Debye Frequency Research Articles

Electronic structure and phonon transport properties of HfSe2 under in-plane strain and finite temperature

The electronic structure and phonon transport properties of HfSe2 under different in-plane strains at finite temperatures are systematically investigated by combining first-principles calculations with machine learning force field molecular dynamics simulations. Within a strain range of -3% to 3%, the electronic band gap value of HfSe2 varies between 0.39 and 0.87 eV. Under compressive strain, the conduction band minimum moves towards the Fermi level, with the distribution of electrons near the valence band maximum becoming more delocalized. This will reduce the scattering of electrons during the transport process, helping to improve the carrier mobility. Under tensile strain, the localization of the density of states near the valence band maximum is strengthened, accompanied by enhanced metallic properties of the Hf-Se bonds, which facilitates the enhancement of the thermoelectric power factor. Both compressive and tensile strains intensify the coupling of phonon normal modes with phonon scattering, and elevating the temperature amplifies this impact. The anharmonicity-induced reduction in phonon frequencies is especially pronounced for modes in the vicinity of the Debye frequency. This not only curtails the phonon lifetimes but also diminishes the lattice thermal conductivity through the enhancement of vibrational coupling among optical branches and the reduction of the group velocity in acoustic branches. These results demonstrate the synergistic effects of strain and temperature on the electronic structure and phonon transport of HfSe2.

Development of size and shape dependent model for various thermodynamic properties of nanomaterials

The models developed in this work are used to study various thermodynamic properties of nanomaterials. A better agreement between theory and experiment indicates the validity of the proposed model. Since the model is simple and easy to use, we extend the theory to understand, how the thermodynamic properties of different nanomaterials depend on size and shape. The results were compared with previous theoretical work and experimental data. We have concluded that the model predicts a better agreement with previous theoretical work and experimental studies. Current research produces thermodynamic models for the Debye frequency, melting entropy, melting enthalpy, and Einstein temperature. To the best of our knowledge, such models are not yet available in the literature that works well.

Pressure and non-ideal axial ratio effects on thermodynamic properties of hexagonal close-packed Mg and Zn metals

ABSTRACT The Debye model has been developed to study the pressure dependence of the extended X-ray absorption fine structure Debye–Waller factor, the Debye frequency and temperature of hexagonal close-packed (hP2) metals. The effects of the non-ideal axial ratio c/a of hP2 structure on these thermodynamic quantities at high pressures have also been considered. Additionally, based on the combination of the Debye model and the Lindemann melting law, we derive the analytic expression of melting temperature of hP2 metals as a function of pressure. Numerical calculations have been implemented for Mg and Zn metals up to 20 and 50 GPa, respectively. We have shown that Debye frequency and temperature, as well as melting temperature of these two metals increase robustly with pressure and non-ideal axial ratio plays important role in these thermodynamic quantities. The remarkable consistency observed between our calculations and various experimental results validates the reliability of the currently presented melting curve. Meanwhile, at high pressure non-ideal axial ratio gives a small contribution to pressure-dependent Debye–Waller factor of Mg (up to 20 GPa) and Zn (beyond 20 GPa), and can be safely neglected in the suggested pressure range.

An equation of state based on the scaling properties of vibrational spectra at high pressure

Inter-atomic forces control vibrational properties and elastic moduli of a solid material. Based on first-principle calculations, it has been reported that, for elemental solids, the Debye frequency scales linearly with density to high accuracy. Combining this with other scaling properties of vibrational frequencies at high pressure, a new equation of state is presented. The proposed equation of state is tested against available experimental data for various kinds of solids at high pressure and room temperature. The quality of description of the compressional behavior of solids by our proposed equation of state is, for many cases, comparable to or better than that with the Vinet EOS.

