Nearly-free Electron Research Articles

Impact of atomic packing and electronic structure on icosahedral short-range order and glass-forming ability of Zr–Cu metallic glasses

ABSTRACT Chemical and topological short-range ordering are important for glass formation in metallic alloys. Yet, it remains little understood from the viewpoint of the electronic bonding among the constituent elements of the alloys. In this work, we study CuxZr100−x, (46 ≤ x ≤ 70) metallic glasses, where the atomic packing efficiency and the electronic structure of the full icosahedra, the key short-range order structures, have been investigated in detail. To capture a realistic picture of the electronic bonding in the icosahedra in the as-quenched metastable state, DFT study of the electronic structure of the icosahedra extracted from classical molecular dynamics simulation is carried out. Results for the CunZr13−n , (4 ≤ n ≤ 9) clusters reveal that Cu6Zr7, Cu7Zr6 and Cu8Zr5 are the most abundant, electronically stable in Cu50Zr50 , Cu58Zr42 and Cu64Zr36, respectively. These three clusters also exhibit pseudo-gap in the density of states at the Fermi level – a feature linked with glass-forming ability according to the nearly-free electron approach. The partial density of states demonstrates the effect of small changes in the stoichiometry of the clusters on the s, p and d states of Cu and Zr in Cu–Cu and Cu–Zr bonding and hence, the stability of the clusters.

Understanding the Electronic Structure and Chemical Bonding in the 2D Fullerene Monolayer.

Recently synthesized two-dimensional (2D) monolayer quasi-hexagonal-phase fullerene (qHPC60) demonstrates excellent thermodynamic stability. Within this monolayer, each fullerene cluster is surrounded by six adjacent C60 cages along an equatorial plane and is connected by both C-C single bonds and [2 + 2] cycloaddition bonds that serve as bridges. In this study, we investigate the stability mechanism of the 2D qHPC60 monolayer by examining the electronic structure and chemical bonding through state-of-the-art theoretical methodologies. Density functional theory (DFT) studies reveal that 2D qHPC60 possesses a moderate direct electronic band gap of 1.46 eV, close to the experimental value (1.6 eV). It is found that the intermolecular bridge bonds play a crucial role in enhancing the charge flow and redistribution among C60 cages, leading to the formation of dual π-aromaticity within the C60 sphere and stabilizing the 2D framework structure. Furthermore, we identify a series of delocalized superatom molecular orbitals (SAMOs) within the 2D qHPC60 monolayer, exhibiting atomic orbital-like behavior and hybridization to form nearly free-electron (NFE) bands with σ/π bonding and σ*/π* antibonding properties. Our findings provide insights into the design and potential applications of NFE bands derived from SAMOs in 2D qHPC60 monolayers.

Strain and Electric Field Engineering of G-ZnO/SnXY (X, Y = S, Se) S-Scheme Heterostructures for Photocatalyst and Electronic Device Applications: A Hybrid DFT Calculation.

Using hybrid density functional theory calculations, we systematically study the biaxial strain and electric field modulated electronic properties of g-ZnO/SnS2, g-ZnO/SnSe2, and g-ZnO/SnSSe S-scheme van der Waals heterostructures (vdWHs). g-ZnO/SnS2 and g-ZnO/SnSSe are found to be promising photocatalysts for water splitting with high solar-to-hydrogen efficiencies, even under acidic, alkaline, and high-stress conditions. The strain effect on the bandgaps of g-ZnO/SnXY is explained in detail according to the correlation between geometry structure and orbital hybridization of SnXY, which could help understand the strain-induced band structure evolutions in other SnXY (X, Y = S, Se)-based vdWHs. It is surprising that under an external electric field, g-ZnO/SnS2, g-ZnO/SnSe2, and g-ZnO/SnSSe can offer the occupied nearly free-electron (NFE) states. In many materials, NFE states are usually unoccupied and is not conducive to the charge transport. The NFE state in g-ZnO/SnSe2 is the most sensitive to the electric field and might be promising electron transport channel in nanoelectronic devices. g-ZnO/SnSe2 might also have application potential in gas sensors and high-temperature superconductors.

Soft X-ray Fermi surface tomography of palladium and rhodium via momentum microscopy

Fermi surfaces of transition metals, which describe all thermodynamical and transport quantities of solids, often fail to be modeled by one-electron mean-field theory due to strong correlations among the valence electrons. In addition, relativistic spin–orbit coupling pronounced in heavier elements lifts the degeneracy of the energy bands and further modifies the Fermi surface. Palladium and rhodium, two 4d metals attributed to show significant spin–orbit coupling and electron correlations, are ideal for a systematic and fundamental study of the two fundamental physical phenomena and their interplay in the electronic structure. In this study, we explored the Fermi surface of the 4d noble metals palladium and rhodium obtained via high-resolution constant initial state momentum microscopy. The complete 3D-Fermi surfaces of palladium and rhodium were tomographically mapped using soft X-ray photon energies from 34 eV up to 660 eV. To fully capture the orbital angular momentum of states across the Fermi surface, the Fermi surface tomography was performed using p- and s- polarized light. Applicability and limitations of the nearly-free electron final state model in photoemission are discussed using a complex band structure model supported by experimental evidence. The significance of spin–orbit coupling and electron correlations across the Fermi surfaces will be discussed within the context of the photoemission results. State-of-the-art fully relativistic Korringa–Kohn–Rostoker (KKR) calculations within the one-step model of photoemission are used to support the experimental results.

Impact of electron correlations on the k-resolved electronic structure of PdCrO2 revealed by Compton scattering

Delafossite PdCrO2 is an intriguing material which displays nearly-free electron and Mott insulating behaviour in different layers. Both angle-resolved photoemission spectroscopy (ARPES) and Compton scattering measurements have established a hexagonal Fermi surface in the material’s paramagnetic phase. However, the Compton experiment detected an additional structure in the projected occupancy which was originally interpreted as an additional Fermi surface feature not seen by ARPES. Here, we revisit this interpretation of the Compton data. State-of-the-art density functional theory (DFT) with dynamical mean field theory (DMFT), the so-called DFT+DMFT method, predicts the Mott insulating state along with a single hexagonal Fermi surface in excellent agreement with ARPES and Compton. However, DFT+DMFT fails to predict the intensity of the additional spectral weight feature observed in the Compton data. We infer that this discrepancy may arise from the DFT+DMFT not being able to correctly predict certain features in the shape and dispersion of the unoccupied quasiparticle band near the Fermi level. Therefore, a theoretical description beyond our DFT+DMFT model is needed to incorporate vital electron interactions, such as inter-layer electron coupling interactions which for PdCrO2 gives rise to the Kondo-like so-called intertwined excitation.

Role of non-d valence electrons for the study of transport properties of some transition metals

In the present communication, the local form of pseudopotential with an effectively single parameter is used to carry out the comparative study of liquid metal resistivity using nearly free electron (NFE) Ziman's approach and transition matrix (T-matrix) Evan's approach. We have proposed a simple method to determine pseudopotential parameters by keeping account of non-d valence electrons. Our results of transport properties particularly T-matrix resistivity are in excellent agreement with experimental results and are better than other theoretical results which proves that the present proposed model is better for the theoretical understanding of transport properties. Moreover, the T-matrix approach for the understanding of liquid metal resistivity of transition metals is more reliable and physically sound. In absence of experimental results and other theoretical results, the study of electron dispersion, Fermi energy and density of states at Fermi energy will be helpful for the understanding of many liquid state properties and provide a base in future for comparison.

