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The recent discovery of correlated insulator states and superconductivity in magic-angle twisted bilayer graphene 1 , 2 has enabled the experimental investigation of electronic correlations in tunable flat-band systems realized in twisted van der Waals heterostructures 3 – 6 . This novel twist angle degree of freedom and control should be generalizable to other two-dimensional systems, which may exhibit similar correlated physics behaviour, and could enable techniques to tune and control the strength of electron–electron interactions. Here we report a highly tunable correlated system based on small-angle twisted bilayer–bilayer graphene (TBBG), consisting of two rotated sheets of Bernal-stacked bilayer graphene. We find that TBBG exhibits a rich phase diagram, with tunable correlated insulator states that are highly sensitive to both the twist angle and the application of an electric displacement field, the latter reflecting the inherent polarizability of Bernal-stacked bilayer graphene 7 , 8 . The correlated insulator states can be switched on and off by the displacement field at all integer electron fillings of the moiré unit cell. The response of these correlated states to magnetic fields suggests evidence of spin-polarized ground states, in stark contrast to magic-angle twisted bilayer graphene. Furthermore, in the regime of lower twist angles, TBBG shows multiple sets of flat bands near charge neutrality, resulting in numerous correlated states corresponding to half-filling of each of these flat bands, all of which are tunable by the displacement field as well. Our results could enable the exploration of twist-angle- and electric-field-controlled correlated phases of matter in multi-flat-band twisted superlattices. Small-angle twisted bilayer–bilayer graphene is tunable by the twist angle and electric and magnetic fields, and can be used to gain further insights into correlated states in two-dimensional superlattices.

Altermagnetism represents an emergent collinear magnetic phase with compensated order and an unconventional alternating even-parity wave spin order in the non-relativistic band structure. We investigate directly this unconventional band splitting near the Fermi energy through spin-integrated soft X-ray angular resolved photoemission spectroscopy. The experimentally obtained angle-dependent photoemission intensity, acquired from epitaxial thin films of the predicted altermagnet CrSb, demonstrates robust agreement with the corresponding band structure calculations. In particular, we observe the distinctive splitting of an electronic band on a low-symmetry path in the Brilliouin zone that connects two points featuring symmetry-induced degeneracy. The measured large magnitude of the spin splitting of approximately 0.6 eV and the position of the band just below the Fermi energy underscores the significance of altermagnets for spintronics based on robust broken time reversal symmetry responses arising from exchange energy scales, akin to ferromagnets, while remaining insensitive to external magnetic fields and possessing THz dynamics, akin to antiferromagnets. The fundamental hallmark of altermagnetism lies in the spin splitting of electronic valence bands. Here, the authors observe splitting in metallic CrSb, revealing an exceptionally large value and energetic placement just below the Fermi energy.

The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology 1 – 18 , which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependent cascade of different symmetry-broken electronic states in a new kagome superconductor, CsV 3 Sb 5 . We reveal, at a temperature far above the superconducting transition temperature T c  ~ 2.5 K, a tri-directional charge order with a 2 a 0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards T c , we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4 a 0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high- T c superconductors and twisted bilayer graphene. A study reveals a temperature-dependent cascade of different symmetry-broken electronic states in the kagome superconductor CsV 3 Sb 5 , and highlights intriguing parallels between vanadium-based kagome metals and materials exhibiting similar electronic phases.

Moiré materials have emerged as a platform for exploring the physics of strong electronic correlations and non-trivial band topology. Here we review the recent progress in semiconductor moiré materials, with a particular focus on transition metal dichalcogenides. Following a brief overview of the general features in this class of materials, we discuss recent theoretical and experimental studies on Hubbard physics, Kane–Mele–Hubbard physics and equilibrium moiré excitons. We also comment on the future opportunities and challenges in the studies of transition metal dichalcogenide and other semiconductor moiré materials.This Review elaborates on the recent developments and the future opportunities and challenges of fundamental research on semiconductor moiré materials, with a particular focus on transition metal dichalcogenides.

Twisted van der Waals heterostructures have latterly received prominent attention for their many remarkable experimental properties and the promise that they hold for realizing elusive states of matter in the laboratory. We propose that these systems can, in fact, be used as a robust quantum simulation platform that enables the study of strongly correlated physics and topology in quantum materials. Among the features that make these materials a versatile toolbox are the tunability of their properties through readily accessible external parameters such as gating, straining, packing and twist angle; the feasibility to realize and control a large number of fundamental many-body quantum models relevant in the field of condensed-matter physics; and finally, the availability of experimental readout protocols that directly map their rich phase diagrams in and out of equilibrium. This general framework makes it possible to robustly realize and functionalize new phases of matter in a modular fashion, thus broadening the landscape of accessible physics and holding promise for future technological applications.Moiré heterostructures have latterly captured the attention of condensed-matter physicists. This Review Article explores the idea of adopting them as a quantum simulation platform that enables the study of strongly correlated physics and topology in quantum materials.

The family of two-dimensional (2D) materials grows day by day, hugely expanding the scope of possible phenomena to be explored in two dimensions, as well as the possible van der Waals (vdW) heterostructures that one can create. Such 2D materials currently cover a vast range of properties. Until recently, this family has been missing one crucial member: 2D magnets. The situation has changed over the past 2 years with the introduction of a variety of atomically thin magnetic crystals. Here we will discuss the difference between magnetic states in 2D materials and in bulk crystals and present an overview of the 2D magnets that have been explored recently. We will focus on the case of the two most studied systems—semiconducting CrI3 and metallic Fe3GeTe2—and illustrate the physical phenomena that have been observed. Special attention will be given to the range of new van der Waals heterostructures that became possible with the appearance of 2D magnets, offering new perspectives in this rapidly expanding field.Until recently, the family of 2D materials was missing one crucial member — 2D magnets. This Review presents an overview of the 2D magnets studied so far and of the heterostructures that can be realized by combining them with other 2D materials.