Oscillatory electro-magneto-kinetics of confined-Stokes-second-problem micro-flows

We semi-analytically investigate the electro-magneto-hydrodynamics of time periodic electroosmotic flow of a Newtonian electrolyte through microchannels with oscillating boundaries, resembling a confined-Stokes-second-problem type system. Herein, a constant orthogonal magnetic field and a constant transverse electric field have been used along with the driving time periodic electric field to have better control over mixing in the microchannel or to augment the pumping. The Poisson–Boltzmann equation has been solved with Debye–Hückel linearization for the thin electric double layer to obtain the electric potential distribution. We determine the flow field for low Hartmann number (Ha) cases by the regular perturbation method. Furthermore, Laplace transformation has been used to solve the flow field for each order in the obtained perturbation series. We have obtained the solution of flow field up to O(Ha) and found an excellent match with the complete numerical solution for our range of Ha. The dependence of flow field on dimensionless parameters, such as Ha, electrokinetic number (M), and Womersley number (Wo), has been discussed thoroughly, where Ha and M are functions of the strength of applied magnetic field and transverse electric field, respectively, and Wo is the function of Debye length, kinematic viscosity, and frequency of the time periodic electric field. Interestingly, for large values Wo, we find wave like motion in the flow field, which induces vorticity as well as better mixing caliber. Additionally, we find that the interplay between Ha and M controls the mixing and modifies the flow rate according to the need. Various combinations of such parameters have been discussed to promote mixing as well as pumping for such strongly coupled microfluidic phenomena.

A criterion for strange metallicity in the Lorenz ratio

The Wiedemann-Franz (WF) law, stating that the Lorenz ratio L = κ/(Tσ) between the thermal and electrical conductivities in a metal approaches a universal constant {L}_{0}={pi }^{2}{k}_{B}^{2}/(3{e}^{2}) at low temperatures, is often interpreted as a signature of fermionic Landau quasi-particles. In contrast, we show that various models of weakly disordered non-Fermi liquids also obey the WF law at T → 0. Instead, we propose using the leading low-temperature correction to the WF law, L(T) − L0 (proportional to the inelastic scattering rate), to distinguish different types of strange metals. As an example, we demonstrate that in a solvable model of a marginal Fermi-liquid, L(T) − L0 ∝ − T. Using the quantum Boltzmann equation (QBE) approach, we find analogous behavior in a class of marginal- and non-Fermi liquids with a weakly momentum-dependent inelastic scattering. In contrast, in a Fermi-liquid, L(T) − L0 is proportional to − T2. This holds even when the resistivity grows linearly with T, due to T − linear quasi-elastic scattering (as in the case of electron-phonon scattering at temperatures above the Debye frequency). Finally, by exploiting the QBE approach, we demonstrate that the transverse Lorenz ratio, Lxy = κxy/(Tσxy), exhibits the same behavior.

Modeling Surface Vibrations and Their Role in Molecular Adsorption: A Generalized Langevin Approach.

The atomic vibrations of a solid surface can play a significant role in the reactions of surface-bound molecules, as well as their adsorption and desorption. Relevant phonon modes can involve the collective motion of atoms over a wide array of length scales. In this paper, we demonstrate how the generalized Langevin equation can be utilized to describe these collective motions weighted by their coupling to individual sites. Our approach builds upon the generalized Langevin oscillator (GLO) model originally developed by Tully. We extend the GLO by deriving parameters from atomistic simulation data. We apply this approach to study the memory kernel of a model platinum surface and demonstrate that the memory kernel has a bimodal form due to coupling to both low-energy acoustic modes and high-energy modes near the Debye frequency. The same bimodal form was observed across a wide variety of solids of different elemental compositions, surface structures, and solvation states. By studying how these dominant modes depend on the simulation size, we argue that the acoustic modes are frozen in the limit of macroscopic lattices. By simulating periodically replicated slabs of various sizes, we quantify the influence of phonon confinement effects in the memory kernel and their concomitant effect on simulated sticking coefficients.