The carrier mobility and sizable bandgap influorinated armchair boron nitride nanoribbons

The electronic transport properties of two-dimensional materials are strongly influenced by the charge carrier mobility and the energy bandgap. Furthermore, the carrier-phonon interaction governs the electrical response of any electrical device at a specific temperature. In light of this, the electron mobility and energy bandgap of fluorine (F) doped armchair Boron Nitride nanoribbons (a-BNNRs) are computed theoretically and analysed further. The acoustical deformation potential (ADP) scattering mechanism is taken into account to determine the mobility of the system. The calculations are carried out in presence of an applied electric field as well as different doping concentrations across a specified temperature range (200–300 K). The computed value of electron mobility for F-BNNR is of the order 104 cm2 V−1 s−1. Such higher magnitude of electron mobility suggests the semiconducting nature of BNNRs. Moreover, the variation of electron mobility as a function of temperature and doping concentration demonstrates a significant reduction in the acoustical phonon-limited electron mobility of fluorine-doped boron nitride nanoribbons. To estimate the energy bandgap, a set of equations are determined from the Fermi velocity expression using the nearly free electron (NFE) model. The computed energy bandgap is found to diminish with the increasing size of the nanoribbon. This behaviour of F-doped a-BNNRs envisages its applications in Visible-IR optical sensors.

Collisional and transport parameters of Cu in the warm dense matter regime calculated using the average atom model

Collisional and transport parameters for Cu are computed using the average atom model. Transition metals such as copper are difficult to model within the framework of the average atom model due to the presence of a narrow band of 3d electrons that mix and hybridize with the broad 4s band of nearly-free electrons. With electron temperature increasing, the 3d electrons play a key role in the thermodynamics and transport properties of Cu (Lin et al 2008 Phys. Rev. B 77 075133), as well as the stability of the lattice (Loboda et al 2011 High Energy Density Phys. 7 361). In this work, the average atom model was used to track the average energy of the 3d band and its evolution with electron temperature. At room temperature, its center is at ∼6 electron volts (eV), a few electron-volts below the Fermi energy, and with electron temperature increasing it sinks relative to it. At electron temperature of about 8 eV the 3d electrons leave the conduction band and become bound. A long-standing problem related to the average ion charge observed by conduction band electrons is addressed and successfully resolved. A work-around has been found that predicts the correct average ion charge, , by formally introducing a third group of electrons: quasi-bound electrons. Benchmarking with published data is made that shows good agreement.

Electrical transport properties of liquid Pb-Li alloys

It is generally observed that electrical transport properties of simple liquid metal based alloys can be explained well in terms of Faber-Ziman theory, 2kF scattering model and finite mean free path approach. However, these approaches give poor description for materials, which show departure from nearly free electron (NFE) model. Taking Pb-Li as a test case of a system showing departure from NFE (which also exhibit compound formation tendency and disparate mass system), a new technique is proposed to compute electrical transport properties using model potential formalism coupled with t-matrix formulation. We have treated valence number of Pb & Li as a parameter in determining phase shifts. Further, rather than calculating phase shift in terms of Muffin-Tin potential, we have used model potential formalism. Present results suggest that compared to other three theoretical approaches mentioned above, present coupling scheme reproduce qualitative features of electrical transport properties of liquid Pb-Li alloys, which can be used further to study electrical transport properties of similar systems.

Electric control of nearly free electron states and ferromagnetism in the transition-metal dichalcogenides monolayers

Using the first-principles calculations, we explore the nearly free electron (NFE) states in the transition-metal dichalcogenides MX 2 (M = Mo, W; X = S, Se, Te) monolayers. It is found that both the external electric field and electron (not hole) injection can flexibly tune the energy levels of the NFE states, which can shift down to the Fermi level and result in novel transport properties. In addition, we find that the valley polarization can be induced by both electron and hole doping in MoTe2 monolayer due to the ferromagnetism induced by the charge injection, which, however, is not observed in other five kinds of MX 2 monolayers. We carefully check band structures of all the MX 2 monolayers, and find that the exchange splitting in the top of the valence band and the bottom of conduction band plays the key role in the ferromagnetism. Our researches enrich the electronic, spintronic, and valleytronic properties of MX 2 monolayers.

