Stoichiometric near room-temperature superconductors (i.e., $H_3S$ and $LaH_{10}$) exhibit so high ground state upper critical field, $B_{c2}(0)>100 T$, that the magnetic phase diagram in these materials cannot be measured in non-destructive experiments. However, recently, Semenok et al (arXiv2203.06500) proposed the idea to explore full magnetic phase diagram in NRTS samples in which the superconducting order parameter is suppressed by the magnetic element doping. If the element is uniformly distributed in the material, then the theory of the electron-phonon mediated superconductivity predicts the suppression of the order parameter in three-dimensional s-wave superconductor. Semenok et al (arXiv2203.06500) experimentally proved this idea by substituting La with the magnetic rare earth Nd in the $La_{1-x}Nd_{x}H_{10-y}$. As a result, $T_c$ in the $La_{1-x}Nd_{x}H_{10-y}$ (x=0.09) decreases to Tc~120 K, and the upper critical field decreases to $B_{c2}(T=41 K)=55 T$. While the exact hydrogen content should be further established in the $La_{1-x}Nd_{x}H_{10-y}$ (because similar $T_c$ suppression was observed in hydrogen deficient $LaH_{10-y}$ reported by Drozdov et al (2019 Nature 569 528)), a significant part of the full magnetic phase diagram for $La_{1-x}Nd_{x}H_{10-y}$ (x=0.09) was measured. Here we analyzed reported Semenok et al (arXiv2203.06500) data for $La_{1-x}Nd_{x}H_{10-y}$ (x=0.09) compressed at P=180 GPa and deduced: (a) Debye temperature, $T_θ=1156 K$; (b) the electron-phonon coupling constant, $λ_{e-ph}=1.65$; (c) the ground state superconducting energy gap, $Δ(0)=20.2 meV$; (d) the gap-to-transition temperature ratio, $2Δ(0)/k_BT_c=4.0$; and (e) the relative jump in specific heat at $T_c$, $ΔC/C=1.68$. The deduced values indicate that $La_{1-x}Nd_{x}H_{10-y}$ (x=0.09; P=180 GPa) is moderately strong coupled s-wave superconductor.
The primary mechanism governing the emergence of near-room-temperature superconductivity in superhydrides is widely accepted to be the electron-phonon interaction. If so, the temperature dependent resistance, R(T), in these materials should obey the Bloch-Grüneisen equation, where the power-law exponent, p, should be equal to the exact integer value of p=5. On the other hand, there is a well-established theoretical result that pure electron-magnon interaction should be manifested by p=3, and p=2 is the value for pure electron-electron interaction. Here we aimed to reveal the type of charge car…
Satterthwaite and Toepke (1970 Phys. Rev. Lett. 25 741) discovered that Th4H15-Th4D15 superhydrides are superconducting but exhibit no isotope effect. As the isotope effect is a fundamental prediction of electron-phonon mediated superconductivity described by Bardeen, Cooper, and Schrieffer (BCS) its absence alludes to some other mechanism. Soon after this work, Stritzker and Buckel (1972 Zeitschrift für Physik A Hadrons and nuclei 257 1-8) reported that superconductors in the PdHx-PdDx system exhibit the reverse isotope effect. Yussouff et al (1995 Solid State Communications 94 549) extended …
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 superc…
Hydrogen-rich superhydrides are promising high-Tc superconductors, with superconductivity experimentally observed near room temperature, as shown in recently discovered lanthanide superhydrides at very high pressures, e.g. LaH10 at 170 GPa and CeH9 at 150 GPa. Superconductivity is believed to be closely related with the high vibrational modes of the bound hydrogen ions. Here we study the limit of extreme pressures (above 200 GPa) where lanthanide hydrides with large hydrogen content have been reported. We focus on LaH16 and CeH16, two prototype candidates for achieving a large electronic contr…
Superhydrides have complex hydrogenic sublattices and are important prototypes for studying metallic hydrogen and high-temperature superconductors. Encouraged by the results on LaH10, in consideration of the differences between La and Pr, Pr-H system is especially worth studying because of the magnetism and valence-band f-electrons in element Pr. Here we successfully synthesized praseodymium superhydrides (PrH9) in laser-heated diamond anvil cells. Synchrotron X-ray diffraction (XRD) analysis demonstrated the presence of previously predicted F43m-PrH9 and unexpected P63/mmc-PrH9 phases. Moreov…
