Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

The applications of graphene and transition metal dichalcogenides in electronics are limited by their zero-bandgap and low mobility, respectively. Here, the authors demonstrate the potential of an emerging layered material—black phosphorous—for thin film electronics and infrared optoelectronics.

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Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics

The optical properties of graphene and emerging two-dimensional materials including transition metal dichalcogenides are reviewed with an emphasis on nanophotonic applications. Two-dimensional materials exhibit diverse electronic properties, ranging from insulating hexagonal boron nitride and semiconducting transition metal dichalcogenides such as molybdenum disulphide, to semimetallic graphene. In this Review, we first discuss the optical properties and applications of various two-dimensional materials, and then cover two different approaches for enhancing their interactions with light: through their integration with external photonic structures, and through intrinsic polaritonic resonances. Finally, we present a narrow-bandgap layered material — black phosphorus — that serendipitously bridges the energy gap between the zero-bandgap graphene and the relatively large-bandgap transition metal dichalcogenides. The plethora of two-dimensional materials and their heterostructures, together with the array of available approaches for enhancing the light–matter interaction, offers the promise of scientific discoveries and nanophotonics technologies across a wide range of the electromagnetic spectrum.

Two-dimensional material nanophotonics

An obstacle to the use of graphene as an alternative to silicon electronics has been the absence of an energy gap between its conduction and valence bands, which makes it difficult to achieve low power dissipation in the OFF state We report a bipolar field-effect transistor that exploits the low density of states in graphene and its one-atomic-layer thickness Our prototype devices are graphene heterostructures with atomically thin boron nitride or molybdenum disulfide acting as a vertical transport barrier They exhibit room-temperature switching ratios of ≈50 and ≈10,000, respectively Such devices have potential for high-frequency operation and large-scale integration

http://repositorium.sdum.uminho.pt/bitstream/1822/21512/1/1112.4999_Science.pdf

Field-effect tunneling transistor based on vertical graphene heterostructures.

Two-dimensional layered materials (2DLMs) have been a central focus of materials research since the discovery of graphene just over a decade ago. Each layer in 2DLMs consists of a covalently bonded, dangling-bond-free lattice and is weakly bound to neighbouring layers by van der Waals interactions. This makes it feasible to isolate, mix and match highly disparate atomic layers to create a wide range of van der Waals heterostructures (vdWHs) without the constraints of lattice matching and processing compatibility. Exploiting the novel properties in these vdWHs with diverse layering of metals, semiconductors or insulators, new designs of electronic devices emerge, including tunnelling transistors, barristors and flexible electronics, as well as optoelectronic devices, including photodetectors, photovoltaics and light-emitting devices with unprecedented characteristics or unique functionalities. We review the recent progress and challenges, and offer our perspective on the exploration of 2DLM-based vdWHs for future application in electronics and optoelectronics. With a dangling-bond-free surface, two dimensional layered materials (2DLMs) can enable the creation of diverse van der Waals heterostructures (vdWHs) without the conventional constraint of lattice matching or process compatibility. This Review discusses the recent advances in exploring 2DLM vdWHs for future electronics and optoelectronics.

Van der Waals heterostructures and devices

Using boron nitride as a substrate for graphene has been suggested as a promising way to reduce the disorder in graphene caused by space fluctuations. It is now shown by scanning tunnelling microscopy that graphene conforms perfectly to boron nitride and the charge fluctuations are minimal compared with the conventionally used substrate, silica. Boron nitride could really be the natural graphene substrate. Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy–momentum dispersion relations which cross at the Dirac point1,2. However, accessing the physics of the low-density region at the Dirac point has been difficult because of disorder that leaves the graphene with local microscopic electron and hole puddles3,4,5. Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges and delicate devices which make local spectroscopic measurements difficult6,7. Recently, it has been shown that placing graphene on hexagonal boron nitride (hBN) yields improved device performance8. Here we use scanning tunnelling microscopy to show that graphene conforms to hBN, as evidenced by the presence of Moire patterns. However, contrary to predictions9,10, this conformation does not lead to a sizeable band gap because of the misalignment of the lattices. Moreover, local spectroscopy measurements demonstrate that the electron–hole charge fluctuations are reduced by two orders of magnitude as compared with those on silicon oxide. This leads to charge fluctuations that are as small as in suspended graphene6, opening up Dirac point physics to more diverse experiments.

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Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride

Graphene has demonstrated great promise for future electronics technology as well as fundamental physics applications because of its linear energy-momentum dispersion relations which cross at the Dirac point[1, 2]. However, accessing the physics of the low density region at the Dirac point has been difficult because of the presence of disorder which leaves the graphene with local microscopic electron and hole puddles[3–5], resulting in a finite density of carriers even at the charge neutrality point. Efforts have been made to reduce the disorder by suspending graphene, leading to fabrication challenges and delicate devices which make local spectroscopic measurements difficult[6, 7]. Recently, it has been shown that placing graphene on hexagonal boron nitride (hBN) yields improved device performance[8]. In this letter, we use scanning tunneling microscopy to show that

STM Spectroscopy of ultra-flat graphene on hexagonal boron nitride

Subdimensional motion occurs when excitations of a system can only move in a lower-dimensional subspace of the full system. This phenomenon occurs both in a class of generalized U(1) gauge theories and in ``fracton'' phases found in certain exactly solvable gapped spin models. Here, the authors present and analyze a more general class of symmetric higher-rank U(1) gauge theories and show how these two cases of subdimensional motion are connected via the Higgs mechanism, which often yields conventional phases but in special cases can drive a symmetric higher-rank U(1) gauge theory into a fracton phase.

Higgs mechanism in higher-rank symmetric U(1) gauge theories

We study strained Hg$_{1-x-y}$Cd$_x$Mn$_y$Te in a magnetic field using a $\bm{k}\cdot\bm{p}$ model and predict that the system is a Weyl semimetal with two nodes in an experimentally reasonable region of the phase diagram. We also predict two signatures of the Weyl semimetal phase which arise from tunability of the Weyl node splitting. First, we find that the Hall conductivity is proportional to the average Mn ion spin and thus is strongly temperature dependent. Second, we find an unusual magnetic field angle dependence of the Hall conductivity; in particular, we predict a peak in $\sigma_{xy}$ as a function of field angle in the $xz$-plane and a finite $\sigma_{yz}$ as the $x$-component of the field goes to 0.

Prediction of a Weyl semimetal in Hg 1 - X - Y Cd x Mn y Te

We re-examine the question of quantum oscillations from surface Fermi arcs and chiral modes in Weyl semimetals. By introducing two tools--semiclassical phase-space quantization and a numerical implementation of a layered construction of Weyl semimetals--we discover several important generalizations to previous conclusions that were implicitly tailored to the special case of identical Fermi arcs on top and bottom surfaces. We show that the phase-space quantization picture fixes an ambiguity in the previously utilized energy-time quantization approach and correctly reproduces the numerically calculated quantum oscillations for generic Weyl semimetals with distinctly curved Fermi arcs on the two surfaces. Based on these methods, we identify a 'magic' magnetic-field angle where quantum oscillations become independent of sample thickness, with striking experimental implications. We also analyze the stability of these quantum oscillations to disorder, and show that the high-field oscillations are expected to persist in samples whose thickness parametrically exceeds the quantum mean free path.

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Daniel Bulmash

Papers

Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride

STM Spectroscopy of ultra-flat graphene on hexagonal boron nitride

Higgs mechanism in higher-rank symmetric U(1) gauge theories

Prediction of a Weyl semimetal in Hg 1 - X - Y Cd x Mn y Te

Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals.