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Magnetic topological materials with coexisting magnetism and non-trivial 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 and a square hysteresis loop near zero magnetic field in all these devices. Upon magnetic field training, a large exchange bias effect is observed in odd but not in even septuple layer (SL) devices. Our theoretical calculations interpret this even-odd layer-dependent exchange bias effect as a consequence of 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., Comment: 23 pages, 4 figures, comments are very much welcome

Interlayer exchange coupling (IEC) between two magnetic layers sandwiched by a nonmagnetic spacer layer plays a critical role in shaping the magnetic properties of such heterostructures. The quantum anomalous Hall (QAH) effect has been realized in a structure composed of two magnetically doped topological insulator (TI) layers separated by an undoped TI layer. The quantized Hall conductance observed in this sandwich heterostructure originates from the combined contribution of the top and bottom surface states. In this work, we employ molecular beam epitaxy to synthesize a series of magnetic TI sandwiches with varying thicknesses of the middle undoped TI layer. The well-quantized QAH effect is observed in all these samples and its critical behavior is modulated by the IEC between the top and bottom magnetic TI layers. Near the plateau phase transition (PPT), we find that thinner QAH samples exhibit a two-dimensional critical metal behavior with nearly temperature-independent longitudinal resistance, whereas thicker QAH samples behave as a three-dimensional insulator with reduced longitudinal resistance at higher temperatures. The IEC-induced critical-metal-to-insulator transition in the QAH PPT regime can be understood through a two-channel Chalker-Coddington network model by tuning inter-channel tunneling. The agreement between experiment and theory strongly supports the QAH PPT within the Kosterlitz-Thouless framework, where the critical metal and disordered insulator phases exist in bound and unbound states of vortex-antivortex pairs, respectively., Comment: 19 pages, 4 figures, comments are very much welcome

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 non-superconducting 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 interaction between 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., Comment: 24 pages, 4 figures, comments are welcome

The plateau phase transition in quantum anomalous Hall (QAH) insulators corresponds to a quantum state wherein a single magnetic domain gives way to multiple magnetic domains and then re-converges 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 (MBE) to grow magnetic topological insulator (TI) multilayers with an asymmetric layer structure and realize the magnetic field-driven plateau phase transition between two QAH states with odd Chern number change {\Delta}C. In multilayer structures with C=+-1 and C=+-2 QAH states, we find two characteristic power-law behaviors between temperature and the scaling variables on the magnetic field at transition points. The critical exponents extracted for the plateau phase transitions with {\Delta}C=1 and {\Delta}C=3 in QAH insulators are found to be nearly identical, specifically, k1~0.390+-0.021 and k2~0.388+-0.015, respectively. We construct a four-layer Chalker-Coddington network model to understand the consistent critical exponents for the plateau phase transitions with {\Delta}C=1 and {\Delta}C=3. This work will motivate further investigations into the critical behaviors of plateau phase transitions with different {\Delta}C in QAH insulators and provide new opportunities for the development of QAH chiral edge current-based electronic and spintronic devices., Comment: 18 pages, 4 figures. Comments are welcome

When two different electronic materials are brought together, the resultant interface often shows unexpected quantum phenomena, including interfacial superconductivity and Fu-Kane topological superconductivity (TSC). Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures formed by stacking together two magnetic materials, a ferromagnetic topological insulator (TI) and an antiferromagnetic iron chalcogenide (FeTe). We discover emergent interface-induced superconductivity in these heterostructures and demonstrate the trifecta occurrence of superconductivity, ferromagnetism, and topological band structure in the magnetic TI layer, the three essential ingredients of chiral TSC. The unusual coexistence of ferromagnetism and superconductivity can be attributed to the high upper critical magnetic field that exceeds the Pauli paramagnetic limit for conventional superconductors at low temperatures. The magnetic TI/FeTe heterostructures with robust superconductivity and atomically sharp interfaces provide an ideal wafer-scale platform for the exploration of chiral TSC and Majorana physics, constituting an important step toward scalable topological quantum computation., Comment: 14 pages, 4 figures. Accepted by Science. Comments are welcome

