Two-dimensional Dirac Materials Research Articles

Colossal infrared and terahertz magneto-optical activity in a two-dimensional Dirac material.

When two-dimensional electron gases (2DEGs) are exposed to a magnetic field, they resonantly absorb electromagnetic radiation via electronic transitions between Landau levels1. In 2DEGs with a Dirac spectrum, such as graphene, theory predicts an exceptionally high infrared magneto-absorption, even at zero doping2-5. However, the measured Landau-level magneto-optical effects in graphene have been much weaker than expected2,6-12 because of imperfections in the samples available for such experiments. Here, we measure magneto-transmission and Faraday rotation in high-mobility encapsulated monolayer graphene using a custom-designed set-up for magneto-infrared microspectroscopy. Our results show strongly enhanced magneto-optical activity in the infrared and terahertz ranges, characterized by absorption of light near to the 50% maximum allowed, 100% magnetic circular dichroism and high Faraday rotation. Considering that sizeable effects have been already observed at routinely achievable magnetic fields, our findings demonstrate the potential of magnetic tuning in 2D Dirac materials for long-wavelength optoelectronics and plasmonics.

Spin-Split Band Hybridization in Graphene Proximitized with α-RuCl3 Nanosheets.

Proximity effects induced in the two-dimensional Dirac material graphene potentially open access to novel and intriguing physical phenomena. Thus far, the coupling between graphene and ferromagnetic insulators has been experimentally established. However, only very little is known about graphene's interaction with antiferromagnetic insulators. Here, we report a low-temperature study of the electronic properties of high quality van der Waals heterostructures composed of a single graphene layer proximitized with α-RuCl3. The latter is known to become antiferromagnetically ordered below 10 K. Shubnikov-de Haas oscillations in the longitudinal resistance together with Hall resistance measurements provide clear evidence for a band realignment that is accompanied by a transfer of electrons originally occupying the graphene's spin degenerate Dirac cones into α-RuCl3 band states with in-plane spin polarization. Left behind are holes in two separate Fermi pockets, only the dispersion of one of which is distorted near the Fermi energy due to spin selective hybridization with these spin polarized α-RuCl3 band states. This interpretation is supported by our density functional theory calculations. An unexpected damping of the quantum oscillations as well as a zero-field resistance upturn close to the Néel temperature of α-RuCl3 suggest the onset of additional spin scattering due to spin fluctuations in the α-RuCl3.

Time-dependent quantum Monte Carlo simulation of electron devices with two-dimensional Dirac materials: A genuine terahertz signature for graphene

An intrinsic electron injection model for linear band two-dimensional (2D) materials, like graphene, is presented and its coupling to a recently developed quantum time-dependent Monte Carlo simulator for electron devices, based on the use of stochastic Bohmian conditional wave functions, is explained. The simulator is able to capture the full (DC, AC, transient and noise) performance of 2D electron devices. In particular, we demonstrate that the injection of electrons with positive and negative kinetic energies is mandatory when investigating high frequency performance of linear band materials with Klein tunneling, while traditional models dealing with holes (defined as the lack of electrons) can lead to unphysical results. We show that the number of injected electrons is bias-dependent, implying that an extra charge is required to get self-consistent results. Interestingly, we provide a successful comparison with experimental DC data. Finally, we predict that a genuine high-frequency signature due to a roughly constant electron injection rate in 2D linear band electron devices (which is missing in 2D parabolic band ones) can be used as a band structure tester.

Unconventional superconductivity in nearly flat bands in twisted bilayer graphene

Flat electronic bands can accommodate a plethora of interaction driven quantum phases, since kinetic energy is quenched therein and electronic interactions therefore prevail. Twisted bilayer graphene, near so-called the "magic angles", features \emph{slow} Dirac fermions close to the charge-neutrality point that persist up to high-energies. Starting from a continuum model of slow, but strongly interacting Dirac fermions, we show that with increasing chemical doping away from the charge-neutrality point, a time-reversal symmetry breaking, valley pseudo-spin-triplet, topological $p+ip$ superconductor gradually sets in, when the system resides at the brink of an anti-ferromagnetic ordering (due to Hubbard repulsion), in qualitative agreement with recent experimental findings. The $p+ip$ paired state exhibits quantized spin and thermal Hall conductivities, polar Kerr and Faraday rotations. Our conclusions should also be applicable for other correlated two-dimensional Dirac materials.

