Tuning the Chern number in quantum anomalous Hall insulators.

A quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has a quantized Hall resistance of h/(Ce2) and vanishing longitudinal resistance under zero magnetic field (where h is the Planck constant, e is the elementary charge, and the Chern number C is an integer)1,2. The QAH effect has been realized in magnetic topological insulators3-9 and magic-angle twisted bilayer graphene10,11. However, the QAH effect at zero magnetic field has so far been realized only for C = 1. Here we realize a well quantized QAH effect with tunable Chern number (up to C = 5) in multilayer structures consisting of alternating magnetic and undoped topological insulator layers, fabricated using molecular beam epitaxy. The Chern number of these QAH insulators is determined by the number of undoped topological insulator layers in the multilayer structure. Moreover, we demonstrate that the Chern number of a given multilayer structure can be tuned by varying either the magnetic doping concentration in the magnetic topological insulator layers or the thickness of the interior magnetic topological insulator layer. We develop a theoretical model to explain our experimental observations and establish phase diagrams for QAH insulators with high, tunable Chern number. The realization of such insulators facilitates the application of dissipationless chiral edge currents in energy-efficient electronic devices, and opens up opportunities for developing multi-channel quantum computing and higher-capacity chiral circuit interconnects.

Electrical switching of the edge current chirality in quantum anomalous Hall insulators.

A quantum anomalous Hall (QAH) insulator is a topological phase in which the interior is insulating but electrical current flows along the edges of the sample in either a clockwise or counterclockwise direction, as dictated by the spontaneous magnetization orientation. Such a chiral edge current eliminates any backscattering, giving rise to quantized Hall resistance and zero longitudinal resistance. Here we fabricate mesoscopic QAH sandwich Hall bar devices and succeed in switching the edge current chirality through thermally assisted spin-orbit torque (SOT). The well-quantized QAH states before and after SOT switching with opposite edge current chiralities are demonstrated through four- and three-terminal measurements. We show that the SOT responsible for magnetization switching can be generated by both surface and bulk carriers. Our results further our understanding of the interplay between magnetism and topological states and usher in an easy and instantaneous method to manipulate the QAH state.

Even-Odd Layer-Dependent Exchange Bias Effect in MnBi2Te4 Chern Insulator Devices.

Magnetic topological materials with coexisting magnetism and nontrivial band structures exhibit many novel quantum phenomena, including the quantum anomalous Hall effect, the axion insulator state, and the Weyl semimetal phase. As a stoichiometric layered antiferromagnetic topological insulator, thin films of MnBi2Te4 show fascinating even-odd layer-dependent physics. In this work, we fabricate a series of thin-flake MnBi2Te4 devices using stencil masks and observe the Chern insulator state at high magnetic fields. Upon magnetic field training, a large exchange bias effect is observed in odd but not in even septuple layer (SL) devices. Through theoretical calculations, we attribute the even-odd layer-dependent exchange bias effect to the contrasting surface and bulk magnetic properties of MnBi2Te4 devices. Our findings reveal the microscopic magnetic configuration of MnBi2Te4 thin flakes and highlight the challenges in replicating the zero magnetic field quantum anomalous Hall effect in odd SL MnBi2Te4 devices.

Engineering Plateau Phase Transition in Quantum Anomalous Hall Multilayers.

The plateau phase transition in quantum anomalous Hall (QAH) insulators corresponds to a quantum state wherein a single magnetic domain gives way to multiple domains and then reconverges back to a single magnetic domain. The layer structure of the sample provides an external knob for adjusting the Chern number C of the QAH insulators. Here, we employ molecular beam epitaxy to grow magnetic topological insulator multilayers and realize the magnetic field-driven plateau phase transition between two QAH states with odd Chern number change ΔC. We find that critical exponents extracted for the plateau phase transitions with ΔC = 1 and ΔC = 3 in QAH insulators are nearly identical. We construct a four-layer Chalker-Coddington network model to understand the consistent critical exponents for the plateau phase transitions with ΔC = 1 and ΔC = 3. This work will motivate further investigations into the critical behaviors of plateau phase transitions with different ΔC in QAH insulators.

Coexistence of Superconductivity and Antiferromagnetism in Topological Magnet MnBi2Te4 Films.

The interface of two materials can harbor unexpected emergent phenomena. One example is interface-induced superconductivity. In this work, we employ molecular beam epitaxy to grow a series of heterostructures formed by stacking together two nonsuperconducting antiferromagnetic materials, an intrinsic antiferromagnetic topological insulator MnBi2Te4 and an antiferromagnetic iron chalcogenide FeTe. Our electrical transport measurements reveal interface-induced superconductivity in these heterostructures. By performing scanning tunneling microscopy and spectroscopy measurements, we observe a proximity-induced superconducting gap on the top surface of the MnBi2Te4 layer, confirming the coexistence of superconductivity and antiferromagnetism in the MnBi2Te4 layer. Our findings will advance the fundamental inquiries into the topological superconducting phase in hybrid devices and provide a promising platform for the exploration of chiral Majorana physics in MnBi2Te4-based heterostructures.

Environmental Doping-Induced Degradation of the Quantum Anomalous Hall Insulators.

The quantum anomalous Hall (QAH) insulator carries dissipation-free chiral edge current and thus provides a unique opportunity to develop energy-efficient transformative information technology. Despite promising advances, the QAH insulator has thus far eluded any practical applications. In addition to its low working temperature, the QAH state in magnetically doped topological insulators usually deteriorates with time in ambient conditions. In this work, we store three QAH devices with similar initial properties in different environments. The QAH device without a protection layer in air shows clear degradation and becomes hole-doped. The QAH device kept in an argon glovebox without a protection layer shows no measurable degradation after 560 h, and the device protected by a 3 nm AlOx protection layer in air shows minimal degradation with stable QAH properties. Our work shows a route to preserve the dissipation-free chiral edge state in QAH devices for potential applications in quantum information technology.

Evolution of Dopant-Concentration-Induced Magnetic Exchange Interaction in Topological Insulator Thin Films.

To date, the quantum anomalous Hall effect has been realized in chromium (Cr)- and/or vanadium(V)-doped topological insulator (Bi,Sb)2Te3 thin films. In this work, we use molecular beam epitaxy to synthesize both V- and Cr-doped Bi2Te3 thin films with controlled dopant concentration. By performing magneto-transport measurements, we find that both systems show an unusual yet similar ferromagnetic response with respect to magnetic dopant concentration; specifically the Curie temperature does not increase monotonically but shows a local maximum at a critical dopant concentration. We attribute this unusual ferromagnetic response observed in Cr/V-doped Bi2Te3 thin films to the dopant-concentration-induced magnetic exchange interaction, which displays evolution from van Vleck-type ferromagnetism in a nontrivial magnetic topological insulator to Ruderman-Kittel-Kasuya-Yosida (RKKY)-type ferromagnetism in a trivial diluted magnetic semiconductor. Our work provides insights into the ferromagnetic properties of magnetically doped topological insulator thin films and facilitates the pursuit of high-temperature quantum anomalous Hall effect.

Crossover from Ising- to Rashba-type superconductivity in epitaxial Bi2Se3/monolayer NbSe2 heterostructures.

A topological insulator (TI) interfaced with an s-wave superconductor has been predicted to host topological superconductivity. Although the growth of epitaxial TI films on s-wave superconductors has been achieved by molecular-beam epitaxy, it remains an outstanding challenge for synthesizing atomically thin TI/superconductor heterostructures, which are critical for engineering the topological superconducting phase. Here we used molecular-beam epitaxy to grow Bi2Se3 films with a controlled thickness on monolayer NbSe2 and performed in situ angle-resolved photoemission spectroscopy and ex situ magnetotransport measurements on these heterostructures. We found that the emergence of Rashba-type bulk quantum-well bands and spin-non-degenerate surface states coincides with a marked suppression of the in-plane upper critical magnetic field of the superconductivity in Bi2Se3/monolayer NbSe2 heterostructures. This is a signature of a crossover from Ising- to Rashba-type superconducting pairings, induced by altering the Bi2Se3 film thickness. Our work opens a route for exploring a robust topological superconducting phase in TI/Ising superconductor heterostructures.

Confinement-Induced Chiral Edge Channel Interaction in Quantum Anomalous Hall Insulators.

In quantum anomalous Hall (QAH) insulators, the interior is insulating but electrons can travel with zero resistance along one-dimensional (1D) conducting paths known as chiral edge channels (CECs). These CECs have been predicted to be confined to the 1D edges and exponentially decay in the two-dimensional (2D) bulk. In this Letter, we present the results of a systematic study of QAH devices fashioned in a Hall bar geometry of different widths under gate voltages. At the charge neutral point, the QAH effect persists in a Hall bar device with a width of only ∼72 nm, implying the intrinsic decaying length of CECs is less than ∼36 nm. In the electron-doped regime, we find that the Hall resistance deviates quickly from the quantized value when the sample width is less than 1 µm. Our theoretical calculations suggest that the wave function of CEC first decays exponentially and then shows a long tail due to disorder-induced bulk states. Therefore, the deviation from the quantized Hall resistance in narrow QAH samples originates from the interaction between two opposite CECs mediated by disorder-induced bulk states in QAH insulators, consistent with our experimental observations.

Zero Magnetic Field Plateau Phase Transition in Higher Chern Number Quantum Anomalous Hall Insulators.

The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states. It can be achieved by either sweeping the magnetic field or tuning the carrier density. The recent realization of the quantum anomalous Hall (QAH) insulators with tunable Chern numbers introduces the channel degree of freedom to the dissipation-free chiral edge transport and makes the study of the quantum phase transition between two topological states under zero magnetic field possible. Here, we synthesized the magnetic topological insulator (TI)/TI pentalayer heterostructures with different Cr doping concentrations in the middle magnetic TI layers using molecular beam epitaxy. By performing transport measurements, we found a potential plateau phase transition between C=1 and C=2 QAH states under zero magnetic field. In tuning the transition, the Hall resistance monotonically decreases from h/e^{2} to h/2e^{2}, concurrently, the longitudinal resistance exhibits a maximum at the critical point. Our results show that the ratio between the Hall resistance and the longitudinal resistance is greater than 1 at the critical point, which indicates that the original chiral edge channel from the C=1 QAH state coexists with the dissipative bulk conduction channels. Subsequently, these bulk conduction channels appear to self-organize and form the second chiral edge channel in completing the plateau phase transition. Our study will motivate further investigations of this novel Chern number change-induced quantum phase transition and advance the development of the QAH chiral edge current-based electronic and spintronic devices.

Even-Odd Layer-Dependent Anomalous Hall Effect in Topological Magnet MnBi2Te4 Thin Films.

Recently, MnBi2Te4 has been demonstrated to be an intrinsic magnetic topological insulator and the quantum anomalous Hall (QAH) effect was observed in exfoliated MnBi2Te4 flakes. Here, we used molecular beam epitaxy (MBE) to grow MnBi2Te4 films with thickness down to 1 septuple layer (SL) and performed thickness-dependent transport measurements. We observed a nonsquare hysteresis loop in the antiferromagnetic state for films with thickness greater than 2 SL. The hysteresis loop can be separated into two AH components. We demonstrated that one AH component with the larger coercive field is from the dominant MnBi2Te4 phase, whereas the other AH component with the smaller coercive field is from the minor Mn-doped Bi2Te3 phase. The extracted AH component of the MnBi2Te4 phase shows a clear even-odd layer-dependent behavior. Our studies reveal insights on how to optimize the MBE growth conditions to improve the quality of MnBi2Te4 films.

Concurrence of quantum anomalous Hall and topological Hall effects in magnetic topological insulator sandwich heterostructures.

