Linear Band Dispersion Research Articles

Intrinsic charge and spin conductivities of doped graphene in the Fermi-liquid regime

The experimental availability of ultra-high-mobility samples of graphene opens the possibility to realize and study experimentally the "hydrodynamic" regime of the electron liquid. In this regime the rate of electron-electron collisions is extremely high and dominates over the electron-impurity and electron-phonon scattering rates, which are therefore neglected. The system is brought to a local quasi-equilibrium described by a set of smoothly varying (in space and time) functions, {\it i.e.} the density, the velocity field and the local temperature. In this paper we calculate the charge and spin conductivities of doped graphene due solely to electron-electron interactions. We show that, in spite of the linear low-energy band dispersion, graphene behaves in a wide range of temperatures as an effectively Galilean invariant system: the charge conductivity diverges in the limit $T \to 0$, while the spin conductivity remains finite. These results pave the way to the description of charge transport in graphene in terms of Navier-Stokes equations.

Towards Wafer-Scale Monocrystalline Graphene Growth and Characterization.

Since its discovery in 2004, graphene has boosted numerous fundamental sciences and technological applications due to its massless Dirac particle-like linear band dispersion, that causes unprecedented physical properties. Among the various methods for synthesizing graphene, chemical vapor deposition is the most suitable approach for scalable production on a wafer scale, which is a critical step for practical applications. Graphene grain boundaries (GGBs), consisting of nonhexagonal carbon rings and therefore modulating the properties of graphene films, are inevitably formed via the merging of adjacent graphene domains with different orientations. Large-area monocrystalline graphene synthesis without forming GGBs has been challenging, let alone observing such boundaries. Here, an up-to-date review is presented of how to grow wafer-scale monocrystalline graphene without GGBs. One approach is to make single domain sizes as large as possible by reducing or passivating the number of nucleation sites. Another approach is to align graphene domains in identical orientations, and then merge them atomically. The recently developed methods for observing graphene orientation and GGBs both at the atomic and macro-scales are also presented. Finally, perspectives for future research in graphene growth are discussed.

Geometric and electronic structures of polymerized C32 fullerenes: Electronic structure tuning by fullerene and carbon nanotube filling

We report first-principles total-energy calculations providing the geometric and electronic structures of polymerized small fullerene C32, and C36- and carbon nanotube (CNT)-filled C32 polymers. We found that the pristine C32 polymer is a semiconductor with a direct bandgap of 1.5 eV, while the filled C32 polymers are metals with the carriers distributed on sp2 carbon atoms in the C32 cage. We also found that the C32 polymer possesses a pair of linear dispersion bands in their valence band because of the π network topology, which is regarded as a graphene-like topology with an internal degree of freedom.

Loss of Linear Band Dispersion and Trigonal Structure in Silicene on Ir(111).

The structure of silicene/Ir(111) was examined on the basis of density functional theory. We have found that Ir(111) preserves the 2D character of silicene but significantly distorts its structure from the trigonal one expected for an isolated silicene. The electronic structure of silicene is strongly hybridized with that of Ir(111) so that silicene on Ir(111) loses its linear band dispersion around the Fermi level, giving rise to a metallic band structure; however, silicene/Ir(111) exhibits a hidden linear-dispersive band, which is related to the linear-dispersive conduction band of an isolated silicene.

First-principles prediction on silicene-based heterobilayers as a promising candidate for FET

The structural and electronic properties of silicene/silicane and silicene/germanene heterobilayers (HBLs) are investigated by using first-principles methods. The results show that the silicene interacts overall with silicane (germanene) with a binding energy of −50∼−70 meV per Si (Ge) atom, suggesting a weakly van der Waals interaction between silicene and substrate. A relative large bandgap with a linear band dispersion of HBLs is opened due to the sublattice symmetry broken by the intrinsic interface dipole between silicene and substrate. Remarkably, the band gap of all these HBLs can also be continually tuned modulated by adjusting the interlayer spacing and strain, independent on the stacking arrangements. Silicene is thus expected to be useful for building high-performance FET channel, which would extend its applicability to possible future nanoelectronics.