Dirac cones in a snub trihexagonal tiling lattice with reflective symmetry breaking

The present models of the two-dimensional (2D) Dirac materials always have reflective symmetry, but the essentiality has never been proved. Here we present an exceptional case: a snub trihexagonal tiling (STT) lattice without reflective symmetry. We demonstrate the existence of Dirac cones in this reflection-symmetry-free lattice by using a single-orbital tight-binding (TB) Hamiltonian. The SST lattice is also topologically nontrivial, because the Dirac cone can be gapped by spin–orbit coupling (SOC) effect associated with robust gapless edge states. Using first-principles calculations, we predict a promising candidate 2D material, Be3C4 monolayer to realize this toy model. The Fermi velocities in this unique lattice are even higher than that in graphene. The stability and plausibility of the Be3C4 monolayer are verified by positive phonon modes, molecular dynamical simulations and mechanical criteria. This work eliminates the need for reflective symmetry in 2D Dirac materials, opening an avenue for designing new 2D Dirac materials.

The origin of intrinsic charge transport for Dirac carbon sheet materials: roles of acetylenic linkage and electron-phonon couplings.

Within the past few years, intriguing graphene Dirac cones have attracted intense interest in novel two-dimensional (2D) Dirac materials as ultrahigh-mobility functional materials. In this work, the phonon-limited charge transport properties of α-graphyne (α-GY), α-graphdiyne (α-GDY), and β-graphyne (β-GY) were investigated using the Boltzmann transport equation within the first-principles framework while considering the electron-phonon coupling (EPC). Despite all three investigated compounds being 2D Dirac carbon materials, each demonstrated distinctly different carrier mobilities by one order of magnitude (2.2 × 104 cm2 V-1 s-1 for α-GY, 2.1 × 103 cm2 V-1 s-1 for α-GDY and 1.9 × 103 cm2 V-1 s-1 for β-GY at room-temperature and a carrier connection of n ∼ 3 × 1012 cm-2). The essential differences in the mobilities of these materials originated from the acetylenic linkage limiting the group velocity and the E2g phonon modes limiting the scattering time. For example, a few uniformly equivalent acetylenic linkages and E2g phonon modes tend to generate high mobilities. A simple mobility relationship was determined using the number of E2g photon modes, allowing for a quick estimation of the mobilities for Dirac materials. α-GY was identified as a promising alternative to graphene for next generation nanoelectronic devices.

Coulomb effects in the absorbance spectra of two-dimensional Dirac materials

A wide range of materials like graphene, topological insulators, and transition-metal dichalcogenides (TMDs) share an interesting property: the low-energy excitations behave as Dirac particles. This emergent behavior of Dirac quasiparticles defines a large class of media that are usually called Dirac materials. In this work we build the foundations of a way to study the linear optical properties of these two-dimensional media. Our approach is based on a Dirac-like formulation of the standard semiconductor Bloch equations used in semiconductor physics. We provide an explicit expression of the linear absorbance, which we call the relativistic Elliott formula, and use it to quantify the variation of the continuum absorbance spectrum with the strength of the Coulomb interaction (the Sommerfeld factor). Our calculations also show how the Coulomb enhancements scales with the band gap and vanishes for zero band gap, shedding light on the behavior of graphene for low-light intensities. The results presented are in good quantitative agreement with published experimental results. Our theory can help researchers to explore the nonlinear interactions of intense, ultrashort pulses with TMDs, and the framework is flexible enough to be adapted to different experimental situations, such as cavities, multilayers, heterostructures, and microresonators.

Light–valley interactions in 2D semiconductors

The emergence of two-dimensional Dirac materials, particularly transition metal dichalcogenides (TMDs), has reinvigorated interest in valleytronics, which utilizes the electronic valley degree of freedom for information storage and processing. Here, we review the basic valley-dependent properties and their experimental demonstrations in single-layer semiconductor TMDs with an emphasis on the effects of band topology and light–valley interactions. We also provide a brief summary of the recent advances on controlling the valley degree of freedom in TMDs with light and other means for potential applications. Valleytronics in single-layer semiconductors is reviewed with an emphasis on controlling the valley degree of freedom with light as well as potential applications.

CUBIT: Capacitive qUantum BIT

In this letter, it is proposed that cryogenic quantum bits can operate based on the nonlinearity due to the quantum capacitance of two-dimensional Dirac materials, and in particular graphene. The anharmonicity of a typical superconducting quantum bit is calculated, and the sensitivity of quantum bit frequency and anharmonicity with respect to temperature are found. Reasonable estimates reveal that a careful fabrication process can reveal expected properties, putting the context of quantum computing hardware into new perspectives.

Research progress on the calculation of carrier mobility for two-dimensional Dirac material

With the development of integrated devices in the direction of increasingly miniaturization, from the end of the last century, computing, communications, automatic control and other aspects of science and technology expressed the urgent expection of new materials. With the discovery of graphene, the study of two-dimensional material system began to reveal new vitality. The special properties of these two-dimensional materials are often related to the carrier mobility. Therefore, studying how to calculate the carrier mobility of two-dimensional materials, especially the Dirac materials, is of double significance for theoretical calculation and application of nanomaterials. In this paper, the theoretical development of the two-dimensional Dirac material mobility is studied in detail. This paper summarizes the commonly used methods and principles in theoretical calculations of materials, including Bloch’s theorem and Density functional theory. The main methods for calculating carrier mobility in two-dimensional materials are introduced in detail, namely Tight-binding models and deformation potential theory.

Terahertz Investigation of Dirac Materials: Graphene and Topological Insulators

Light-matter interaction in two-dimensional Dirac materials exhibits intriguing features in comparison to conventional semiconductors. Recent discoveries of graphene and three-dimensional topological insulators (TIs) have demonstrated novel terahertz (THz) optoelectronics, such that control over the electronic properties of Dirac-type carriers can be conducted by optical techniques. In this paper, we review recent investigations of graphene and TIs using broadband THz radiation and ultrashort optical pulses. After discussing state-of-the-art progress in graphene and TI investigations (Sec. I), we present ultrafast optical techniques that employ optical-pump THz-probe spectroscopy (Sec. II). In Sec. III, broadband THz responses in Dirac materials are examined according to semi-classical theories, and corresponding physical rationales are extended to elucidate Dirac plasmons in graphene and TIs (Sec. IV). Finally, brief summaries with research outlooks for future THz applications of graphene and TIs are provided (Sec. V).

Nonlinear and anisotropic polarization rotation in two-dimensional Dirac materials

We predict nonlinear optical polarization rotation in two dimensional massless Dirac systems including graphene and 8-$Pmmn$ borophene. When illuminated, a continuous wave optical field leads to a nonlinear steady state of photo-excited carriers in the medium. The photo-excited population inversion and the inter-band coherence gives rise to a finite transverse optical conductivity, $\sigma_{xy} (\omega)$. This in turn leads to definitive signatures in associated Kerr and Faraday polarization rotation, which are measurable in a realistic experimental scenario.

