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Moiré quantum matter has emerged as a materials platform in which correlated and topological phases can be explored with unprecedented control. Among them, magic-angle systems constructed from two or three layers of graphene have shown robust superconducting phases with unconventional characteristics 1 – 5 . However, direct evidence of unconventional pairing remains to be experimentally demonstrated. Here we show that magic-angle twisted trilayer graphene exhibits superconductivity up to in-plane magnetic fields in excess of 10 T, which represents a large (2–3 times) violation of the Pauli limit for conventional spin-singlet superconductors 6 , 7 . This is an unexpected observation for a system that is not predicted to have strong spin–orbit coupling. The Pauli-limit violation is observed over the entire superconducting phase, which indicates that it is not related to a possible pseudogap phase with large superconducting amplitude pairing. Notably, we observe re-entrant superconductivity at large magnetic fields, which is present over a narrower range of carrier densities and displacement fields. These findings suggest that the superconductivity in magic-angle twisted trilayer graphene is likely to be driven by a mechanism that results in non-spin-singlet Cooper pairs, and that the external magnetic field can cause transitions between phases with potentially different order parameters. Our results demonstrate the richness of moiré superconductivity and could lead to the design of next-generation exotic quantum matter. A large violation of the Pauli limit and re-entrant superconductivity in a magnetic field is reported for magic-angle twisted trilayer graphene, suggesting that the spin configuration of the superconducting state of this material is unlikely to consist of spin singlets.

On-chip spectrometers with compact footprints are being extensively investigated owing to their promising future in critical applications such as sensing, surveillance and spectral imaging. Most existing miniaturized spectrometers use large arrays of photodetection elements to capture different spectral components of incident light, from which its spectrum is reconstructed. Here, we demonstrate a mid-infrared spectrometer in the 2–9 µm spectral range, utilizing a single tunable black phosphorus photodetector with an active area footprint of only 9 × 16 µm2, along with a unique spectral learning procedure. Such a single-detector spectrometer has a compact size at the scale of the operational wavelength. Leveraging the wavelength and bias-dependent responsivity matrix learned from the spectra of a tunable blackbody source, we reconstruct unknown spectra from their corresponding photoresponse vectors. Enabled by the strong Stark effect and the tunable light–matter interactions in black phosphorus, our single-detector spectrometer shows remarkable potential in the reconstruction of the spectra of both monochromatic and broadband light. Furthermore, its ultracompact structure that is free from bulky interferometers and gratings, together with its electrically reconfigurable nature, may open up pathways towards on-chip mid-infrared spectroscopy and spectral imaging.A single-photodetector spectrometer based on black phosphorus is demonstrated in the wavelength range from 2 to 9 μm. The footprint is 9 × 16 μm2. The spectrometer is free from bulky interferometers and gratings, and is electrically reconfigurable.

Devices that rely on the manipulation of excitons—bound pairs of electrons and holes—hold great promise for realizing efficient interconnects between optical data transmission and electrical processing systems. Although exciton-based transistor actions have been demonstrated successfully in bulk semiconductor-based coupled quantum wells 1 – 3 , the low temperature required for their operation limits their practical application. The recent emergence of two-dimensional semiconductors with large exciton binding energies 4 , 5 may lead to excitonic devices and circuits that operate at room temperature. Whereas individual two-dimensional materials have short exciton diffusion lengths, the spatial separation of electrons and holes in different layers in heterostructures could help to overcome this limitation and enable room-temperature operation of mesoscale devices 6 – 8 . Here we report excitonic devices made of MoS 2 –WSe 2 van der Waals heterostructures encapsulated in hexagonal boron nitride that demonstrate electrically controlled transistor actions at room temperature. The long-lived nature of the interlayer excitons in our device results in them diffusing over a distance of five micrometres. Within our device, we further demonstrate the ability to manipulate exciton dynamics by creating electrically reconfigurable confining and repulsive potentials for the exciton flux. Our results make a strong case for integrating two-dimensional materials in future excitonic devices to enable operation at room temperature. Heterobilayer excitonic devices consisting of two different van der Waals materials, in which excitons are shared between the layers, exhibit electrically controlled switching actions at room temperature.

Quantum geometric properties of Bloch wave functions in solids, that is, Berry curvature and the quantum metric, are known to significantly influence the ground- and excited-state behaviour of electrons 1 – 5 . The bulk photovoltaic effect (BPVE), a nonlinear phenomenon depending on the polarization of excitation light, is largely governed by the quantum geometric properties in optical transitions 6 – 10 . Infrared BPVE has yet to be observed in graphene or moiré systems, although exciting strongly correlated phenomena related to quantum geometry have been reported in this emergent platform 11 – 14 . Here we report the observation of tunable mid-infrared BPVE at 5 µm and 7.7 µm in twisted double bilayer graphene (TDBG), arising from the moiré-induced strong symmetry breaking and quantum geometric contribution. The photoresponse depends substantially on the polarization state of the excitation light and is highly tunable by external electric fields. This wide tunability in quantum geometric properties enables us to use a convolutional neural network 15 , 16 to achieve full-Stokes polarimetry together with wavelength detection simultaneously, using only one single TDBG device with a subwavelength footprint of merely 3 × 3 µm 2 . Our work not only reveals the unique role of moiré engineered quantum geometry in tunable nonlinear light–matter interactions but also identifies a pathway for future intelligent sensing technologies in an extremely compact, on-chip manner. Tunable quantum geometric properties of moiré graphene enable the use of a convolutional neural network to simultaneously decipher the light polarization, power and wavelength in a subwavelength-scale smart device.