Switchable two-dimensional electrides: A first-principles study

Electrides, with excess anionic electrons confined in their empty space, are promising for uses in catalysis, nonlinear optics and spin-electronics. However, the application of electrides is limited by their high chemical reactivity with the environmental agents. In this work, we report the discovery of a group of two-dimensional (2D) moonolayer electrides with the presence of switchable nearly free electron (NFE) states in their electronic structures. Unlike conventional electrides, which are metals with floating electrons forming the partially occupied bands close to the Fermi level, the switchable electrides are chemically much less active semiconductors holding the NFE states that are 0.3-1.5 eV above the Fermi level. According to a high throughput search, we identified 12 2D candidates that possess such low-energy NFE states. Among them, 11 2D materials can likely be exfoliated from the known layered materials. Under external forces, such as a compressive strain, these NFE states stemming from the surface image potential will be pushed downward to cross the Fermi level. Remarkably, the critical semiconductor-metal transition can be achieved by a strain as low as 3% in 2D monolayer Na$_2$Pd$_3$O$_4$. As such, the switchable 2D electrides may provide an ideal platform for exploring novel quantum phenomena and modern electronic device applications.

Effect of Hybridization in PdAlY-(Ni/Au/Ir) Metallic Glasses Thin Films on Electrical Resistivity

Thin film metallic glasses (MGs) are promising materials for electronic applications. While the transport properties of MGs are composition dependent, the influence of hybridization on the resistivity has not been investigated systematically. We implement a correlative experimental and computational approach utilizing thin film deposition, electrical resistivity measurements, synchrotron X-ray diffraction and ab initio calculations to explore the relationship between the fraction of hybridized bonds present in PdAlY-M glasses with M=Ir,Au,Ni, where the electrical behaviour is dominated by d-electrons. The strong bonds hybridization in PdAlY-Ir yields a high resistivity of 175 µΩm, while the weakly hybridized bonds in PdAlY-M MGs (M=Au,Ni) result in lower resistivities of 114 and 92 µΩm, respectively. We propose that an increase in the fraction of hybridized states yields an increased room temperature resistivity. Whereas nearly-free electron model applies to the weakly hybridized systems, where the density of states at the Fermi level determines the resistivity.

Absence of diagonal force constants in cubic Coulomb crystals.

The quasi-harmonic model proposes that a crystal can be modelled as atoms connected by springs. We demonstrate how this viewpoint can be misleading: a simple application of Gauss’s law shows that the ion–ion potential for a cubic Coulomb system can have no diagonal harmonic contribution and so cannot necessarily be modelled by springs. We investigate the repercussions of this observation by examining three illustrative regimes: the bare ionic, density tight-binding and density nearly-free electron models. For the bare ionic model, we demonstrate the zero elements in the force constants matrix and explain this phenomenon as a natural consequence of Poisson’s law. In the density tight-binding model, we confirm that the inclusion of localized electrons stabilizes all major crystal structures at harmonic order and we construct a phase diagram of preferred structures with respect to core and valence electron radii. In the density nearly-free electron model, we verify that the inclusion of delocalized electrons, in the form of a background jellium, is enough to counterbalance the diagonal force constants matrix from the ion–ion potential in all cases and we show that a first-order perturbation to the jellium does not have a destabilizing effect. We discuss our results in connection to Wigner crystals in condensed matter, Yukawa crystals in plasma physics, as well as the elemental solids.

Theoretical and experimental evaluation of thermoelectric performance of alkaline earth filled skutterudite compounds

