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The quantum anomalous Hall effect in graphene, predicted by first-principles calculations, is induced by the proximity effect of a magnetic topological insulator. Our model further reveals a rich phase diagram in graphene/MnBi 2 Te 4 heterostructures.
We predict the emergence of a state of matter with intertwined ferromagnetism, charge order, and topology in fractionally filled moiré superlattice bands. Remarkably, these quantum anomalous Hall crystals exhibit a quantized integer Hall conductance that is different than expected from the filling and Chern number of the band. Microscopic calculations show that this phase is robustly favored at half-filling (𝜈 =1/2) at larger twist angles of the twisted semiconductor bilayer 𝑡MoTe 2 .
We study particle-hole symmetry at the integer quantum Hall plateau transition using composite fermion mean-field theory. Because this theory implicitly includes some electron-electron interactions, it also has applications to certain fractional quantum Hall plateau transitions. Previous work [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] using this approach showed that the diffusive quantum criticality of this transition is described by a nonlinear sigma model with topological θ = π term. This result, which holds for both the Dirac and Halperin, Lee, and Read composite fermion theories, signifies an emergent particle-hole (reflection) symmetry of the integer (fractional) quantum Hall transition. Here we consider the stability of this result to various particle-hole symmetry-violating perturbations. In the presence of quenched disorder that preserves particle-hole symmetry, we find that finite longitudinal conductivity at this transition requires the vanishing of a symmetry-violating composite fermion effective mass, which if present would generally lead to θ ≠ π and a corresponding violation of particle-hole symmetric electrical transport σ xy ≠ $\frac1{2}$$\frac{e^2}{h}$ . When the disorder does not preserve particle-hole symmetry, we find that θ can vary continuously within the diffusive regime. Our results call for further study of the universality of the quantum Hall plateau transition.
We study interaction-driven edge reconstruction in a quantum spin Hall insulator described by the Bernevig-Hughes-Zhang model with Kanamori-Hubbard interactions using the real-space density matrix renormalization group method in both the grand-canonical and canonical ensembles. For a two-dimensional cylinder with a smooth edge, we identify discrete particle-number transitions that lead to a spin-polarized edge state stabilized by an emergent ferromagnetic exchange interaction. The reconstruction is orbital-selective, occurring predominantly in the 𝑠-orbital channel. Our results reveal a microscopic mechanism for emergent fluctuating moments at the edge that could compromise the topological protection of helical edge states by time-reversal symmetry.
Here, the interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with twofold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that an QAH state is stabilized when the interaction strength exceeds the energy scale controlling the separation between the Dirac points. Through numerical simulations, we verify the existence of the QAH phase with spontaneous time-reversal symmetry breaking and quantized Chern number C = 1.
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.
Fractional Chern insulators (FCI) with fractionally quantized Hall conductance at fractional fillings and an extended quantum anomalous Hall (EQAH) crystal with an integer quantized Hall conductance over an extended region of doping were recently observed in pentalayer graphene. One particularly puzzling observation is the transition between the EQAH and FCI regimes, driven either by temperature or electrical current. Here, in this study, we propose a scenario to understand these transitions based on the topologically protected gapless edge modes that are present in both the FCI and EQAH phases and should be most relevant at temperature scales below the energy gap. Our consideration is based on the simple assumption that the edge velocity in FCI is smaller than that in EQAHE and thus contributes to a higher entropy. We further argue that domains with opposite fractionally quantized Hall conductance are ubiquitous in the devices due to disorder, which gives rise to a network of edge modes. The velocity of the edge modes between domains is further reduced due to edge reconstruction. The edge velocity can also be reduced by current when the occupation of the edge mode approaches the gap edge. The edge entropy therefore drives the transition from EQAH to FCI either by temperature or current at a nonzero temperature.