First-principles design of silicene/Sc2CF2 heterojunction as a promising candidate for field effect transistor

Experimentally, it is challenging to epitaxially grow silicene on conventional semiconductor substrate. Here, we explore high-quality van de Waals silicene/Sc2CF2 heterojunction (HTJ) using first-principles calculations, and we predict that the Dirac cone of silicene maintains in the band gap of Sc2CF2 substrate. The nearly linear band dispersion of silicene with a sizable gap (36–48 meV) is obtained in all HTJs due to the sublattice symmetry broken by the intrinsic interface dipole. Remarkably, the band gap of all these HTJs can be effectively modulated by the interlayer spacing and strain. These findings are promising for high-performance FETs with high carrier mobilities operating at room temperature in nanoelectronics.

Gate tunable relativistic mass and Berry's phase in topological insulator nanoribbon field effect devices.

Transport due to spin-helical massless Dirac fermion surface state is of paramount importance to realize various new physical phenomena in topological insulators, ranging from quantum anomalous Hall effect to Majorana fermions. However, one of the most important hallmarks of topological surface states, the Dirac linear band dispersion, has been difficult to reveal directly in transport measurements. Here we report experiments on Bi2Te3 nanoribbon ambipolar field effect devices on high-κ SrTiO3 substrates, where we achieve a gate-tuned bulk metal-insulator transition and the topological transport regime with substantial surface state conduction. In this regime, we report two unambiguous transport evidences for gate-tunable Dirac fermions through π Berry's phase in Shubnikov-de Haas oscillations and effective mass proportional to the Fermi momentum, indicating linear energy-momentum dispersion. We also measure a gate-tunable weak anti-localization (WAL) with 2 coherent conduction channels (indicating 2 decoupled surfaces) near the charge neutrality point, and a transition to weak localization (indicating a collapse of the Berry's phase) when the Fermi energy approaches the bulk conduction band. The gate-tunable Dirac fermion topological surface states pave the way towards a variety of topological electronic devices.

Two-dimensional mineral [Pb2BiS3][AuTe2]: high-mobility charge carriers in single-atom-thick layers.

Two-dimensional (2D) electronic systems are of wide interest due to their richness in chemical and physical phenomena and potential for technological applications. Here we report that [Pb2BiS3][AuTe2], known as the naturally occurring mineral buckhornite, hosts 2D carriers in single-atom-thick layers. The structure is composed of stacking layers of weakly coupled [Pb2BiS3] and [AuTe2] sheets. The insulating [Pb2BiS3] sheet inhibits interlayer charge hopping and confines the carriers in the basal plane of the single-atom-thick [AuTe2] layer. Magneto-transport measurements on synthesized samples and theoretical calculations show that [Pb2BiS3][AuTe2] is a multiband semimetal with a compensated density of electrons and holes, which exhibits a high hole carrier mobility of ∼1360 cm(2)/(V s). This material possesses an extremely large anisotropy, Γ = ρ(c)/ρ(ab) ≈ 10(4), comparable to those of the benchmark 2D materials graphite and Bi2Sr2CaCu2O(6+δ). The electronic structure features linear band dispersion at the Fermi level and ultrahigh Fermi velocities of 10(6) m/s, which are virtually identical to those of graphene. The weak interlayer coupling gives rise to the highly cleavable property of the single crystal specimens. Our results provide a novel candidate for a monolayer platform to investigate emerging electronic properties.

Dirac Cones in two-dimensional conjugated polymer networks.

Linear electronic band dispersion and the associated Dirac physics has to date been limited to special-case materials, notably graphene and the surfaces of three-dimensional (3D) topological insulators. Here we report that it is possible to create two-dimensional fully conjugated polymer networks with corresponding conical valence and conduction bands and linear energy dispersion at the Fermi level. This is possible for a wide range of polymer types and connectors, resulting in a versatile new family of experimentally realisable materials with unique tuneable electronic properties. We demonstrate their stability on substrates and possibilities for doping and Dirac cone distortion. Notably, the cones can be maintained in 3D-layered crystals. Resembling covalent organic frameworks, these materials represent a potentially exciting new field combining the unique Dirac physics of graphene with the structural flexibility and design opportunities of organic-conjugated polymer chemistry.