Magnetic topological states refer to a class of exotic phases in magnetic materials with their 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 10nm. The thick QAH insulators in the three-dimensional(3D) regime are limited, largely due to inevitable bulk carriers being introduced in thick magnetic TI samples. Here, we employ molecular beam epitaxy (MBE) to synthesize magnetic TI trilayers with a thickness of up to ~106 nm. We find these samples exhibit well-quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field. By varying magnetic dopants, gate voltages, temperature, and external magnetic fields, we examine the properties of these thick QAH insulators and demonstrate the robustness of the 3D QAH effect. The realization of the well-quantized 3D QAH effect indicates that the nonchiral side surface states of our 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., Comment: 24 pages, 5 figures. Comments are welcome

Over the last decade, the possibility of realizing topological superconductivity (TSC) has generated much excitement, mainly due to the potential use of its excitations (Majorana zero modes) in a fault-tolerant topological quantum computer 1,2. TSC can be created in electronic systems where the topological and superconducting orders coexist3, motivating the continued exploration of candidate material platforms to this end. Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures that host emergent interfacial superconductivity when a non-superconducting antiferromagnet (FeTe) is interfaced with a topological insulator (TI) (Bi, Sb)2Te3 wherein the chemical potential can be tuned through varying the Bi/Sb ratio. By performing in-vacuo angle-resolved photoemission spectroscopy (ARPES) and ex-situ electrical transport measurements, we find that the superconducting transition temperature and the upper critical magnetic field are suppressed when the chemical potential approaches the Dirac point. This observation implies a direct correlation between the interfacial superconductivity and Dirac electrons of the TI layer. We provide evidence to show that the observed interfacial superconductivity and its chemical potential dependence is the result of the competition between the Ruderman-Kittel-Kasuya-Yosida-type ferromagnetic coupling mediated by Dirac surface states and antiferromagnetic exchange couplings that generate the bicollinear antiferromagnetic order in the FeTe layer. The Dirac-fermion-assisted interfacial superconductivity in (Bi,Sb)2Te3/FeTe heterostructures provides a new approach to probe TSC and Majorana physics in hybrid devices and potentially constitutes an alternative platform for topological quantum computation., Comment: 32 pages and 4 figures. Accepted by Nature Communications

An axion insulator is a three-dimensional (3D) topological insulator (TI), in which the bulk maintains the time-reversal symmetry or inversion symmetry but the surface states are gapped by surface magnetization. The axion insulator state has been observed in molecular beam epitaxy (MBE)-grown magnetically doped TI sandwiches and exfoliated intrinsic magnetic TI MnBi2Te4 flakes with an even number layer. All these samples have a thickness of ~10 nm, near the 2D-to-3D boundary. The coupling between the top and bottom surface states in thin samples may hinder the observation of quantized topological magnetoelectric response. Here, we employ MBE to synthesize magnetic TI sandwich heterostructures and find that the axion insulator state persists in a 3D sample with a thickness of ~106 nm. Our transport results show that the axion insulator state starts to emerge when the thickness of the middle undoped TI layer is greater than ~3 nm. The 3D hundred-nanometer-thick axion insulator provides a promising platform for the exploration of the topological magnetoelectric effect and other emergent magnetic topological states, such as the high-order TI phase., Comment: 25 pages, 5 figures. Comments are very much welcome

The quantum anomalous Hall (QAH) insulator is a topological quantum state with quantized Hall resistance and zero longitudinal resistance in the absence of an external magnetic field. The QAH insulator carries spin-polarized dissipation-free chiral edge current and thus provides a unique opportunity to develop energy-efficient transformative information technology. Despite promising advances on the QAH effect over the past decade, the QAH insulator has thus far eluded any practical applications. In addition to its low working temperature, the QAH state in magnetically doped topological insulator (TI) films/heterostructures usually deteriorates with time in ambient conditions. In this work, we prepare three QAH devices with similar initial properties and store them in different environments to investigate the evolution of their transport properties. The QAH device without a protection layer in air show clear degradation and becomes hole-doped with the charge neutral point shifting significantly to positive gate voltages. The QAH device kept in an argon glove box without a protection layer shows no measurable degradation after 560 hours 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., Comment: 18 pages, 4 figures. A REU project. Comments are welcome