Prediction of nodal-line fermion and phonon-mediated superconductivity in bilayer α-borophene

The electron deficiency of boron allows the formation of a variety of monolayer or few-layer two-dimensional structures (borophenes) with interesting physical properties. Recent experiments have also confirmed that interlayer covalent bonding makes the bilayer structure more stable than the monolayer. In this work based on α-borophene, we propose three free-stranding bilayer structures with dynamic stability. In these three metallic structures, the electronic band crossings around Fermi level form nodal lines. All these structures also exhibit strong electron-phonon couplings. The Bardeen–Cooper–Schrieffer superconducting critical temperature T c of the type-II structure went as high as 28.2 K, which was further improved to 32.0 K by the enhancement effect of Li adatom at the Debye frequency. However, no increase in critical temperature was observed in other Li-doping cases. Specifically, Li intercalation inside the bilayer causes a significant abrupt decrease in the critical temperature of type-I structure. Our results indicated that the bilayer borophene would be an ideal platform for the coexistence of topological electronic states and superconducting states.

Temperature effects on thermodynamic properties of rare-earth ytterbium

Thermodynamic quantities (including Debye temperature and frequency, atomic mean-square displacement, specific heats at constant volume and constant pressure, linear thermal expansion coefficient, and total entropy) of face-centered cubic ytterbium metal have been studied by means of the statistical moment method in statistical mechanics. This theoretical approach allows us to calculate these thermodynamic quantities taking into account the anharmonicity of lattice vibrations. Numerical calculations for ytterbium have been conducted in temperature range from 0 K to 1100 K using Lennard-Jones potential to describe the interaction between ytterbium atoms. Our derived results are compared with those of mean-field potential approach as well as previous experimental data showing the good agreement. We have shown that the atomic mean-square displacement contains the zero-point vibration (quantum effect) at low temperature. At high temperature it changes linearly with respect to temperature. Furthermore, our theoretical calculations have also pointed out the anharmonic contribution to specific heat at constant volume of ytterbium metal is negative with temperature. This research presents an effective statistical approach to study temperature effects on thermodynamic quantities of materials.

The two-gap BCS model in the large-N approximation within a field-theory approach

We study the continuum version of the two-gap BCS model in (3 + 1)D within the large-N approximation. We calculate the effective potential of the model which depends on two independent energy gaps σ and Δ, where σ describes the Cooper pair made of electrons that belong to the same internal symmetry whereas Δ describes the Cooper pair of electrons that have a different internal symmetry. The effective potential is calculated by considering that the Debye frequency is an ultraviolet cutoff Λ, which is meant to describe the physical lattice of 3D superconductors. Our main result shows that the extra gap provides a possible inter-band phase transition that may be either a stable or metastable phase, depending on the competion between the coupling constants of the model. We also derive the critical temperature below which the phases may be observed.

Weyl conjecture and thermal radiation of finite systems

In this work, corrections for the Weyl law and Weyl conjecture in d dimensions are obtained and effects related to the polarization and area term are analyzed. The derived formalism is applied on the quasithermodynamics of the electromagnetic field in a finite d-dimensional box within a semi-classical treatment. In this context, corrections to the Stefan–Boltzmann law are obtained. Special attention is given to the two-dimensional scenario, since it can be used in the characterization of experimental setups. Another application concerns acoustic perturbations in a quasithermodynamic generalization of Debye model for a finite solid in d dimensions. Extensions and corrections for known results and usual formulas, such as the Debye frequency and Dulong–Petit law, are calculated.