Silicane as an Inert Substrate of Silicene: A Promising Candidate for FET

Opening up a band gap without lowering high carrier mobility and finding a suitable substrate material are a challenge for designing silicon-based nanodevices. Using density functional theory calculations incorporating vdW corrections, we find that the semiconducting silicane monolayer is free of dangling bonds, providing an ideal substrate for silicene to sit on. The nearly linear band dispersion character of silicene with a sizable band gap (44–61 meV) opening is obtained in all heterobilayers (HBLs). We also find that the effective masses of electrons and holes near the Dirac point (ranging from 0.033 to 0.045m0) are very small in HBLs, and thus high carrier mobility (105cm2 V–1 s–1) of silicene is expected. These characteristics of HBLs can be flexibly modulated by applying bias voltage or strain, suitable for the high-performance FET channel operating at room temperature.

Tunable electronic properties induced by a defect-substrate in graphene/BC3 heterobilayers.

We perform first-principles calculations to study the geometric, energetics and electronic properties of graphene supported on BC3 monolayer. The results show that overall graphene interacts weakly with BC3 monolayer via van der Waals interaction. The energy gap of graphene can be up to ∼0.162 eV in graphene/BC3 heterobilayers (G/BC3 HBLs), which is large enough for the gap opening at room temperature. We also find that the interlayer spacing and in-plane strain can tune the band gap of G/BC3 HBLs effectively. Interestingly, the characteristics of a Dirac cone with a nearly linear band dispersion relationship of graphene can be preserved, accompanied by a small electron effective mass, and thus the higher carrier mobility is still expected. These findings provide a possible way to design effective FETs out of graphene on a BC3 substrate.

Novel band structures in silicene on monolayer zinc sulfide substrate

Opening a sizable band gap in the zero-gap silicene without lowering the carrier mobility is a key issue for its application in nanoelectronics. Based on first-principles calculations, we find that the interaction energies are in the range of −0.09‒0.3 eV per Si atom, indicating a weak interaction between silicene and ZnS monolayer and the ABZn stacking is the most stable pattern. The band gap of silicene can be effectively tuned ranging from 0.025 to 1.05 eV in silicene and ZnS heterobilayer (Si/ZnS HBL). An unexpected indirect–direct band gap crossover is also observed in HBLs, dependent on the stacking pattern, interlayer spacing and external strain effects on silicene. Interestingly, the characteristics of Dirac cone with a nearly linear band dispersion relation of silicene can be preserved in the ABS pattern which is a metastable state, accompanied by a small electron effective mass and thus the carrier mobility is expected not to degrade much. These provide a possible way to design effective FETs out of silicene on a ZnS monolayer.

Pinpoint operando analysis of the electronic states of a graphene transistor using photoelectron nanospectroscopy

Graphene is a promising material for next-generation devices owing to its excellent electronic properties. Graphene devices do not, however, exhibit the high performance that is expected considering graphene’s intrinsic electronic properties. Operando, i.e., gate-controlled, photoelectron nanospectroscopy is needed to observe electronic states in device operation conditions. We have achieved, for the first time, pinpoint operando core-level photoelectron nanospectroscopy of a channel of a graphene transistor. The direct relationship between the graphene’s binding energy and the Fermi level is reproduced by a simulation assuming linear band dispersion. This operando nanospectroscopy will bridge the gap between electronic properties and device performance.

Beyond graphene: stable elemental monolayers of silicene and germanene.

