Solid-state materials have recently emerged as a new stage of strong-field physics and attosecond science. The mechanism of the electron dynamics driven by an ultrashort intense laser pulse is under intensive discussion. Here we theoretically discuss momentum-space strong-field electron dynamics in graphene and crystalline dielectrics and semiconductors. First, within massless Dirac fermion and tight-binding models for graphene, we rigorously derive intraband displacement and interband transition, which form the basis for understanding solid-state strong-field physics including high-harmonic generation (HHG). Then, based on the time-dependent Schrödinger equation for a one-dimensional model crystal, we introduce a simple, multiband, momentum-space three-step model that incorporates intraband displacement, interband tunneling, and recombination with a valence band hole. We also analyze how the model is modified by electron-hole interaction. Finally, actual three-dimensional materials are investigated. We present a time-dependent density-matrix method whose results for HHG are compared with experimental measurement results. Moreover, we describe the dynamical Franz-Keldysh effect in femtosecond time resolution, i.e., the time-dependent modulation of a dielectric function under an intense laser field, using a real-time time-dependent density functional theory.
We propose a simple formula for fitting the electron mean free paths in solids both at high and at low electron energies. The free-electron-gas approximation used for predicting electron mean free paths is no longer valid at low energies (E < 50 eV), as the band structure effects become significant at those energies. Therefore we include the results of the band structure calculations in our fit. Finally, we apply the fit to 9 elements and 2 compounds.
The solidification behavior of a eutectic AlCu specimen is investigated via in situ scanning transmission electron microscope (STEM) experiments. Solidification conditions are varied by imposing various cooling conditions via a micro-electro-mechanical system (MEMS) based membrane. The methodology allows the use of material processed by a melting and casting route close to industrial metallurgically fabricated material for in situ STEM solidification studies. Different rapid solidification morphologies could be obtained solely on a single specimen by the demonstrated strategy. Additional post-…
A full quantum mechanical theory for the spontaneous emission from excitons simultaneously coupled to electronic excitations and anharmonic phonons in solid is developed. Origin of detailed structures, such as zero-phonon line splitting, Fano lineshape near one phonon sideband, strong second-order phonon Stokes line, asymmetric phonon anti-Stokes lines, and two-electron satellites as well as their phonon replicas recently revealed in the low-temperature photoluminescence of ZnO, has been identified by quantitative calculations from the theory.
The possibility of a solid state electron electric dipole moment (EDM) experiment based on Gadolinium Iron Garnet (GdIG) is investigated. GdIG appears to exhibit superparamagnetism and this effect can be used to enhance the electric-field-induced EDM signal at relatively a high temperatures, as compared to a simple paramagnetic system such as Gadolinium Gallium Garnet. The sensitivity of a GdIG based experiment might be large enough that an improvement by over three orders of magnitude, compared to the existing electron EDM limit, could be obtained at a modest temperature of 4 K, assuming that…
Lecture notes used in a graduate-level Introduction to Solid State Physics course at Cornell University, to serve as a supplement to textbooks at the level of Ashcroft & Mermin.
Inelastic scattering of electrons incident on a solid surface is determined by the two properties: (i) electronic response of the target system and (ii) the detailed quantum-mechanical motion of the projectile electron inside and in the vicinity of the target. We emphasize the equal importance of the second ingredient, pointing out the fundamental limitations of the conventionally used theoretical description of the electron energy-loss spectroscopy (EELS) in terms of the ``energy-loss functions''. Our approach encompasses the dipole and impact scattering as specific cases, with the emphasis o…
A general formula for the orbital magnetic moment of interacting electrons in solids is derived using the many-electron Green function method. The formula factorizes into two parts, a part that contains the information about the one-particle band structure of the system and a part that contains the effects of exchange and correlations carried by the Green function. The derived formula provides a convenient means of including the effects of exchange and correlations beyond the commonly used local density approximation of density functional theory.
Ultrafast electron dynamics of solids after an absorption of femtosecond laser pulse is governed by electron-electron, electron-phonon, phonon-electron, and phonon-phonon collisions. It is of importance to construct a framework for interpreting experimental observations correctly. In this paper we review recent developments of modeling the relaxation dynamics of solids. We discuss the ultrafast relaxation in respect to the effective temperature dynamics and the excess energy dynamics.
A procedure is developed to rigorously decompose experimental loss spectra of medium-energy electrons reflected from solid surfaces into contributions due to surface and volume electronic excitations. This can be achieved by analysis of two spectra acquired under different experimental conditions, e.g. measured at two different energies and/or geometrical configurations. The input parameters of this procedure comprise the elastic scattering cross section and the inelastic mean free path for volume scattering. The (normalized) differential inelastic mean free path as well as the differential su…
Theoretical calculations of core electron binding energies are important for aiding the interpretation of experimental core level photoelectron spectra. In previous work, the $Δ$-Self-Consistent-Field ($Δ$-SCF) method based on density functional theory has been shown to yield highly accurate 1s and 2p binding energies in free molecules. However, most experimental work is concerned with solids, not gases. In this study, we demonstrate the application of the all-electron $Δ$-SCF method to periodic systems. A consideration of the experimentally accessible points of reference leads to the definiti…
Nonequilibrium electron dynamics in solids is an important subject from both fundamental and technological points of view. The recent development of laser technology has enabled us to study ultrafast electron dynamics in the time domain. First-principles calculation is a powerful tool for analyzing such complex electron dynamics and clarifying the physics behind the experimental observation. In this article, we review the recent development of the first-principles calculation for light-induced electron dynamics in solids by revising its application to recent attosecond experiments. The electro…
We propose a simple linear scaling expression in reciprocal space for evaluating the ion--electron potential of crystalline solids. The expression replaces the long-range ion--electron potential with an equivalent localized charge distribution and corresponding boundary conditions on the unit cell. Given that no quadratic scaling structure factor is required---as used in traditional methods---the expression shows inherent linear behavior, and is well suited to simulating large-scale systems within orbital-free density functional theory. The scheme is implemented in the ATLAS software package a…
We study the electrodynamics of Dirac electrons in solids (e.g., bismuth) by comparing it with quantum electrodynamics (QED). It is shown that Lorentz covariance associated with the Dirac electrons in solids results in a remarkable correlation between the dielectric and diamagnetic properties, leading to a significant enhancement in the permittivity directly linked to the well-known phenomenon of large diamagnetism.
We propose an efficient basis expansion for electron orbitals to describe real-time electron dynamics in crystalline solids. Although a conventional grid representation in the three-dimensional Cartesian coordinates works robustly, it requires a large amount of computational resources. To reduce computational costs, we consider an expansion using basis functions with a truncation. A simple choice employing eigenstates of the ground state Hamiltonian with a truncation turned out to be useless. We have found that adding occupied eigenstates of nearby $k$-points to the truncated basis functions c…
Quantum chemistry is one of the most promising near-term applications of quantum computers. Quantum algorithms such as variational quantum eigen solver (VQE) and variational quantum deflation (VQD) algorithms have been mainly applied for molecular systems and there is a need to implement such methods for periodic solids. Using Wannier tight-binding Hamiltonian (WTBH) approaches, we demonstrate the application of VQE and VQD to accurately predict both electronic and phonon bandstructure properties of several elemental as well as multi-component solid-state materials. We apply VQE-VQD calculatio…
We include the treatment of quadrupolar fields beyond the Fröhlich interaction in the first-principles electron-phonon vertex in semiconductors. Such quadrupolar fields induce long-range interactions that have to be taken into account for accurate physical results. We apply our formalism to Si (nonpolar), GaAs, and GaP (polar) and demonstrate that electron mobilities show large errors if dynamical quadrupoles are not properly treated.
We use photoemission spectroscopy to study electronic structures of pristine and K-doped solid picene. The valence band spectrum of pristine picene consists of three main features with no state at the Fermi level (EF), while that of K-doped picene has three structures similar to those of pristine picene with new states near EF, consistent with the semiconductor-metal transition. The K-induced change cannot be explained with a simple rigid-band model of pristine picene, but can be interpreted by molecular orbital calculations considering electron-intramolecular-vibration interaction. Excellent …
We present {\it ab initio} density-functional calculations of molecular solids formed from C$_{28}$-derived closed-shell fullerenes. Solid C$_{28}$H$_4$ is found to bind weakly and exhibits many of the electronic structure features of solid C$_{60}$ with an enhanced electron-phonon interaction potential. We show that chemical doping of this structure is feasible, albeit more restrictive than its C$_{60}$ counterpart, with an estimated superconducting transition temperature exceeding those of the alkali-doped C$_{60}$ solids.
Features of electronic currents in solids are truly diverse depending on circumstances, e.g. non-equilibrium transport currents leading to dissipation and persistent currents flowing in equilibrium. Differences between these currents may be clear in many cases, while there are some where they are not. Results of theoretical studies on the latter cases will be introduced briefly focusing on the inter-band effects of magnetic fields in orbital magnetisms and Hall effects of Dirac electrons.
The possibility of solid solution formation in high entropy alloys (HEAs) has been calculated for alloys with four to seven elements, using a rule previously reported. Thirty elements were included: transition elements of the fourth, fifth and sixth periods of the periodic table, and aluminum. A total of 2,799,486 systems were analyzed. The percentage of solid solutions that would be formed in HEAs decreases from 35.9% to 26.4%, as the number of elements increases from four to seven. The structure of the solid solutions, fcc, bcc or a mixture of fcc and bcc, that would be formed, has been pred…
The exact-exchange (EXX) potential, which is obtained by solving the optimized-effective potential (OEP) equation, is compared to various approximate semilocal exchange potentials for a set of selected solids (C, Si, BN, MgO, Cu$_{2}$O, and NiO). This is done in the framework of the linearized augmented plane-wave method, which allows for a very accurate all-electron solution of electronic structure problems in solids. In order to assess the ability of the semilocal potentials to approximate the EXX-OEP, we considered the EXX total energy, electronic structure, electric-field gradient, and mag…
A Monte Carlo scheme is described where the secondary electron generation has been incorporated. The initial position of a secondary electron due to Fermi sea excitation is assumed to be where the inelastic collision took place, while the polar and azimuth angles of secondary electrons can be calculated in two different ways. The first one assumes a random direction of the secondary electrons, corresponding to the idea that slow secondary electrons should be generated with spherical symmetry. Such an approach violates momentum conservation. The second way of calculating the polar and azimuth a…
Electrical double layers play a key role in a variety of electrochemical systems. The mean free path of secondary electrons in aqueous solutions is on the order of a nanometer, making them suitable for probing of ultrathin electrical double layers at solid-liquid electrolyte interfaces. Employing graphene as an electron-transparent electrode in a two-electrode electrochemical system, we show that the secondary electron yield of the graphene-liquid interface depends on the ionic strength and concentration of electrolyte and applied bias at the remote counter electrode. These observations have b…
A general theoretical framework for the study of electronic stopping of particle projectiles in crystalline solids is proposed. It neither relies on perturbative or linear response approximations, nor on an ideal metal host. Instead, it exploits the discrete translational symmetries in a space-time diagonal determined by a projectile with constant velocity moving along a trajectory with crystalline periodicity. This allows for the characterisation of (stroboscopically) stationary solutions, by means of Floquet theory for time-periodic systems. Previous perturbative and non-linear jellium model…
We present an approach for reconstructing the distribution of electronic internal quantum pressure in the electronic continuum of solids from the experimental electron density. Using the formalism of the density functional theory, we obtain the spatial inner-crystal map of the quantum pressure. The results are visualized via the indicator of quantum pressure focusing (IQPF) which reveals the regions where the pressure is concentrated or depleted due to the quantum effects. IQPF contains all quantum electron shell structure-forming contributions resulting from kinetic, exchange and correlation …
In this short viewpoint, we discuss the assignment of ionic charges in solids. We argue that formal oxidation states serve a useful function, and that absolute values of partial charges should be interpreted and applied with caution; the charge assigned can never be definitive and depends on the type of property studied and the type of analysis performed. Careful analysis can be used to avoid unphysical conclusions such as a recent report on the Ti(III) nature of Ti in stoichiometric TiO$_2$.
We describe the software package SPEX, which allows first-principles calculations of quasiparticle and collective electronic excitations in solids using techniques from many-body perturbation theory. The implementation is based on the full-potential linearized augmented-plane-wave (FLAPW) method, which treats core and valence electrons on an equal footing and can be applied to a wide range of materials, including transition metals and rare earths. After a discussion of essential features that contribute to the high numerical efficiency of the code, we present illustrative results for quasipart…
Over the last decade, researchers have been working to improve a crucial aspect of quantum computing to predict Hamiltonian energy of solids. Quantum algorithms such as Variational Quantum Eigensolver (VQE) and Variational Quantum Deflation (VQD) have been used to study the molecular systems. However, there is growing interest in adapting and applying these methods to periodic solid-state materials. In this work, we have integrated first-principles density functional theory with VQE and VQD algorithms and utilizing the Wannier Tight-Binding Hamiltonian (WTBH) method to predict the electronic c…
Core-electron x-ray photoelectron spectroscopy is a powerful technique for studying the electronic structure and chemical composition of molecules, solids and surfaces. However, the interpretation of measured spectra and the assignment of peaks to atoms in specific chemical environments is often challenging. Here, we address this problem and introduce a parameter-free computational approach for calculating absolute core-electron binding energies. In particular, we demonstrate that accurate absolute binding energies can be obtained from the total energy difference of the ground state and a stat…
We present a linear scaling formulation for the solution of the all-electron Coulomb problem in crystalline solids. The resulting method is systematically improvable and well suited to large-scale quantum mechanical calculations in which the Coulomb potential and energy of a continuous electronic density and singular nuclear density are required. Linear scaling is achieved by introducing smooth, strictly local neutralizing densities to render nuclear interactions strictly local, and solving the remaining neutral Poisson problem for the electrons in real space. While the formulation includes si…
We present accurate many-body results of the electronic densities in several solid materials, including Si, NaCl, and Cu. These results are obtained using the ab initio auxiliary-field quantum Monte Carlo (AFQMC) method working in a plane-wave basis with norm-conserving, multiple-projector pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables and correlation functions other than the ground-state energy requires back-propagation, whose adaption and implementation in the plane-wave basis AFQMC framework are discussed in the present pa…
La-doped ASnO3 (A = Ba, Sr) have great potential as advanced transparent oxide semiconductors due to their large optical bandgap and relatively high electron mobility. The bandgap of Ba1-xSrxSnO3 solid solution increases from 3.2 eV (BaSnO3) to 4.6 eV (SrSnO3) with x. However, the increase in the bandgap is accompanied by reductions in the electrical conductivity. The versatility in the changes in the electrical properties are not trivial, and the property optimization has been challenging. Here we propose a simple metric for quantifying the transport properties of ASnO3. We investigated the e…
A survey is presented of current investigations of the impact of band structure effects on various aspects of the interaction of charged particles with real solids. The role that interband transitions play in the decay mechanism of bulk plasmons is addressed, and results for plasmon linewidths in Al and Si are discussed. {\it Ab initio} calculations of the electronic energy loss of ions moving in Al and Si are also presented, within linear response theory, from a realistic description of the one-electron band structure and a full treatment of the dynamic electronic response of valence electron…
We study the effect of quantum vibronic coupling on the electronic properties of carbon allotropes, including molecules and solids, by combining path integral first principles molecular dynamics (FPMD) with a colored noise thermostat. In addition to avoiding several approximations commonly adopted in calculations of electron-phonon coupling, our approach only adds a moderate computational cost to FPMD simulations and hence it is applicable to large supercells, such as those required to describe amorphous solids. We predict the effect of electron-phonon coupling on the fundamental gap of amorph…
In this brief review we discuss the transient processes in solids under irradiation with femtosecond X-ray free-electron-laser (FEL) pulses and swift-heavy ions (SHI). Both kinds of irradiation produce highly excited electrons in a target on extremely short timescales. Transfer of the excess electronic energy into the lattice may lead to observable target modifications such as phase transitions and damage formation. Transient kinetics of material excitation and relaxation under FEL or SHI irradiation are comparatively discussed. The same origin for the electronic and atomic relaxation in both …
We develop a numerical Brillouin-zone integration scheme for real-time propagation of electronic systems with time-dependent density functional theory. This scheme is based on the decomposition of a large simulation into a set of small independent simulations. The performance of the decomposition scheme is examined in both linear and nonlinear regimes by computing the linear optical properties of bulk silicon and high-order harmonic generation. The decomposition of a large simulation into a set of independent simulations can improve the efficiency of parallel computation by reducing communicat…
We have developed a novel multiscale computational scheme to describe coupled dynamics of light electromagnetic field with electrons and atoms in crystalline solids, where first-principles molecular dynamics based on time-dependent density functional theory is used to describe the microscopic dynamics. The method is applicable to wide phenomena in nonlinear and ultrafast optics. To show usefulness of the method, we apply it to a pump-probe measurement of coherent phonon in diamond where a Raman amplification takes place during the propagation of the probe pulse.
Progress toward the realization of quantum computers requires persistent advances in their constituent building blocks - qubits. Novel qubit platforms that simultaneously embody long coherence, fast operation, and large scalability offer compelling advantages in the construction of quantum computers and many other quantum information systems. Electrons, ubiquitous elementary particles of nonzero charge, spin, and mass, have commonly been perceived as paradigmatic local quantum information carriers. Despite superior controllability and configurability, their practical performance as qubits via …
We show theoretically that nonrelativistic nearly-free electrons in solids should experience a trembling motion (Zitterbewegung, ZB) in absence of external fields, similarly to relativistic electrons in vacuum. The Zitterbewegung is directly related to the influence of periodic potential on the free electron motion. The frequency of ZB is $ω\approx E_g/\hbar$, where $E_g$ is the energy gap. The amplitude of ZB is determined by the strength of periodic potential and the lattice period and it can be of the order of nanometers. We show that the amplitude of ZB does not depend much on the width of…
A heavy-mass electron state is realized in a doped valence bond solid (Ti1-xVx)2O3. In this system, itinerant holes mediate the mainly ferromagnetic RKKY interaction between the localized magnetic moments and become readily spin-polarized under a magnetic field, while showing large negative magnetoresistance. In spite of the ferromagnetic interaction among the carriers, their effective mass is found to be 1 or 2 orders of magnitude larger than that of usual doped semiconductors. Such strong mass renormalization is ascribable to the polaron formation on the Ti-dimer, where the spin-singlet stat…
We extend the semi-classical trajectory description for the high-order harmonic generation~(HHG) from solids by integrating the effect of electron-scattering. Comparing the extended semi-classical trajectory model with a one-dimensional quantum mechanical simulation, we find that the multi-plateau feature of the HHG spectrum is formed by Umklapp scattering under the electron-hole acceleration dynamics by laser fields. Furthermore, by tracing the scattered trajectories in real-space, the model fairly describes the emitted photon energy and the emission timing of the HHG even in the higher plate…
We study the structural and electronic properties of phase III of solid hydrogen using accurate many-electron theories and compare to state-of-the-art experimental findings. The atomic structures of phase III modelled by C2/c-24 crystals are fully optimized on the level of second-order perturbation theory, demonstrating that previously employed structures optimized on the level of approximate density functionals exhibit errors in the H$_2$ bond lengths that cause significant discrepancies in the computed quasi particle band gaps and vibrational frequencies compared to experiment. Using the new…
Solid He is studied in the pressure and temperature ranges 1-40 TPa and 0-10,000 K using first-principles methods. Anharmonic vibrational properties are calculated within a self-consistent field framework, including the internal and free energies, density-pressure relation, stress tensor, thermal expansion, and the electron-phonon coupling renormalization of the electronic band gap. We find that an accurate description of electron-phonon coupling requires us to use a non-perturbative approach. The metalization pressure of 32.9 TPa at 0 K is larger than found previously. The vibrational effects…
The interaction between electronic and nuclear spins in the presence of external magnetic fields can be described by a spin Hamiltonian, with parameters obtained from first principles, electronic structure calculations. We describe an approach to compute these parameters, applicable to both molecules and solids, which is based on Density Functional Theory (DFT) and real-space, all-electron calculations using finite elements (FE). We report results for hyperfine tensors, zero field splitting tensors (spin-spin component) and nuclear quadrupole tensors of a series of molecules and of the nitroge…
The relativistic Dirac equation covers the fundamentals of electronic phenomena in solids and as such it effectively describes the electronic states of the topological insulators like Bi$_2$Se$_3$ and Bi$_2$Te$_3$. Topological insulators feature gapless surface states and, moreover, magnetic doping and resultant ferromagnetic ordering break time-reversal symmetry to realize quantum anomalous Hall and Chern insulators. Here we focus on the bulk and investigate the mutual coupling of electronic and magnetic properties of Dirac electrons. Without carrier doping, spiral magnetic orders cause a fer…
Electronic structure of the manganese oxide solid is studied by the quantum Monte Carlo (QMC) methods. The trial wavefunctions are built using orbitals from unrestricted Hartree-Fock and Density Functional Theory, and the electron-electron correlation is recovered by the fixed-node QMC. The correlation effects are significant and QMC estimations of the gap and cohesion show a very good agreement with experiment. Comparison with hybrid functional results points out the importance of the exact exchange for improvement of the Density Functional description of transition metal oxide systems.
We propose a mechanism of long-range coherent coupling between nuclear spins to be used as qubits in solid-state semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which in turn interact with the two-dimensional electron gas. An effective two-spin interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of qubit decoherence and consider possibilities for gate control of the interaction between neighboring qubits. The resulting quantum computing scheme retains all the gate-control and me…
Traditional classifications of crystalline phases focus on nuclear degrees of freedom. Through examination of both electronic and nuclear structure, we introduce the concept of an electronic plastic crystal. Such a material is classified by crystalline nuclear structure, while localized electronic degrees of freedom - here lone pairs - exhibit orientational motion at finite temperatures. This orientational motion is an emergent phenomenon arising from the coupling between electronic structure and polarization fluctuations generated by collective motions, such as phonons. Using ab initio molecu…