Moiré systems made from stacked two-dimensional materials host correlated and topological states that can be electrically controlled with applied gate voltages. One prevalent form of topological state that can occur are Chern insulators that display a quantum anomalous Hall effect. Here we manipulate Chern domains in an interaction-driven quantum anomalous Hall insulator made from twisted monolayer–bilayer graphene and observe chiral interface states at the boundary between different domains. By tuning the carrier concentration, we stabilize neighbouring domains of opposite Chern number that then provide topological interfaces devoid of any structural boundaries. This allows the wavefunction of chiral interface states to be directly imaged using a scanning tunnelling microscope. In conclusion, our theoretical analysis confirms the chiral nature of observed interface states and allows us to determine the characteristic length scale of valley polarization reversal across neighbouring Chern domains.
It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a non-Abelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. Here, this may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED 3 to 3+1 dimensions. In addition we discuss a (3+1)-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.
The thermal Hall conductance K of the fractional quantum Hall state at filling fraction ν = 5/2 has recently been measured to be K = 2.5π 2 $k$$^{2}_{B}$T/3h [M. Banerjee et al. Nature (London) 559, 205 (2018)]. Here, the half-integer value of this result (in units of π 2 $k$$^{2}_{B}$T/3h) provides strong evidence for the presence of a Majorana edge mode and a corresponding quantum Hall state hosting quasiparticles with non-Abelian statistics. Whether this measurement points to the realization of the PH-Pfaffian or the anti-Pfaffian state has been the subject of debate. Here we consider the implications of this measurement for anti-Pfaffian edge-state transport. We show that in the limit of strong Coulomb interaction and an approximate spin degeneracy in the lowest Landau level, the anti-Pfaffian state admits low-temperature edge phases that are consistent with the Hall conductance measurements. Furthermore, these edge phases can exhibit fully equilibrated electrical transport coexisting with partially equilibrated heat transport over a range of temperatures. Through a study of the kinetic equations describing low-temperature electrical and heat transport of these edge states, we determine regimes of parameter space, controlling the interactions between the different edge modes that agree with experiment.
Abstract Van der Waals heterostructures offer great versatility to tailor unique interactions at the atomically flat interfaces between dissimilar layered materials and induce novel physical phenomena. By bringing monolayer 1 T’ WTe 2 , a two-dimensional quantum spin Hall insulator, and few-layer Cr 2 Ge 2 Te 6 , an insulating ferromagnet, into close proximity in an heterostructure, we introduce a ferromagnetic order in the former via the interfacial exchange interaction. The ferromagnetism in WTe 2 manifests in the anomalous Nernst effect, anomalous Hall effect as well as anisotropic magnetoresistance effect. Using local electrodes, we identify separate transport contributions from the metallic edge and insulating bulk. When driven by an AC current, the second harmonic voltage responses closely resemble the anomalous Nernst responses to AC temperature gradient generated by nonlocal heater, which appear as nonreciprocal signals with respect to the induced magnetization orientation. Our results from different electrodes reveal spin-polarized edge states in the magnetized quantum spin Hall insulator.
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.
We report that topological materials often exhibit remarkably linear nonsaturating magnetoresistance (LMR), which is both of scientific and technological importance. However, the role of topologically nontrivial states in the emergence of such a behavior has eluded clear demonstration in experiments. Here, by reducing the coupling between the topological surface states (TSS) and the bulk carriers, we controllably tune the LMR behavior in Pt 1-x Au x LuSb into distinct plateaus in Hall resistance, which we show arise from a quantum Hall phase. This allowed us to reveal how smearing of the Landau levels, which otherwise gives rise to a quantum Hall phase, results in an LMR behavior due to strong interaction between the TSS with a positive g factor and the bulk carriers. We establish that controlling the coupling strength between the surface and the bulk carriers in topological materials can bring about dramatic changes in their magnetotransport behavior. In addition, our work outlines a strategy to reveal macroscopic physical observables of TSS in compounds with a semimetallic bulk band structure, as is the case in multifunctional Heusler compounds, thereby opening up opportunities for their utilization in hybrid quantum structures.
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.
