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The synthesis of bulk crystals, thin films and nanostructures plays a seminal role in expanding the frontiers of quantum materials. Crystal growers accomplish this by creating materials aimed at harnessing the complex interplay between quantum wavefunctions and various factors such as dimensionality, topology, Coulomb interactions and symmetry. This Review provides a synthesis perspective on how this discovery of quantum materials takes place. After introducing the general paradigms that arise in this context, we provide a few examples to illustrate how thin-film growers in particular exploit quantum confinement, topology, disorder and interfacial heterogeneity to realize new quantum materials. The exploration of the properties and applications of quantum materials relies on advances in synthesis techniques. The approaches pursued to realize thin films and other materials revealing emergent quantum behaviour are reviewed here.

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. The coexistence of chiral edge states and chiral spin textures in magnetic topological insulator sandwiches provides a platform for proof-of-concept dissipationless spin-textured spintronic applications.

When a three-dimensional ferromagnetic topological insulator thin film is magnetized out-of-plane, conduction ideally occurs through dissipationless, one-dimensional (1D) chiral states that are characterized by a quantized, zero-field Hall conductance. The recent realization of this phenomenon, the quantum anomalous Hall effect, provides a conceptually new platform for studies of 1D transport, distinct from the traditionally studied quantum Hall effects that arise from Landau level formation. An important question arises in this context: how do these 1D edge states evolve as the magnetization is changed from out-of-plane to in-plane? We examine this question by studying the field-tilt-driven crossover from predominantly edge-state transport to diffusive transport in Cr x (Bi,Sb) 2− x Te 3 thin films. This crossover manifests itself in a giant, electrically tunable anisotropic magnetoresistance that we explain by employing a Landauer–Büttiker formalism. Our methodology provides a powerful means of quantifying dissipative effects in temperature and chemical potential regimes far from perfect quantization. When magnetized out-of-plane, three-dimensional ferromagnetic topological insulator thin films exhibit the quantum anomalous Hall effect. Here, the authors follow the evolution of this dissipationless chiral edge transport effect as the magnetization is brought in-plane under an applied magnetic field.

The large spin−orbit coupling in topological insulators results in helical spin-textured Dirac surface states that are attractive for topological spintronics. These states generate an efficient spin−orbit torque on proximal magnetic moments. However, memory or logic spin devices based upon such switching require a non-optimal three-terminal geometry, with two terminals for the writing current and one for reading the state of the device. An alternative two-terminal device geometry is now possible by exploiting the recent discovery of the unidirectional spin Hall magnetoresistance in heavy metal/ferromagnet bilayers and unidirectional magnetoresistance in magnetic topological insulators. Here, we report the observation of such unidirectional magnetoresistance in a technologically relevant device geometry that combines a topological insulator with a conventional ferromagnetic metal. Our devices show a figure of merit (magnetoresistance per current density per total resistance) that is more than twice as large as the highest reported values in all-metal Ta/Co bilayers. Unidirectional spin Hall magnetoresistance enables the new spintronic devices but is limited by the low amplitude or working temperature. Here, the authors report the large unidirectional spin Hall magnetoresistance in a topological insulator and ferromagnetic metal bilayer system at relatively higher temperature.

A quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has a quantized Hall resistance of h /( Ce 2 ) 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 insulators 3 – 9 and magic-angle twisted bilayer graphene 10 , 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. The number of edge channels in quantum anomalous Hall insulators is controlled by varying either the magnetic dopant concentration or the interior spacer layer thickness, yielding Chern numbers up to 5.

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 κ ~ 0.38 ± 0.02 in agreement with recent high-precision numerical results on the correlation length exponent of the Chalker–Coddington model at ν ~ 2.6, rather than the generally-accepted value of 2.33. Understanding the critical scaling behaviors of quantum phase transitions can provide profound physical implications. Here, the authors report temperature dependence of the derivative of longitudinal resistance at a magnetic-field induced quantum phase transition between the quantum anomalous Hall insulator to the axion insulator in magnetic topological insulator sandwich samples.

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 the consequence of non-zero Berry curvature in momentum space. Here, we fabricate TI/magnetic TI heterostructures and find that the sign of the AH effect in the magnetic TI layer can be changed from being positive to negative with increasing the thickness of the top TI layer. Our first-principles calculations show that the built-in electric fields at the TI/magnetic TI interface influence the band structure of the magnetic TI layer, and thus lead to a reconstruction of the Berry curvature in the heterostructure samples. Based on the interface-induced AH effect with a negative sign in TI/V-doped TI bilayer structures, we create an artificial “topological Hall effect”-like feature in the Hall trace of the V-doped TI/TI/Cr-doped TI sandwich heterostructures. Our study provides a new route to create the Berry curvature change in magnetic topological materials that may lead to potential technological applications. Berry curvature connects to exotic electronic phases hence it provides important insights to understand quantum materials. Here, the authors report sign change of the anomalous Hall effect resulted from Berry curvature change at the interface of a topological insulator/magnetic topological insulator heterostructure.

The rapid discovery of two-dimensional (2D) van der Waals (vdW) quantum materials has led to heterostructures that integrate diverse quantum functionalities such as topological phases, magnetism, and superconductivity. In this context, the epitaxial synthesis of vdW heterostructures with well-controlled interfaces is an attractive route towards wafer-scale platforms for systematically exploring fundamental properties and fashioning proof-of-concept devices. Here, we use molecular beam epitaxy to synthesize a vdW heterostructure that interfaces two material systems of contemporary interest: a 2D ferromagnet (1T-CrTe 2 ) and a topological semimetal (ZrTe 2 ). We find that one unit-cell (u.c.) thick 1T-CrTe 2 grown epitaxially on ZrTe 2 is a 2D ferromagnet with a clear anomalous Hall effect. In thicker samples (12 u.c. thick CrTe 2 ), the anomalous Hall effect has characteristics that may arise from real-space Berry curvature. Finally, in ultrathin CrTe 2 (3 u.c. thickness), we demonstrate current-driven magnetization switching in a full vdW topological semimetal/2D ferromagnet heterostructure device. Van der Waals heterostructures offer the potential of integrating multiple material layers into a single device to achieve new functionalities. Here, Ou et al combine ZrTe 2 , a topological semimetal, with CrTe 2 , a 2D ferromagnet, in a single heterostructure and demonstrate spin-orbit torque switching of the 2D ferromagnet by current in the topological semimetal.

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.