72 results found
Kahk JM, Lischner J, 2022, Predicting core electron binding energies in elements of the first transition series using the Δ-self-consistent-field method., Faraday Discussions, Vol: 236, Pages: 364-373, ISSN: 1359-6640
The Δ-Self-Consistent-Field (ΔSCF) method has been established as an accurate and computationally efficient approach for calculating absolute core electron binding energies for light elements up to chlorine, but relatively little is known about the performance of this method for heavier elements. In this work, we present ΔSCF calculations of transition metal (TM) 2p core electron binding energies for a series of 60 molecular compounds containing the first row transition metals Ti, V, Cr, Mn, Fe and Co. We find that the calculated TM 2p3/2 binding energies are less accurate than the results for the lighter elements with a mean absolute error (MAE) of 0.73 eV compared to experimental gas phase photoelectron spectroscopy results. However, our results suggest that the error depends mostly on the element and is rather insensitive to the chemical environment. By applying an element-specific correction to the binding energies the MAE is reduced to 0.20 eV, similar to the accuracy obtained for the lighter elements.
Arrigo R, Aureau D, Bhatt P, et al., 2022, In situ methods: discoveries and challenges: general discussion, FARADAY DISCUSSIONS, Vol: 236, Pages: 219-266, ISSN: 1359-6640
Lischner J, Jin H, Ferreira A, et al., 2022, Plasmon-induced hot carriers from interband and intraband transitions in large noble metal nanoparticles, Physical Review X, ISSN: 2160-3308
Hot electrons generated from the decay of localized surface plasmons in metallic nanostructureshave the potential to transform photocatalysis, photodetection and other optoelectronic applications.However, the understanding of hot-carrier generation in realistic nanostructures, in particular therelative importance of interband and intraband transitions, remains incomplete. Here we reporttheoretical predictions of hot-carrier generation rates in spherical nanoparticles of the noble metalssilver, gold and copper with diameters up to 30 nanometers consisting of more than one millionatoms obtained from an atomistic linear-scaling approach. As the nanoparticle size increases therelative importance of interband transitions from d-bands to sp-bands relative to surface-enabled spband to sp-band transitions increases. We find that the hot-hole generation rate is characterized bya peak at the onset of the d-bands, while the position of the corresponding peak in the hot-electrondistribution can be controlled through the illumination frequency. In contrast, intraband transitionsgive rise to hot electrons, but relatively cold holes. Importantly, increasing the dielectric constantof the environment removes hot carriers generated from interband transitions, while increasing thenumber of hot carriers from intraband transitions. The insights resulting from our work enable thedesign of nanoparticles for specific hot-carrier applications through their material composition, sizeand dielectric environment.
Aghajanian M, Mostofi A, Lischner J, 2022, Electronic structure of monolayer and bilayer black phosphorus with charged defects, Physical Review Materials, Vol: 6, Pages: 1-13, ISSN: 2475-9953
We use an atomistic approach to study the electronic properties of monolayer and bilayer black phosphorus in the vicinity of a charged defect. In particular, we combine screened defect potentials obtained from first-principles linear response theory with large-scale tight-binding simulations to calculate the wave functions and energies of bound acceptor and donor states. As a consequence of the anisotropic band structure, the defect states in these systems form distorted hydrogenic orbitals with a different ordering from that in isotropic materials. For the monolayer, we study the dependence of the binding energies of charged adsorbates on the defect height and the dielectric constant of a substrate in an experimental setup. We also compare our results with an anisotropic effective mass model and find quantitative and qualitative differences when the charged defect is close to the black phosphorus or when the screening from the substrate is weak. For the bilayer, we compare results for charged adsorbates and charged intercalants and find that intercalants induce more prominent secondary peaks in the local density of states because they interact strongly with electronic states on both layers. These insights can be directly tested in scanning tunneling spectroscopy measurements and enable a detailed understanding of the role of Coulomb impurities in electronic devices.