One-dimensional (1D) topologically protected states are usually formed at the interface between two-dimensional (2D) materials with different topological invariants. Therefore, 1D chiral interface channels (CICs) can be created at the boundary of two quantum anomalous Hall (QAH) insulators with different Chern numbers. Such a QAH junction can function as a chiral edge current distributer at zero magnetic field, but its realization remains challenging. Here, by employing an in-situ mechanical mask, we use molecular beam epitaxy (MBE) to synthesize QAH insulator junctions, in which two QAH insulators with different Chern numbers are connected along a 1D junction. For the junction between C = 1 and C = -1 QAH insulators, we observe quantized transport and demonstrate the appearance of the two parallel propagating CICs along the magnetic domain wall at zero magnetic field. Moreover, since the Chern number of the QAH insulators in magnetic topological insulator (TI)/TI multilayers can be tuned by altering magnetic TI/TI bilayer periods, the junction between two QAH insulators with arbitrary Chern numbers can be achieved by growing different periods of magnetic TI/TI on the two sides of the sample. For the junction between C = 1 and C = 2 QAH insulators, our quantized transport shows that a single CIC appears at the interface. Our work lays down the foundation for the development of QAH insulator-based electronic and spintronic devices, topological chiral networks, and topological quantum computations., Comment: 20 pages, 4 figures, comments are welcome

In quantum anomalous Hall (QAH) insulators, the interior is insulating but electrons can travel with zero resistance along one-dimensional conducting paths known as chiral edge channels (CECs). These CECs have been predicted to be confined to the one-dimensional (1D) edges and exponentially decay in the two-dimensional (2D) bulk. In this work, we present the results of a systematic study of QAH devices fashioned in a Hall bar geometry of different widths. 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 um. Our theoretical calculations suggest that 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., Comment: 19 pages, 5 figures, comments are welcome

A quantum anomalous Hall (QAH) insulator is a topological state of matter, in which the interior is insulating but electrical current flows along the edges of the sample, in either clockwise (right-handed) or counter-clockwise (left-handed) direction dictated by the spontaneous magnetization orientation. Such chiral edge current (CEC) eliminates any backscattering, giving rise to quantized Hall resistance and zero longitudinal resistance. In this work, we fabricate mesoscopic QAH sandwich (i.e. magnetic topological insulator (TI)/TI/magnetic TI) Hall bar devices and succeed in switching the CEC chirality in QAH insulators through spin-orbit torque (SOT) by applying a current pulse and suitably controlled gate voltage. The well-quantized QAH states with opposite CEC chiralities are demonstrated through four- and three-terminal measurements before and after SOT switching. Our theoretical calculations show that the SOT that enables the magnetization switching can be generated by both bulk and surface carriers in QAH insulators, in good agreement with experimental observations. Current pulse-induced switching of the CEC chirality in QAH insulators will not only advance our knowledge in the interplay between magnetism and topological states but also expedite easy and instantaneous manipulation of the QAH state in proof-of-concept energy-efficient electronic and spintronic devices as well as quantum information applications., Comment: 24 pages, 5 figures, comments are welcome

Two essential ingredients for the quantum anomalous Hall (QAH) effect, i.e. topological and magnetic orders, can be combined by doping magnetic ions into a topological insulator (TI) film. Through this approach, the QAH effect has been realized in chromium (Cr)- and/or vanadium (V)-doped TI (Bi,Sb)2Te3 thin films. In this work, we synthesize both V- and Cr-doped Bi2Te3 thin films with controlled dopant concentration using molecular beam epitaxy (MBE). By performing magneto-transport measurements, we find that both systems show an unusual but 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. Our angle-resolved photoemission spectroscopy (ARPES) measurements show that the Cr/V doping introduces hole carriers into Bi2Te3, which consequently move the chemical potential toward the charge neutral point. In addition, the Cr/V doping also reduces the spin-orbit coupling of Bi2Te3 which drives it from a nontrivial TI to a trivial semiconductor. The unusual ferromagnetic response observed in Cr/V-doped Bi2Te3 thin films is attributed to the dopant-concentration-induced magnetic exchange interaction, which displays the evolution from the van Vleck-type ferromagnetism in a nontrivial magnetic TI to the Ruderman-Kittel-Kasuya-Yosida (RKKY)-type ferromagnetism in a trivial diluted magnetic semiconductor. Our work provides insights into the ferromagnetic properties of magnetically doped TI thin films and facilitates the pursuit of high-temperature QAH effect., Comment: 17 pages, 4 figures. Comments are welcome

