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At least 145 records · Page 8

Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials

It is well known that a nonvanishing Hall conductivity requires broken time-reversal symmetry. However, we demonstrate that Hall-like currents can occur in second-order response to external electric fields in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the driving frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. The nonlinear Hall coefficient is a rank-two pseudotensor, whose form is determined by point group symmetry. We discus optimal conditions to observe this effect and propose candidate two- and three-dimensional materials, including topological crystalline insulators, transition metal dichalcogenides, and Weyl semimetals.

36 MATERIALS SCIENCE↗

Quantum anomalous Hall effect in perfectly compensated collinear antiferromagnetic thin films

Here, we show that the quantum anomalous Hall effect almost always occurs in magnetic topological insulator thin films whenever the top and bottom surface layer magnetizations are parallel at some temperature, independent of the interior layer magnetization configuration. Using this criterion, we identify structures that have a quantum anomalous Hall effect even though they have collinear magnetic structures with no net magnetization, and discuss strategies for realizing these interesting magnetic states experimentally.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Analytical theory and possible detection of the ac quantum spin Hall effect

Here, we develop an analytical theory of the low-frequency ac quantum spin Hall (QSH) effect based upon the scattering matrix formalism. It is shown that the ac QSH effect can be interpreted as a bulk quantum pumping effect. When the electron spin is conserved, the integer-quantized ac spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes, which also equal to the bulk spin Chern numbers of the QSH material. Furthermore, a possible experimental scheme by using ferromagnetic metals as electrodes is proposed to detect the topological ac spin current by electrical means.

36 MATERIALS SCIENCE↗

Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride

The quantum anomalous Hall (QAH) effect is sometimes observed in twisted bilayer graphene (tBG) when it is nearly aligned with an encapsulating hexagonal boron nitride (hBN) layer. We propose that the appearance or absence of the QAH effect in individual devices could be related to commensurability between the graphene/graphene and graphene/hBN moiré patterns. We identify a series of points in the (θ GG , θ GBN ) twist-angle space at which the two moiré patterns are commensurate, allowing moiré band theory to be applied, and we show that the band Chern numbers are in this case sensitive to a rigid in-plane hBN displacement. Given this property, we argue that the QAH effect is likely only when (i) the (θ GG , θ GBN ) twist-angle-pair is close enough to a commensurate point that the two moiré patterns yield a supermoiré pattern with a sufficiently long length scale, and (ii) the supermoiré has a percolating topologically nontrivial QAH phase. For twist angles far from commensurability, the hBN layer acts as a source of disorder that can destroy the QAH effect. Our proposal can explain a number of current experimental observations. Finally, further experimental studies that can test this proposal more directly are suggested.

36 MATERIALS SCIENCE↗

Perspective–The Elusive Quantum Anomalous Hall Effect in MnBi 2 Te 4 : Materials

Observation of the quantum anomalous Hall effect (QAHE) in MnBi 2 Te 4 flakes is one of the most exciting results in the study of the intrinsic magnetic topological insulator MnBi 2 Te 4 and related compounds. However, reproducing this fascinating result has been found to be challenging. The quality of starting MnBi 2 Te 4 single crystals is believed to be the key factor. An interesting and important question to address is what is the right quality to enable the QAHE. In this perspective, we present possible approaches to tuning the magnetic and topological properties of MnBi 2 Te 4 by using lattice imperfections, strain, stacking sequence, and interactions between the substrate and flakes/films. It is of critical importance to eventually identify the factor(s) responsible for the realization of QAHE. This paper is part of the JES/JSS Joint Focus Issue In Honor of John Goodenough: A Centenarian Milestone.

36 MATERIALS SCIENCE↗

Chiral transport along magnetic domain walls in the quantum anomalous Hall effect

The recent prediction, and subsequent discovery, of the quantum anomalous Hall (QAH) effect in thin films of the three-dimensional ferromagnetic topological insulator (MTI) (Cr$_y$Bi$_x$Sb$_{1-x-y}$)$_2$Te$_3$ has opened new possibilities for chiral-edge-state-based devices in zero external magnetic field. Like the $\nu=1$ quantum Hall system, the QAH system is predicted to have a single chiral edge mode circulating along the boundary of the film. Backscattering of the chiral edge mode should be suppressed, as recently verified by the observation of well-quantized Hall resistivities $\rho_{yx} = \pm h/e^2$, along with longitudinal resistivities as low as a few ohms. Dissipationless 1D conduction is also expected along magnetic domain walls. Here, we intentionally create a magnetic domain wall in a MTI and study electrical transport along the domain wall. We present the first observation of chiral transport along domain walls, in agreement with theoretical predictions. We present further evidence that two modes equilibrate and co-propagate along the length of the domain wall.