The behaviour of strongly correlated materials, and in particular unconventional superconductors, has been studied extensively for decades, but is still not well understood. This lack of theoretical understanding has motivated the development of experimental techniques for studying such behaviour, such as using ultracold atom lattices to simulate quantum materials. Here we report the realization of intrinsic unconventional superconductivity—which cannot be explained by weak electron–phonon interactions—in a two-dimensional superlattice created by stacking two sheets of graphene that are twisted relative to each other by a small angle. For twist angles of about 1.1°—the first ‘magic’ angle—the electronic band structure of this ‘twisted bilayer graphene’ exhibits flat bands near zero Fermi energy, resulting in correlated insulating states at half-filling. Upon electrostatic doping of the material away from these correlated insulating states, we observe tunable zero-resistance states with a critical temperature of up to 1.7 kelvin. The temperature–carrier-density phase diagram of twisted bilayer graphene is similar to that of copper oxides (or cuprates), and includes dome-shaped regions that correspond to superconductivity. Moreover, quantum oscillations in the longitudinal resistance of the material indicate the presence of small Fermi surfaces near the correlated insulating states, in analogy with underdoped cuprates. The relatively high superconducting critical temperature of twisted bilayer graphene, given such a small Fermi surface (which corresponds to a carrier density of about 10 11 per square centimetre), puts it among the superconductors with the strongest pairing strength between electrons. Twisted bilayer graphene is a precisely tunable, purely carbon-based, two-dimensional superconductor. It is therefore an ideal material for investigations of strongly correlated phenomena, which could lead to insights into the physics of high-critical-temperature superconductors and quantum spin liquids. A superlattice consisting of two graphene sheets twisted relative to each other by a specific amount exhibits superconductivity when doped electrostatically, with a relatively high critical temperature. Twisted graphene strengthens electronic interactions In 1957, John Bardeen, Leon Cooper, and John Robert Schrieffer came up with the first theory of superconductivity to describe how some materials can conduct electricity with no electrical resistance. However, there are many superconductive materials that cannot be described using this theory. Understanding the mechanism of unconventional superconductivity could help scientists engineer materials with higher transition temperatures. Pablo Jarillo-Herrero and colleagues now show that when two graphene sheets are twisted by a certain angle they exhibit unconventional superconductivity, with features similar to high-temperature superconducting cuprates. This system can easily be tuned through both the twist angle and electric fields, so could provide a new two-dimensional platform for understanding the origin of high-temperature superconductivity. Elsewhere in this issue, the same team reports that twisting graphene sheets in this manner also creates an insulating state that appears to be driven by strong electronic interactions, consistent with a Mott-like insulator phase.

The discovery of correlated states and superconductivity in magic-angle twisted bilayer graphene (MATBG) established a new platform to explore interaction-driven and topological phenomena. However, despite multitudes of correlated phases observed in moiré systems, robust superconductivity appears the least common, found only in MATBG and more recently in magic-angle twisted trilayer graphene. Here we report the experimental realization of superconducting magic-angle twisted four-layer and five-layer graphene, hence establishing alternating twist magic-angle multilayer graphene as a robust family of moiré superconductors. This finding suggests that the flat bands shared by the members play a central role in the superconductivity. Our measurements in parallel magnetic fields, in particular the investigation of Pauli limit violation and spontaneous rotational symmetry breaking, reveal a clear distinction between the N  = 2 and N  > 2-layer structures, consistent with the difference between their orbital responses to magnetic fields. Our results expand the emergent family of moiré superconductors, providing new insight with potential implications for design of new superconducting materials platforms. Superconductivity is reported in magic-angle twisted four-layer and five-layer graphene systems. While they find that all magic-angle graphene systems fit into a unified hierarchy of systems that share a set of flat bands in their electronic band structures, they also report that there is a key distinction between magic-angle twisted bilayer graphene and the other family members, related to the difference in the way the electrons move between the layers in a magnetic field.

