the polarization proposed by Ezawa in the presence of intrinsic SOC (Non-Patent Document 15). Since the staggered magnetic field can be realized by an antiferromagnetic (AFM) insulator, a compact and stable device based on the topological state of FIG.

As a material that realizes our idea, we pay attention to the d-electron system of the perovskite structure (Non-patent Document 25). First, a perovskite insulator ABO ₃ having a G-type AFM order on magnetic B atoms is selected. As first described by Xiao et al. (Non-Patent Document 9), along the [111] direction, B atoms constitute a stack of buckled honeycomb lattices, and this stack provides atomic accuracy. It can be grown by state-of-the-art molecular beam epitaxy (MBE) (Non-patent Document 26). During the growth process, the single-buckled atomic layer of B atoms is replaced with that of non-magnetic B ′ atoms, and the element B ′ is selected in a conjugate manner with B so as to constitute a d ⁸ configuration. For B'-d electrons on the buckled honeycomb lattice, the intrinsic SOC increases, the uniform electric field causes the staggered potential of the two sublattices, and the G-type AFM ordering of the B atoms on both sides provides the AFM exchange field To do. The material design provides a magnetic field that is purely an exchange field, thereby avoiding leakage magnetic fields from permanent ferromagnets. The effectiveness of the present invention has been confirmed by performing first-principles calculations on several materials. In the transition metal perovskite, an intrinsic SOC of tens of meV has been identified, which is an order of magnitude larger than silicene and enables the use of new topological states beyond room temperature.

[Effective model and state diagram]
We describe our approach based on the 4-band Hamiltonian of electrons on a honeycomb lattice buckled under an AFM exchange magnetic field and a uniform electric field perpendicular to the plane (in d ⁸ systems where the electronic structure contains two degenerate eg orbitals, Effective H ₀ can be obtained by reducing the 4-band Hamiltonian to the 2-band Hamiltonian using k · p perturbation theory).

Holds around two non-equivalent K and K ′ points, where the z-axis is along the [111] direction of the perovskite structure; σ is a sublattice Pauli matrix, τ _z = ± 1 and s _z = ± 1 is a binary degree of freedom indicating valleys and spins. The first two terms are due to the same nearest neighbor hopping as simple graphene (see the note in parentheses just before Equation 1), and the third term is inherent in having a positive coupling coefficient λ> 0 by definition. It is of SOC, which can be increased by heavier host transition metal atoms and buckled structures, the fourth term is obtained by the uniform potential on the buckled structure, and the last term is the AFM exchange It is a magnetic field. The chemical potential is set to 0 and all energy is measured in this study in units of nearest hopping integral. As will be shown later, this model Hamiltonian shows the low energy physics of a transition metal oxide having a perovskite structure grown along the [111] direction.

The behavior of the system in adjusting the potential V while the M field and λ are fixed is clarified as follows, which directly corresponds to our material design and experimental operation. When 0 <M <λ, the gap at V = 0 is topologically non-trivial for both spin-up and spin-down channels and characterizes the QSHE state (see FIG. 1 (c)). As shown in FIG. 2 (b), when V increases, the gap of the spin-up channel decreases, and when V = λ−M, after closing at the K ′ point (τ _z = −1), again. open. This quantum phase transition makes the spin-up channel trivial, while the spin-down channel remains non-trivial. This insulating state in which only one spin channel exhibits a non-trivial gap is different from other topological states such as QSHE and QAHE as described by Ezawa (Non-Patent Document 15). When V becomes even larger, the spin-down channel gap shrinks, and when V = λ + M, it closes at the K point (τ _z = 1) and then opens again, which also makes the spin-down channel self-evident, and the system becomes A trivial insulating state is obtained by the second quantum phase transition.

For M> λ, the system exhibits a trivial gap in both spin-up and spin-down channels at V = 0 (see FIG. 1 (c)). As can be seen in FIG. 2 (c), when V is large, the gap of the spin down channel is reduced at τ _z = −1 and closed again at V = M−λ, so that it opens again, thereby causing spin down. The channel becomes topological. As V becomes even larger, the spin-down channel gap shrinks at τ _z = 1, closes at V = λ + M, and then reopens, thereby putting the system into a trivial insulator state.