We study the impact of a time-dependent external driving of the lattice phonons in a minimal model of a BCS superconductor. Upon evaluating the driving-induced vertex corrections of the phonon-mediated electron-electron interaction, we show that parametric phonon driving can be used to elevate the critical temperature $T_c$, while a dipolar phonon drive has no effect. We provide simple analytic expressions for the enhancement factor of $T_c$. Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction also shows that phonon anharmonicities further amplify $T_c$. Our results hol…
A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the renormalization approach. The effective electron-electron interaction for Cooper pairs does not contain any singularities. Furthermore, it is found that phonon-induced particle-hole excitations only contribute to the attractive electron-electron interaction if their energy difference is smaller than the phonon energy.
Room temperature superconductivity has been achieved under high pressure in an organically derived carbonaceous sulfur hydride with a critical superconducting transition temperature (Tc) of 288 kelvin. This development is part of a new class of dense, hydrogen rich materials with remarkably high critical temperatures. Metal superhydrides are a subclass of these materials that provide a different and potentially more promising route to very high Tc superconductivity. The most promising binary metal superhydrides contain alkaline or rare earth elements, and recent experimental observations of La…
The discoveries of high-temperature superconductivity in H3S and LaH10 have excited the search for superconductivity in compressed hydrides. In contrast to rapidly expanding theoretical studies, high-pressure experiments on hydride superconductors are expensive and technically challenging. Here we experimentally discover superconductivity in two new phases,Fm-3m-CeH10 (SC-I phase) and P63/mmc-CeH9 (SC-II phase) at pressures that are much lower (<100 GPa) than those needed to stabilize other polyhydride superconductors. Superconductivity was evidenced by a sharp drop of the electrical resistanc…
The use of high pressure to realize superconductivity in the vicinity of room temperature has a long history, much of it focused on achieving this in hydrogen rich materials. This paper provides a brief overview of the work presented at this May 2018 conference, together with background on motivation and techniques, the theoretical predictions of superconductivity in lanthanum hydride, and the subsequent experimental confirmation. Theoretical calculations using density functional based structure search methods combined with BCS type models predicted a new class of dense, hydrogen rich material…
We theoretically study the pump-probe response of nonequilibrium BCS superconductors coupled to optical phonons. For ultrashort pump pulses a nonadiabatic regime emerges, which is characterized by oscillations of the superconducting order parameter as well as by the generation of coherent phonons. Using the density-matrix formalism, we compute the pump-probe response in the nonadiabatic regime of the coupled Bogoliubov quasiparticle-phonon system and determine the signatures of the order parameter and of the phonon oscillations in the pump-probe conductivity. We find that the nonadiabatic dyna…
The isotope effect in the superconducting transition temperature is anomalous if the isotope coefficient $α<0$ or $α>1/2$. In this work, we show that such anomalous behaviors can naturally arise within the Bardeen-Cooper-Schrieffer framework if both phonon and non-phonon modes coexist. Different from the case of the standard Eliashberg theory (with only phonon) in which $α\le1/2$, the isotope coefficient can now take arbitrary values in the simultaneous presence of phonon and the other non-phonon mode. In particular, most strikingly, a pair-breaking phonon can give rise to large isotope coeffi…
We systematically explore the exquisiteness of Bardeen-Cooper-Schriefer(BCS) theory where the BCS-type electron-phonon interaction is unambiguously reinforced as the only viable superglue in cuprate superconductors because phonon-induced scattering is effectively nil for Cooper pairs (in its original form), and also phonons are never required to Bose-condense. Here, we prove that (i) the Cooper-pair binding energy can be strengthened to obtain high superconductor transition temperature (Tsc) and (ii) the existence of a generalized electron-phonon potential operator that can induce the finite-t…