Two-dimensional materials are one of the most active areas of nanomaterials research. Here we report the structural stability, electronic and vibrational properties of different monolayer configurations of the group IV elemental materials silicene and germanene. The structure of the stable configuration is calculated and for planar and low (<1 Å) atomic buckling configurations, analysis of the electronic band structure reveals linear band dispersion giving rise to massless Dirac Fermions with a Fermi velocity about two-thirds that of graphene. Monolayer stability is shown to be directly attributed to the phonons present with the instability being driven by the out-of-plane ZA and ZO phonon modes. Long momentum relaxation lengths and high carrier mobilities are predicted for silicene and germanene based devices as carrier relaxation via phonon scattering is found to be inhibited as the electron-optical phonon coupling matrix elements are calculated to be small, being about a factor of 25 times smaller than in graphene. The consequences for phonon scattering, high energy electrical transport and integration of elemental monolayers into electronic devices are further discussed.

Migdal's theorem and electron-phonon vertex corrections in Dirac materials

Migdal's theorem plays a central role in the physics of electron-phonon interactions in metals and semiconductors, and has been extensively studied theoretically for parabolic band electronic systems in three-, two-, and one-dimensional systems over the last fifty years. In the current work, we theoretically study the relevance of Migdal's theorem in graphene and Weyl semimetals which are examples of 2D and 3D Dirac materials, respectively, with linear and chiral band dispersion. Our work also applies to 2D and 3D topological insulator systems. In Fermi liquids, the renormalization of the electron-phonon vertex scales as the ratio of sound ($v_s$) to Fermi ($v_F$) velocity, which is typically a small quantity. In two- and three-dimensional quasirelativistic systems, such as undoped graphene and Weyl semimetals, the one loop electron-phonon vertex renormalization, which also scales as $\eta=v_s/v_F$ as $\eta \rightarrow 0$, is, however, enhanced by an ultraviolet \emph{logarithmic divergent correction}, arising from the linear, chiral Dirac band dispersion. Such enhancement of the electron-phonon vertex can be significantly softened due to the logarithmic increment of the Fermi velocity, arising from the long range Coulomb interaction, and therefore, the electron-phonon vertex correction does not have a logarithmic divergence at low energy. Otherwise, the Coulomb interaction does not lead to any additional renormalization of the electron-phonon vertex. Therefore, electron-phonon vertex corrections in two- and three-dimensional Dirac fermionic systems scale as $v_s/v^0_F$, where $v^0_F$ is the bare Fermi velocity, and small when $v_s \ll v^0_F$. These results, although explicitly derived for the intrinsic undoped systems, should hold even when the chemical potential is tuned away from the Dirac points.

Broken symmetry induced band splitting in theAg2Gesurface alloy on Ag(111)

We report a study of the atomic and electronic structures of the ordered ${\mathrm{Ag}}_{2}\mathrm{Ge}$ surface alloy containing ⅓ monolayer of Ge. Low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), and angle-resolved photoelectron spectroscopy (ARPES) data reveal a symmetry breaking of the expected \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 periodicity, which is established for other ${\mathrm{Ag}}_{2}$$M$ alloys ($M$ = Bi, Sb, Pb, and Sn). The deviation from a simple \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 structure manifests itself as a splitting of diffraction spots in LEED, as a striped structure with a 6\ifmmode\times\else\texttimes\fi{} periodicity including a distortion of the local hexagonal structure in STM, and as a complex surface band structure in ARPES that is quite different from those of the other ${\mathrm{Ag}}_{2}$$M$ alloys. These results are interesting in view of the differences in the atomic and electronic structures exhibited by different group IV elements interacting with Ag(111). Pb and Sn form \ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3 surface alloys on Ag(111), of which ${\mathrm{Ag}}_{2}\mathrm{Pb}$ shows a surface band structure with a clear spin-orbit split. Si and C form silicene and graphene structures, respectively, with linear band dispersions and the formation of Dirac cones as reported for graphene. The finding that ${\mathrm{Ag}}_{2}\mathrm{Ge}$ deviates from the ideal (\ensuremath{\surd}3 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}3) ${\mathrm{Ag}}_{2}\mathrm{Sn}$ and ${\mathrm{Ag}}_{2}\mathrm{Pb}$ surface alloys makes Ge an interesting ``link'' between the heavy group IV elements (Sn, Pb) and the light group IV elements (Si, C).