The quantum anomalous Hall (QAH) effect is a consequence of non-zero Berry curvature in momentum space. The QAH insulator harbours dissipation-free chiral edge states in the absence of an external magnetic field. However, the topological Hall (TH) effect, a hallmark of chiral spin textures, is a consequence of real-space Berry curvature. Here, by inserting a topological insulator (TI) layer between two magnetic TI layers, we realized the concurrence of the TH effect and the QAH effect through electric-field gating. The TH effect is probed by bulk carriers, whereas the QAH effect is characterized by chiral edge states. The appearance of the TH effect in the QAH insulating regime is a consequence of chiral magnetic domain walls that result from the gate-induced Dzyaloshinskii-Moriya interaction and occurs during the magnetization reversal process in the magnetic TI sandwich samples. The coexistence of chiral edge states and chiral spin textures provides a platform for proof-of-concept dissipationless spin-textured spintronic applications.

Observation of Interfacial Antiferromagnetic Coupling between Magnetic Topological Insulator and Antiferromagnetic Insulator.

Inducing magnetic orders in a topological insulator (TI) to break its time reversal symmetry has been predicted to reveal many exotic topological quantum phenomena. The manipulation of magnetic orders in a TI layer can play a key role in harnessing these quantum phenomena toward technological applications. Here we fabricated a thin magnetic TI film on an antiferromagnetic (AFM) insulator Cr2O3 layer and found that the magnetic moments of the magnetic TI layer and the surface spins of the Cr2O3 layers favor interfacial AFM coupling. Field cooling studies show a crossover from negative to positive exchange bias clarifying the competition between the interfacial AFM coupling energy and the Zeeman energy in the AFM insulator layer. The interfacial exchange coupling also enhances the Curie temperature of the magnetic TI layer. The unique interfacial AFM alignment in magnetic TI on AFM insulator heterostructures opens a new route toward manipulating the interplay between topological states and magnetic orders in spin-engineered heterostructures, facilitating the exploration of proof-of-concept TI-based spintronic and electronic devices with multifunctionality and low power consumption.

Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures.

The "magnetoelectric effect" arises from the coupling between magnetic and electric properties in materials. The Z_{2} invariant of topological insulators (TIs) leads to a quantized version of this phenomenon, known as the topological magnetoelectric (TME) effect. This effect can be realized in a new topological phase called an "axion insulator" whose surface states are all gapped but the interior still obeys time reversal symmetry. We demonstrate such a phase using electrical transport measurements in a quantum anomalous Hall (QAH) sandwich heterostructure, in which two compositionally different magnetic TI layers are separated by an undoped TI layer. Magnetic force microscopy images of the same sample reveal sequential magnetization reversals of the top and bottom layers at different coercive fields, a consequence of the weak interlayer exchange coupling due to the spacer. When the magnetization is antiparallel, both the Hall resistance and Hall conductance show zero plateaus, accompanied by a large longitudinal resistance and vanishing longitudinal conductance, indicating the realization of an axion insulator state. Our findings thus show evidence for a phase of matter distinct from the established QAH state and provide a promising platform for the realization of the TME effect.

Correlated metals as transparent conductors.

The fundamental challenge for designing transparent conductors used in photovoltaics, displays and solid-state lighting is the ideal combination of high optical transparency and high electrical conductivity. Satisfying these competing demands is commonly achieved by increasing carrier concentration in a wide-bandgap semiconductor with low effective carrier mass through heavy doping, as in the case of tin-doped indium oxide (ITO). Here, an alternative design strategy for identifying high-conductivity, high-transparency metals is proposed, which relies on strong electron-electron interactions resulting in an enhancement in the carrier effective mass. This approach is experimentally verified using the correlated metals SrVO3 and CaVO3, which, despite their high carrier concentration (>2.2 × 10(22) cm(-3)), have low screened plasma energies (<1.33 eV), and demonstrate excellent performance when benchmarked against ITO. A method is outlined to rapidly identify other candidates among correlated metals, and strategies are proposed to further enhance their performance, thereby opening up new avenues to develop transparent conductors.

