Electron-phonon Interaction Function Research Articles

Reconstruction of the Electron–Phonon Interaction Function for Superconductors Using Inhomogeneous Point-Contacts and Correction Background in Yanson Spectra

Reconstruction of the Electron–Phonon Interaction Function for Superconductors Using Inhomogeneous Point-Contacts and Correction Background in Yanson Spectra

ВОССТАНОВЛЕНИЕ ФУНКЦИИ ЭЛЕКТРОН-ФОНОННОГО ВЗАИМОДЕЙСТВИЯ В СВЕРХПРОВОДНИКАХ С ПОМОЩЬЮ НЕОДНОРОДНЫХ МИКРОКОНТАКТОВ И КОРРЕКЦИЯ ФОНА В СПЕКТРАХ ЯНСОНА

The application of inhomogeneous niobium point-contacts in the superconducting stata for reconstructing the electron-phonon interaction function is considered. The method is based on the use of the nonlinearity of current-voltage curve, which is due to the inelastic processes of suppressing excess point contact current when nonequilibrium phonons are scattered from the electrons undergoing Andreev reflection. A new model of background occurrence in point-contact Yanson spectra and some ways to correct this background are proposed.

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.

The unbalanced phonon-induced superconducting state on a square lattice beyond the static boundary

The paper presents our verification of induction of the superconducting state on a square lattice by the linear electron–phonon interaction for values of the unbalance parameter (γ=λD∕λND) less than γC=0.42. Symbols λD and λND denote the values of the coupling constant in the diagonal and the non-diagonal channel of the self-energy. Calculations were carried out using the Eliashberg equations, in which the order parameter (Δkiωn) and the wave function renormalising factor (Zkiωn) depend explicitly on the Matsubara frequency (ωn) and the wave vector (k). The value of γC in the static boundary (Δkiωn→Δkiωn=1), equal to (0.93), is significantly greater than the obtained limit value of 0.42. Values of the thermodynamic functions of the superconducting state determined for our assumptions are significantly different from the values calculated in accordance with the BCS theory. The results were obtained for the electron–phonon interaction function explicitly dependent on the momentum transfer between electron states.

Recovery of the electron–phonon interaction function in superconducting tantalum ballistic contacts

The experimentally observed nonlinearities of the current–voltage characteristics (CVCs) of tantalum-based point homo- and heterocontacts in both normal and superconducting states related to electron–phonon interaction (EPI) were analyzed. It was taken into account that additional nonlinearity of CVCs arising upon contact transition to the superconducting state (superconducting spectral component) is formed not only near the constriction in the region roughly equal to the contact diameter (as is the case for the normal state, and as predicted theoretically for the superconducting state), but also in a markedly larger region that is about the size of the coherence length. In this case, a considerable role in the formation of this superconducting component is played by nonequilibrium phonons with low group velocity, which account for the experimentally observed sharpening of the phonon peaks in the EPI spectra (the second derivatives of the CVCs) during the superconducting transition of the contacts, instead of the theoretically expected peak broadening (spreading), and for the increase in the superconducting contribution to the point contact spectrum in the low and medium energy regions. The high-energy part of the EPI spectrum changes much less significantly during the superconducting transition, which is attributable to suppression of the excess contact current by nonequilibrium quasi-particles. A detailed procedure was proposed for the recovery of the EPI spectral function from the point contact spectrum contribution (the second derivative of the CVC) that arises during the superconducting transition of one or both contacting metals.

Point-contact spectroscopy of electron-phonon interaction in superconductors

The possibility to reconstruct the electron-phonon interaction (EPI) function was demonstrated for S–c–N and S–c–S point contacts using the superconducting inelastic contribution to the excess current caused by Andreev reflection processes. Superconductors with both weak (Sn, Al) and strong (Pb, In) EPI were considered. It was shown that in the latter case it is necessary to account for the elastic component of current which is related to the frequency dependence of the superconducting energy gap arising due to electron-phonon renormalization of the energy spectrum of the superconductor.

Reconstruction of the electron-phonon interaction function in Ta, 2H-NbSe2 and MgB2 from spectra of S–c–N microcontacts

Using Ta, 2H-NbSe2 and MgB2 as an example it is shown that it is possible to reconstruct qualitatively a function of the electron-phonon interaction from microcontact spectra in a superconducting state. The limits and the restrictions of this method are also shown. The results obtained are compared with available literature data.