Kalha C, Ratcliff LE, Gutierrez Moreno JJ, et al., 2022, Lifetime effects and satellites in the photoelectron spectrum of tungsten metal, PHYSICAL REVIEW B, Vol: 105, ISSN: 2469-9950
Maity I, Mostofi AA, Lischner J, 2022, Chiral valley phonons and flat phonon bands in moire materials, PHYSICAL REVIEW B, Vol: 105, ISSN: 2469-9950
Fischer A, Goodwin ZAH, Mostofi AA, et al., 2022, Unconventional superconductivity in magic-angle twisted trilayer graphene, npj Quantum Materials, Vol: 7, Pages: 1-10, ISSN: 2397-4648
Magic-angle twisted trilayer graphene (MATTG) recently emerged as a highly tunable platform for studying correlated phases of matter, such as correlated insulators and superconductivity. Superconductivity occurs in a range of doping levels that is bounded by van Hove singularities, which stimulates the debate of the origin and nature of superconductivity in this material. In this work, we discuss the role of spin-fluctuations arising from atomic-scale correlations in MATTG for the superconducting state. We show that in a phase diagram as a function of doping (ν) and temperature, nematic superconducting regions are surrounded by ferromagnetic states and that a superconducting dome with Tc ≈ 2 K appears between the integer fillings ν = −2 and ν = −3. Applying a perpendicular electric field enhances superconductivity on the electron-doped side which we relate to changes in the spin-fluctuation spectrum. We show that the nematic unconventional superconductivity leads to pronounced signatures in the local density of states detectable by scanning tunneling spectroscopy measurements.
Zauchner MG, Dal Forno S, Cśanyi G, et al., 2021, Predicting polarizabilities of silicon clusters using local chemical environments, Machine Learning: Science and Technology, Vol: 2, Pages: 1-16, ISSN: 2632-2153
Calculating polarizabilities of large clusters with first-principles techniques is challenging because of the unfavorable scaling of computational cost with cluster size. To address this challenge, we demonstrate that polarizabilities of large hydrogenated silicon clusters containing thousands of atoms can be efficiently calculated with machine learning methods. Specifically, we construct machine learning models based on the smooth overlap of atomic positions (SOAP) descriptor and train the models using a database of calculated random-phase approximation polarizabilities for clusters containing up to 110 silicon atoms. We first demonstrate the ability of the machine learning models to fit the data and then assess their ability to predict cluster polarizabilities using k-fold cross validation. Finally, we study the machine learning predictions for clusters that are too large for explicit first-principles calculations and find that they accurately describe the dependence of the polarizabilities on the ratio of hydrogen to silicon atoms and also predict a bulk limit that is in good agreement with previous studies.
Wentink M, Gaberle J, Aghajanian M, et al., 2021, Substitutional tin acceptor states in black phosphorus, The Journal of Physical Chemistry C, Vol: 125, Pages: 22883-22889, ISSN: 1932-7447
Nominally pure black phosphorus (BP) is commonly found to be a p-type semiconductor, suggesting the ubiquitious presence of impurity species or intrinsic, charged defects. Moreover, scanning tunneling microscopy (STM) images of black phosphorus reveal the presence of long-range double-lobed defect features superimposed onto the surface atomic lattice. We show that both the p-type doping of BP and the defect features observed in STM images can be attributed to substitutional tin impurities. We show that black phosphorus samples produced through two common synthesis pathways contain tin impurities, and we demonstrate that the ground state of substitutional tin impurities is negatively charged for a wide range of Fermi level positions within the BP band gap. The localized negative charge of the tin impurities induces hydrogenic states in the band gap, and it is the 2p level that sits at the valence band edge that gives rise to the double-lobed features observed in STM images.
Liou F, Tsai H-Z, Aikawa AS, et al., 2021, Imaging Reconfigurable Molecular Concentration on a Graphene Field-Effect Transistor, NANO LETTERS, Vol: 21, Pages: 8770-8776, ISSN: 1530-6984
Baek H, Brotons-Gisbert M, Campbell A, et al., 2021, Optical read-out of Coulomb staircases in a moiré superlattice via trapped interlayer trions, Nature Nanotechnology, Vol: 16, Pages: 1237-1243, ISSN: 1748-3387
Moiré patterns with a superlattice potential can be formed by vertically stacking two layered materials with a relative twist or lattice constant mismatch. In transition metal dichalcogenide-based systems, the moiré potential landscape can trap interlayer excitons (IXs) at specific atomic registries. Here, we report that spatially isolated trapped IXs in a molybdenum diselenide/tungsten diselenide heterobilayer device provide a sensitive optical probe of carrier filling in their immediate environment. By mapping the spatial positions of individual trapped IXs, we are able to spectrally track the emitters as the moiré lattice is filled with excess carriers. Upon initial doping of the heterobilayer, neutral trapped IXs form charged IXs (IX trions) uniformly with a binding energy of ~7 meV. Upon further doping, the empty superlattice sites sequentially fill, creating a Coulomb staircase: stepwise changes in the IX trion emission energy due to Coulomb interactions with carriers at nearest-neighbour moiré sites. This non-invasive, highly local technique can complement transport and non-local optical sensing techniques to characterize Coulomb interaction energies, visualize charge correlated states, or probe local disorder in a moiré superlattice.
