Intraband Contributions Research Articles

Ab initio-simulated optical response of hot electrons in gold and ruthenium

Optical femtosecond pump-probe experiments allow to measure the dynamics of ultrafast heating of metals with high accuracy. However, the theoretical analysis of such experiments is often complicated because of the indirect connection of the measured signal and the desired temperature transients. Establishing such a connection requires an accurate model of the optical constants of a metal, depending on both the electron temperature T e and the lattice temperature T l . In this paper, we present first-principles simulations of the two-temperature scenario with T e ≫ T l , showing the optical response of hot electrons to laser irradiation in gold and ruthenium. Comparing our simulations with the Kubo-Greenwood approach, we discuss the influence of electron-phonon and electron-electron scattering on the intraband contribution to optical constants. Applying the simulated optical constants to the analysis of ultrafast heating of ruthenium thin films we highlight the importance of the latter scattering channel to understand the measured heating dynamics.

χ(2) and χ(3) enhancement by arylamine substituents in aromatic conjugated polyenyne polymers

In this work, we have determined the χ(1), χ(2), and χ(3) NLO properties of NH2substituted aromatic polyenynes in ortho, meta, and para positions. It is worth noting that Mednis-Genkin’s approximation takes into account the intraband contribution with a derivate of the dipole valence-conduction band moment transition, unlike, for example, Ward’s summation-over-sates (SOS) methodology, which considers the difference of these states. Indeed, we have selected these polymers because of the high asymmetry in their molecular wavefunction. In this way, the calculated χ(3) values of the para-NH2 substituted aromatic polyenyne with a higher degree of polymerization are near 1 X 10−7 esu. For its part, the ortho polymer has higher values, of the order of 1 X 10−6 esu, due to its high transition dipole moment. We have also found that the energy band distribution in the para position of these polymers produces van Hove points, which have a negligible proportion of the NLO properties, compared with singularity regions 1 and 2, which have a contribution of 100 %. These regions are due to the wavefunction coefficients’ first and second-order derivatives. Besides, without considering border effects nor correlation effects, and only the variation of excitation energy, we have calculated that the quaternary monomeric oligomers of these polymers have almost similar values of χ(2) and χ(3). Then, it implies building a methodology to synthesize the polymers to avoid canceling the NLO-χ(2) and -χ(3) values.

Physical Origin of Color Changes in Lutetium Hydride under Pressure

Recently, near-ambient superconductivity was claimed in nitrogen-doped lutetium hydride (LuH3–δ N ε ). Unfortunately, all follow-up research still cannot find superconductivity signs in successfully synthesized lutetium dihydride (LuH2) and N-doped LuH2±x N y . However, a similar intriguing observation was the pressure-induced color changes (from blue to pink and subsequent red). The physical understanding of its origin and the correlation between the color, crystal structure, and chemical composition of Lu–H–N is still lacking. In this work, we systematically investigated the optical properties of LuH2 and LuH3, and the effects of hydrogen vacancies and nitrogen doping using the first-principles calculations by considering both interband and intraband contributions. Our results demonstrate that the evolution of reflectivity peaks near blue and red light, which is driven by changes in the band gap and Fermi velocity of free electrons, resulting in the blue-to-red color change under pressure. In contrast, LuH3 exhibits gray and no color change up to 50 GPa. Furthermore, we investigated the effects of hydrogen vacancies and nitrogen doping on its optical properties. Hydrogen vacancies can significantly decrease the pressure of blue-to-red color change in LuH2 but do not have a noticeable effect on the color of LuH3. The N-doped LuH2 with the substitution of a hydrogen atom at the tetrahedral position maintains the color change when the N-doping concentration is low. As the doping level increases, this trend becomes less obvious, while other N-doped structures do not show a blue-to-red color change. Our results can clarify the origin of the experimental observed blue-to-red color change in lutetium hydride and also provide a further understanding of the potential N-doped lutetium dihydride.

Wavelength scaling of high harmonic yields and cutoff energies in solids driven by mid-infrared pulses.