Electron-phonon interaction function in the layered dichalcogenide 2Ha-TaSe2

Point-contact spectroscopy is used to investigate experimentally the electron-phonon interaction spectrum in the layered quasi-two-dimensional dichalcogenide 2Ha-TaSe2. The measurements are performed on 2Ha-TaSe2∕Cu heterocontacts. The point-contact spectra reflecting the effects of the electron-phonon interaction are recorded in the spectral regime of current flow and delocalization of the electronic states near point contacts for small momentum free-path lengths of electrons. The electron-phonon interaction function in this compound is determined for the first time. Calculations of important integral parameters of the electron-phonon system of the experimental material confirm the good reproducibility of the results.

Point-contact spectrum of the electron-phonon interaction in mercury

A method is proposed for creating mercury point-contacts for point-contact spectroscopy. In this method point-contacts are produced at low temperature between mercury-coated metal substrate electrodes. The coatings are produced by exposing the electrodes to mercury at room temperature. The nonlinear part of the normal-state resistance of the contacts is studied experimentally, after which the point-contact electron-phonon interaction function is reconstructed. The experimental results are in good agreement with existing data on the tunneling effect in superconductors. Specifically, good agreement obtains for the positions of the main peak of the electron-phonon interaction function, the maximum phonon frequency, and the numerical values of the average and rms phonon frequencies.

Low Temperature Properties and Superconductivity of LuB12

We have investigated the low temperature properties of LuB12 by measuring its magnetic susceptibility, heat capacity, and electrical resistivity, as well as by point-contact spectroscopy using both the spear-anvil type technique and mechanically controllable break junctions. Our specific heat measurements and point - contact spectroscopy results indicate that LuB12 is a simple weak-coupling BCS-type superconductor with TC ≈ 0.4 K, a superconducting energy gap of 2 Δ ≈ 0.12 meV, and a very small critical field BC ≈ 1 mT. From the dU/dI(U) characteristics in the superconducting state, the energy gap 2Δ, the critical current IC and the Andreev-reflection excess current Iex as a function of normal-state point contact resistance RN have been determined. At low RN all three parameters are strongly suppressed, possibly due to the self-magnetic field. At contacts with large RN the model of resistively and capacitively shunted Josephson junctions (RCSJ) allowed us to estimate the superconducting current plasma frequency and the Josephson coupling energy. Moreover, from the d2U/d I2(U) spectra in the normal state the (point-contact) electron-phonon interaction function and the characteristic phonon energies of LuB12 have been determined.

Point-contact spectroscopy of LuB12

We have investigated LuB12 point-contacts between 0.1 K to 4.2 K using both the spear-anvil type technique and mechanically controllable break junctions. Our results of the superconducting energy gap 2Δ0≈0.12 meV and the critical current indicate that LuB12 is a BCS-type superconductor. From the d2U/dI2(U) spectra in the normal state the (point-contact) electron-phonon interaction function of LuB12 has been determined.

Spectroscopy of the electron–phonon interaction in the layered two-dimensional dichalcogenide 1T–VSe2

The vibrational spectra of the layered two-dimensional transition-metal dichalcogenide 1T–VSe2 are investigated by the methods of point-contact and Raman spectroscopy. The measured point-contact spectra and the Raman scattering spectra contain features that coincide in position and relative intensity. Various regimes of current passage (ballistic, diffusive, and thermal) in 1T–VSe2/Cu point contacts are investigated. Both direct and inverse point-contact spectra are recorded, the former demonstrating the effect of the electron–phonon interaction in 1T–VSe2 and the latter reflecting the destruction of localization of the electronic states in the region near the contact, which leads to growth of the contact conductance. A study of the point contacts in the regime of small energy and momentum mean free paths of the electrons reveals nonlinearities caused by a phase transition of the material to a state with a charge density wave. The point-contact electron–phonon interaction function, previously unknown for this compound, is recovered from the data, and the values of the mean and rms phonon frequencies in 1T–VSe2 are calculated. An estimate of the Debye temperature is made.

