Dirac Cone Material Research Articles

Dirac fermions collimation in heterostructures based on tilted Dirac cone materials

This paper aims to theoretically analyze the behavior of Dirac fermions in a tilted Dirac cone material, particularly those interacting with a barrier potential. Our results show that the degree of tilt in the y-direction can lead to different collimations of Dirac fermion beams relative to the Fermi and confinement surfaces. We have highlighted a range of results, including the conical geometry by illustrating the active surfaces and their geometric parameters in reciprocal space. To study the transmission probability, we have conducted numerical analyses, considering various system configurations and different external and internal physical parameters to characterize the fermionic transport behavior in a proposed heterostructure. Additionally, we examined the transmission of Dirac fermions in relation to the refractive indices and refraction between the different media constituting the system, discussing the tunneling effect and the Klein paradox in relation to various physical parameters. Our findings lay the groundwork for the development of controllable electronic devices using Dirac fermion collimation, governed by the tilt parameter, enabling precise manipulation and enhanced functionality.

Quantum oscillations of pseudomagnetoresistance in tunable tilt-mismatch Dirac-cone junction

This paper presents research on the quantum oscillation of pseudomagnetoresistance (PMR) in tilted Dirac cone material junctions. Dirac cones are linear energy dispersions that arise in materials like graphene, which is a two-dimensional material with unique electronic properties. The presence of a tilted Dirac cone in the energy spectrum of these materials introduces interesting phenomena such as pseudomagnetism and anisotropic quantum transport. By applying strain, we can control the direction of the tilted Dirac cone in graphene and investigate the pseudomagnetotransport properties of this system. Magnetoresistance is a real effect that arises from the Lorentz force acting on the charge carriers, while PMR is a geometric effect that arises from the tilted Dirac cone and the crystal lattice structure of the material. Using computational methods for finite-superlattice materials and the transfer-matrix method, our results show that the quantum beating pattern of PMR is more pronounced with an increased number of barriers. Additionally, we observe that the amplitude and period of the modulation depend on the strength and orientation of the tilted-induced pseudomagnetic field. We demonstrate that the PMR behavior can be tuned and optimized for specific applications, potentially leading to improvements in the design and optimization of graphene-based devices such as sensors, transistors, and quantum computers, which rely on the PMR behavior of graphene.

4-6 carbophene: A two-dimensional carbon material with Dirac cone and superior activity for electrochemical oxygen reduction reactions

The positive exploration of efficient and cost-effective electrocatalysts for the oxygen reduction reaction (ORR) is crucial for the sustainable development of energy conversion and storage technologies. Recently, a new type of two-dimensional (2D) carbon crystals, called 4-6 carbophene, has been successfully synthesized. It consists of a four-carbon ring and a six-carbon ring. In this work, we have discovered that 4-6 carbophene is a two-dimensional Dirac cone material through density-functional theory (DFT) calculations. Therefore, we further investigated the oxygen reduction reaction on 4-6 carbophene to understand its catalytic properties. The results demonstrate that on 4-6 carbophene, the ORR prefers a direct four-electron pathway. Under acidic conditions, the ORR overpotential of 4-6 carbophene is as low as 0.59 V, which is comparable to some metal benchmark catalysts, demonstrating that 4-6 carbophene is a metal-free ORR candidate catalyst. In addition, the richly charged carbon atoms on 4-6 carbophene exhibit remarkable charge transfer when binding to the adsorbed intermediates. This results in a strong binding strength. Thus, 4-6 carbophene has favorable ORR catalytic activity. This work not only provides promising low-cost catalysts in pure carbon materials for ORR, promoting the development of metal-free ORR catalysts, but also enhances the understanding of Dirac cone two-dimensional materials for applications in catalysis.

MX6C2H monolayers: The novel two-dimensional tunable Dirac cone materials family and quantum spin Hall insulators

Two-dimensional (2D) Dirac cone materials have many interesting physical properties. Therefore, people have been trying to find 2D materials with Dirac cones. Here, based on first principle calculations, we studied a new 2D Dirac cone material family MX6C2H monolayers (M = N,P,As and Sb, X = C,Si,Ge and Sn). The calculation of the cohesive energy indicated that the MX6C2H sheets have excellent energy stability. And the phonon spectrum showed their excellent dynamical stability. The electronic calculation revealed that the 2D MX6C2H monolayers have graphene-like band structures and ultra-high Fermi velocities comparable to graphene. The spin–orbit–coupling effect can open a sizable topological band gap in SbSn6C2H monolayer so that it can be effectively classified as quantum spin Hall insulators. In addition, the Dirac cone of PC6C2H monolayer can be adjusted by applying in-plane uniaxial strain, which is much easier than that of graphene. These interesting properties indicate that the novel 2D MX6C2H system has potential application value in nanoelectronics.

A family of robust Dirac cone materials: two-dimensional hexagonal M3X2 (M = Zn/Cd/Hg, X = Si/Ge).

The fascinating Dirac cone, which has produced some excellent properties in graphene, such as ballistic charge transport, ultra-high carrier mobility and the quantum Hall effect, has motivated researchers to design and study more two dimensional (2D) Dirac materials. In this work, we have designed a family of 2D Dirac cone materials M3X2 (M = Zn/Cd/Hg, X = Si/Ge) and studied their superior properties by first principles calculation. The calculated cohesive energy, phonon dispersion and ab initio molecular dynamics confirmed the energetic, dynamic and thermodynamic stability of Zn3Ge2, Cd3Ge2, Hg3Si2, and Cd3Si2 monolayers. It was found that the intrinsic Dirac cones exist in the electronic structure of the Zn3Ge2, Cd3Ge2, Hg3Si2 and Cd3Si2 monolayers. Their Fermi velocities are from 3.26 × 105 m s-1 to 4.32 × 105 m s-1 (8.2 × 105 m s-1 for graphene). It is noteworthy that the Dirac cone in the M3X2 structure is robust. It is independent of external strain (from -7% to +19%) and can also be preserved as one-dimensional zigzag nanoribbons and multilayers (from two to three-layers). Our work shows that the novel M3X2 Dirac cone materials are an important candidate for high-speed nanoelectronic devices.

Two-dimensional anisotropic Dirac materials PtN4C2 and Pt2N8C6 with quantum spin and valley Hall effects

We propose two different two-dimensional topological Dirac materials, planar ${\mathrm{PtN}}_{4}{\mathrm{C}}_{2}$ and ${\mathrm{Pt}}_{2}{\mathrm{N}}_{8}{\mathrm{C}}_{6}$, which exhibit graphenelike electronic structures with linearly dispersive Dirac-cone states exactly at the Fermi level. Moreover, the Dirac cone is anisotropic, resulting in anisotropic Fermi velocities and making it possible to realize orientation-dependent quantum devices. Using first-principles electronic structure calculations, we have systemically studied the structural, electronic, and topological properties. We find that spin-orbit coupling opens a sizable topological band gap so that the materials can be classified as quantum spin Hall insulators as well as quantum valley Hall insulators. Helical edge states that reside in the insulating band gap connecting the bulk conduction and valence bands are observed. Our work not only expands the Dirac-cone material family, but also provides another avenue to search for more two-dimensional topological quantum spin and valley Hall insulators.

Design and modulation of two-dimensional Dirac materials in beryllium/boron-based binary monolayers

In the periodic table, beryllium (Be) and boron (B) as typical light element are near neighbors of carbon (C). Survey the electron-deficiency in Be and B as compared with C, if introducing external electrons in principle can offset the electron-deficiency, it seems that a Dirac cone have a possibility to exist in Be/B-based structures, like as C-structure (e.g., graphene). Motivated by this inference, here we selected elements P/Se as electron-rich donors to make up special Be/B-based binary compositions (BeP2/B2Se) being isoelectronic with graphene. Using a global structure search method combined with first-principles calculation, we identified three stable two-dimensional (2D) monolayers, namely o-BeP2, α-B2Se and β-B2Se. As expected, these three monolayers are verified to possess intrinsic or strain-inducing Dirac cone. When applied with a 6% compressive strain, the o-BeP2 even can be converted to Dirac cone material. The two low-lying B2Se monolayers (α-B2Se and β-B2Se) possess a hexagonal honeycomb lattice, showing a natural Dirac cone and their Fermi velocities are in the same order of that of graphene. These configurations can be further expanded to the isoelectronic BeAs2 and B2S stoichiometries and a Dirac cone can be found. This isoelectronic strategy offers a possible route to design the 2D Dirac material in Be/B-based binary compounds.

CuP: A new type of anisotropic and very stable Dirac cone material

Abstract The anisotropic Dirac cone has the advantage of anisotropic carrier mobility, which is different from other Dirac materials and can be applied to direction-dependent quantum devices. By first-principle calculation, we systematically research the Dirac cone and quantum properties of CuP. The calculation results show that CuP monolayer is a new type of anisotropic Dirac material. In addition, there is no virtual frequency in the phonon spectrum of this structure. At 300 K, the CuP monolayer can be remained well and there is no loose fracture of the structure. Based on grounds of Born criteria, CuP monolayer has good mechanical stability. Interestingly, considering the effect of spin-orbit coupling (SOC), the Dirac cone does not open the band gap. Moreover, the addition of stress does not destroy the Dirac cone. The material is mechanically and thermally stable. The results of Poisson's ratio and Young's modulus show that the structure has obvious anisotropy. It is worth noting that, the Fermi velocity to the right is 2.3 × 105 m/s and the left is 4.5 × 105 m/s, which is in the same order of magnitude as the Fermi velocity of graphene (8.0 × 105 m/s). The calculation results provide an ideal basis for the design of directional electron transport devices in spintronics.

Ultra-low-loss on-chip zero-index materials

Light travels in a zero-index medium without accumulating a spatial phase, resulting in perfect spatial coherence. Such coherence brings several potential applications, including arbitrarily shaped waveguides, phase-mismatch-free nonlinear propagation, large-area single-mode lasers, and extended superradiance. A promising platform to achieve these applications is an integrated Dirac-cone material that features an impedance-matched zero index. Although an integrated Dirac-cone material eliminates ohmic losses via its purely dielectric structure, it still entails out-of-plane radiation loss, limiting its applications to a small scale. We design an ultra-low-loss integrated Dirac cone material by achieving destructive interference above and below the material. The material consists of a square array of low-aspect-ratio silicon pillars embedded in silicon dioxide, featuring easy fabrication using a standard planar process. This design paves the way for leveraging the perfect spatial coherence of large-area zero-index materials in linear, nonlinear, and quantum optics.

Undamped transverse electric mode in undoped two-dimensional tilted Dirac cone materials

Transverse electric (TE) modes can not propagate through the conducting solids. This is because the continuum of particle-hole excitations of conductors contaminates with the TE mode and dampes it out. But in solids hosting tilted Dirac cone (TDC) that admit a description in terms of a modified Minkowski spacetime, the new spacetime structure remedies this issue and therefore a tilted Dirac cone material (TDM) supports the propagation of an undamped TE mode which is sustained by density fluctuations. The resulting TE mode propagates at fermionic velocities which strongly confines the mode to the surface of the two-dimensional (2D) TDM.

Tunable tilted anisotropy of massless Dirac fermion in magnetic Kronig-Penney-type graphene

Modulation effects of alternating periodic electrostatic scalar and magnetic vector potentials on the anisotropic and the tilt characteristics of Dirac cone in a semi-infinite graphene was theoretically investigated using the transfer matrix technique. To study its anisotropic behavior, we characterized the geometry deformation of superlattice Dirac cone by introducing the tilt parameter, eccentricity, and group velocity. We found that the Dirac cone anisotropy and tilt effect depend on the amplitude of the periodically modulated scalar and/or vector potentials. As the results of tuning the coupled periodic scalar and vector potentials, four different phases of Dirac fermions emerged and were categorized through a phase diagram of the tilt parameter. For a strong coupled modulation, the tilt parameter becomes larger than one and the type-II Dirac cone phase emerged. We also found that pairs of extra Dirac points can be induced by a very high periodic scalar modulation coupled with a low periodic vector modulation. Moreover, strong modulation caused the Fermi contour to deform from a closed contour into an opened contour, introducing an electron-hole pocket on the graphene. Our results demonstrate the possibility to control the anisotropic behavior of the electronic structure of graphene, which might lead to an artificial tilted Dirac cone material and direction-dependent quantum devices.

Two-dimensional hexagonal Zn3Si2 monolayer: Dirac cone material and Dirac half-metallic manipulation**Projectsupported by the National Natural Science Foundation of China (Grant Nos. 11674136 and 11564022), Yunnan Province for Recruiting High-Caliber Technological Talents, China (Grant No. 1097816002), ReserveTalents for Yunnan Young and Middle-aged Academic and Technical Leaders, China (Grant No. 2017HB010), the Academic Qinglan Project of KUST (Grant No. 1407840010), the Analysis

The fascinating Dirac cone in honeycomb graphene, which underlies many unique electronic properties, has inspired the vast endeavors on pursuing new two-dimensional (2D) Dirac materials. Based on the density functional theory method, a 2D material Zn3Si2 of honeycomb transition-metal silicide with intrinsic Dirac cones has been predicted. The Zn3Si2 monolayer is dynamically and thermodynamically stable under ambient conditions. Importantly, the Zn3Si2 monolayer is a room-temperature 2D Dirac material with a spin–orbit coupling energy gap of 1.2 meV, which has an intrinsic Dirac cone arising from the special hexagonal lattice structure. Hole doping leads to the spin polarization of the electron, which results in a Dirac half-metal feature with single-spin Dirac fermion. This novel stable 2D transition-metal-silicon-framework material holds promises for electronic device applications in spintronics.