The effect of driving wavelengths on high harmonic generation (HHG) have long been a fundamental research topic. However, despite of abundant efforts, the investigation of wavelength scaling of HHG in solids is still confined within the scope of theoretical predictions. In this work, we for the first time to the best of our knowledge, experimentally reveal wavelength scaling of HHG yields and cutoff energy in three typical solid media (namely pristine crystals GaSe, CdTe and polycrystalline ZnSe), driven in a broad mid-infrared (MIR) range from 4.0 to 8.7 µm. It is revealed that when the driving wavelength is shorter than 6.5-7.0 µm, HHG yields decrease monotonously with the MIR driving wavelengths, while they rise abruptly by 1-3 orders of magnitude driven at longer wavelength and exhibit a crest at 7.5 µm. In addition, the cutoff energies are found independent on driving wavelengths across the broad MIR pump spectral range. We propose that the interband mechanism dominates the HHG process when the driving wavelength is shorter than 6.5-7.0 µm, and as the driving wavelength increases, intraband contribution leads to an abrupt rise of the HHG yields, which is verified by the HHG polarization measurement driven at 3.0 and 7.0 µm. This work not only experimentally demonstrate the wavelength scaling of HHG in solids, but more importantly blazes the trail for optimizing the HHG performance by choosing a driving wavelength and provides experimental method to distinguish the interband and intraband dynamics.

Extracting quantum-geometric effects from Ginzburg-Landau theory in a multiband Hubbard model

We first apply functional-integral approach to a multiband Hubbard model near the critical pairing temperature, and derive a generic effective action that is quartic in the fluctuations of the pairing order parameter. Then we consider time-reversal-symmetric systems with uniform (i.e., at both low-momentum and low-frequency) pairing fluctuations in a unit cell, and derive the corresponding time-dependent Ginzburg-Landau (TDGL) equation. In addition to the conventional intraband contribution that depends on the derivatives of the Bloch bands, we show that the kinetic coefficients of the TDGL equation have a geometric contribution that is controlled by both the quantum-metric tensor of the underlying Bloch states and their band-resolved quantum-metric tensors. Furthermore we show that thermodynamic properties such as London penetration depth, GL coherence length, GL parameter and upper critical magnetic field have an explicit dependence on quantum geometry.

Unfolding the Origin of the Ultrafast Optical Response of Titanium Nitride

AbstractUltrafast plasmonics is driving growing interest for the search of novel plasmonic materials, overcoming the main limitations of noble metals. In this framework, titanium nitride (TiN) is brought in the spotlight for its refractory properties combined with an extremely fast electron‐lattice cooling time (<100 fs) compared to gold (≈ 1 ps). Despite the results reported in literature, a clear‐cut explanation of the origin of the ultrafast and giant optical response of TiN‐based materials upon excitation with femtosecond laser pulses is still missing. To address this issue, an original model is introduced, capable of unfolding the modulation of TiN optical properties on a broad bandwidth, starting from the variations of electronic and lattice temperatures following ultrafast photoexcitation. The numerical analysis is validated on ultrafast pump–probe spectroscopy experiments on a simple structure, a TiN film on glass. This approach enables a complete disentanglement of the interband and intraband contributions to the permittivity modulation. Moreover, it is also shown that, varying the synthesis conditions of the TiN film, not only the static, but also the dynamical optical response can be efficiently tuned. These findings pave the way for a breakthrough in the field: the design of TiN‐based ultrafast nanodevices for all‐optical modulation of light.

Efficient full frequency GW for metals using a multipole approach for the dielectric screening

The properties of metallic systems with important and structured excitations at low energies, such as Cu, are challenging to describe with simple models like the plasmon pole approximation (PPA), and more accurate and sometimes prohibitive full frequency approaches are usually required. In this paper we propose a numerical approach to $GW$ calculations on metals that takes into account the frequency dependence of the screening via the multipole approximation (MPA), an accurate and efficient alternative to current full-frequency methods that was recently developed and validated for semiconductors and overcomes several limitations of PPA. We now demonstrate that MPA can be successfully extended to metallic systems by optimizing the frequency sampling for this class of materials and introducing a simple method to include the $\mathbf{q}\to 0$ limit of the intra-band contributions. The good agreement between MPA and full frequency results for the calculations of quasi-particle energies, polarizability, self-energy and spectral functions in different metallic systems confirms the accuracy and computational efficiency of the method. Finally, we discuss the physical interpretation of the MPA poles through a comparison with experimental electron energy loss spectra for Cu.

Quantum Oscillations of Interlayer Conductivity in a Multilayer Topological Insulator

Quantum and difference oscillations of interlayer conductivity in a multilayer system of thin films of topological insulators (TIs) are investigated. Due to the linearity of the carrier spectrum in such a system, new features of quantum oscillations arise. In particular, the frequencies of de Haas–van Alfvén and Shubnikov–de Haas oscillations depend quadratically on the chemical potential, rather than linearly as in systems with parabolic carrier spectrum. For the same reason, the temperature damping factor of oscillations contains the chemical potential. This is due to the nonequidistant character of the Landau levels: the higher the chemical potential, the smaller the distance between Landau levels. However, the beat frequencies, as well as the frequencies of slow oscillations, do not depend on the chemical potential; in this sense, the behavior of these systems is similar to that of conventional non-Dirac systems. Finally, in the Born approximation (in the second order cross-diagram technique), we considered the general case when the interlayer conductivity takes into account both intra- and interband transitions. We have shown that the contribution of intraband transitions is insignificant for the conductivity oscillations in the absence of magnetic impurities. However, in the presence of a Dirac point in the spectrum, a linear (in magnetic field) intraband contribution to conductivity arises from the zero Landau level. At low temperatures, this contribution is exponentially small compared to the intraband contribution and vanishes at zero temperature.

First-principle study on electronic structures and optical properties of Au-Cu intermetallic compounds

The optical properties of Au-Cu intermetallic compounds can be tailored by varying the components, which advances their promising applications in plasmonics and optical metamaterials. However, physical insight on how components tailor the electronic structures and optical properties of those Au-Cu intermetallic compounds still lacks. In this work, first-principle study on the electronic structures and optical properties of three intermetallic compounds Au 3 Cu, AuCu and AuCu 3 is presented. The influence of components on the electronic structure, electron-phonon coupling, dielectric function and electrical resistivity are fully investigated. The calculation of dielectric function is divided into interband and intraband part. The calculated interband dielectric function show large differences compared with that of pure Au and pure Cu, with an absorption peak emerging at low energy of around 0.3 eV. The temperature effect of intraband dielectric function is investigated by considering electron-phonon interaction. By superimposing the interband and intraband contribution, the total dielectric function of AuCu 3 and AuCu shows an overall good agreement with available experimental data in literature. The calculated electron-phonon coupling strength of Au 3 Cu is higher than that of pure Au and Cu, whereas, the results of AuCu and AuCu 3 are lower than them. In addition, the calculated electrical resistivity of all the three Au-Cu compounds are larger than that of pure Au and Cu. • The changes of electronic structure, electron-phonon coupling strength, and optical properties for different components are presented. • The electron-phonon coupling strength of AuCu and AuCu 3 is lower than that of pure Au and Cu. • The electrical resistivity of Au-Cu compound is higher than pure Au and Cu.

Effective-mass tensor of the two-body bound states and the quantum-metric tensor of the underlying Bloch states in multiband lattices

By considering an on-site attraction between a spin-$\ensuremath{\uparrow}$ and a spin-$\ensuremath{\downarrow}$ fermion in a multiband tight-binding lattice, here we study the two-body spectrum and derive an exact relation between the inverse of the effective-mass tensor of the lowest bound states and the quantum-metric tensor of the underlying Bloch states. In addition to the intraband (or the so-called conventional) contribution that depends only on the single-particle spectrum and the interband (or the so-called geometric) contribution that is controlled by the quantum metric, our generalized relation has an additional interband contribution that depends on the so-called band-resolved quantum metric. All of our analytical expressions are applicable to those multiband lattices that simultaneously exhibit time-reversal symmetry and fulfill the condition on spatially uniform pairing. As a nontrivial illustration we analyze the two-body problem in a kagome lattice with nearest-neighbor hoppings, and we show that the exact relation provides a perfect benchmark.

Disentangling Orbital Magnetic Susceptibility with Wannier Functions

Orbital magnetic susceptibility involves rich physics such as interband effects despite of its conceptual simplicity. In order to appreciate the rich physics related to the orbital magnetic susceptibility, it is essential to derive a formula to decompose the susceptibility into the contributions from each band. Here, we propose a scheme to perform this decomposition using the modified Wannier functions. The derived formula nicely decomposes the susceptibility into intraband and interband contributions, and from the other aspect, into itinerant and local contributions. The validity of the formula is tested in a couple of simple models. Interestingly, it is revealed that the quality of the decomposition depends on the degree of localization of the used Wannier functions. The formula here complements another formula using Bloch functions, or the formula derived in the semiclassical theory, which deepens our understanding of the orbital magnetic susceptibility and may serve as a foundation of a better computational method. The relationship to the Berry curvature in the present scheme is also clarified.

Diamagnetic and paramagnetic Meissner effect from odd-frequency pairing in multiorbital superconductors

The Meissner effect is one of the defining properties of superconductivity, with a conventional superconductor completely repelling an external magnetic field. In contrast to this diamagnetic behavior, odd-frequency superconducting pairing has often been seen to produce a paramagnetic Meissner effect, which instead makes the superconductor unstable due to the attraction of magnetic field. In this work we study how both even- and odd-frequency superconducting pairing contributes to the Meissner effect in a generic two-orbital superconductor with a tunable odd-frequency pairing component. By dividing the contributions to the Meissner effect into intra- and inter-band processes, we find that the odd-frequency pairing actually generates both dia- and paramagnetic Meissner responses, determined by the normal-state band structure. More specifically, for materials with two electron-like (hole-like) low-energy bands we find that the odd-frequency inter-band contribution is paramagnetic but nearly canceled by a diamagnetic odd-frequency intra-band contribution. Combined with a diamagnetic even-frequency contribution, such superconductors thus always display a large diamagnetic Meissner response to an external magnetic field, even in the presence of large odd-frequency pairing. For materials with an inverted, or topological, band structure, we find the odd-frequency inter-band contribution to instead be diamagnetic and even the dominating contribution to the Meissner effect in the near-metallic regime. Taken together, our results show that odd-frequency pairing in multi-orbital superconductors does not generate a destabilizing paramagnetic Meissner effect and can even generate a diamagnetic response in topological materials.

Ultrafast laser-driven many-body dynamics and Kondo coherence collapse

Ultrafast laser pulse has provided a systematic way to inspect the dynamics of electrons in condensed matter systems. In this paper, by means of time-dependent density matrix renormalization group, we study an ultrafast laser driven Kondo lattice model, in which conduction electrons are strongly coupled with magnetically local moments. The single-particle spectral function due to strong correlation effects and photon emission in the non-equilibrium states under laser driving are calculated. We find laser field excited collective doublon-hole pairs and an associated transient melting of Kondo coherence phase, signifying the collapse of Kondo energy gap. Moreover, we show that the photon emission, induced by a strong laser field, exhibits a different intensity characteristics than in the equilibrium Kondo insulator, which could be explained by the Kondo collapse and related suppression of both intra-band and inter-band contribution in Kondo melting liquid. These theoretical insight is accessible with time- and angle-resolved photoemission spectroscopy and high-harmonic generation spectroscopy, and will stimulate the investigation of nonequilibrium dynamics and nonlinear phenomenon in heavy fermion systems.

Dynamical polarizability of graphene with spatial dispersion

We perform a detailed analysis of electronic polarizability of graphene with different theoretical approaches. From Kubo's linear response formalism, we give a general expression of frequency and wave-vector dependent polarizability within the random phase approximation. Four theoretical approaches have been applied to the single-layer graphene and their differences are on the band-overlap of wavefunctions. By comparing with the \textit{ab initio} calculation, we discuss the validity of methods used in literature. Our results show that the tight-binding method is as good as the time-demanding \textit{ab initio} approach in calculating the polarizability of graphene. Moreover, due to the special Dirac-cone band structure of graphene, the Dirac model reproduces results of the tight-binding method for energy smaller than \SI{3}{\electronvolt}. For doped graphene, the intra-band transitions dominate at low energies and can be described by the Lindhard formula for two-dimensional electron gases. At zero temperature and long-wavelength limit, with the relaxation time approximation, all theoretical methods reduce to a long-wave analytical formula and the intra-band contributions agree to the Drude polarizability of graphene. Effects of electrical doping and temperature are also discussed. This work may provide a solid reference for researches and applications of the screening effect of graphene.

Microscopic analysis of high harmonic generation in semiconductors with degenerate bands

Based on the multiband semiconductor Bloch equations a microscopic approach to high-harmonic generation in crystalline solids which is able to properly describe degenerate bands and band crossings is presented and analyzed. It is well known that numerical band structure calculations typically provide electronic wave functions with an undetermined $k$-dependent phase which results in matrix elements which contain arbitrary $k$-dependent phases. In addition, such approaches usually mix degenerate bands and bands with an energy difference smaller than the numerical precision in an arbitrary way for each point in $k$ space. These ambiguities are problematic if one considers the dynamics induced by electric fields since the matrix elements of the position operator involve a derivative of the wave functions with respect to $k$. When the light-matter interaction is described in the length gauge, the problem of arbitrary phases and degenerate subspace mixing of Bloch states is solved by adopting a smooth gauge transformation along the field direction. The results obtained within this method are validated by comparing with calculations in the velocity gauge. Although we obtain in both gauges the same overall result, the length gauge is advantageous since it converges with a smaller number of bands and thus requires significantly less numerical effort than the velocity gauge. Also a unique distinction between inter- and intraband contributions and thus an instructive physical interpretation is possible in the length gauge whereas in the velocity gauge this is unclear. The computed polarization-direction-dependent high-harmonic spectra agree well with experimental data reported for GaAs. Furthermore, it is demonstrated that, under proper conditions, the Berry curvature is largely responsible for the even-order harmonics which are polarized perpendicular to the driving field.

Polarization Flipping of Even-Order Harmonics in Monolayer Transition-Metal Dichalcogenides

We present a systematic study of the crystal-orientation dependence of high-harmonic generation in monolayer transition-metal dichalcogenides, WS 2 and MoSe 2 , subjected to intense linearly polarized midinfrared laser fields. The measured spectra consist of both odd- and even-order harmonics, with a high-energy cutoff extending beyond the 15th order for a laser-field strength around ~1 V/nm. In WS 2 , we find that the polarization direction of the odd-order harmonics smoothly follows that of the laser field irrespective of the crystal orientation, whereas the direction of the even-order harmonics is fixed by the crystal mirror planes. Furthermore, the polarization of the even-order harmonics shows a flip in the course of crystal rotation when the laser field lies between two of the crystal mirror planes. By numerically solving the semiconductor Bloch equations for a gapped-graphene model, we qualitatively reproduce these experimental features and find the polarization flipping to be associated with a significant contribution from interband polarization. In contrast, high-harmonic signals from MoSe 2 exhibit deviations from the laser-field following of odd-order harmonics and crystal-mirror-plane following of even-order harmonics. We attribute these differences to the competing roles of the intraband and interband contributions, including the deflection of the electron-hole trajectories by nonparabolic crystal bands.

Longitudinal and anomalous Hall conductivity of a general two-band model

We derive and analyze the longitudinal and the anomalous Hall conductivity for a general momentum-block-diagonal two-band model. This model captures a broad spectrum of physically very different systems including N\'eel antiferromagnetic and spiral spin density waves as well as models that involve spin-orbit interaction and are known to show topological properties. We present a complete microscopic derivation for finite temperature and constant scattering rate $\Gamma$ that is diagonal and equal, but arbitrarily large for both bands. We identify two criteria that allow for a unique and physically motivated decomposition of the conductivities. On the one hand, we distinguish intraband and interband contributions that are defined by the involved quasiparticle spectral functions. On the other hand, we distinguish symmetric and antisymmetric contributions that are defined by the symmetry under the exchange of the current and the electric field directions. The (symmetric) intraband contributions generalize the formula of standard Boltzmann transport theory, which is valid only in the clean limit (small $\Gamma$), whereas the interband contributions capture interband coherence effects beyond independent quasiparticles. We show that the symmetric interband contribution is a correction only present for finite $\Gamma$ and is controlled by the quantum metric. The antisymmetric interband contributions generalize the formula of the anomalous Hall conductivity in terms of the Berry curvature to finite $\Gamma$. We study the clean (small $\Gamma$) and dirty (large $\Gamma$) limit analytically. The connection between the presented derivation and the Bastin and Streda formalism is given. We apply our results to a Chern insulator, a ferromagnetic multi-d-orbital, and a spiral spin density wave model.

Optical and plasmonic properties of twisted bilayer graphene: Impact of interlayer tunneling asymmetry and ground-state charge inhomogeneity

We present a theoretical study of the local optical conductivity, plasmon spectra, and thermoelectric properties of twisted bilayer graphene (TBG) at different filling factors and twist angles $\theta$. Our calculations are based on the electronic band structures obtained from a continuum model that has two tunable parameters, $u_0$ and $u_1$, which parametrize the intra-sublattice inter-layer and inter-sublattice inter-layer tunneling rate, respectively. In this Article we focus on two key aspects: i) we study the dependence of our results on the value of $u_0$, exploring the whole range $0\leq u_0\leq u_1$; ii) we take into account effects arising from the intrinsic charge density inhomogeneity present in TBG, by calculating the band structures within the self-consistent Hartree approximation. At zero filling factor, i.e. at the charge neutrality point, the optical conductivity is quite sensitive to the value of $u_0$ and twist angle, whereas the charge inhomogeneity brings about only modest corrections. On the other hand, away from zero filling, static screening dominates and the optical conductivity is appreciably affected by the charge inhomogeneity, the largest effects being seen on the intra-band contribution to it. These findings are also reflected by the plasmonic spectra. We compare our results with existing ones in the literature, where effects i) and ii) above have not been studied systematically. As natural byproducts of our calculations, we obtain the Drude weight and Seebeck coefficient. The former displays an enhanced particle-hole asymmetry stemming from the inhomogeneous ground-state charge distribution. The latter is shown to display a broad sign-changing feature even at low temperatures ($\approx 5~{\rm K}$) due to the reduced slope of the bands, as compared to those of single-layer graphene.

Spin-Reorientation-Induced Band Gap in Fe_{3}Sn_{2}: Optical Signatures of Weyl Nodes.

Temperature- and frequency-dependent infrared spectroscopy identifies two contributions to the electronic properties of the magnetic kagome metal Fe_{3}Sn_{2}: two-dimensional Dirac fermions and strongly correlated flat bands. The interband transitions within the linearly dispersing Dirac bands appear as a two-step feature along with a very narrow Drude component due to intraband contribution. Low-lying absorption features indicate flat bands with multiple van Hove singularities. Localized charge carriers are seen as a Drude peak shifted to finite frequencies. The spectral weight is redistributed when the spins are reoriented at low temperatures; a sharp mode appears suggesting the opening of a gap due to the spin reorientation as the sign of additional Weyl nodes in the system.

Electron energy loss spectroscopy of bulk gold with ultrasoft pseudopotentials and the Liouville-Lanczos method

The implementation of ultrasoft pseudopotentials into time-dependent density-functional perturbation theory is detailed for both the Sternheimer approach and the Liouville-Lanczos (LL) method, and equations are presented in the scalar relativistic approximation for periodic solids with finite momentum transfer q. The LL method is applied to calculations of the electron energy loss (EEL) spectrum of face-centered cubic bulk Au both at vanishing and finite q. Our study reveals the richness of the physics underlying the various contributions to the density fluctuation in gold. In particular, our calculations suggest the existence in gold of two quasi-separate 5d and 6s electron gasses, each one oscillating with its own frequency at resp. 5.1 eV and 10.2 eV. We find that the contribution near 2.2 eV comes from 5d to 6s interband transitions modified by the intraband contribution to the real part of the dielectric function, which we call a mixed excitation.