A topological insulator (TI) interfaced with an s-wave superconductor has been predicted to host an unusual form of superconductivity known as topological superconductivity (TSC). Molecular beam epitaxy (MBE) has been the primary approach in the scalable synthesis of the TI/superconductor heterostructures. Although the growth of epitaxial TI films on s-wave superconductors has been achieved, it remains an outstanding challenge for synthesizing atomically thin TI/superconductor heterostructures, which are critical for engineering the TSC phase. Here, we used MBE to grow Bi2Se3 films with the controlled thickness on monolayer NbSe2 and performed in-situ angle-resolved photoemission spectroscopy and ex-situ magneto-transport measurements on these Bi2Se3/monolayer NbSe2 heterostructures. We found that the emergence of Rashba-type bulk quantum well bands and spin-nondegenerate 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 the signature of a crossover from Ising- to Rashba-type superconducting pairings, induced by altering Bi2Se3 film thickness. Our work opens a new route for exploring a robust TSC phase in TI/Ising superconductor heterostructures., Comment: 27 pages, 4 pages, comments are welcome

The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states through 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 penta-layer heterostructures with different Cr doping concentrations in the middle magnetic TI layers using molecular beam epitaxy (MBE). By performing transport measurements, we found a zero magnetic field quantum phase transition between the C = 1 and C = 2 QAH states. In tuning the transition, the Hall resistance monotonically decreases from h/e2 to h/2e2, 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., Comment: 19 pages, 4 figures, Comments are welcome

When a ferromagnet is placed in contact with a superconductor, owing to incompatible spin order, the Cooper pairs from the superconductor cannot survive more than one or two nanometers inside the ferromagnet. This is confirmed in the measurements of ferromagnetic nickel (Ni) nanowires contacted by superconducting niobium (Nb) leads. However, when a 3 nm thick copper oxide (CuO) buffer layer made by exposing an evaporated or a sputtered 3 nm Cu film to air, is inserted between the Nb electrodes and the Ni wire, the spatial extent of the superconducting proximity range is dramatically increased from 2 to a few tens of nanometers. Scanning transmission electron microscope study confirms the formation of a 3 nm thick CuO layer when an evaporated Cu film is exposed to air. Magnetization measurements of such a 3 nm CuO film on a SiO2/Si substrate and on Nb/SiO2/Si show clear evidence of ferromagnetism. One way to understand the long-range proximity effect in the Ni nanowire is that the CuO buffer layer with ferromagnetism facilitates the conversion of singlet superconductivity in Nb into triplet supercurrent along the Ni nanowires., Comment: 23 pages, 4 figures, 2 tables. Comments are welcome

A central theme in condensed matter physics is to create and understand the exotic states of matter by incorporating magnetism into topological materials. One prime example is the quantum anomalous Hall (QAH) state. Recently, MnBi2Te4 has been demonstrated to be an intrinsic magnetic topological insulator and the 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 non-square hysteresis loop in the antiferromagnetic state for films with thickness greater than 2 SL. The hysteresis loop can be separated into two AH components. Through careful analysis, we demonstrated that one AH component with the larger coercive field is from the dominant MnBi2Te4 phase, while the other AH component with the smaller coercive field is from the minor Mn-doped Bi2Te3 phase in the samples. The extracted AH component of the MnBi2Te4 phase shows a clear even-odd layer-dependent behavior, a signature of antiferromagnetic thin films. Our studies reveal insights on how to optimize the MBE growth conditions to improve the quality of MnBi2Te4 films, in which the QAH and other exotic states are predicted., Comment: 23 pages, 4 figures, comments are welcome

We use magnetotransport in dual-gated magnetic topological insulator heterostructures to map out a phase diagram of the topological Hall and quantum anomalous Hall effects as a function of the chemical potential (primarily determined by the back gate voltage) and the asymmetric potential (primarily determined by the top gate voltage). A theoretical model that includes both surface states and valence band quantum well states allows the evaluation of the variation of the Dzyaloshinskii-Moriya interaction and carrier density with gate voltages. The qualitative agreement between experiment and theory provides strong evidence for the existence of a topological Hall effect in the system studied, opening up a new route for understanding and manipulating chiral magnetic spin textures in real space., Comment: Minor corrections to original submission