Kahk JM, Michelitsch GS, Maurer RJ, et al., 2021, Core Electron Binding Energies in Solids from Periodic All-Electron Delta-Self-Consistent-Field Calculations, JOURNAL OF PHYSICAL CHEMISTRY LETTERS, Vol: 12, Pages: 9353-9359, ISSN: 1948-7185
Goodwin Z, Klebl L, Vitale V, et al., 2021, Flat bands, electron interactions and magnetic order in magic-angle mono-trilayer graphene, Physical Review Materials, Vol: 5, ISSN: 2475-9953
Starting with twisted bilayer graphene, graphene-based moiré materials have recently been established as a new platform for studying strong electron correlations. In this paper, we study twisted graphene monolayers on trilayer graphene and demonstrate that this system can host flat bands when the twist angle is close to the magic angle of 1.16∘. When monolayer graphene is twisted on ABA trilayer graphene, the flat bands are not isolated, but are intersected by a Dirac cone with a large Fermi velocity. In contrast, graphene twisted on ABC trilayer graphene (denoted AtABC) exhibits a gap between flat and remote bands. Since ABC trilayer graphene and twisted bilayer graphene are known to host broken-symmetry phases, we further investigate the ostensibly similar magic-angle AtABC system. We study the effect of electron-electron interactions in AtABC using both Hartree theory and an atomic Hubbard theory to calculate the magnetic phase diagram as a function of doping, twist angle, and perpendicular electric field. Our analysis reveals a rich variety of magnetic orderings, including ferromagnetism and ferrimagnetism, and demonstrates that a perpendicular electric field makes AtABC more susceptible to magnetic ordering.
Vitale V, Atalar K, Mostofi AA, et al., 2021, Flat band properties of twisted transition metal dichalcogenide homo- andheterobilayers of MoS2, MoSe2, WS2 and WSe2, 2D Materials, Vol: 8, ISSN: 2053-1583
Twisted bilayers of two-dimensional materials, such as twisted bilayergraphene, often feature flat electronic bands that enable the observation ofelectron correlation effects. In this work, we study the electronic structureof twisted transition metal dichalcogenide (TMD) homo- and heterobilayers thatare obtained by combining MoS$_2$, WS$_2$, MoSe$_2$ and WSe$_2$ monolayers, andshow how flat band properties depend on the chemical composition of the bilayeras well as its twist angle. We determine the relaxed atomic structure of thetwisted bilayers using classical force fields and calculate the electronic bandstructure using a tight-binding model parametrized from first-principlesdensity-functional theory. We find that the highest valence bands in thesesystems can derive either from $\Gamma$-point or $K$/$K'$-point states of theconstituent monolayers. For homobilayers, the two highest valence bands arecomposed of monolayer $\Gamma$-point states, exhibit a graphene-like dispersionand become flat as the twist angle is reduced. The situation is morecomplicated for heterobilayers where the ordering of $\Gamma$-derived and$K$/$K'$-derived states depends both on the material composition and also thetwist angle. In all systems, qualitatively different band structures areobtained when atomic relaxations are neglected.
Goebel A, Rubio A, Lischner J, 2021, Light-Induced Charge Transfer from Transition-Metal-Doped Aluminum Clusters to Carbon Dioxide, JOURNAL OF PHYSICAL CHEMISTRY A, Vol: 125, Pages: 5878-5885, ISSN: 1089-5639
Lu Q, Martins H, Kahk JM, et al., 2021, Layer-resolved many-electron interactions in delafossite PdCoO2 from standing-wave photoemission spectroscopy, COMMUNICATIONS PHYSICS, Vol: 4, ISSN: 2399-3650
Klebl L, Goodwin Z, Mostofi AA, et al., 2021, Importance of long-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene, Physical Review B, Vol: 103, Pages: 1-7, ISSN: 2469-9950
Electron-electron interactions are intrinsically long ranged, but many models of strongly interacting electrons only take short-ranged interactions into account. Here, we present results of atomistic calculations including both long-ranged and short-ranged electron-electron interactions for the magnetic phase diagram of twisted bilayer graphene and demonstrate that qualitatively different results are obtained when long-ranged interactions are neglected. In particular, we use Hartree theory augmented with Hubbard interactions and calculate the interacting spin susceptibility at a range of doping levels and twist angles near the first magic angle to identify the dominant magnetic instabilities. At the magic angle, mostly antiferromagnetic order is found, while ferromagnetism dominates at other twist angles. Moreover, long-ranged interactions significantly increase the twist angle window in which strong correlation phenomena can be expected. These findings are in good agreement with available experimental data.