Skutterudite compounds are one of the most promising thermoelectric materials that can be used for intermediate power generation applications because of their excellent thermoelectric and mechanical properties. In spite of extensive research efforts during the past two decades, there is still a lack of full understanding of the electronic and thermal transport in these compounds. In the present study, we carry out a combined experimental and theoretical investigation of the electronic and thermal transport properties of alkaline earth-filled (Ca,Sr,Ba)0.2Co4Sb12 skutterudites in the temperature range from 300 ​K to 800 ​K. The experimental work includes structural properties probed by PXRD and EMPA for phase purity and composition analysis. Theoretical values of the temperature dependent electronic transport parameters were determined using the nearly-free electron approximation, and various phonon thermal conductivity contributions were studied using the Debye isotropic continuum model and the theory of Price for the bipolar contribution. The theoretical and experimental transport parameters were found in good agreement with each other. They confirm that both Ba and Sr filled skutterudites are highly degenerate semiconductors, while the heat transport in the Ca filled compound is dominated by the bipolar contribution at temperatures above 300 ​K. The Sr filled skutterudite shows the highest Seebeck coefficient, likely due to its lowest donor ionisation energy. From our detailed theoretical investigations, it is seen that the key mechanism to control the phonon thermal conduction is originated from the interaction between mass defects and phonons. The maximum ZT value obtained 0.14 for Sr0.2Co4Sb12 compound at 800 ​K likely indicate that Sr is more effective filler among the alkaline earth metals.

Theoretical calculation of the free energy of mixing of liquid transition-metal alloys using a bond-order potential and thermodynamic perturbation theory

Here, we demonstrate an extensive theoretical analysis of the free energy of mixing of liquid transition-metal alloys. The interatomic interaction is modeled by a semi-empirical potential, where the contributions from nearly-free and tight-binding electrons are described by the pseudopotential perturbation theory and the bond-order tight-binding potential, respectively. The liquid structure and the structure-dependent part of the free energy are calculated through the Weeks-Chandler-Anderson (WCA) approach with the non-additive hard-sphere reference system. The calculated free energy of mixing values shows reasonable agreement with experimental values, especially for alloys with small differences in group numbers for their components.

Realizing nearly-free-electron like conduction band in a molecular film through mediating intermolecular van der Waals interactions

Collective molecular physical properties can be enhanced from their intrinsic characteristics by templating at material interfaces. Here we report how a black phosphorous (BP) substrate concatenates a nearly-free-electron (NFE) like conduction band of a C60 monolayer. Scanning tunneling microscopy reveals the C60 lowest unoccupied molecular orbital (LUMO) band is strongly delocalized in two-dimensions, which is unprecedented for a molecular semiconductor. Experiment and theory show van der Waals forces between C60 and BP reduce the inter-C60 distance and cause mutual orientation, thereby optimizing the π-π wave function overlap and forming the NFE-like band. Electronic structure and carrier mobility calculations predict that the NFE band of C60 acquires an effective mass of 0.53–0.70 me (me is the mass of free electrons), and has carrier mobility of ~200 to 440 cm2V−1s−1. The substrate-mediated intermolecular van der Waals interactions provide a route to enhance charge delocalization in fullerenes and other organic semiconductors.

Comparative study of transport properties using transition metal model potential (TMMP) for 16 liquid metals

We propose a pseudopotential of Kumar form with two parameters, the core radius ( $$r_{\mathrm{c}}$$ ) and the model radius ( $$r_{\mathrm{m}}$$ ), which in practice is reduced to a single-parameter potential taking $$r_{\mathrm{m}}$$ as the experimental atomic radius. The validity of the presently used pseudopotential is verified by carrying out a detailed study of transport properties of 16 liquid metals. The results of the liquid metal resistivities using the nearly free electron (NFE) Ziman’s approach and the single-site t-matrix approach are presented and compared with the experimental as well as other theoretical findings. Such comparative study confirms that the t-matrix approach is more appropriate and physically sound for a theoretical understanding of liquid metal resistivity, particularly in the case of transition metals. Furthermore, thermoelectric powers are also calculated using the present method and compared with the available experimental and theoretical results.