(TaSe4)2I, a quasi-one-dimensional (1D) crystal, shows a characteristic temperature-driven metal-insulator phase transition. Above the charge density wave (CDW) temperature Tc, (TaSe4)2I has been predicted to harbor a Weyl semimetal phase. Below Tc, it becomes an axion insulator. Here, we performed angle-resolved photoemission spectroscopy (ARPES) measurements on the (110) surface of (TaSe4)2I and observed two sets of Dirac-like energy bands in the first Brillion zone, which agree well with our first-principles calculations. Moreover, we found that each Dirac band exhibits an energy splitting of hundreds of meV under certain circumstances. In combination with core level measurements, our theoretical analysis showed that this Dirac band splitting is a result of surface charge polarization due to the loss of surface iodine atoms. Our findings here shed new light on the interplay between band topology and CDW order in Peierls compounds and will motivate more studies on topological properties of strongly correlated quasi-1D materials., Comment: 18 pages, 4 figures. Comments are welcome

The quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has quantized Hall resistance of h/Ce2 and vanishing longitudinal resistance under zero magnetic field, where C is called the Chern number. The QAH effect has been realized in magnetic topological insulators (TIs) and magic-angle twisted bilayer graphene. Despite considerable experimental efforts, the zero magnetic field QAH effect has so far been realized only for C = 1. Here we used molecular beam epitaxy to fabricate magnetic TI multilayers and realized the QAH effect with tunable Chern number C up to 5. The Chern number of these QAH insulators is tuned by varying the magnetic doping concentration or the thickness of the interior magnetic TI layers in the multilayer samples. A theoretical model is developed to understand our experimental observations and establish phase diagrams for QAH insulators with tunable Chern numbers. The realization of QAH insulators with high tunable Chern numbers facilitates the potential applications of dissipationless chiral edge currents in energy-efficient electronic devices and opens opportunities for developing multi-channel quantum computing and higher-capacity chiral circuit interconnects., Comment: Accepted version (27 pages, 4 figures). Comments are welcome

The Berry phase picture provides important insights into the electronic properties of condensed matter systems. The intrinsic anomalous Hall (AH) effect can be understood as a consequence of non-zero Berry curvature in momentum space. The realization of the quantum anomalous Hall effect provided conclusive evidence for the intrinsic mechanism of the AH effect in magnetic topological insulators (TIs). Here we fabricated magnetic TI/TI heterostructures and found both the magnitude and sign of the AH effect in the magnetic TI layer can be altered by tuning the TI thickness and/or the electric gate voltage. The sign change of the AH effect with increasing TI thickness is attributed to the charge transfer across the TI and magnetic TI layers, consistent with first-principles calculations. By fabricating the magnetic TI/TI/magnetic TI sandwich heterostructures with different dopants, we created an artificial topological Hall (TH) effect-like feature in Hall traces. This artificial TH effect is induced by the superposition of two AH effects with opposite signs instead of the formation of chiral spin textures in the samples. Our study provides a new route to engineer the Berry curvature in magnetic topological materials that may lead to potential technological applications., Comment: 28 pages, 5 figures. Accepted version

The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase transition. Similar to the quantum Hall plateau to plateau transition, the QAH to axion insulator transition can also be understood by the Chalker-Coddington network model. We extract a critical exponent k~ 0.38 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker-Coddington model at v ~ 2.6, rather than the generally-accepted value of 2.33., Comment: 24 pages, 4 figures, comments are welcome