Roman Castellanos L, Hess O, Lischner J, 2021, Dielectric engineering of hot carrier generation by quantized plasmons in embedded silver nanoparticles, The Journal of Physical Chemistry C: Energy Conversion and Storage, Optical and Electronic Devices, Interfaces, Nanomaterials, and Hard Matter, Vol: 125, Pages: 3081-3087, ISSN: 1932-7447
Understanding and controlling properties of plasmon-induced hot carriers is a key step toward next-generation photovoltaic and photocatalytic devices. Here, we uncover a route to engineering hot-carrier generation rates of silver nanoparticles by designed embedding in dielectric host materials. Extending our recently established quantum-mechanical approach to describe the decay of quantized plasmons into hot carriers we capture both external screening by the nanoparticle environment and internal screening by silver d-electrons through an effective electron–electron interaction. We find that hot-carrier generation can be maximized by engineering the dielectric host material such that the energy of the localized surface plasmon coincides with the highest value of the nanoparticle joint density of states. This allows us to uncover a path to control the energy of the carriers and the amount produced, for example, a large number of relatively low-energy carriers are obtained by embedding in strongly screening environments.
Liang X, Goodwin ZAH, Vitale V, et al., 2020, Effect of bilayer stacking on the atomic and electronic structure of twisted double bilayer graphene, Physical Review B, Vol: 102, Pages: 155146 – 1-155146 – 12, ISSN: 2469-9950
Twisted double bilayer graphene has recently emerged as an interesting moiré material that exhibits strong correlation phenomena that are tunable by an applied electric field. Here we study the atomic and electronic properties of three different graphene double bilayers: double bilayers composed of two AB stacked bilayers (AB/AB), double bilayers composed of two AA stacked bilayers (AA/AA), as well as heterosystems composed of one AB and one AA bilayer (AB/AA). The atomic structure is determined using classical force fields. We find that the inner layers of the double bilayer exhibit significant in-plane and out-of-plane relaxations, similar to twisted bilayer graphene. The relaxations of the outer layers depend on the stacking: atoms in AB bilayers follow the relaxations of the inner layers, while atoms in AA bilayers attempt to avoid higher-energy AA stacking. For the relaxed structures, we calculate the electronic band structures using the tight-binding method. All double bilayers exhibit flat bands at small twist angles, but the shape of the bands depends sensitively on the stacking of the outer layers. To gain further insight, we study the evolution of the band structure as the outer layers are rigidly moved away from the inner layers, while preserving their atomic relaxations. This reveals that the hybridization with the outer layers results in an additional flattening of the inner-layer flat band manifold. Our results establish AA/AA and AB/AA twisted double bilayers as interesting moiré materials with different flat band physics compared to the widely studied AB/AB system.
Song W, Stein Scholtis E, sherrel P, et al., 2020, Electronic Structure Influences on the Formation of the Solid Electrolyte Interphase, Energy and Environmental Science, ISSN: 1754-5692
Kahk J, Lovelock K, Kuusik I, et al., 2020, Frontier orbitals and quasiparticle energy levels in ionic liquids, npj Computational Materials, Vol: 6, Pages: 1-7, ISSN: 2057-3960
Room temperature ionic liquids play an important role in many technological applications and a detailed understanding of their frontier molecular orbitals is required to optimize interfacial barriers,reactivity and stability with respect to electron injection and removal. In this work, we calculate quasiparticle energy levels of ionic liquids using first-principles many-body perturbation theory within the GW approximation and compare our results to various mean-field approaches, including semilocal and hybrid density-functional theory and Hartree-Fock. We find that the mean-field results depend qualitatively and quantitatively on the treatment of exchange-correlation effects, while GW calculations produce results that are in excellent agreement with experimental photoelectron spectra of gas phase ion pairs and ionic liquids. These results establish the GW approach as a valuable tool for understanding the electronic structures of ionic liquids.