Low-frequency phase diagram of irradiated graphene and a periodically driven spin- 12 XY chain

We study the Floquet phase diagram of two-dimensional Dirac materials such as graphene and the one-dimensional (1D) spin-1/2 $XY$ model in a transverse field in the presence of periodic time-varying terms in their Hamiltonians in the low drive frequency ($\omega$) regime where standard $1/\omega$ perturbative expansions fail. For graphene, such periodic time dependent terms are generated via the application of external radiation of amplitude $A_0$ and time period $T = 2\pi/\omega$, while for the 1D $XY$ model, they result from a two-rate drive protocol with time-dependent magnetic field and nearest-neighbor couplings between the spins. Using the adiabatic-impulse method, we provide several semi-analytic criteria for the occurrence of changes in the topology of the phase bands of such systems. For irradiated graphene, we point out the role of the symmetries of $H(t)$ and $U$ behind such topology changes. Our analysis reveals that at low frequencies, phase band topology changes may also happen at $t= T/3, 2T/3$ (apart from $t=T$). We chart out the phase diagrams at $t=T/3, 2T/3,\, {\rm and }\, T$ as a function of $A_0$ and $T$ using exact numerics, and compare them with the prediction of the adiabatic-impulse method. We show that several characteristics of these phase diagrams can be analytically understood from results obtained using the adiabatic-impulse method and point out the crucial contribution of the high-symmetry points in the graphene Brillouin zone to these diagrams. Finally we study the 1D $XY$ model with a two-rate driving protocol using the adiabatic-impulse method and exact numerics revealing a phase band crossing at $t=T/2$ and $k=\pi/2$. We also study the anomalous end modes generated by such a drive. We suggest experiments to test our theory.

Phase Transitions of the Polariton Condensate in 2D Dirac Materials.

For the quantum well in an optical microcavity, the interplay of the Coulomb interaction and the electron-photon (e-ph) coupling can lead to the hybridizations of the exciton and the cavity photon known as polaritons, which can form the Bose-Einstein condensate above a threshold density. Additional physics due to the nontrivial Berry phase comes into play when the quantum well consists of the gapped two-dimensional Dirac material such as the transition metal dichalcogenide MoS_{2} or WSe_{2}. Specifically, in forming the polariton, the e-ph coupling from the optical selection rule due to the Berry phase can compete against the Coulomb electron-electron (e-e) interaction. We find that this competition gives rise to a rich phase diagram for the polariton condensate involving both topological and symmetry breaking phase transitions, with the former giving rise to the quantum anomalous Hall and the quantum spin Hall phases.

Chaos in Dirac Electron Optics: Emergence of a Relativistic Quantum Chimera.

We uncover a remarkable quantum scattering phenomenon in two-dimensional Dirac material systems where the manifestations of both classically integrable and chaotic dynamics emerge simultaneously and are electrically controllable. The distinct relativistic quantum fingerprints associated with different electron spin states are due to a physical mechanism analogous to a chiroptical effect in the presence of degeneracy breaking. The phenomenon mimics a chimera state in classical complex dynamical systems but here in a relativistic quantum setting-henceforth the term "Dirac quantum chimera," associated with which are physical phenomena with potentially significant applications such as enhancement of spin polarization, unusual coexisting quasibound states for distinct spin configurations, and spin selective caustics. Experimental observations of these phenomena are possible through, e.g., optical realizations of ballistic Dirac fermion systems.

Excitonic instability in optically pumped three-dimensional Dirac materials

Recently it was suggested that transient excitonic instability can be realized in optically-pumped two-dimensional (2D) Dirac materials (DMs), such as graphene and topological insulator surface states. Here we discuss the possibility of achieving a transient excitonic condensate in optically-pumped three-dimensional (3D) DMs, such as Dirac and Weyl semimetals, described by non-equilibrium chemical potentials for photoexcited electrons and holes. Similar to the equilibrium case with long-range interactions, we find that for pumped 3D DMs with screened Coulomb potential two possible excitonic phases exist, an excitonic insulator phase and the charge density wave phase originating from intranodal and internodal interactions, respectively. In the pumped case, the critical coupling for excitonic instability vanishes; therefore, the two phases coexist for arbitrarily weak coupling strengths. The excitonic gap in the charge density wave phase is always the largest one. The competition between screening effects and the increase of the density of states with optical pumping results in a reach phase diagram for the transient excitonic condensate. Based on the static theory of screening, we find that under certain conditions for the value of the dimensionless coupling constant screening in 3D DMs can be weaker than in 2D DMs. Furthermore, we identify the signatures of the transient excitonic condensate that could be probed by scanning tunneling spectroscopy, photoemission and optical conductivity measurements. Finally, we provide estimates of critical temperatures and excitonic gaps for existing and hypothetical 3D DMs.