A quantum anomalous Hall (QAH) insulator coupled to an s-wave superconductor is predicted to harbor a topological superconducting phase, the elementary excitations of which (i.e. Majorana fermions) can form topological qubits upon non-Abelian braiding operations. A recent transport experiment interprets the half-quantized two-terminal conductance plateau as the presence of chiral Majorana fermions in a millimeter-size QAH-Nb hybrid structure. However, there are concerns about this interpretation because non-Majorana mechanisms can also generate similar signatures, especially in a disordered QAH system. Here, we fabricated QAH-Nb hybrid structures and studied the QAH-Nb contact transparency and its effect on the corresponding two-terminal conductance. When the QAH film is tuned to the metallic regime by electric gating, we observed a sharp zero-bias enhancement in the differential conductance, up to 80% at zero magnetic field. This large enhancement suggests high probability of Andreev reflection and transparent interface between the magnetic topological insulator (TI) and Nb layers. When the magnetic TI film is in the QAH state with well-aligned magnetization, we found that the two-terminal conductance is always half-quantized. Our experiment provides a comprehensive understanding of the superconducting proximity effect observed in QAH-superconductor hybrid structures and shows that the half-quantized conductance plateau is unlikely to be induced by chiral Majorana fermions., Comment: 17 pages, 4 figures. Comments are welcome. Supplementary materials will be provided upon request

The quantum anomalous Hall (QAH) effect is a quintessential consequence of non-zero Berry curvature in momentum-space. The QAH insulator harbors dissipation-free chiral edge states in the absence of an external magnetic field. On the other hand, the topological Hall (TH) effect, a transport hallmark of the chiral spin textures, is a consequence of real-space Berry curvature. While both the QAH and TH effects have been reported separately, their coexistence, a manifestation of entangled chiral edge states and chiral spin textures, has not been reported. Here, by inserting a TI layer between two magnetic TI layers to form a sandwich heterostructure, we realized a concurrence of the TH effect and the QAH effect through electric field gating. The TH effect is probed by bulk carriers, while the QAH effect is characterized by chiral edge states. The appearance of TH effect in the QAH insulating regime is the consequence of chiral magnetic domain walls that result from the gate-induced Dzyaloshinskii-Moriya interaction and occur during the magnetization reversal process in the magnetic TI sandwich samples. The coexistence of chiral edge states and chiral spin textures potentially provides a unique platform for proof-of-concept dissipationless spin-textured spintronic applications., Comment: 22 pages, 4 figures, the accepted version for Nature Materials

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 towards 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 multi-functionality and low power consumption., Comment: 18 pages, 4 figures. Comments are welcome

The Dirac electrons occupying the surface states (SSs) of topological insulators (TIs) have been predicted to exhibit many exciting magneto-transport phenomena. Here we report on the first experimental observation of an unconventional planar Hall effect (PHE) and an electrically gate-tunable hysteretic planar magnetoresistance (PMR) in EuS/TI heterostructures, in which EuS is a ferromagnetic insulator (FMI) with an in-plane magnetization. In such exchange-coupled FMI/TI heterostructures, we find a significant (suppressed) PHE when the in-plane magnetic field is parallel (perpendicular) to the electric current. This behavior differs from previous observations of the PHE in ferromagnets and semiconductors. Furthermore, as the thickness of the 3D TI films is reduced into the 2D limit, in which the Dirac SSs develop a hybridization gap, we find a suppression of the PHE around the charge neutral point indicating the vital role of Dirac SSs in this phenomenon. To explain our findings, we outline a symmetry argument that excludes linear-Hall mechanisms and suggest two possible non-linear Hall mechanisms that can account for all the essential qualitative features in our observations., Comment: 17 pages, 4 figures, accepted by Phys. Rev. B

We observed a novel voltage peak in the proximity effect induced superconducting gold (Au) nanowire while cooling the sample through the superconducting transition temperature. The voltage peak turned into dip in the warming process. The voltage peak (or dip) was found to be closely related to the emergence (vanishing) of the proximity induced superconductivity in the Au nanowire. The amplitude of the voltage signal depends on the temperature scanning rate and it cannot be detected when the temperature is changed slower than 0.03 K/min. This transient feature suggests the non-equilibrium property of the effect. The voltage peak could be understood by Ginzburg-Landau model as a combined result of the emergence of Cooper pairs with relatively lower free energy in W contact and the non-equilibrium diffusion of Cooper pairs and quasiparticles.

Topological crystalline insulator (TCI) is a recently-discovered topological phase of matter. It possesses multiple Dirac surface states, which are protected by the crystal symmetry. This is in contrast to the time reversal symmetry that is operative in the well-known topological insulators. In the presence of a Zeeman field and/or strain, the multiple Dirac surface states are gapped. The high-Chern-number quantum anomalous Hall (QAH) state is predicted to emerge if the chemical potential resides in all the Zeeman gaps. Here, we use molecular beam epitaxy to grow 12 double layer (DL) pure and Cr-doped SnTe (111) thin film on heat-treated SrTiO3 (111) substrate using a quintuple layer of insulating (Bi0.2Sb0.8)2Te3 topological insulator as a buffer film. The Hall traces of Cr-doped SnTe film at low temperatures display square hysteresis loops indicating long-range ferromagnetic order with perpendicular anisotropy. The Curie temperature of the 12DL Sn0.9Cr0.1Te film is ~ 110 K. Due to the chemical potential crossing the bulk valence bands, the anomalous Hall resistance of 12DL Sn0.9Cr0.1Te film is substantially lower than the predicted quantized value (~1/4 h/e2). It is possible that with systematic tuning the chemical potential via chemical doping and electrical gating, the high-Chern-number QAH state can be realized in the Cr-doped SnTe (111) thin film., Comment: 20 pages, 5 figures, accepted by Phys. Rev. B

The 'magnetoelectric effect' arises from the coupling between magnetic and electric properties in materials. The Z2 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 evidences for a phase of matter distinct from the established QAH state and provide a promising platform for the realization of the TME effect., Comment: 18-page manuscript + 24-page supplementary materials. Accepted by PRL

The possible realization of dissipationless chiral edge current in a topological insulator / magnetic insulator heterostructure is based on the condition that the magnetic proximity exchange coupling at the interface is dominated by the Dirac surface states of the topological insulator. Here we report a polarized neutron reflectometry observation of Dirac electrons mediated magnetic proximity effect in a bulk-insulating topological insulator (Bi$_{0.2}$Sb$_{0.8}$)$_{2}$Te$_{3}$ / magnetic insulator EuS heterostructure. We are able to maximize the proximity induced magnetism by applying an electrical back gate to tune the Fermi level of topological insulator to be close to the charge neutral point. A phenomenological model based on diamagnetic screening is developed to explain the suppressed proximity induced magnetism at high carrier density. Our work paves the way to utilize the magnetic proximity effect at the topological insulator/magnetic insulator hetero-interface for low-power spintronic applications., Comment: 5 pages main text with 4 figures; 2 pages supplemental materials; suggestions and discussions are welcomed

The exact mechanism responsible for the tenfold enhancement of superconducting transition temperature (Tc) in a monolayer iron selenide (FeSe) on SrTiO3(STO) substrate over that of bulk FeSe, is an open issue. We present here a coordinated study of electrical transport and low temperature electron energy-loss spectroscopy (EELS) measurements on FeSe/STO films of various thicknesses. Our EELS mapping across the FeSe/STO interface shows direct evidence of band-bending caused by electrons transferred from STO to FeSe layer. The transferred electrons were found to accumulate only within the first two atomic layers of FeSe films near the STO substrate. Our transport results found a positive backgate applied from STO is particularly effective in enhancing Tc of the films while minimally changing the carrier density. We suggest that the positive backgate tends to 'pull' the transferred electrons in FeSe films closer to the interface and thus further enhances both their coupling to interfacial phonons and the electron-electron interaction within FeSe films, thus leading to a huge enhancement of Tc in FeSe films., Comment: Submitted to Nature Communications on 24th June 2016. Comments are welcome

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 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 (QAH) 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., Comment: 17 pages, 4 figures. Accepted by PRL. Comments are welcome

The quantum anomalous Hall (QAH) effect is predicted to possess, at zero magnetic field, chiral edge channels that conduct 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 two orders of magnitude smaller than the Curie temperature of ferromagnetism., Comment: main text+supporting materials. This is the accepted version for PRL. Comments are welcome

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 as 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/e2 (~3.35+-1.76 ohm), Hall conductance reaching 0.9998+-0.0006e2/h and the Hall angle becoming as high as 89.993+-0.004degree at T=25mK. Further advantage of this system comes from the fact that it is a hard ferromagnet with a large coercive field (Hc>1.0T) and a relative high Curie temperature. This realization of robust QAH state in hard FMTIs is a major step towards dissipationless electronic applications without external fields., Comment: 16 pages, 4 figures, this is the final version, accepted by Nature Materials, forthcoming

We demonstrate by high resolution low temperature electron energy loss spectroscopy (EELS) measurements that the long range ferromagnetic (FM) order in vanadium (V)-doped topological insulator Sb$_2$Te$_3$ has the nature of van Vleck-type ferromagnetism. The positions and the relative amplitudes of two core-level peaks (L$_3$ and L$_2$) of the V EELS spectrum show unambiguous change when the sample is cooled from room temperature to T=10K. Magnetotransport and comparison of the measured and simulated EELS spectra confirm that these changes originate from onset of FM order. Crystal field analysis indicates that in V-doped Sb$_2$Te$_3$, partially filled core states contribute to the FM order. Since van Vleck magnetism is a result of summing over all states, this magnetization of core level verifies the van Vleck-type ferromagnetism in a direct manner., Comment: 5 pages, 5 figures

The resonant period drop observed at low temperatures in torsional oscillators containing solid helium had been interpreted as a signature of supersolid. However, it was found that the shear modulus increase found in solid helium at the same low temperature could also decrease the resonant period of the torsional oscillator. We report the results of a study in two different torsional oscillators that were specially designed to minimize the shear modulus effect and maximize any possible supersolid response. We were able to place an upper limit on the nonclassical rotational inertia or supersolid fraction of $4\times10^{-6}$. Moreover, we have repeated an earlier experiment on hcp $^3$He solid, which shows similar low temperature stiffening as in hcp $^4$He. We found that the small drop of the resonant period measured in the hcp $^3$He sample is comparable in size to that found in the hcp $^4$He samples. These results strongly suggest that the resonant period drop reported in most torsional oscillator studies in the last decade is primarily a consequence of the shear modulus stiffening effect.

In this review, we present a summary of some recent experiments on topological insulators (TIs) and superconducting nanowires and films. Electron-electron interaction (EEI), weak anti-localization (WAL) and anisotropic magneto-resistance (AMR) effect found in TI films by transport measurements are reported. Then, transport properties of superconducting films, bridges and nanowires and proximity effect in non-superconducting nanowires are described. Finally, the interplay between TIs and superconductors (SCs) is also discussed.

We report thermal conductivity measurements of porous Vycor glass when it is empty and when the pores are filled with helium between 0.06 and 0.5 K. The filling of liquid 3He and liquid 4He inside the Vycor pores brings about respectively two and three fold reduction of the thermal conductivity as compared with empty Vycor. This dramatic reduction of thermal conductivity, not seen with solid 3He and 4He in the pores, is the consequence of hydrodynamic sound modes in liquid helium that greatly facilitate the quantum tunneling of the two-level systems (TLS) in Vycor and enhance the scattering of the thermal phonons in the silica network., Comment: 5 pages, 3 figures

In 2004, Kim and Chan (KC) carried out torsional oscillator (TO) measurements of solid helium confined in porous Vycor glass and found an abrupt drop in the resonant period below 200 mK. The period drop was interpreted as probable experimental evidence of nonclassical rotational inertia (NCRI). This experiment sparked considerable activities in the studies of superfluidity in solid helium. More recent ultrasound and TO studies, however, found evidence that shear modulus stiffening is responsible for at least a fraction of the period drop found in bulk solid helium samples. The experimental configuration of KC makes it unavoidable to have a small amount of bulk solid inside the torsion cell containing the Vycor disc. We report here the results of a new helium in Vycor experiment with a design that is completely free from any bulk solid shear modulus stiffening effect. We found no measureable period drop that can be attributed to NCRI.

The transport properties of superconducting single crystal Pb nanowires of 55 nm and 70 nm diameter are studied by standard four electrodes method. Resistance-temperature (R-T) scans and magneto-resistance (R-H) measurements show a series of resistance steps with increasing temperature and magnetic field as the wires are brought toward the normal state. The resistance-current (R-I) scans at different temperature and magnetic field show that the increase in R with I is punctuated with sharp steps at specific current values. We interpret these steps as consequence of phase slip centers (PSCs) in the superconducting wires enhanced by the presence of the normal Pt electrodes.