Tsai H-Z, Lischner J, Omrani AA, et al., 2020, A molecular shift register made using tunable charge patterns in one-dimensional molecular arrays on graphene, Nature Electronics, Vol: 3, Pages: 598-603, ISSN: 2520-1131
The ability to tune the electronic properties of molecular arrays is an important step in the development of molecule-scale electronic devices. However, control over internal device charge distributions by tuning interactions between molecules has proved challenging. Here, we show that gate-tunable charge patterning can occur in one-dimensional molecular arrays on graphene field-effect transistors. One-dimensional molecular arrays are fabricated using an edge-templated self-assembly process that allows organic molecules (F4TCNQ) to be precisely positioned on graphene devices. The charge configurations of the molecular arrays can be reversibly switched between different collective charge states by tuning the graphene Fermi level via a back-gate electrode. Charge pinning at the ends of the molecular arrays allows the charge state of the entire array to be controlled by adding or removing an edge molecule and changing the total number of molecules in an array between odd and even integers. Charge patterns altered in this way propagate down the array in a cascade effect, allowing the array to function as a charge-based molecular shift register. An extended multi-site Anderson impurity model is used to quantitatively explain this behaviour.
Goodwin Z, Vitale V, Liang X, et al., 2020, Hartree theory calculations of quasiparticle properties in twisted bilayer graphene, Physical Review B: Condensed Matter and Materials Physics, Vol: 2, ISSN: 1098-0121
A detailed understanding of interacting electrons in twisted bilayer graphene(tBLG) near the magic angle is required to gain insights into the physicalorigin of the observed broken symmetry phases including correlated insulatorstates and superconductivity. Here, we present extensive atomistic Hartreetheory calculations of the electronic properties of tBLG in the (semi-)metallicphase as function of doping and twist angle. Specifically, we calculatequasiparticle properties, such as the band structure, density of states (DOS)and local density of states (LDOS), which are directly accessible inphotoemission and tunnelling spectroscopy experiments. We find thatquasiparticle properties change significantly upon doping - an effect which isnot captured by tight-binding theory. In particular, we observe that thepartially occupied bands flatten significantly which enhances the density ofstates at the Fermi level and explains the experimentally observed Fermi levelpinning. We predict a clear signature of this band flattening in the LDOS inthe AB/BA regions of tBLG which can be tested in scanning tunnelingexperiments. We also study the dependence of quasiparticle properties on thedielectric environment of tBLG and discover that these properties aresurprisingly robust as a consequence of the strong internal screening. Finally,we present a simple analytical expression for the Hartree potential whichenables the determination of quasiparticle properties without the need forself-consistent calculations.
Stepanov P, Das I, Lu X, et al., 2020, Untying the insulating and superconducting orders in magic-angle graphene, Nature, Vol: 583, Pages: 375-378, ISSN: 0028-0836
The coexistence of superconducting and correlated insulating states in magic-angle twisted bilayer graphene1-11 prompts fascinating questions about their relationship. Independent control of the microscopic mechanisms that govern these phases could help uncover their individual roles and shed light on their intricate interplay. Here we report on direct tuning of electronic interactions in this system by changing the separation distance between the graphene and a metallic screening layer12,13. We observe quenching of correlated insulators in devices with screening layer separations that are smaller than the typical Wannier orbital size of 15 nanometres and with twist angles that deviate slightly from the magic angle of 1.10 ± 0.05 degrees. Upon extinction of the insulating orders, the vacated phase space is taken over by superconducting domes that feature critical temperatures comparable to those in devices with strong insulators. In addition, we find that insulators at half-filling can reappear in small out-of-plane magnetic fields of 0.4 tesla, giving rise to quantized Hall states with a Chern number of 2. Our study suggests re-examination of the often-assumed 'parent-and-child' relation between the insulating and superconducting phases in moiré graphene, and suggests a way of directly probing the microscopic mechanisms of superconductivity in strongly correlated systems.