Superfluidlike Mass Flow Through 8 µm Thick Solid

We report the observation of superfluidlike mass flow through coin-shaped 8 µm thick solid ^{4}He samples sandwiched between superfluid leads. Mass flow is found from the melting pressure to at least 30 bar with a concomitant decrease in the onset temperature from 1 to 0.25 K. The mass-flow rate is found to be sample dependent and can be enhanced by thermal annealing. The flow rate decreases with temperature and decays nearly exponentially with the pressure of the samples. The dissipation associated with the mass flow decreases with temperature and becomes superfluidlike near 0.1 K. In contrast to earlier studies on centimeter-thick samples, we do not see a sharp cutoff in the mass-flow rate at low temperature.

High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator.

The discovery of the quantum Hall (QH) effect led to the realization of a topological electronic state with dissipationless currents circulating in one direction along the edge of a two-dimensional electron layer under a strong magnetic field. The quantum anomalous Hall (QAH) effect shares a similar physical phenomenon to that of the QH effect, whereas its physical origin relies on the intrinsic spin-orbit coupling and ferromagnetism. Here, we report the experimental observation of the QAH state in V-doped (Bi,Sb)2Te3 films with the zero-field longitudinal resistance down to 0.00013 ± 0.00007h/e(2) (~3.35 ± 1.76 Ω), Hall conductance reaching 0.9998 ± 0.0006e(2)/h and the Hall angle becoming as high as 89.993° ± 0.004° at T = 25 mK. A further advantage of this system comes from the fact that it is a hard ferromagnet with a large coercive field (Hc > 1.0 T) and a relative high Curie temperature. This realization of a robust QAH state in hard ferromagnetic topological insulators (FMTIs) is a major step towards dissipationless electronic applications in the absence of external fields.

Observation of the Quantum Anomalous Hall Insulator to Anderson Insulator Quantum Phase Transition and its Scaling Behavior.

Fundamental insight into the nature of the quantum phase transition from a superconductor to an insulator in two dimensions, or from one plateau to the next or to an insulator in the quantum Hall effect, has been revealed through the study of its scaling behavior. Here, we report on the experimental observation of a quantum phase transition from a quantum-anomalous-Hall insulator to an Anderson insulator in a magnetic topological insulator by tuning the chemical potential. Our experiment demonstrates the existence of scaling behavior from which we extract the critical exponent for this quantum phase transition. We expect that our work will motivate much further investigation of many properties of quantum phase transition in this new context.

Surface superconductivity in thin cylindrical Bi nanowire.

The physical origin and the nature of superconductivity in nanostructured Bi remains puzzling. Here, we report transport measurements of individual cylindrical single-crystal Bi nanowires, 20 and 32 nm in diameter. In contrast to nonsuperconducting Bi nanoribbons with two flat surfaces, cylindrical Bi nanowires show superconductivity below 1.3 K. However, their superconducting critical magnetic fields decrease with their diameter, which is the opposite of the expected behavior for thin superconducting wires. Quasiperiodic oscillations of magnetoresistance were observed in perpendicular fields but were not seen in the parallel orientation. These results can be understood by a model of surface superconductivity with an enhanced surface-to-bulk volume in small diameter wires, where the superconductivity originates from the strained surface states of the nanowires due to the surface curvature-induced stress.

Zero-Field Dissipationless Chiral Edge Transport and the Nature of Dissipation in the Quantum Anomalous Hall State.

The quantum anomalous Hall (QAH) effect is predicted to possess, at a zero magnetic field, chiral edge channels that conduct a spin polarized current without dissipation. While edge channels have been observed in previous experimental studies of the QAH effect, their dissipationless nature at a zero magnetic field has not been convincingly demonstrated. By a comprehensive experimental study of the gate and temperature dependences of local and nonlocal magnetoresistance, we unambiguously establish the dissipationless edge transport. By studying the onset of dissipation, we also identify the origin of dissipative channels and clarify the surprising observation that the critical temperature of the QAH effect is 2 orders of magnitude smaller than the Curie temperature of ferromagnetism.