Energetics and electronic structures of polymerized cyclobutadiene

We investigated electronic and geometric properties of polymerized cyclobutadiene (C4) as a metallic form of a two-dimensional carbon allotrope using first-principles calculations. Our calculations show that the polymerized structure is stable with a total energy that is slightly higher than that of C60 fullerene and close to that of small fullerene polymers. This two-dimensional covalent network with tetragonal symmetry is a metal with linear dispersion bands at the Fermi level due to the inflection point in the cosine bands. We also studied the stable stacking arrangement and electronic structures of layered system comprising the C4 polymer. The calculations show that the AA stacking is a favorable stacking arrangement among four representative stacking structures. Although small but substantial interlayer interaction, electronic structures of the layered system of C4 polymer are almost the same as that of the monolayer of C4 polymer.

Operando Spectromicroscopy Observation of Many-Body Effects in Graphene Device

Linear band dispersion causes peculiar behaviour of device interfaces in graphene transistors. The vanishment of density of states (DOS) near the Dirac point due to the linear band dispresion renormalizes quasiparticles behaviours of electrons, i.e. many-body effects, such as excitonic effects and the Anderson orthogonality catastrophe (AOC) which occur through the interactions of conduction electrons with holes. For this reason, we have studied the impact of the excitonic effects and the AOC on graphene device performance by using x-ray absorption spectromicroscopy on an actual graphene transistor in operation. Our work shows that the excitonic effect and the AOC are tunable by gate bias or metal contacts, both of which alter the Fermi energy. In addition, it is found that these many-body effects are orbital-specifi c, appreciable many-body effects on π * orbital, while negligible on σ * orbital.

The Electronic Properties of Graphene Adsorbed on the (111) HfO2 Surface – A First Principles Study

Using density functional theory calculations, we have investigated the electronic properties of graphene monolayer adsorbed on the HfO2 substrate. Our main research interest here is to explore the reason why the HfO2 substrate can significantly degrade the transport properties of the adsorbed graphene layer as revealed in the recent experiments. Our calculated results show that graphene monolayer is bounded to the HfO2 surface via the van der Waals interaction with a binding energy of around 25∼40% larger than that on a SiO2 substrate. The band gap opening at the Dirac point was found to be comparable to that on a silanol SiO2 surface, but the induced charge accumulation at the graphene/HfO2 interface is at least one order of magnitude larger than that between graphene and the silanol SiO2 surface. Moreover, when graphene monolayer was placed on top of the substrate containing an O vacancy, the adsorbed graphene layer becomes n-type doped primarily due to the charge transfer from the O vacancy site in the HfO2 substrate. Our results further show that the strong interaction between surface O vacancy and the graphene layer not only can result in a relatively larger band gap opening at the Dirac point but also can degrade the linear band dispersion in the band structure of monolayer graphene.

First-principles study of graphene adsorbed on WS2 monolayer

We perform first-principles calculations to study the energetics and electronic properties of graphene adsorbed on WS2 surface (G/WS2). We find that the graphene can be bound to WS2 monolayer with an interlayer spacing of about 3.9 ´Å with a binding energy of −21–32 meV per carbon atom dependent on graphene adsorption arrangement, suggesting a weak interaction between graphene and WS2. The nearly linear band dispersion character of graphene can be preserved in G/WS2 system, with a sizable band gap, depending on graphene stacking patterns on WS2 and the distance between graphene and WS2 monolayer. More interestingly, when the interlayer spacing is larger than 3.0 ´Å, the energy-gap opening is mainly determined by the distortion of the isolated graphene peeled from WS2 surface, independent on the WS2 substrate. Further tight-binding model analysis demonstrates that the origin of semiconducting properties can be well understood by the variation of on-site energy of graphene induced by WS2 substrate.