Borophosphene: A New Anisotropic Dirac Cone Monolayer with a High Fermi Velocity and a Unique Self-Doping Feature.

Two-dimensional (2D) Dirac cone materials exhibit linear energy dispersion at the Fermi level, where the effective masses of carriers are very close to zero and the Fermi velocity is ultrahigh, only 2-3 orders of magnitude lower than the light velocity. Such Dirac cone materials have great promise in high-performance electronic devices. Herein, we have employed the genetic algorithm methods combined with first-principles calculations to propose a new 2D anisotropic Dirac cone material, an orthorhombic boron phosphide (BP) monolayer named borophosphene. Molecular dynamics simulation and phonon dispersion have been used to evaluate the dynamic and thermal stability of borophosphene. Because of the unique arrangements of B-B and P-P dimers, the mechanical and electronic properties are highly anisotropic. Of great interest is the fact that the Dirac cone of the borophosphene is robust, independent of in-plane biaxial and uniaxial strains, and can also be observed in its one-dimensional zigzag nanoribbons and armchair nanotubes. The Fermi velocities are ∼105 m/s, on the same order of magnitude as that of graphene. By using a tight-binding model, the origin of the Dirac cone of borophosphene is analyzed. Moreover, a unique feature of self-doping can be induced by the in-plane biaxial and uniaxial strains of borophosphene and the curvature effect of nanotubes, which is greatly beneficial for realizing high-speed carriers (holes). Our results suggest that the borophosphene holds great promise for high-performance electronic devices, which could promote experimental and theoretical studies for further exploring the potential applications of other 2D Dirac cone sheets.

Negative differential thermal conductance in a borophane normal metal–superconductor junction

We study the charge and heat transport in a normal metal/superconductor (NS) junction of the tilted anisotropic Dirac cone material borophane, using the extended Blonder–Tinkham–Klapwijk formalism. In spite of the large mismatch in the Fermi wave vector of the normal metal and superconductor sides of the borophane NS junction, the electron–hole conversion happens with unit probability at normal incidences. Furthermore, in the heavily doped superconducting regime, for heavily doped normal borophane, the electron–hole conversion happens with unit probability, at almost any incident angle. Finding the dependence of the differential Andreev conductance on the Fermi energy and excitation energy gives us a handle to distinguish specular from retro Andreev reflection. We numerically find that, independent of the Fermi energy, the temperature dependence of the differential thermal conductance in borophane can be modelled as an inverse Gaussian function, reflecting the d-wave symmetry of the borophane superconductor. We propose a scheme for achieving negative differential thermal conductance, as a key building block of thermal circuits, at intermediate Fermi energies. Our findings will have potential applications in developing borophane-based thermal management and signal manipulation mesoscopic structures such as heat transistors, heat diodes, and thermal logic gates.

Computational study of silicene nanoribbon tunnel field-effect transistor

Stable room temperature operation of field-effect transistor (FET) based on two-dimensional silicon (silicene) has recently been reported. Like graphene, silicene is a Dirac cone material. Silicene-based devices provide high off-state leakage current due to lack of a significant bandgap. However, quantum confined silicene nanoribbon (SiNR) shows observable bandgap which can be used for making switching transistors for digital integrated circuit design. Contrary to metal oxide semiconductor FET (MOSFET), tunnel field-effect transistor (TFET) overcomes the physical limit of scaling of supply voltage. In this work, we present structure and characteristics of SiNR TFET using atomistic simulation based on self-consistent solution of 3D Poisson and Schrodinger equations within the non-equilibrium Green’s function formalism. Performances are also compared with the International Technology Roadmap for Semiconductors projected high performance requirements of 2026 nMOSFETs.

Theoretical prediction of HfB2 monolayer, a two-dimensional Dirac cone material with remarkable Fermi velocity.

Searching for new two-dimensional (2D) Dirac cone materials has been popular since the discovery of graphene with a Dirac cone structure. Based on density functional theory (DFT) calculations, we theoretically designed a HfB2 monolayer as a new 2D Dirac material by introducing the transition metal Hf into a graphene-like boron framework. This newly predicted HfB2 monolayer has pronounced thermal and kinetic stabilities along with a Dirac cone with a massless Dirac fermion and Fermi velocities (3.59 × 105 and 6.15 × 105 m s−1) comparable to that of graphene (8.2 × 105 m s−1). This study enriches the diversity and promotes the application of 2D Dirac cone materials.

A New Anisotropic Dirac Cone Material: A B2S Honeycomb Monolayer.