Reconstruction of electron-phonon interaction function from temperature dependence of electrical resistivity for metals

The determination of the electron phonon interaction function (EPIF) from the temperature dependence of the electrical resistivity (TDER) for metals within a selected moderate temperature range is numerically demonstrated based on the general theory of the amplitude phase retrieval problem and an iterative algorithm. From the model calculation, the convergent solution can be obtained; however,the profile of the recovered EPIF depends on the initial frequency distribution used in the algorithm since this inversion problem is inherently ill posed. In order to get reasonable result,it is necessary to introduce additional information about the feature of the EPIF for guiding the choice of the initial distribution. The algorithm can also furnish a robust reconstruction of EPIF from TDER contaminated with random noise. It means that this algorithm is relatively stable and insensitive to external perturbation; therefore in a sense, the presented algorithm overcomes the ill posedness of the inversion problem.

Point-contact spectroscopy of YNi5

Abstract PC spectra of YNi 5 intermetallic compound homocontacts and heterocontacts with Cu have been measured in the ballistic regime. Phonon maxima at characteristic energies of 4, 8, 18 and 30 meV have been observed in the electron-phonon interaction function. The phonon parts of PC spectra of RENi 5 (RE  La, Ce, Pr, Sm, Y) compounds with isomorphous lattice structure are similar which corresponds to small differences between lattice constants of these materials.

On inversion of normal metal tunnelling data

A short summary of the theoretical and experimental status of elastic tunnelling between normal metals is given. Methods for the determination of the electron-phonon interaction function, alpha 2F( omega ), from the conductance. sigma ( omega ), of a normal metal tunnel junction are presented and their performance is discussed. A complete list of sum rules applicable to the inversion procedures is given for the first time. Elimination of the thermal smearing of the conductance data with the help of the fast Fourier transform algorithm and the regularization method is described. The possibility of the existence of 'interference' between the elastic and inelastic parts of the tunnelling current is discussed for conductivity data of Pb and Sn.

POINT-CONTACT SPECTROSCOPY OF THE ELECTRON-PHONON INTERACTION IN SmNi5

The measured point-contact (PC) spectra of the heterocontact between oriented hexagonal single crystal of SmNi 5 and Cu in ballistic and thermal regime are presented. The PC spectrum (the second derivative of I–V characteristic - d 2 I/dV 2( eV )) is directly proportional to the electron-quasiparticle interaction (EQI) function. The absence of the magnetic field effect on the energy position of the characteristic peaks until 10T is the confirmation of the phonon origin. The phonon part of the EQI function is similar to the electron-phonon interaction function for LaNi 5.

Investigation of the energy gap and phonon structure in tunneling junctions of the Bi 2Sr 2CaCu 2O 8 single crystal cleavages

Tunneling junctions of the point-contact type of Bi 2 Sr 2 CaCu 2 O 8 single crystals have been studied, a natural oxide of aluminium electrode serving as a tunneling barrier. The ratio 2Δ/ kT c =5–6 was obtained in this investigation. A phenomenological model was applied for describing the behaviour of tunneling characteristics. From the numerical calculations and on the basis of this model, the phonon singularities in tunneling characteristics were treated by the standard program for the solutions of the Eliashberg equations and the electron-phonon interaction function, α 2 ( ω ) F ( ω ), was found.

Effect of coherent twin boundaries on the electron-phonon interaction in single crystals of tin

Electron-phonon interaction near the twinning plane in a single crystal of tin in normal state is studied experimentally using the method of the point contact spectroscopy. Considerable softening of the electron-phonon interaction function is observed. The order of magnitude of the increase of superconducting transtion temperature near the twinning plane is estimated.

Far-infrared properties of high T c superconductors

The results of calculations of the optical conductivity σ( ω, T) and reflectivity R( ω, T) are presented. These calculations were carried out in the frame of the Eliashberg theory, the function of electron-phonon interaction being obtained from tunneling measurements. The obtained frequency and temperature dependencies have a rather good agreement with experimental data.

Point-contact spectroscopy of the electron-phonon interaction in LaNi5

The electron-phonon interaction in LaNi5 is studied by point-contact spectroscopy. The spectrum corresponding to the electron-phonon interaction function g (the phonon density of states modulated by the matrix element of the electron-phonon interaction) is found. The functiong is used to analyze the point-contact spectra of PrNi5, where besides the electron-phonon contribution there is also an interaction between the conduction electrons and the crystal electric field levels of the Pr3+ ion.