If consideration is given to symmetry in the above analysis, a detailed state diagram as shown in FIG. 2A can be constructed. A new topological state is realized when the absolute values of the three fields | V |, | M |, and | λ | are triangular, which is between three degrees of freedom σ _z , τ _z and s _z . Demonstrate that weaving is important for new topological conditions. FIG. 2 (d) shows a typical band structure of a zigzag ribbon of a buckled honeycomb lattice, with two edge states that intersect at the Fermi level and are localized on two opposing edges (FIG. 1 ( see e)). This state diagram is similar to that of Non-Patent Document 15, except that in this state diagram, the state with the same churn number is in the diagonal direction, and in Non-Patent Document 15, it is in the same half space, This is due to the difference in control field between the two Hamiltonians.

Experiment

[Realization of materials]
In the perovskite ABO ₃ material shown in FIG. 3 (a), A and B constitute two simple cubic lattices that penetrate each other. Octahedral cage constituted by six oxygen around the transition metal B generates a doublet e _g and triplet t _{2 g} trajectory of d electrons. In the [111] direction, a simple cubic structure can be seen as a stack of buckled honeycomb lattices as shown in FIGS. 3 (b) and (c). The new coordinates, unique SOC between the two e _g orbitals appears. With regard to material synthesis, perovskite structures can be grown with atomic accuracy in the [111] direction due to recent advances in laser molecular beam epitaxy (MBE) technology (Non-patent Document 26). All of these, as first shown by Xiao et al., Make d electrons in the perovskite structure a very promising platform for realizing topological states (Non-Patent Document 9).

Many transition metal oxides having a perovskite structure are known as wide gap antiferromagnetic insulators. As a subgroup of these materials, take the so-called G-type AMF order in which the spins are antiferromagnetically aligned in the two sublattices of the buckled honeycomb lattice. In the present invention, this is a base for realizing a porologic state by material design and magnetic field operation. One buckled layer of B is replaced by the nonmagnetic element B ′, resulting in B′-d electrons on a single layer of the buckled honeycomb lattice, which are derived from the G-type AMF ordering of the matrix ABO ₃ . Subject to an AFM exchange field (in fact, there are two magnetic configurations. From first-principles calculations performed by the inventor, those that cause the desired AFM magnetization in the AB′O ₃ layer always have lower energy I found out)

There is a gap (10 Dq) between the e _g and t _2g orbits, which excludes the t _2g orbit from low energy physics. In each unit cell, two B 'atom, to contribute a total of four e _g orbitals. The band structure of these four orbits is given by a tightly bound Hamiltonian with a hopping integral shown by the Slater-Coster form, as shown in FIG. 3 (d). Two dispersion bands intersecting the two flat bands can be seen. Xiao et al. (9, 18, 19) focused on flat bands and constructed interesting scenarios for topological states based on strong electronic correlations by using the d ⁷ (t ⁶ _2g e ¹ _g ) configuration. . Here we focus on the two dispersion bands that meet at the Fermi level by considering the d ⁸ (t ⁶ _2g e ² _g ) system.

In order to verify the above idea, first principles calculations, the base material LaCrO ₃ in order to achieve a ^{_{d 8 (t 6 2g e 2}} g) based on the honeycomb lattice buckle, La ₂ Ag ₂ O ₆ or This was carried out on a system in which a single layer of La ₂ Au ₂ O ₆ was inserted. The ultra-unit cell used for the calculation has 6 layers with the structure (La ₂ B ′ ₂ O ₆ ) / (La ₂ B ₂ O ₆ ) ₅ . The calculation is a generalized gradient in the parameterization of Perdew, Burke, and Ehzorhof (PBE) for exchange correlation as realized in the Vienna non-empirical simulation package (VASP) (Non-Patent Document 28). This is done using density functional theory (DFT) within an approximation (GGA) approach. The bulk lattice constant is set to 3.85 設定 for LaCrO ₃ and the atomic position is relaxed in the ultra-unit cell. The on-site Coulomb interaction of 3d electrons in Cr is handled by the Dudarev method (Non-patent Document 29) with an effective U value (U _eff = U−J = 5.4 eV). It was confirmed that the main results are valid for windows with large U values. The momentum space mesh is 6 × 6 × 1 and the cut-off energy is 440 eV.

FIGS. 4A and 4B show the band structures of LaCrAgO and LaCrAuO obtained from the GGA + U + SOC calculation. First, two flat bands and two dispersion bands close to the Fermi level in FIG. 3D are realized in the two materials. Two gaps in K and K ′ that were not in FIG. 3 (b) of the tightly bound model were brought about by AFM exchange fields from LaCrO ₃ and SOC. From the two gaps at K and K ′, the AFM exchange field and SOC are M = 0.141 eV and λ = 7.3 meV for LaCrAgO, and M = 0.166 eV and λ = 32.91 meV for LaCrAuO. Calculated. Calculations were also made for several other possible materials and the results are listed in Table 1, which shows the AFM order and SOC parameters determined from the GGA + U + SOC calculation, and for KNiInF and KNiTlF, The electron configurations of In ²⁺ and Tl ²⁺ are 5s ¹ and 6s ¹ . Since the maximum non-trivial gap is indicated by 2λ, the results from the first-principles calculation show that a topological material can be realized at about 660K, which is sufficiently higher than room temperature (2λ = 65.82 meV for LaCrAuO). I understand that there is. A typical electric field that realizes the new topological state is about 0.1 V / Å.

[application]
This new topological state, possibly achievable at room temperature, is ideal for spintronics applications because it provides a spin-polarized quantized edge current that is robust to both nonmagnetic and magnetic defects. This is because this spin polarization can be adjusted by reversing the electric field. This is ideal for current transport in the grid due to the characteristics of non-dissipative current.

By using two replicas of the new topological state, a “composite QSHE insulator” can be realized. As shown in FIG. 5 (a), we manufacture two pairs of electrodes with opposite bias voltages (ie, two upper and two lower square plates with rounded corners). Can do. Two patches show a state with opposite chirality and spin. The spin Hall conductivity can be measured using this apparatus. As shown in FIG. 5 (b), a positive spin current I _s is when injected from the left electrode, the spin-up current outgoing flows along the left electrode the upper edge of the upper patch (upward The dark colored solid curve), the incoming spin-down current flows into the left electrode along the straight line between the two electrodes (green solid line), resulting in zero charge current. Since the charge current flows only at the upper edge and accumulates charge there, the Hall voltage drop between the upper and lower edges of the device can be detected. When compared to previously realized QSHE, time-reversal symmetry destructive perturbations, such as magnetic fields or magnetic impurities, do not backscatter reverse charge currents due to spin-up and spin-down at the center of the device, The reason is that the charge current is then distributed in different patches as shown in FIG. 5 (b).

[Discussion]
Although this topological state is slightly reversed because the inversion symmetry with respect to the honeycomb lattice plane is broken by the electric field, it is robust to the existing Rashba SOC (Non-patent Documents 22 and 23). In fact, in graphene, it is known that a non-obvious band gap closes when λ _R > λ, and QSHE is destroyed by mixing of two spin channels by Rashba SOC (Non-Patent Document 4). For example, in a new topological state with V = M> 0, a gap of 2 (2M-λ) is opened in the spin-up channel, while the gap of the spin-down channel is 2λ. Since M >> λ as shown in Table 1, even a Rashba SOC that is more powerful than the intrinsic one,

You cannot mix two spin channels to close the gap.

  The material of the present invention is optimal for quantum devices such as spintronic devices and current transport in power transmission networks.

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Claims (1)

An electric field tunable topological insulator using a perovskite structure, in which a perovskite G-type antiferromagnetic insulator is grown in the [111] direction, and a magnetic element at the B site in the perovskite structure is formed in one atomic unit layer. A topological insulator that replaces a non-magnetic element and d-electrons hops on a single buckled honeycomb lattice.