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Abstract Two-dimensional (2D) materials have drawn immense interests in scientific and technological communities, owing to their extraordinary properties and their tunability by gating, proximity, strain and external fields. For electronic applications, an ideal 2D material would have high mobility, air stability, sizable band gap, and be compatible with large scale synthesis. Here we demonstrate air stable field effect transistors using atomically thin few-layer PdSe₂sheets that are sandwiched between hexagonal BN (hBN), with large saturation current > 350 μA/μm, and high field effect mobilities of ~ 700 and 10,000 cm²/Vs at 300 K and 2 K, respectively. At low temperatures, magnetotransport studies reveal unique octets in quantum oscillations that persist at all densities, arising from 2-fold spin and 4-fold valley degeneracies, which can be broken by in-plane and out-of-plane magnetic fields toward quantum Hall spin and orbital ferromagnetism. 

The quantum anomalous Hall effect (QAHE) is a robust topological phenomenon that features quantized Hall resistance at zero magnetic field. We report the QAHE in a rhombohedral pentalayer graphene-monolayer tungsten disulfide (WS₂) heterostructure. Distinct from other experimentally confirmed QAHE systems, this system has neither magnetic element nor moiré superlattice effect. The QAH states emerge at charge neutrality and feature Chern numbersC= ±5 at temperatures of up to about 1.5 kelvin. This large QAHE arises from the synergy of the electron correlation in intrinsic flat bands of pentalayer graphene, the gate-tuning effect, and the proximity-induced Ising spin-orbit coupling. Our experiment demonstrates the potential of crystalline two-dimensional materials for intertwined electron correlation and band topology physics and may enable a route for engineering chiral Majorana edge states. 

BACKGROUND Optical sensing devices measure the rich physical properties of an incident light beam, such as its power, polarization state, spectrum, and intensity distribution. Most conventional sensors, such as power meters, polarimeters, spectrometers, and cameras, are monofunctional and bulky. For example, classical Fourier-transform infrared spectrometers and polarimeters, which characterize the optical spectrum in the infrared and the polarization state of light, respectively, can occupy a considerable portion of an optical table. Over the past decade, the development of integrated sensing solutions by using miniaturized devices together with advanced machine-learning algorithms has accelerated rapidly, and optical sensing research has evolved into a highly interdisciplinary field that encompasses devices and materials engineering, condensed matter physics, and machine learning. To this end, future optical sensing technologies will benefit from innovations in device architecture, discoveries of new quantum materials, demonstrations of previously uncharacterized optical and optoelectronic phenomena, and rapid advances in the development of tailored machine-learning algorithms. ADVANCES Recently, a number of sensing and imaging demonstrations have emerged that differ substantially from conventional sensing schemes in the way that optical information is detected. A typical example is computational spectroscopy. In this new paradigm, a compact spectrometer first collectively captures the comprehensive spectral information of an incident light beam using multiple elements or a single element under different operational states and generates a high-dimensional photoresponse vector. An advanced algorithm then interprets the vector to achieve reconstruction of the spectrum. This scheme shifts the physical complexity of conventional grating- or interference-based spectrometers to computation. Moreover, many of the recent developments go well beyond optical spectroscopy, and we discuss them within a common framework, dubbed “geometric deep optical sensing.” The term “geometric” is intended to emphasize that in this sensing scheme, the physical properties of an unknown light beam and the corresponding photoresponses can be regarded as points in two respective high-dimensional vector spaces and that the sensing process can be considered to be a mapping from one vector space to the other. The mapping can be linear, nonlinear, or highly entangled; for the latter two cases, deep artificial neural networks represent a natural choice for the encoding and/or decoding processes, from which the term “deep” is derived. In addition to this classical geometric view, the quantum geometry of Bloch electrons in Hilbert space, such as Berry curvature and quantum metrics, is essential for the determination of the polarization-dependent photoresponses in some optical sensors. In this Review, we first present a general perspective of this sensing scheme from the viewpoint of information theory, in which the photoresponse measurement and the extraction of light properties are deemed as information-encoding and -decoding processes, respectively. We then discuss demonstrations in which a reconfigurable sensor (or an array thereof), enabled by device reconfigurability and the implementation of neural networks, can detect the power, polarization state, wavelength, and spatial features of an incident light beam. OUTLOOK As increasingly more computing resources become available, optical sensing is becoming more computational, with device reconfigurability playing a key role. On the one hand, advanced algorithms, including deep neural networks, will enable effective decoding of high-dimensional photoresponse vectors, which reduces the physical complexity of sensors. Therefore, it will be important to integrate memory cells near or within sensors to enable efficient processing and interpretation of a large amount of photoresponse data. On the other hand, analog computation based on neural networks can be performed with an array of reconfigurable devices, which enables direct multiplexing of sensing and computing functions. We anticipate that these two directions will become the engineering frontier of future deep sensing research. On the scientific frontier, exploring quantum geometric and topological properties of new quantum materials in both linear and nonlinear light-matter interactions will enrich the information-encoding pathways for deep optical sensing. In addition, deep sensing schemes will continue to benefit from the latest developments in machine learning. Future highly compact, multifunctional, reconfigurable, and intelligent sensors and imagers will find applications in medical imaging, environmental monitoring, infrared astronomy, and many other areas of our daily lives, especially in the mobile domain and the internet of things. Schematic of deep optical sensing. The n -dimensional unknown information ( w ) is encoded into an m -dimensional photoresponse vector ( x ) by a reconfigurable sensor (or an array thereof), from which w′ is reconstructed by a trained neural network ( n ′ = n and w′   ≈   w ). Alternatively, x may be directly deciphered to capture certain properties of w . Here, w , x , and w′ can be regarded as points in their respective high-dimensional vector spaces ℛ n , ℛ m , and ℛ n ′ .