The critical current of a superconductor can be different for opposite directions of current flow when both time-reversal and inversion symmetry are broken. Such non-reciprocal behaviour creates a superconducting diode and has recently been experimentally demonstrated by breaking these symmetries with an applied magnetic field or by the construction of a magnetic tunnel junction. Here we report an intrinsic superconducting diode effect that is present at zero external magnetic field in mirror-symmetric twisted trilayer graphene. Such non-reciprocal behaviour, with sign that can be reversed through training with an out-of-plane magnetic field, provides direct evidence of the microscopic coexistence between superconductivity and time-reversal symmetry breaking. In addition to the magnetic-field trainability, we show that the zero-field diode effect can be controlled by varying the carrier density or twist angle. A natural interpretation for the origin of the intrinsic diode effect is an imbalance in the valley occupation of the underlying Fermi surface, which probably leads to finite-momentum Cooper pairing and nematicity in the superconducting phase. A superconducting diode effect is observed at zero magnetic field in twisted trilayer graphene. This suggests that time-reversal symmetry is intrinsically broken and leads to pairing between electrons with non-zero centre-of-mass momentum.

Materials research has driven the development of modern nano-electronic devices. In particular, research in magnetic thin films has revolutionized the development of spintronic devices 1 , 2 because identifying new magnetic materials is key to better device performance and design. Van der Waals crystals retain their chemical stability and structural integrity down to the monolayer and, being atomically thin, are readily tuned by various kinds of gate modulation 3 , 4 . Recent experiments have demonstrated that it is possible to obtain two-dimensional ferromagnetic order in insulating Cr 2 Ge 2 Te 6 (ref. 5 ) and CrI 3 (ref. 6 ) at low temperatures. Here we develop a device fabrication technique and isolate monolayers from the layered metallic magnet Fe 3 GeTe 2 to study magnetotransport. We find that the itinerant ferromagnetism persists in Fe 3 GeTe 2 down to the monolayer with an out-of-plane magnetocrystalline anisotropy. The ferromagnetic transition temperature, T c , is suppressed relative to the bulk T c of 205 kelvin in pristine Fe 3 GeTe 2 thin flakes. An ionic gate, however, raises T c to room temperature, much higher than the bulk T c . The gate-tunable room-temperature ferromagnetism in two-dimensional Fe 3 GeTe 2 opens up opportunities for potential voltage-controlled magnetoelectronics 7 – 11 based on atomically thin van der Waals crystals. Monolayers of Fe 3 GeTe 2 exhibit itinerant ferromagnetism with an out-of-plane magnetocrystalline anisotropy; ionic gating raises the ferromagnetic transition temperature of few-layer Fe 3 GeTe 2 to room temperature.

When electric conductors differ from their mirror image, unusual chiral transport coefficients appear that are forbidden in achiral metals, such as a non-linear electric response known as electronic magnetochiral anisotropy (eMChA) 1 – 6 . Although chiral transport signatures are allowed by symmetry in many conductors without a centre of inversion, they reach appreciable levels only in rare cases in which an exceptionally strong chiral coupling to the itinerant electrons is present. So far, observations of chiral transport have been limited to materials in which the atomic positions strongly break mirror symmetries. Here, we report chiral transport in the centrosymmetric layered kagome metal CsV 3 Sb 5 observed via second-harmonic generation under an in-plane magnetic field. The eMChA signal becomes significant only at temperatures below T ′ ≈ 35 K, deep within the charge-ordered state of CsV 3 Sb 5 ( T CDW  ≈ 94 K). This temperature dependence reveals a direct correspondence between electronic chirality, unidirectional charge order 7 and spontaneous time-reversal symmetry breaking due to putative orbital loop currents 8 – 10 . We show that the chirality is set by the out-of-plane field component and that a transition from left- to right-handed transport can be induced by changing the field sign. CsV 3 Sb 5 is the first material in which strong chiral transport can be controlled and switched by small magnetic field changes, in stark contrast to structurally chiral materials, which is a prerequisite for applications in chiral electronics. Change of chirality from left- to right-handed transport in the layered kagome metal CsV 3 Sb 5 can be controlled by small magnetic field changes, a required feature for chiral electronic applications.

Finite-momentum Cooper pairing is an unconventional form of superconductivity that is widely believed to require finite magnetization. Altermagnetism is an emerging magnetic phase with highly anisotropic spin-splitting of specific symmetries, but zero net magnetization. Here, we study Cooper pairing in metallic altermagnets connected to conventional s -wave superconductors. Remarkably, we find that the Cooper pairs induced in the altermagnets acquire a finite center-of-mass momentum, despite the zero net magnetization in the system. This anomalous Cooper-pair momentum strongly depends on the propagation direction and exhibits unusual symmetric patterns. Furthermore, it yields several unique features: (i) highly orientation-dependent oscillations in the order parameter, (ii) controllable 0- π transitions in the Josephson supercurrent, (iii) large-oblique-angle Cooper-pair transfer trajectories in junctions parallel with the direction where spin splitting vanishes, and (iv) distinct Fraunhofer patterns in junctions oriented along different directions. Finally, we discuss the implementation of our predictions in candidate materials such as RuO 2 and KRu 4 O 8 . An altermagnet has highly anisotropic spin splitting but zero net magnetization. Here, S.-B. Zhang et al. theoretically study the behavior of s -wave superconductor/altermagnet hybrid structures, finding that Cooper pairs in the proximitized altermagnet have an anisotropic non-zero momentum.