The first principle calculation of two-dimensional Dirac materials

As the size of integrated device becoming increasingly small, from the last century, semiconductor industry is facing the enormous challenge to break the Moore’s law. The development of calculation, communication and automatic control have emergent expectation of new materials at the aspect of semiconductor industrial technology and science. In spite of silicon device, searching the alternative material with outstanding electronic properties has always been a research point. As the discovery of graphene, the research of two-dimensional Dirac material starts to express new vitality. This essay studied the development calculation of 2D material’s mobility and introduce some detailed information of some approximation method of the first principle calculation.

Helical Level Structure of Dirac Potential Wells.

In graphene and other massless two-dimensional Dirac materials, Klein tunneling compromises electron confinement, and momentum-space contours can be assigned a Berry phase which is either zero or π. Consequently, in such systems the energy spectrum of circular potential wells exhibits an interesting discontinuity as a function of magnetic field B: for a given angular momentum the ladder of eigen-resonances is split at an energy-dependent critical field B c. Here we show that introducing a mass term Δ in the Hamiltonian bridges this discontinuity in such a way that states below B c are adiabatically connected to states above B c whose principal quantum number differs by unity depending on the sign of Δ. In the B-Δ plane, the spectrum of these circular resonators resembles a spiral staircase, in which a particle prepared in the ∣n, m⟩ resonance state can be promoted to the ∣n± 1, m⟩ state by an adiabatic circuit of the Hamiltonian about B c, the sign depending on the direction of the circuit. We explain the phenomenon in terms of the evolving Berry phase of the orbit, which in such a circuit changes adiabatically by 2π.

C4N3H monolayer: A two-dimensional organic Dirac material with high Fermi velocity

Searching for two-dimensional (2D) organic Dirac materials, which have more adaptable practical applications in comparing with inorganic ones, is of great significance and has been ongoing. However, only two kinds of these materials with low Fermi velocity have been discovered so far. Herein, we report the design of an organic monolayer with C$_4$N$_3$H stoichiometry which possesses fascinating structure and good stability in its free-standing state. More importantly, we demonstrate that this monolayer is a semimetal with anisotropic Dirac cones and very high Fermi velocity. This Fermi velocity is roughly one order of magnitude larger than that in 2D organic Dirac materials ever reported, and is comparable to that in graphene. The Dirac states in this monolayer arise from the extended $\pi$-electron conjugation system formed by the overlapping 2\emph{p}$_z$ orbitals of carbon and nitrogen atoms. Our finding opens a door for searching more 2D organic Dirac materials with high Fermi velocity.

Experimental realization of two-dimensional Dirac nodal line fermions in monolayer Cu2Si

Topological nodal line semimetals, a novel quantum state of materials, possess topologically nontrivial valence and conduction bands that touch at a line near the Fermi level. The exotic band structure can lead to various novel properties, such as long-range Coulomb interaction and flat Landau levels. Recently, topological nodal lines have been observed in several bulk materials, such as PtSn4, ZrSiS, TlTaSe2 and PbTaSe2. However, in two-dimensional materials, experimental research on nodal line fermions is still lacking. Here, we report the discovery of two-dimensional Dirac nodal line fermions in monolayer Cu2Si based on combined theoretical calculations and angle-resolved photoemission spectroscopy measurements. The Dirac nodal lines in Cu2Si form two concentric loops centred around the Γ point and are protected by mirror reflection symmetry. Our results establish Cu2Si as a platform to study the novel physical properties in two-dimensional Dirac materials and provide opportunities to realize high-speed low-dissipation devices.