Rhombohedral-stacked multilayer graphene hosts a pair of flat bands touching at zero energy, which should give rise to correlated electron phenomena that can be tuned further by an electric field. Moreover, when electron correlation breaks the isospin symmetry, the valley-dependent Berry phase at zero energy may give rise to topologically non-trivial states. Here we measure electron transport through hexagonal boron nitride-encapsulated pentalayer graphene down to 100 mK. We observed a correlated insulating state with resistance at the megaohm level or greater at charge density n  = 0 and displacement field D  = 0. Tight-binding calculations predict a metallic ground state under these conditions. By increasing D , we observed a Chern insulator state with C  = −5 and two other states with C  = −3 at a magnetic field of around 1 T. At high D and n , we observed isospin-polarized quarter- and half-metals. Hence, rhombohedral pentalayer graphene exhibits two different types of Fermi-surface instability, one driven by a pair of flat bands touching at zero energy, and one induced by the Stoner mechanism in a single flat band. Our results establish rhombohedral multilayer graphene as a suitable system for exploring intertwined electron correlation and topology phenomena in natural graphitic materials without the need for moiré superlattice engineering. Pentalayer graphene in the rhombohedral stacking order exhibits rich phases including a correlated insulator, isospin-polarized metals and Chern insulators. These findings demonstrate electron-correlated and topological states in crystalline 2D materials without the need for a moiré superlattice.

Chern insulators, which are the lattice analogues of the quantum Hall states, can potentially manifest high-temperature topological orders at zero magnetic field to enable next-generation topological quantum devices 1 – 3 . Until now, integer Chern insulators have been experimentally demonstrated in several systems at zero magnetic field 3 – 8 , whereas fractional Chern insulators have been reported in only graphene-based systems under a finite magnetic field 9 , 10 . The emergence of semiconductor moiré materials 11 , which support tunable topological flat bands 12 , 13 , provides an opportunity to realize fractional Chern insulators 13 – 16 . Here we report thermodynamic evidence of both integer and fractional Chern insulators at zero magnetic field in small-angle twisted bilayer MoTe 2 by combining the local electronic compressibility and magneto-optical measurements. At hole filling factor ν  = 1 and 2/3, the system is incompressible and spontaneously breaks time-reversal symmetry. We show that they are integer and fractional Chern insulators, respectively, from the dispersion of the state in the filling factor with an applied magnetic field. We further demonstrate electric-field-tuned topological phase transitions involving the Chern insulators. Our findings pave the way for the demonstration of quantized fractional Hall conductance and anyonic excitation and braiding 17 in semiconductor moiré materials. Thermodynamic evidence of both integer and fractional Chern insulators at zero magnetic field is reported in small-angle twisted bilayer MoTe 2 by combining the local electronic compressibility and magneto-optical measurements.

The interplay between spontaneous symmetry breaking and topology can result in exotic quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) state, which exhibits an integer quantum Hall effect at zero magnetic field owing to intrinsic ferromagnetism 1 – 3 . In the presence of strong electron–electron interactions, fractional QAH (FQAH) states at zero magnetic field can emerge 4 – 8 . These states could host fractional excitations, including non-Abelian anyons—crucial building blocks for topological quantum computation 9 . Here we report experimental signatures of FQAH states in a twisted molybdenum ditelluride (MoTe 2 ) bilayer. Magnetic circular dichroism measurements reveal robust ferromagnetic states at fractionally hole-filled moiré minibands. Using trion photoluminescence as a sensor 10 , we obtain a Landau fan diagram showing linear shifts in carrier densities corresponding to filling factor v  = −2/3 and v  = −3/5 ferromagnetic states with applied magnetic field. These shifts match the Streda formula dispersion of FQAH states with fractionally quantized Hall conductance of σ x y = − 2 3 e 2 h and σ x y = − 3 5 e 2 h , respectively. Moreover, the v  = −1 state exhibits a dispersion corresponding to Chern number −1, consistent with the predicted QAH state 11 – 14 . In comparison, several non-ferromagnetic states on the electron-doping side do not disperse, that is, they are trivial correlated insulators. The observed topological states can be electrically driven into topologically trivial states. Our findings provide evidence of the long-sought FQAH states, demonstrating MoTe 2 moiré superlattices as a platform for exploring fractional excitations. Signatures of fractional quantum anomalous Hall states at zero magnetic field are observed in a fractionally filled moiré superlattice in a molybdenum ditelluride twisted bilayer.

An electronic double layer, subjected to a high magnetic field, can form an exciton condensate: a Bose–Einstein condensate of Coulomb-bound electron–hole pairs. Now, exciton condensation is reported for a graphene/boron-nitride/graphene structure. An exciton condensate is a Bose–Einstein condensate of electron and hole pairs bound by the Coulomb interaction 1 , 2 . In an electronic double layer (EDL) subject to strong magnetic fields, filled Landau states in one layer bind with empty states of the other layer to form an exciton condensate 3 , 4 , 5 , 6 , 7 , 8 , 9 . Here we report exciton condensation in a bilayer graphene EDL separated by hexagonal boron nitride. Driving current in one graphene layer generates a near-quantized Hall voltage in the other layer, resulting in coherent exciton transport 4 , 6 . Owing to the strong Coulomb coupling across the atomically thin dielectric, quantum Hall drag in graphene appears at a temperature ten times higher than previously observed in a GaAs EDL. The wide-range tunability of densities and displacement fields enables exploration of a rich phase diagram of Bose–Einstein condensates across Landau levels with different filling factors and internal quantum degrees of freedom. The observed robust exciton condensation opens up opportunities to investigate various many-body exciton phases.