The anomalous Hall effect is a fundamental transport process in solids arising from the spin-orbit coupling. In a quantum anomalous Hall insulator, spontaneous magnetic moments and spin-orbit coupling combine to give rise to a topologically nontrivial electronic structure, leading to the quantized Hall effect without an external magnetic field. Based on first-principles calculations, we predict that the tetradymite semiconductors Bi2Te3, Bi2Se3, and Sb2Te3 form magnetically ordered insulators when doped with transition metal elements (Cr or Fe), in contrast to conventional dilute magnetic semiconductors where free carriers are necessary to mediate the magnetic coupling. In two-dimensional thin films, this magnetic order gives rise to a topological electronic structure characterized by a finite Chern number, with the Hall conductance quantized in units of e2/h (where e is the charge of an electron and h is Planck's constant).

In topological insulators, spin–orbit coupling and time-reversal symmetry combine to form a novel state of matter predicted to have exotic physical properties.

The ability to detect light over a broad spectral range is central for practical optoelectronic applications, and has been successfully demonstrated with photodetectors of two-dimensional layered crystals such as graphene and MoS 2 . However, polarization sensitivity within such a photodetector remains elusive. Here we demonstrate a linear-dichroic broadband photodetector with layered black phosphorus transistors, using the strong intrinsic linear dichroism arising from the in-plane optical anisotropy with respect to the atom-buckled direction, which is polarization sensitive over a broad bandwidth from about 400 nm to 3750 nm. Especially, a perpendicular built-in electric field induced by gating in the transistor geometry can spatially separate the photo-generated electrons and holes in the channel, effectively reducing their recombination rate, and thus enhancing the performance for linear dichroism photodetection. This provides practical functionality using anisotropic layered black phosphorus, thereby enabling novel optical and optoelectronic device applications. Corresponding author: hyhwang@stanford.edu, yicui@stanford.edu. 2Confined electronic systems in layered two-dimensional (2D) crystals are host to many emerging electronic, spintronic and photonic phenomena, 1, 2, 3 including quantum Hall and Dirac electrons in graphene 4, 5, 6 and topological surface states in topological insulators 7, 8 . Experimentally identifying new functionalities of two-dimensional materials is a challenging and rewarding frontier, enabled by recent advances in materials and device fabrication. One example is the valley polarization control using circularly polarized light in the non-centrosymmetric MoS 2 monolayer and resulting potential valleytronics applications. 9, 10,11 Other examples include recent demonstrations of novel electronic and optoelectronic applications of the well-known layered material black phosphorus (BP), such as high-mobility field effect transistors and linear-polarization dependent optical absorption. 12,13,14 Therefore, further discovering new properties and functionalities utilizing known layered materials is of practical importance and great current interest. 14,15,16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 As a potential functionality for layered 2D materials, linear dichroism (LD) is an electromagnetic spectroscopy probing different absorption of light polarized parallel or perpendicular to an orientation axis. It directly depends on the conformation and orientation of material/device structures, where they are either intrinsically oriented in an anisotropic crystal structure 27, 28 or extrinsically oriented in anisotropic device patterns 29, 30 . Compared to the hexagonal in-plane lattice in other 2D materials such as graphene and MoS 2 , which are insensitive to the linear polarization of incident light, the layered BP crystal with a rectangular in-plane lattice has a highly-anisotropic structure along the x and y directions (defined in Fig. 1a), where every two rows of P atoms alternatel...