Facile mechanism to induce topological transition in MXene

We have investigated the electronic structure of the Sc2C(OH)2 MXene interfacing with a polar AlN multi-layer or a hydrogenated AlN surface. Density functional theory calculations reveal that the nearly free electron (NFE) states of the MXene shift down when the MXene is in contact with a polar flat surface. The Sc2C(OH)2/AlN heterostructure shows a Dirac cone and inversion in the band structure. The H-s, Sc-d, and C-p orbitals are involved in the band-inversion. The electronic structure of Sc2C(OH)2/AlN heterostructure is found to be topological since the topological invariant Z2=1. We suggest that a band inversion can be induced by contacting with any flat insulating polar surface that has no excess surface-charge. However, it is crucial that the MXene surface is not perturbed (e.g., by dangling bonds). As a proof of concept, we have investigated the electronic structure of Sc2C(OH)2 adsorbed on a hydrogenated AlN surface and observed band inversion. The band dispersions of the adsorbed MXene are reminiscent of a Weyl semi-metal. The adsorption on a polar material is a facile method to induce a topological electronic structure in the Sc2C(OH)2 MXene, which may be utilized in various device applications.

Amplification of intense light fields by nearly free electrons.

Light can be used to modify and control properties of media, as in the case of electromagnetically induced transparency or, more recently, for the generation of slow light or bright coherent XUV and X-ray radiation. Particularly unusual states of matter can be created by light fields with strengths comparable to the Coulomb field that binds valence electrons in atoms, leading to nearly-free electrons oscillating in the laser field and yet still loosely bound to the core [1,2]. These are known as Kramers-Henneberger states [3], a specific example of laser-dressed states [2]. Here, we demonstrate that these states arise not only in isolated atoms [4,5], but also in rare gases, at and above atmospheric pressure, where they can act as a gain medium during laser filamentation. Using shaped laser pulses, gain in these states is achieved within just a few cycles of the guided field. The corresponding lasing emission is a signature of population inversion in these states and of their stability against ionization. Our work demonstrates that these unusual states of neutral atoms can be exploited to create a general ultrafast gain mechanism during laser filamentation.

Isolating lattice from electronic contributions in thermal transport measurements of metals and alloys above ambient temperature and an adiabatic model

From femtosecond spectroscopy (fs-spectroscopy) of metals, electrons and phonons reequilibrate nearly independently, which contrasts with models of heat transfer at ordinary temperatures ([Formula: see text] K). These electronic transfer models only agree with thermal conductivity [Formula: see text] data at a single temperature, but do not agree with thermal diffusivity [Formula: see text] data. To address the discrepancies, which are important to problems in solid state physics, we separately measured electronic (ele) and phononic (lat) components of [Formula: see text] in many metals and alloys over [Formula: see text]290–1100 K by varying measurement duration and sample length in laser-flash experiments. These mechanisms produce distinct diffusive responses in temperature versus time acquisitions because carrier speeds [Formula: see text] and heat capacities [Formula: see text] differ greatly. Electronic transport of heat only operates for a brief time after heat is applied because [Formula: see text] is high. High [Formula: see text] is associated with moderate [Formula: see text], long lengths, low electrical resistivity, and loss of ferromagnetism. Relationships of [Formula: see text] and [Formula: see text] with physical properties support our assignments. Although [Formula: see text] reaches [Formula: see text] near 470 K, it is transient. Combining previous data on [Formula: see text] with each [Formula: see text] provides mean free paths and lifetimes that are consistent with [Formula: see text] K fs-spectroscopy, and new values at high [Formula: see text]. Our findings are consistent with nearly-free electrons absorbing and transmitting a small fraction of the incoming heat, whereas phonons absorb and transmit the majority. We model time-dependent, parallel heat transfer under adiabatic conditions which is one-dimensional in solids, as required by thermodynamic law. For noninteracting mechanisms, [Formula: see text]. For metals, this reduces to [Formula: see text] above [Formula: see text]20 K, consistent with our measurements, and shows that Meissner’s equation [Formula: see text] is invalid above [Formula: see text]20 K. For one mechanism with multiple, interacting carriers, [Formula: see text]. Thus, certain dynamic behaviors of electrons and phonons in metals have been misunderstood. Implications for theoretical models and technological advancements are briefly discussed.