Superconductivity out of a non-Fermi liquid: Free energy analysis

In this paper, we present in-depth analysis of the condensation energy $E_c$ for a superconductor in a situation when superconductivity emerges out of a non-Fermi liquid due to pairing mediated by a massless boson. This is the case for electronic-mediated pairing near a quantum-critical point in a metal, for pairing in SYK-type models, and for phonon-mediated pairing in the properly defined limit, when the dressed Debye frequency vanishes. We consider a subset of these quantum-critical models, in which the pairing in a channel with a proper spatial symmetry is described by an effective $0+1$ dimensional model with the effective dynamical interaction $V(\Omega_m) = {\bar g}^\gamma/|\Omega_m|^\gamma$, where $\gamma$ is model-specific (the $\gamma$-model). In previous papers, we argued that the pairing in the $\gamma$ model is qualitatively different from that in a Fermi liquid, and the gap equation at $T=0$ has an infinite number of topologically distinct solutions, $\Delta_n (\omega_m)$, where an integer $n$, running between $0$ and infinity, is the number of zeros of $\Delta_n (\omega_m)$ on the positive Matsubara axis. This gives rise to the set of extrema of $E_c$ at $E_{c,n}$, of which $E_{c,0}$ is the global minimum. The spectrum $E_{c,n}$ is discrete for a generic $\gamma <2$, but becomes continuous at $\gamma = 2-0$. Here, we discuss in more detail the profile of the condensation energy near each $E_{c,n}$ and the transformation from a discrete to a continuous spectrum at $\gamma \to 2$. We also discuss the free energy and the specific heat of the $\gamma$-model in the normal state.

Interaction bulk-boundary relation and its applications towards symmetry breaking and beyond

In this article, we propose a simple but general scaling relation between interactions in a gapped bulk topological matter and gapless interacting surface states. We explicitly illustrate such a generic bulk-boundary relation (BBR) for a few specific interactions in a topological quantum matter, where we can perform dimensional reduction of a microscopic bulk theory to project out interacting surfaces. We have examined renormalization effects of the gapped bulk fermions on the interacting topological surface fermions. As simple applications, we utilize effective interacting quantum fields implied by BBR to explore feasibility of routes to various fascinating emergent phenomena on surfaces including emergent Majorana fermions induced by spontaneous symmetry breaking. We obtain sufficient conditions for these interacting surface phenomena to take place. We have also found that for given bulk electron-phonon interactions and when ${\mathrm{\ensuremath{\Omega}}}_{D}\ensuremath{\ge}m$, the phonon-mediated interactions on the surface are strongest if the bulk Debye frequency ${\mathrm{\ensuremath{\Omega}}}_{D}$ matches $m$, the mass gap of the topological matter.

Heuristic bounds on superconductivity and how to exceed them

What limits the value of the superconducting transition temperature (Tc) is a question of great fundamental and practical importance. Various heuristic upper bounds on Tc have been proposed, expressed as fractions of the Fermi temperature, TF, the zero-temperature superfluid stiffness, ρs(0), or a characteristic Debye frequency, ω0. We show that while these bounds are physically motivated and are certainly useful in many relevant situations, none of them serve as a fundamental bound on Tc. To demonstrate this, we provide explicit models where Tc/TF (with an appropriately defined TF), Tc/ρs(0), and Tc/ω0 are unbounded.

Thermal conduction in a densified oxide glass: Insights from lattice dynamics

Thermal conductivity is an important property of oxide glasses, but its structural origins remain largely unknown. Here, we provide detailed modal information on thermal conductivity in a calcium aluminosilicate glass by relying on recent advances in lattice dynamics methods. We probe various structural features using molecular dynamics simulations by densifying the glass at pressures up to 100 GPa and studying the vibrational, mechanical, and thermal properties. We demonstrate good agreement between these simulations and complementary experiments, both of which indicate significant pressure-induced alteration of mechanical moduli, vibrational density of states, boson peak behavior, and thermal conductivity. We also find an intriguing correlation between the boson peak frequency and the total thermal conductivity in both the current glass series and a lithium borate glass series reported in literature. This correlation scales with the Debye frequency, suggesting that both parameters are associated with the transformation of the elastic medium under pressure.

