Electron-phonon Spectral Function Research Articles

First-principles calculations on the intrinsic resistivity of realistic metals: a case study of monolayer V2N.

The Ziman resistivity formula is extensively employed to calculate the intrinsic resistivity of realistic metals using recent works of first-principles calculations. Owing to the approximation, Allen's generalization, which relates the solution of the Boltzmann transport equation (BTE) for metals to the transport electron-phonon (e-ph) spectral function, the applicability of the Ziman resistivity formula still needs to be discussed. In this work, we perform first-principles calculations of the intrinsic resistivity of the V2N monolayer, a kind of MXene material, by employing the Ziman resistivity formula and the iterative solution of BTE. We find that in the wide temperature range of 50-1400 K, the intrinsic resistivity of the V2N monolayer obtained by means of the two approaches, has the same order of magnitude. However the Ziman resistivity formula fails to correctly describe the Fermi level dependence of the intrinsic resistivity of the V2N monolayer. The underlying reason is that the band edge of the V2N and hence Van Hove singularity (VHS), is near the shifted Fermi level. We suggest a modified Ziman resistivity formula which is valid even if there is a band edge at the Fermi level.

Effects of anisotropy and disorder on the superconducting properties of niobium

We report results for the superconducting transition temperature and anisotropic energy gap for pure niobium based on Eliashberg’s equations and electron and phonon band structures computed from density functional theory. The electronic band structure is used to construct the Fermi surface and calculate the Fermi velocity at each point on the Fermi surface. The phonon bands are in excellent agreement with inelastic neutron scattering data. The corresponding phonon density of states and electron–phonon coupling define the electron–phonon spectral function, α2F(p, p′; ω), and the corresponding electron–phonon pairing interaction, which is the basis for computing the superconducting properties. The electron–phonon spectral function is in good agreement with existing tunneling spectroscopy data except for the spectral weight of the longitudinal phonon peak at ℏωLO = 23 meV. We obtain an electron–phonon coupling constant of λ = 1.057, renormalized Coulomb interaction μ⋆ = 0.218, and transition temperature Tc = 9.33 K. The corresponding strong-coupling gap at T = 0 is modestly enhanced, Δ0 = 1.55 meV, compared to the weak-coupling BCS value Δ0wc=1.78kBTc=1.43meV. The superconducting gap function exhibits substantial anisotropy on the Fermi surface. We analyze the distribution of gap anisotropy and compute the suppression of the superconducting transition temperature using a self-consistent T-matrix theory for quasiparticle-impurity scattering to describe niobium doped with non-magnetic impurities. We compare these results with experimental results on niobium SRF cavities doped with nitrogen impurities.

Classification of superconducting transition temperature over 150K of metal polyhydrides using support vector machine

The search for room-temperature superconductors have shed light on metal polyhydrides as their superconducting transition temperature (TC) vary from a few kelvins to near-room temperatures. One major drawback in the quest for hydrogen-based superconductors is that the calculation of TC through the electron-phonon spectral function consumes large amount of time and computational resources. Here we propose a method of using the support vector machine (SVM) to classify the ranges of TC of the metal polyhydrides without actual calculation of the electron-phonon spectral function. The input variables are chosen based on the effect of hydrogen atoms and the electron localization function (ELF). These set of features can be obtained quickly from the electronics simulations, compare with the actual spectral function calculations. We found that the SVM can classify the superconductors with accuracy over 80 percent with respect to all the metal polyhydrides in the dataset. Our goal of this work is to help screen for the high value of TC of the hydrogen-based compounds, and reduce the time required for the direct calculations of TC.

Ab initio calculations for the transport properties of metals within Boltzmann transport theory: From equilibrium to nonequilibrium heating regime

The paper offers an approach to ab initio calculations for predicting the electron transport properties of solid-state metals in a case of nonequilibrium heating. Formulas for the electrical resistivity (also static conductivity) and thermal conductivity of metals at different electron and lattice temperatures were derived within a method proposed by Allen [Phys. Rev. B 17, 3725 (1978)] for the solution of the Boltzmann transport equation. The approach works well under equilibrium heating too when electron and lattice temperatures are equal. It performs most effectively if it is necessary to allow for the Fermi smearing of the electron distribution function over quantum states and the energy dependence of the electron-phonon spectral function. Four metals---Cu, Ag, Au and Pd---are considered as examples. We succeeded to reproduce well the temperature dependencies of electrical resistivity and thermal conductivity of studied metals in a wide range of temperatures under equilibrium heating. For the nonequilibrium regime of heating, calculations reproduce quite well the temporal evolution of the static electrical conductivity of gold, observed in recent experiments for the interaction of thin gold foils with ultrashort laser pulses.

The Pseudopotential Approach within Density-Functional Theory: The Case of Atomic Metallic Hydrogen

Internal energies, enthalpies, phonon dispersion curves, and superconductivity of atomic metallic hydrogen are calculated. The standard use of pseudopotentials in density-functional theory are compared with full Coulomb-potential, all-electron linear muffin-tin orbital calculations. Quantitatively similar results are found as far as internal energies are concerned. Larger differences are found for phase-transition pressures; significant enough to affect the phase diagram. Electron–phonon spectral functions α2F(ω) also show significant differences. Against expectation, the estimated superconducting critical-temperature Tc of the first atomic metallic phase I41/amd (Cs-IV) at 500 GPa is actually higher.

Temperature-dependent electron-phonon spectral function and the intrinsic resistivity of a metal: A case study of monolayer Ti2N

The transport spectral function of electron-phonon ($e$-ph) interaction in the double $\ensuremath{\delta}$-function approximation (DDFA) is extensively employed to calculate the intrinsic resistivity (arising from $e$-ph scattering) of metallic materials in recent works of first-principles calculations. In contrast, a more fundamental transport spectral function with the Fermi smearing effect due to finite temperature ($T$) and nonzero phonon frequency is less involved. In this work, we perform first-principles calculations of the intrinsic resistivity of ${\mathrm{Ti}}_{2}\mathrm{N}$ monolayer, a potential MXene material, by employing the two kinds of spectral function. We find that the spectral function with the DDFA fails to describe correctly the temperature dependence of the intrinsic resistivity of ${\mathrm{Ti}}_{2}\mathrm{N}$ monolayer at $T>250$ K, much lower than the Debye temperature. The underlying reason is that ${\mathrm{Ti}}_{2}\mathrm{N}$ monolayer has a multisheet Fermi surface formed by several bands, and some band edges are very close to the Fermi surface. Our results suggest that the transport spectral function with the Fermi smearing effect, instead of the one with the DDFA, is always adequate for studying the intrinsic resistivity of realistic materials on the level of first-principles calculations. In addition, we give a brief remark on the intrinsic resistivity of ${\mathrm{Ti}}_{2}\mathrm{N}$ monolayer, in contrast with other typical two-dimensional materials, which is significant from the viewpoint of application of such an MXene material.

Migdal-Eliashberg theory of multi-band high-temperature superconductivity in field-effect-doped hydrogenated (111) diamond

We perform single- and multi-band Migdal-Eliashberg (ME) calculations with parameters exctracted from density functional theory (DFT) simulations to study superconductivity in the electric-field-induced 2-dimensional hole gas at the hydrogenated (111) diamond surface. We show that according to the Eliashberg theory it is possible to induce a high-Tc superconducting phase when the system is field-effect doped to a surface hole concentration of 6×1014 cm−2, where the Fermi level crosses three valence bands. Starting from the band-resolved electron-phonon spectral functions α2Fjj′(ω) computed ab initio, we iteratively solve the self-consistent isotropic Migdal-Eliashberg equations, in both the single-band and the multi-band formulations, in the approximation of a constant density of states at the Fermi level. In the single-band formulation, we find Tc≈40 K, which is enhanced between 4% and 8% when the multi-band nature of the system is taken into account. We also compute the multi-band-sensitive quasiparticle density of states to act as a guideline for future experimental works.

Hybrid acousto-electromagnetic metamaterial superconductors

Recent theoretical and experimental studies demonstrated that an electromagnetic metamaterial approach is capable of drastically increasing the critical temperature Tc of composite metamaterial superconductors. This progress was achieved by engineering the frequency-dependant dielectric response function of the metamaterial. Here we further extend this approach by introducing the concept of hybrid acousto-electromagnetic hyperbolic metamaterial superconductors, which are projected to exhibit strongly enhanced superconducting properties due to artificially engineered broadband divergency of the Eliashberg electron-phonon spectral density function α2F(ω). Based on the developed approach, a hybrid acousto-electromagnetic metamaterial is proposed, which is made of LSCO/STO nano-alloy.

Strong Electron-Phonon Coupling and its Influence on the Transport and Optical Properties of Hole-Doped Single-Layer InSe.

We show that hole states in recently discovered single-layer InSe are strongly renormalized by the coupling with acoustic phonons. The coupling is enhanced significantly at moderate hole doping (∼10^{13} cm^{-2}) due to hexagonal warping of the Fermi surface. While the system remains dynamically stable, its electron-phonon spectral function exhibits sharp low-energy resonances, leading to the formation of satellite quasiparticle states near the Fermi energy. Such many-body renormalization is predicted to have two important consequences. First, it significantly suppresses charge carrier mobility reaching ∼1 cm^{2} V^{-1} s^{-1} at 100K in a freestanding sample. Second, it gives rise to unusual temperature-dependent optical excitations in the midinfrared region. Relatively small charge carrier concentrations and realistic temperatures suggest that these excitations may be observed experimentally.

Pressure effect on the superconducting and the normal state of β−Bi2Pd

The pressure effect up to 24.0 kbar on superconducting and normal-state properties of $\ensuremath{\beta}\ensuremath{-}\mathrm{B}{\mathrm{i}}_{2}\mathrm{Pd}$ single crystal (${T}_{\mathrm{c}}\ensuremath{\approx}4.98\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ at ambient pressure) has been investigated by measurements of the electrical resistivity. In addition, we have performed the heat capacity measurements in the temperature range 0.7--300 K at ambient pressure. The recent calculations of electronic density of states, electron-phonon interaction spectral function, and phonon density of states of $\ensuremath{\beta}\ensuremath{-}\mathrm{B}{\mathrm{i}}_{2}\mathrm{Pd}$ [Zheng and Margine, Phys. Rev. B 95, 014512 (2017)], are used to fit the resistivity and the heat capacity data. In the superconducting state we have focused on the influence of pressure on the superconducting transition temperature ${T}_{\mathrm{c}}$ and upper critical field ${H}_{\mathrm{c}2}$ and a negative effect with $d{T}_{\mathrm{c}}/dp=--0.025\phantom{\rule{0.16em}{0ex}}\mathrm{K}/\mathrm{kbar}$ and $d{H}_{\mathrm{c}2}/dp=--8\phantom{\rule{0.16em}{0ex}}\mathrm{mT}/\mathrm{kbar}$ is found. A simplified Bloch-Gr\uneisen model was used to analyze the pressure effect on the temperature dependence of the normal-state resistivity. The obtained results point to a decrease of the electron-phonon coupling parameter \ensuremath{\lambda} and to a shift of phonon frequencies to higher values with pressure. Moreover, the temperature dependence of the normal-state resistivity follows a ${T}^{2}$ dependence above ${T}_{\mathrm{c}}$ up to about 25 K. Together with the enhanced value of Sommerfeld coefficient $\ensuremath{\gamma}=13.23\phantom{\rule{0.16em}{0ex}}\mathrm{mJ}\phantom{\rule{0.16em}{0ex}}\mathrm{mo}{\mathrm{l}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{K}}^{\ensuremath{-}2}$ these results point to a certain role of the electron-electron interaction in the superconducting pairing mechanism in $\ensuremath{\beta}\ensuremath{-}\mathrm{B}{\mathrm{i}}_{2}\mathrm{Pd}$.

Electron-phonon coupling mechanisms for hydrogen-rich metals at high pressure

The mechanisms for strong electron-phonon coupling predicted for hydrogen-rich alloys with high superconducting critical temperature ($T_c$) are examined within the Migdal-Eliashberg theory. Analysis of the functional derivative of $T_c$ with respect to the electron-phonon spectral function shows that at low pressures, when the alloys often adopt layered structures, bending vibrations have the most dominant effect. At very high pressures, the H-H interactions in two-dimensional (2D) and three-dimensional (3D) extended structures are weakened, resulting in mixed bent (libration) and stretch vibrations, and the electron-phonon coupling process is distributed over a broad frequency range leading to very high $T_c$.

Revisiting optical properties of MgB2 with a high-quality sample prepared by a HPCVD method

We investigated a high-quality MgB2 thin film with a thickness of ~1000 nm on an Al2O3 substrate using optical spectroscopy. We measured the reflectance spectra of the film at various temperatures both below, and above, the superconducting transition temperature, Tc simeq 40 K. An earlier study showed that when the sample surface is exposed to air the optical properties of the surface change immediately, however, the saturated change is negligibly small in the far-infrared region. The optical conductivity spectrum in the normal state shows two (narrow and broad) Drude modes, with the narrow Drude mode being dominant in the low frequency region below 1000 cm−1. Our study, which uses a good-quality sample, provides more reliable data on the optical properties of MgB2, in a similar spectral range. The optical data is analyzed further using an extended Drude model, and the electron-phonon spectral density function, α2F(ω), is extracted. The spectral density function α2F(ω) features two peaks: a small one near 114 cm−1, and a strong peak around the 550 cm−1 where the B-B bond stretching phonon exists. Our data in the superconducting state does not show the expected energy shift of the onset of scattering associated with the α2F(ω) peaks.

Critical temperature of metallic hydrogen sulfide at 225-GPa pressure

The Eliashberg theory generalized for electron—phonon systems with a nonconstant density of electron states and with allowance made for the frequency behavior of the electron mass and chemical potential renormalizations is used to study T c in the SH3 phase of hydrogen sulfide under pressure. The phonon contribution to the anomalous electron Green’s function is considered. The pairing within the total width of the electron band and not only in a narrow layer near the Fermi surface is taken into account. The frequency and temperature dependences of the complex mass renormalization ReZ(ω), the density of states N(e) renormalized by the electron—phonon interactions, and the electron—phonon spectral function obtained computationally are used to calculate the anomalous electron Green’s function. A generalized Eliashberg equation with a variable density of electron states has been solved. The frequency dependence of the real and imaginary parts of the order parameter in the SH3 phase has been obtained. The value of T c ≈ 177 K in the SH3 phase of hydrogen sulfide at pressure P = 225 GPa has been determined by solving the system of Eliashberg equations.

Ab initio determination of effective electron–phonon coupling factor in copper

The electron temperature Te dependent electron density of states g(ε), Fermi–Dirac distribution f(ε), and electron–phonon spectral function α2F(Ω) are computed as prerequisites before achieving effective electron–phonon coupling factor Ge–ph. The obtained Ge–ph is implemented into a molecular dynamics (MD) and two-temperature model (TTM) coupled simulation of femtosecond laser heating. By monitoring temperature evolutions of electron and lattice subsystems, the result utilizing Ge–ph from ab initio calculation shows a faster decrease of Te and increase of Tl than those using Ge–ph from phenomenological treatment. The approach of calculating Ge–ph and its implementation into MD–TTM simulation is applicable to other metals.

Electron-phonon Coupling and the Superconducting Phase Diagram of the LaAlO3-SrTiO3 Interface.

The superconductor at the LaAlO3—SrTiO3 interface provides a model system for the study of two-dimensional superconductivity in the dilute carrier density limit. Here we experimentally address the pairing mechanism in this superconductor. We extract the electron—phonon spectral function from tunneling spectra and conclude, without ruling out contributions of further pairing channels, that electron—phonon mediated pairing is strong enough to account for the superconducting critical temperatures. Furthermore, we discuss the electron—phonon coupling in relation to the superconducting phase diagram. The electron—phonon spectral function is independent of the carrier density, except for a small part of the phase diagram in the underdoped region. The tunneling measurements reveal that the increase of the chemical potential with increasing carrier density levels off and is zero in the overdoped region of the phase diagram. This indicates that the additionally induced carriers do not populate the band that hosts the superconducting state and that the superconducting order parameter therefore is weakened by the presence of charge carriers in another band.

Comparison of pressurized sulfur hydride with conventional superconductors

A recent report that sulfur hydride under pressure is an electron-phonon superconductor with a Tc of 190 K has been met with much excitement although it is yet to be confirmed. Based on several electron-phonon spectral density functions already available from density functional theory, we find that the electron-phonon spectrum is near optimum for Tc with a particularly large value of its characteristic phonon energy omega_ln which is due to the small hydrogen mass. We find that the thermodynamic universal BCS ratios are near those for Pb and Nb3Sn. We suggest that optical measurements could be a useful tool to establish the existence and nature of the superconductivity in this system. Conventional superconductors are in the impurity-dominated dirty limit. By contrast sulfur hydride will be in the clean limit because of its large energy gap scale. The AC optical conductivity will display distinct and separate signatures of the superconducting gap in the low-energy impurity-dominated range of the optical spectrum and additional phonon structures at higher energies where the clean limit applies.

Study of the superconducting phase in silicene under biaxial tensile strain

The electron-doped silicene under the influence of the biaxial tensile strain is predicted to be the phonon-mediated superconductor. By using the Eliashberg formalism, we investigate the thermodynamic properties of the superconducting silicene in the case when the tension is 5% and the electron doping equals 3.5×1014cm−2. Under such conditions, silicene monolayer is expected to exhibit the highest superconducting transition temperature (TC). In particular, based on the electron–phonon spectral function and assuming a wide range of the Coulomb pseudopotential values (μ⋆∈〈0.1,0.3〉) it is stated that the superconducting transition temperature decreases from 18.7K to 11.6K. Similar behavior is observed in the case of the zeroth temperature superconducting energy gap at the Fermi level: 2Δ(0)∈〈6.68,3.88〉 meV. Other thermodynamic parameters differ from the predictions of the Bardeen–Cooper–Schrieffer theory. In particular, the ratio of the energy gap to the critical temperature changes in the range from 4.14 to 3.87. The ratio of the specific heat jump to the specific heat in the normal state takes the values from 2.19 to 2.05, and the ratio of the critical temperature and specific heat in the normal state to the thermodynamic critical field increases from 0.143 to 0.155. It is also determined that the maximum value of the electron effective mass equals 2.11 of the electron band mass.

Electronic structure, phonon spectra and electron–phonon interaction in ScB2

The electronic structure, Fermi surface, angle dependence of the cyclotron masses and extremal cross sections of the Fermi surface, phonon spectra, electron–phonon Eliashberg and transport spectral functions, temperature dependence of electrical resistivity of the ScB2 diboride were investigated from first principles using the fully relativistic and full potential linear muffin-tin orbital methods. The calculations of the dynamic matrix were carried out within the framework of the linear response theory. A good agreement with experimental data of electron–phonon spectral functions, electrical resistivity, cyclotron masses and extremal cross sections of the Fermi surface was achieved.

Comparative study of the electronic structure, phonon spectra, and electron-phonon interaction of ZrB2and TiB2

The electronic structure, optical and x-ray absorption spectra, angle dependence of the cyclotron masses and extremal cross sections of the Fermi surface, phonon spectra, electron-phonon Eliashberg and transport spectral functions, temperature dependence of electrical resistivity of the MB2 (M=Ti and Zr) diborides were investigated from first principles using the full potential linear muffin-tin orbital method. The calculations of the dynamic matrix were carried out within the framework of the linear response theory. A good agreement with experimental data of optical and x-ray absorption spectra, phonon spectra, electron-phonon spectral functions, electrical resistivity, cyclotron masses and extremal cross sections of the Fermi surface was achieved.

Electronic structure, phonon spectra, and anisotropy of electron–phonon interaction in scandium

AbstractThe anisotropy of transport function, electronic structure, Fermi surface, phonon spectra, electron–phonon spectral function, orbital dependence of the cyclotron masses, and extremal cross sections of the Fermi surface of Sc were investigated from first principles using the full potential linear muffin‐tin orbital method. The calculations of the dynamic matrix were carried out within the framework of the linear response theory. A good agreement with experimental data of phonon spectra, electrical resistivity, cyclotron masses, and extremal cross sections of the Fermi surface in high symmetry directions was achieved.