36 MATERIALS SCIENCE↗

Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure

Quantum geometry in condensed matter physics has two components: the real part quantum metric and the imaginary part Berry curvature. Whereas the effects of Berry curvature have been observed through phenomena such as the quantum Hall effect in 2D electron gases and the anomalous Hall effect (AHE) in ferromagnets, quantum metric has rarely been explored. Here, in this paper, we report a nonlinear Hall effect induced by quantum metric dipole by interfacing even-layered MnBi 2 Te 4 with black phosphorus. The quantum metric nonlinear Hall effect switches direction upon reversing the AFM spins and exhibits distinct scaling that is independent of the scattering time. Our results open the door to discovering quantum metric responses predicted theoretically and pave the way for applications that bridge nonlinear electronics with AFM spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Approaching quantum anomalous Hall effect in proximity-coupled YIG/graphene/h-BN sandwich structure

Quantum anomalous Hall state is expected to emerge in Dirac electron systems such as graphene under both sufficiently strong exchange and spin-orbit interactions. In pristine graphene, neither interaction exists; however, both interactions can be acquired by coupling graphene to a magnetic insulator as revealed by the anomalous Hall effect. Here, we show enhanced magnetic proximity coupling by sandwiching graphene between a ferrimagnetic insulator yttrium iron garnet (YIG) and hexagonal-boron nitride (h-BN) which also serves as a top gate dielectric. By sweeping the top-gate voltage, we observe Fermi level-dependent anomalous Hall conductance. As the Dirac point is approached from both electron and hole sides, the anomalous Hall conductance reaches ¼ of the quantum anomalous Hall conductance 2e 2 /h. The exchange coupling strength is determined to be as high as 27 meV from the transition temperature of the induced magnetic phase. YIG/graphene/h-BN is an excellent heterostructure for demonstrating proximity-induced interactions in two-dimensional electron systems.

36 MATERIALS SCIENCE↗

Microwave spectroscopic observation of distinct electron solid phases in wide quantum wells

In high magnetic fields, two-dimensional electron systems can form a number of phases in which interelectron repulsion plays the central role, since the kinetic energy is frozen out by Landau quantization. These phases include the well-known liquids of the fractional quantum Hall effect, as well as solid phases with broken spatial symmetry and crystalline order. Solids can occur at the low Landau-filling termination of the fractional quantum Hall effect series but also within integer quantum Hall effects. Here we present microwave spectroscopy studies of wide quantum wells that clearly reveal two distinct solid phases, hidden within what in d.c. transport would be the zero diagonal conductivity of an integer quantum-Hall-effect state. Explanation of these solids is not possible with the simple picture of a Wigner solid of ordinary (quasi) electrons or holes.

42 ENGINEERING↗

Ordering mechanism and quantum anomalous Hall effect of magnetically doped topological insulators

We investigate magnetic ordering and the quantum anomalous Hall effect (QAHE) in Cr-doped topological insulators using systematic first-principles calculations, explaining the mechanism responsible for ferromagnetic order and the reason why Sb 2 Te 3 is a better QAHE host than Bi 2 Se 3 or Bi 2 Te 3 . In this work, we conclude that these magnetic topological insulators have relatively long-range exchange interactions within quintuple layers and weak interactions between quintuple layers. Our analyses for the spin splitting of the topological surface states suggest that the temperature at which the QAHE occurs in these materials can be enhanced significantly by Mo-Cr co-doping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Quantum anomalous Hall effect in magnetic topological insulators

The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. Here, we give a theoretical introduction to the quantum anomalous Hall (QAH) effect based on magnetic topological insulators in two-dimensions (2D) and three-dimensions (3D). In 2D topological insulators, magnetic order breaks the symmetry between the counter-propagating helical edge states, and as a result, the quantum spin Hall effect can evolve into the QAH effect. In 3D, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. We present the phase diagram in thin films of a magnetic topological insulator and review the basic mechanism of ferromagnetic order in magnetically doped topological insulators. We also review the recent experimental observation of the QAH effect. Furthermore, we discuss more recent theoretical work on the coexistence of the helical and chiral edge states, multi-channel chiral edge states, the theory of the plateau transition, and the thickness dependence in the QAH effect.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Origin of the quasi-quantized Hall effect in ZrTe 5

The quantum Hall effect (QHE) is traditionally considered to be a purely two-dimensional (2D) phenomenon. Recently, however, a three-dimensional (3D) version of the QHE was reported in the Dirac semimetal ZrTe 5 . It was proposed to arise from a magnetic-field-driven Fermi surface instability, transforming the original 3D electron system into a stack of 2D sheets. Here, we report thermodynamic, spectroscopic, thermoelectric and charge transport measurements on such ZrTe 5 samples. The measured properties: magnetization, ultrasound propagation, scanning tunneling spectroscopy, and Raman spectroscopy, show no signatures of a Fermi surface instability, consistent with in-field single crystal X-ray diffraction. Instead, a direct comparison of the experimental data with linear response calculations based on an effective 3D Dirac Hamiltonian suggests that the quasi-quantization of the observed Hall response emerges from the interplay of the intrinsic properties of the ZrTe 5 electronic structure and its Dirac-type semi-metallic character.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

3D Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred‐Nanometer Thickness

Magnetic topological states refer to a class of exotic phases in magnetic materials with the non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state, which is a zero magnetic field manifestation of the quantum Hall effect. Current research in this direction focuses on QAH insulators with a thickness of less than 10 nm. Here, molecular beam epitaxy (MBE) is employed to synthesize magnetic TI trilayers with a thickness of up to ≈106 nm. It is found that these samples exhibit well-quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field. By varying the magnetic dopants, gate voltages, temperature, and external magnetic fields, the properties of these thick QAH insulators are examined and the robustness of the 3D QAH effect is demonstrated. The realization of the well-quantized 3D QAH effect indicates that the nonchiral side surface states of the thick magnetic TI trilayers are gapped and thus do not affect the QAH quantization. The 3D QAH insulators of hundred-nanometer thickness provide a promising platform for the exploration of fundamental physics, including axion physics and image magnetic monopole, and the advancement of electronic and spintronic devices to circumvent Moore's law.

36 MATERIALS SCIENCE↗

Intrinsic Quantum Anomalous Hall Effect with In-Plane Magnetization: Searching Rule and Material Prediction

So far, most theoretically predicted and experimentally confirmed quantum anomalous Hall effects (QAHEs) are limited in two-dimensional (2D) materials with out-of-plane magnetization. In this Letter, starting from 2D nodal-line semimetal, a general rule for searching QAHE with in-plane magnetization is mapped out. Because of spin-orbital coupling, we found that the magnetization will prefer an in-plane orientation if the orbital of degenerate nodal-line states at the Fermi level have the same absolute value of magnetic quantum number. Moreover, depending on the broken or conserved mirror symmetry, either a QAHE or 2D semimetal can be realized. Based on first principles calculations, we further predict a real material of monolayer LaCl to be an intrinsic QAHE with in-plane magnetization. By tuning the directions of in-plane magnetization, the QAHE in LaCl demonstrates a threefold rotational symmetry with a Chern number of either +1 or –1 , and the transition point is characterized by a 2D semimetal phase. All these features are quantitatively reproduced by tight-binding model calculations, revealing the underlying physics clearly. Here, our results greatly extend the scope for material classes of QAHE and hence stimulate immediate experimental interest.

2-dimensional systems↗

Intrinsic quantum anomalous Hall effect in the kagome lattice Cs 2 LiMn 3 F 12

In a kagome lattice, the time reversal symmetry can be broken by a staggered magnetic flux emerging from ferromagnetic ordering and intrinsic spin-orbit coupling, leading to several well-separated nontrivial Chern bands and intrinsic quantum anomalous Hall effect. Based on this idea and ab initio calculations, we propose the realization of the intrinsic quantum anomalous Hall effect in the single layer Cs 2 Mn 3 F 12 kagome lattice and on the (001) surface of a Cs 2 LiMn 3 F 12 single crystal by modifying the carrier coverage on it, where the band gap is around 20 meV. Furthermore, a simplified tight binding model based on the in-plane ddσ antibonding states is constructed to understand the topological band structures of the system.

36 MATERIALS SCIENCE↗

Thickness-independent transport in thin (001)-oriented cadmium arsenide films

The three-dimensional Dirac semimetal is a parent phase for a variety of topological phases that can be generated by tuning parameters in material growth or device operation. Notably, it has recently been found that cadmium arsenide, which is ordinarily a three-dimensional Dirac semimetal, can nevertheless realize a three-dimensional topological insulator in (001)-oriented films about 50-nm thick. In this work, we study the quantum Hall effect in thin (001)-oriented cadmium arsenide films, their thickness ranging from 12 to 24 nm. When the carrier density is kept approximately constant across the different films, quantum transport reveals an identical underlying picture. The result is shown to be consistent with the transport's origin in the surface states of a three-dimensional topological insulator, but problematic for a perspective in which the quantum Hall effect originates from the confined subbands of the bulk band structure. As a result, these thin-film results complement previous studies of the quantum Hall effect in 50-nm-thick films.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Alloying vanadium in Mn Bi 2 Te 4 for robust ferromagnetic coupling and quantum anomalous Hall effect

The intrinsic antiferromagnetic (AFM) interlayer coupling in the two-dimensional magnetic topological insulator MnBi 2 Te 4 places a restriction on realizing a stable quantum anomalous Hall effect (QAHE) [Y. Deng et al., Science 367, 895 (2020)]. Through density functional theory calculations, we demonstrate the possibility of tuning the AFM coupling to the ferromagnetic coupling in Mn Bi 2 Te 4 films by alloying about 50% V with Mn. As a result, the QAHE can be achieved without alternation with the even or odd septuple layers. This provides a practical strategy to get a robust QAHE in ultrathin Mn Bi 2 Te 4 films, rendering them attractive for technological innovations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