Equation of state, thermoelastic properties and melting curves of some intermetallic compounds LiBC, MgB2 and TiB2

The equation of state based on the approximation of Saxena et al. has been used to obtain thermoelastic properties such as the pressure-volume-temperature relationship, bulk modulus and its pressure derivative for some intermetallic compounds viz. LiBC, MgB2 and TiB2 up to a pressure of 200 GPa and temperature up to 2000 K. The model for density dependence of Debye frequency recently developed by Roy and Sarkar is used in the present study to determine melting curves of intermetallic compounds with the help of the Lindemann law of melting. The melting slope for TiB2 is found to be much lower than the melting slopes for LiBC and MgB2. The models used in the present study for determining thermoelastic properties and melting curves are based on simple analytical formulations. They are capable of making rapid estimations of the studied properties.

Incoherent excitation of coherent Higgs oscillations in superconductors

We investigate theoretically the excitation of Higgs oscillations of the order parameter in superconductors by incoherent short pulses of light with frequency much larger than the superconducting gap. The excitation amplitude of the Higgs mode is controlled by a single parameter which is determined by the total number of quasiparticles excited by the pulse. This fact can be traced back to the universality of the shape of the light-induced quasiparticle cascade at energy below the Debye frequency and above the gap.

Low thermal conductivity in franckeite heterostructures.

Layered crystals are known to be good candidates for bulk thermoelectric applications as they open new ways to realise highly efficient devices. Two dimensional materials, isolated from layered materials, and their stacking into heterostructures have attracted intense research attention for nanoscale applications due to their high Seebeck coefficient and possibilities to engineer their thermoelectric properties. However, integration to thermoelectric devices is problematic due to their usually high thermal conductivities. Reporting on thermal transport studies between 150 and 300 K, we show that franckeite, a naturally occurring 2D heterostructure, exhibits a very low thermal conductivity which combined with its previously reported high Seebeck coefficient and electrical conductance make it a promising candidate for low dimensional thermoelectric applications. We find cross- and in-plane thermal conductivity values at room temperature of 0.70 and 0.88 W m-1 K-1, respectively, which is one of the lowest values reported today for 2D-materials. Interestingly, a 1.77 nm thick layer of franckeite shows very low thermal conductivity similar to one of the most widely used thermoelectric material Bi2Te3 with the thickness of 10-20 nm. We show that this is due to the low Debye frequency of franckeite and scattering of phonon transport through van der Waals interface between different layers. This observation open new routes for high efficient ultra-thin thermoelectric applications.

Room-temperature superconductivity in boron- and nitrogen-doped lanthanum superhydride

Recent theoretical and experimental studies of hydrogen-rich materials at megabar pressures (i.e., >100 GPa) have led to the discovery of very high-temperature superconductivity in these materials. Lanthanum superhydride LaH$_{10}$ has been of particular focus as the first material to exhibit a superconducting critical temperature (T$_c$) near room temperature. Experiments indicate that the use of ammonia borane as the hydrogen source can increase the conductivity onset temperatures of lanthanum superhydride to as high as 290 K. Here we examine the doping effects of B and N atoms on the superconductivity of LaH$_{10}$ in its fcc (Fm-3m) clathrate structure at megabar pressures. Doping at H atomic positions strengthens the H$_{32}$ cages of the structure to give higher phonon frequencies that enhance the Debye frequency and thus the calculated T$_c$. The predicted T$_c$ can reach 288 K in LaH$_{9.985}$N$_{0.015}$ within the average high-symmetry structure at 240 GPa.

EXAFS Debye-Waller Factors of B2-FeAl Alloys

This work develops the anharmonic correlated Debye model to study the temperature-dependent extended X-ray absorption fine structure (EXAFS) Debye-Waller factors (DWFs) of B2-FeAl alloys. We derived the analytical expressions of the EXAFS DWF and Debye frequency as functions of temperature. Numerical calculations were performed for Fe1-yAly alloys with various Al concentration (y = 0.35, 0.40, 0.45 and 0.50) in which Fe-Al alloys still maintained B2 structure. The good agreement between our theoretical results with previous data verifies our developed theory. Our calculations show that DWFs of Fe1-yAly alloys increase robustly when temperature and/or Al concentration in Fe1-yAly alloys increase. The increasing of DWF will cause the reduction of the amplitude of EXAFS.