Different from the isotropic Dirac cones existing in other two-dimensional (2D) materials, anisotropic Dirac cones have the merit of anisotropic carrier mobility for applications in direction-dependent quantum devices. Motivated by the recent experimental finding of an anisotropic Dirac cone in borophene, here we report a new 2D anisotropic Dirac cone material, B2S monolayer, identified by using a global structure search method and first-principles calculation combined with a tight-binding model. The B2S monolayer is found to be stable mechanically, thermally, and dynamically and exhibits an anisotropic Dirac cone exactly at the Fermi level, showing a Fermi velocity of 106 m/s in the same order of magnitude as that of graphene. Moreover, B2S monolayer is the first anisotropy Dirac cone material with a pristine honeycomb structure stabilized by S in free-standing conditions where each atom has four valence electrons on average being isoelectronic to C. This study would expand the Dirac cone material family with new features.

Electron Correlations in an Organic Dirac-Cone Material

Electron Correlations in an Organic Dirac-Cone Material

Finding correlations in a Dirac-cone material

2D Materials Researchers have long been on the lookout for signatures of electron-electron interactions in materials whose electrons have linear energy dispersions represented by Dirac cones, such as graphene. However, these effects have remained frustratingly small. Hirata et al. used nuclear

Silicene Nanoribbon Tunnel Field Effect Transistor

Scaling of metal oxide semiconductor field effect transistor (MOSFET) following the Moore’s law is approaching to its near end as the power dissipation at the chip level is becoming increasingly difficult to reduce [1]. The International Technology Roadmap for Semiconductors (ITRS) considers several non-classical devices as a future replacement of silicon-based MOSFETs among which tunnel field effect transistor (TFET) is found to be promising [2, 3]. Compared to bulk three dimensional material based TFETs, study of TFETs based on two dimensional atomically thick materials have shown potential to operate at low supply voltage with a low subthreshold slope (SS) compared to 60mV/decade in conventional MOSFETs [4]. Different forms of two dimensional materials are studied such as Dirac cone materials (graphene, silicene, gemanene, stanene), transition metal dichalcogenides (TMD), transition oxides (TO) and topological insulators (TI). Compared to the study of TFET based on other two dimensional materials, silicene TFET remained large unexplored. Silicene is the two dimensional atomically thick planer form of bulk silicon. Stable room temperature operation of FET based on silicene has recently been reported [5]. Like graphene, silicene is a Dirac cone material with devices which provide high off-state leakage current due to the lack of a significant bandgap. However, quantum confined silicene nanoribbon (SiNR) shows observable bandgap making it suitable for digital applications [6]. Moreover, being an allotrope of silicon, silicene is also expected to be suitable for fabrication technology. Here, we present our work on SiNR TFET using atomistic simulation based on self-consistent solution of the 3D Poisson and Schrödinger equations within the non-equilibrium Green’s function (NEGF) formalism. SiNR has two types of edges, armchair and zigzag. We have considered armchair configuration in our study for a channel length of 10nm of a double gate SiNR TFET. Source and drain are 10nm each. Our default SiNR width is ~4nm providing a band gap of 1.42eV. Top and bottom gate oxides of our studied TFET are 2nm of SiO2. The effective tight binding Hamiltonian is adopted from the work of Voon et al. [7] and is simulated using the simulation code proposed in [8] for Si-Si bond length of 2.25Å and hoping integral of -6.43eV with -1.12eV correction at the SiNR edges [7]. The n+-type source and p+-type drain are doped with a molecular fraction of 0.001. A drain source voltage (VDS) of 0.3V is considered in this work. The studied SiNR TFET provides an on/off current ratio of ~107 with an average steep subthreshold slope (SS) of 6mV/decade for VDS=0.3V. A record low ~0.75x10-11pW/μm off-state leakage power is estimated. We have found that the leakage level increases as the supply voltage increases. The off-state leakage current increases to 0.6pA/μm as VDS increases from 0.3V to 0.95V. As the width of SiNR increases and the corresponding band gap decreases, leakage current also increases at small band gap with a reduction in on/off current ratio. The steep subthreshold slope of our studied SiNR TFET suits low power operation. With a suitable high-k dielectric and low gate oxide thickness, on-state drive current can be improved. Performance of SiNR TFET is also compared with ITRS projected high performance (HP) requirements of 2026 nMOSFET where SiNR TFET exceeds the performance of 2026 nMOSFET by 1014 times less power dissipation at 103 times higher on/off current ratio. Acknowledgement: Part of the work is supported by the United States Air Force Research Laboratory under agreement number FA9453-10-1-0002. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon.