Graphene is very popular because of its many fascinating properties, but its lack of an electronic bandgap has stimulated the search for 2D materials with semiconducting character. Transition metal dichalcogenides (TMDCs), which are semiconductors of the type MX2, where M is a transition metal atom (such as Mo or W) and X is a chalcogen atom (such as S, Se or Te), provide a promising alternative. Because of its robustness, MoS2 is the most studied material in this family. TMDCs exhibit a unique combination of atomic-scale thickness, direct bandgap, strong spin–orbit coupling and favourable electronic and mechanical properties, which make them interesting for fundamental studies and for applications in high-end electronics, spintronics, optoelectronics, energy harvesting, flexible electronics, DNA sequencing and personalized medicine. In this Review, the methods used to synthesize TMDCs are examined and their properties are discussed, with particular attention to their charge density wave, superconductive and topological phases. The use of TMCDs in nanoelectronic devices is also explored, along with strategies to improve charge carrier mobility, high frequency operation and the use of strain engineering to tailor their properties. Two-dimensional transition metal dichalcogenides (TMDCs) exhibit attractive electronic and mechanical properties. In this Review, the charge density wave, superconductive and topological phases of TMCDs are discussed, along with their synthesis and applications in devices with enhanced mobility and with the use of strain engineering to improve their properties.

2D transition metal dichalcogenides

We report the experimental discovery of intrinsic ferromagnetism in Cr 2 Ge 2 Te 6 atomic layers by scanning magneto-optic Kerr microscopy. In this 2D van der Waals ferromagnet, unprecedented control of transition temperature is realized via small magnetic fields.

Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals

In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

Physical Review B

The isolation of graphene has triggered an avalanche of studies into the spin-dependent physical properties of this material, as well as graphene-based spintronic devices Here we review the experimental and theoretical state-of-art concerning spin injection and transport, defect-induced magnetic moments, spin-orbit coupling and spin relaxation in graphene Future research in graphene spintronics will need to address the development of applications such as spin transistors and spin logic devices, as well as exotic physical properties including topological states and proximity-induced phenomena in graphene and other 2D materials

Graphene Spintronics

We present k.p Hamiltonians parametrized by ab initio density functional theory calculations to describe the dispersion of the valence and conduction bands at their extrema (the K , Q , Γ , and M points of the hexagonal Brillouin zone) in atomic crystals of semiconducting monolayer transition metal dichalcogenides (TMDCs). We discuss the parametrization of the essential parts of the k.p[ Hamiltonians for MoS2 , MoSe2 , MoTe2 , WS2 , WSe2 , and WTe2 , including the spin-splitting and spin-polarization of the bands, and we briefly review the vibrational properties of these materials. We then use k.p theory to analyse optical transitions in two-dimensional TMDCs over a broad spectral range that covers the Van Hove singularities in the band structure (the M points). We also discuss the visualization of scanning tunnelling microscopy maps.

https://iopscience.iop.org/article/10.1088/2053-1583/2/2/022001/pdf

k · p theory for two-dimensional transition metal dichalcogenide semiconductors

We present $\mathbf{k}\cdotp\mathbf{p}$ Hamiltonians parametrised by {\it ab initio} density functional theory calculations to describe the dispersion of the valence and conduction bands at their extrema (the $K$, $Q$, $\Gamma$, and $M$ points of the hexagonal Brillouin zone) in atomic crystals of semiconducting monolayer transition metal dichalcogenides. We review the parametrisation of the essential parts of the $\mathbf{k}\cdotp\mathbf{p}$ Hamiltonians for MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, including the spin-splitting and spin-polarisation of the bands, and we discuss the vibrational properties of these materials. We then use $\mathbf{k}\cdotp\mathbf{p}$ theory to analyse optical transitions in two-dimensional transition metal dichalcogenides over a broad spectral range that covers the Van Hove singularities in the band structure (the $M$ points). We also discuss the visualisation of scanning tunnelling microscopy maps.

k.p theory for two-dimensional transition metal dichalcogenide semiconductors

The electronic band structure of graphene in the presence of spin-orbit coupling and transverse electric field is investigated from first principles using the linearized augmented plane-wave method. The spin-orbit coupling opens a gap of $24\text{ }\ensuremath{\mu}\text{eV}$ (0.28 K) at the $K({K}^{\ensuremath{'}})$ point. It is shown that the previously accepted value of $1\text{ }\ensuremath{\mu}\text{eV}$, coming from the $\ensuremath{\sigma}\text{\ensuremath{-}}\ensuremath{\pi}$ mixing, is incorrect due to the neglect of $d$ and higher orbitals whose contribution is dominant due to symmetry reasons. The transverse electric field induces an additional (extrinsic) Bychkov-Rashba-type splitting of $10\text{ }\ensuremath{\mu}\text{eV}$ (0.11 K) per V/nm, coming from the $\ensuremath{\sigma}\text{\ensuremath{-}}\ensuremath{\pi}$ mixing. A ``miniripple'' configuration with every other atom shifted out of the sheet by less than 1% differs little from the intrinsic case.

Band-structure topologies of graphene: Spin-orbit coupling effects from first principles

The spin-orbit coupling in graphene induces spectral gaps at the high-symmetry points. The relevant gap at the $\ensuremath{\Gamma}$ point is similar to the splitting of the $p$ orbitals in the carbon atom, being roughly 8.5 meV. The splitting at the $\mathrm{K}$ point is orders of magnitude smaller. Earlier tight-binding theories indicated the value of this intrinsic gap of $1\text{ }\ensuremath{\mu}\text{eV}$, based on the $\ensuremath{\sigma}\text{\ensuremath{-}}\ensuremath{\pi}$ coupling. All-electron first-principles calculations give much higher values, between 25 and $50\text{ }\ensuremath{\mu}\text{eV}$, due to the presence of the orbitals of the $d$ symmetry in the Bloch states at $\mathrm{K}$. A realistic multiband tight-binding model is presented to explain the effects the $d$ orbitals play in the spin-orbit coupling at $\mathrm{K}$. The $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\sigma}$ coupling is found irrelevant to the value of the intrinsic spin-orbit-induced gap. On the other hand, the extrinsic spin-orbit coupling (of the Bychkov-Rashba type), appearing in the presence of a transverse electric field, is dominated by the $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\sigma}$ hybridization, in agreement with previous theories. Tight-binding parameters are obtained by fitting to first-principles calculations, which also provide qualitative support for the model when considering the trends in the spin-orbit-induced gap in graphene under strain. Finally, an effective single-orbital next-nearest-neighbor hopping model accounting for the spin-orbit effects is derived.

/pdf/tight-binding-theory-of-the-spin-orbit-coupling-in-graphene-3yf8o527ip.pdf

Martin Gmitra

Papers

Graphene Spintronics

k · p theory for two-dimensional transition metal dichalcogenide semiconductors

k.p theory for two-dimensional transition metal dichalcogenide semiconductors

Band-structure topologies of graphene: Spin-orbit coupling effects from first principles

Tight-binding theory of the spin-orbit coupling in graphene