Berens J, Bichelmaier S, Fernando NK, et al., 2020, Effects of nitridation on SiC/SiO(2)structures studied by hard X-ray photoelectron spectroscopy, JOURNAL OF PHYSICS-ENERGY, Vol: 2, ISSN: 2515-7655
Li L, Zhang J, Myeong G, et al., 2020, Gate-tunable reversible rashba-edelstein effect in a few-layer graphene/2H-TaS2 heterostructure at room temperature., ACS Nano, Vol: 14, Pages: 5251-5259, ISSN: 1936-0851
We report the observation of current-induced spin polarization, the Rashba-Edelstein effect (REE), and its Onsager reciprocal phenomenon, the spin galvanic effect (SGE), in a few-layer graphene/2H-TaS2 heterostructure at room temperature. Spin-sensitive electrical measurements unveil full spin-polarization reversal by an applied gate voltage. The observed gate-tunable charge-to-spin conversion is explained by the ideal work function mismatch between 2H-TaS2 and graphene, which allows for a strong interface-induced Bychkov-Rashba interaction with a spin-gap reaching 70 meV, while keeping the Dirac nature of the spectrum intact across electron and hole sectors. The reversible electrical generation and control of the nonequilibrium spin polarization vector, not previously observed in a nonmagnetic material, are elegant manifestations of emergent two-dimensional Dirac Fermions with robust spin-helical structure. Our experimental findings, supported by first-principles relativistic electronic structure and transport calculations, demonstrate a route to design low-power spin-logic circuits from layered materials.
Goodwin Z, Vitale V, Corsetti F, et al., 2020, Critical role of device geometry for the phase diagram of twisted bilayer graphene, Physical Review B: Condensed Matter and Materials Physics, Vol: 101, Pages: 1-8, ISSN: 1098-0121
The effective interaction between electrons in two-dimensional materials can be modified by their environment, enabling control of electronic correlations and phases. Here, we study the dependence of electronic correlations in twisted bilayer graphene (tBLG) on the separation to the metallic gate(s) in two device configurations. Using an atomistic tight-binding model, we determine the Hubbard parameters of the flat bands as a function of gate separation, taking into account the screening from the metallic gate(s), the dielectric spacer layers, and the tBLG itself. We determine the critical gate separation at which the Hubbard parameters become smaller than the critical value required for a transition from a correlated insulator state to a (semi)metallic phase. We show how this critical gate separation depends on twist angle, doping, and the device configuration. These calculations may help rationalize the reported differences between recent measurements of tBLG's phase diagram and suggest that correlated insulator states can be screened out in devices with thin dielectric layers.
Castellanos LR, Kahk JM, Hess O, et al., 2020, Generation of plasmonic hot carriers from d-bands in metallic nanoparticles, Journal of Chemical Physics, Vol: 152, ISSN: 0021-9606
We present an approach to master the well-known challenge of calculating the contribution of d-bands to plasmon-induced hot carrier rates in metallic nanoparticles. We generalize the widely used spherical well model for the nanoparticle wavefunctions to flat d-bands using the envelope function technique. Using Fermi’s golden rule, we calculate the generation rates of hot carriers after the decay of the plasmon due to transitions either from a d-band state to an sp-band state or from an sp-band state to another sp-band state. We apply this formalism to spherical silver nanoparticles with radii up to 20 nm and also study the dependence of hot carrier rates on the energy of the d-bands. We find that for nanoparticles with a radius less than 2.5 nm, sp-band state to sp-band state transitions dominate hot carrier production, while d-band state to sp-band state transitions give the largest contribution for larger nanoparticles.
Aghajanian M, Schuler B, Cochrane KA, et al., 2020, Resonant and bound states of charged defects in two-dimensional semiconductors, Physical Review B: Condensed Matter and Materials Physics, Vol: 101, Pages: 1-6, ISSN: 1098-0121
A detailed understanding of charged defects in two-dimensional semiconductors is needed for the development of ultrathin electronic devices. Here, we study negatively charged acceptor impurities in monolayer WS2 using a combination of scanning tunneling spectroscopy and large-scale atomistic electronic structure calculations. We observe several localized defect states of hydrogenic wave function character in the vicinity of the valence band edge. Some of these defect states are bound, while others are resonant. The resonant states result from the multivalley valence band structure of WS2, whereby localized states originating from the secondary valence band maximum at Γ hybridize with continuum states from the primary valence band maximum at K/K′. Resonant states have important consequences for electron transport as they can trap mobile carriers for several tens of picoseconds.
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