A quantum anomalous Hall (QAH) insulator coupled to an s-wave superconductor is predicted to harbor chiral Majorana modes. A recent experiment interprets the half-quantized two-terminal conductance plateau as evidence for these modes in a millimeter-size QAH-niobium hybrid device. However, non-Majorana mechanisms can also generate similar signatures, especially in disordered samples. Here, we studied similar hybrid devices with a well-controlled and transparent interface between the superconductor and the QAH insulator. When the devices are in the QAH state with well-aligned magnetization, the two-terminal conductance is always half-quantized. Our experiment provides a comprehensive understanding of the superconducting proximity effect observed in QAH-superconductor hybrid devices and shows that the half-quantized conductance plateau is unlikely to be induced by chiral Majorana fermions in samples with a highly transparent interface.
Intrinsic magnetic topological insulators offer low disorder and large magnetic band gaps for robust magnetic topological phases operating at higher temperatures. By controlling the layer thickness, emergent phenomena such as the quantum anomalous Hall (QAH) effect and axion insulator phases have been realized. Furthermore, these observations occur at temperatures significantly lower than the Néel temperature of bulk MnBi 2 Te 4 , and measurement of the magnetic energy gap at the Dirac point in ultrathin MnBi 2 Te 4 has yet to be achieved. Critical to achieving the promise of this system is a direct measurement of the layer-dependent energy gap and verification of a temperature-dependent topological phase transition from a large band gap QAH insulator to a gapless TI paramagnetic phase. Here we utilize temperature-dependent angle-resolved photoemission spectroscopy to study epitaxial ultrathin MnBi 2 Te 4 . We directly observe a layer-dependent crossover from a 2D ferromagnetic insulator with a band gap greater than 780 meV in one septuple layer (1 SL) to a QAH insulator with a large energy gap (>70 meV) at 8 K in 3 and 5 SL MnBi 2 Te 4 . The QAH gap is confirmed to be magnetic in origin, as it becomes gapless with increasing temperature above 8 K.
The evolution of the physical properties of 2D material from monolayer limit to the bulk reveals unique consequences from dimension confinement and provides a distinct tuning knob for applications. Monolayer 1T'-phase transition metal dichalcogenides (1T'-TMDs) with ubiquitous quantum spin Hall (QSH) states are ideal 2D building blocks of various 3D topological phases. However, the stacking geometry has been previously limited to the bulk 1T'-WTe 2 type. Here, the novel 2M-TMDs consisting of translationally stacked 1T'-monolayers are introduced as promising material platforms with tunable inverted bandgaps and interlayer coupling. By performing advanced polarization-dependent angle-resolved photoemission spectroscopy as well as first-principles calculations on the electronic structure of 2M-TMDs, a topology hierarchy is revealed: 2M-WSe 2 , MoS 2 , and MoSe 2 are weak topological insulators (WTIs), whereas 2M-WS 2 is a strong topological insulator (STI). Further demonstration of topological phase transitions by tunning interlayer distance indicates that band inversion amplitude and interlayer coupling jointly determine different topological states in 2M-TMDs. Finally, it is proposed that 2M-TMDs are parent compounds of various exotic phases including topological superconductors and promise great application potentials in quantum electronics due to their flexibility in patterning with 2D materials.
Not long ago, it was shown that a discrete time crystal can be realized if a quantum system is periodically driven to a non-equilibrium state. Proof-of-concept experiments are reported by two groups using trapped ions and nitrogen-vacancy centers in diamond, respectively. The concept of discrete time crystals vividly demonstrates that the coherence time of a quantum system may be enhanced by driving the system out of equilibrium. In this project, we want to test this novel concept in another canonical quantum system, the quantum Hall system in a two-dimensional electron gas (2DEG). Compared to other systems, quantum Hall magnetism (QHM) in high quality, industry-compatible GaAs/AlGaAs heterostructures allows for detailed and quantitative studies in a particularly simple and clean environment. This detailed knowledge should help achieve longer coherence times in a driven QHM system. This report will detail the results from a recent study on the stability of the quantum Hall skyrmions (QHS) state at a Landau level filling close to ν = 1 by measuring its current-voltage (I-V) breakdown characteristics under radio-frequency (RF) radiations. We observe that the critical current increases visibly when the RF frequency is right at the Larmor frequency of 75As nuclei, where the hyperfine interaction between electron and nuclear spins perturbs the QHS state most significantly. We believe that this observation is consistent with the novel concept that the coherence time of a quantum system may be enhanced by driving the system out of equilibrium.