By recognizing the vital importance of two-hole Cooper pairs (CPs) in addition to the usual two-electron ones in a strongly-interacting many-electron system, the concept of CPs was re-examined with striking conclusions. Based on this, Bose-Einstein condensation (BEC) theory has been generalized to include not boson-boson interactions (also neglected in BCS theory) but rather boson-fermion (BF)interaction vertices reminiscent of the Frohlich electron-phonon interaction in metals. Unlike BCS theory, the GBEC model is not a mean-field theory restricted to weak-coupling as it can be diagonalized e…
The search for room-temperature superconducting materials has been at the center of modern research for decades. The recent discovery of high-temperature superconductivity, under extreme pressure in hydrogen-rich materials, is a tremendous achievement in this research front. This discovery offers a route in the search for room temperature superconductivity at ambient pressure. The superconductivity of these hydrogen-rich materials was confirmed by the observation of zero-resistance, isotope effects, effect of magnetic field, and other standard properties. However, some of the experimental feat…
In this communication we report the interplay of the normal electron-phonon (EP) interaction, dynamic Jahn-Teller (DJT) distortion and superconductivity in high temperature superconductors in presence of a static lattice strain. This model consists of a degenerate two orbital band separated by Jahn-Teller (JT) energy modified by the DJT interaction in the conduction band. The superconductivity is assumed to be s-wave type present in the same band. The interaction Hamiltonian is solved by Green's function method and a modified BCS gap equation is obtained with a modified conduction band energy …
In a superconductor electrons form pairs for which the end states of normal and umklapp scattering may overlap. This cuts electron pairing off at a phonon frequency, $ω_c$, low compared with the Debye frequency, $ω_D$. Using this insight, correct values of $2Δ/k_BT_c$ (average error 8.9%) for 12 superconductive metals, including Hg and Pb, are achieved from simple BCS formalism with an average $ω_c/ω_D$ of 0.148: Landau's idea of a Fermi liquid may cover strong-coupling superconductors. The cancellation between normal and umklapp scattering may be more important than a strong electron-phonon i…
We predict a strong enhancement of the critical temperature in a conventional Bardeen-Cooper-Schrieffer (BCS) superconductor in the presence of a bosonic condensate of exciton-polaritons. The effect depends strongly on the ratio of the cutoff frequencies for phonon and exciton-polariton mediated BCS superconductivity, respectively. We also discuss a possible design of hybrid semiconductor-superconductor structures suitable for the experimental observation of such an effect.
We investigate the dynamical effects of pairing interaction on superconductivity in BCS-BEC crossover by studying the Holstein model at half-filling where the electron-phonon coupling $g$ controls the crossover. The dynamical mean-field theory was employed in combination with the numerical renormalization group technique. The dynamical effects induce distinct features such as absenceof the dispersion back-bending of Bogoliubov quasi-particles, non-monotonous coupling dependence of the pairing gap, and the soft phonon spectrum due to the Goldstone mode of local pair phase fluctuations. Also int…
We report the results of low-temperature heat capacity measurements of the pnictide oxide superconductor BaTi$_2$Sb$_2$O doped with sodium. The temperature and field dependent heat capacity data are well described by a single-gap BCS theory. The estimated values for the normal state Sommerfeld constant, the heat capacity jump at $T_c$, and the electron-phonon coupling constant are in favor of a conventional weak coupling superconductivity mediated by electron-phonon interaction. The results are discussed with regard to and compared with recent first principle calculations.
MgB_2 is considered as a binary system with 2D electrons. The classic BCS theory is applied to this system. The transition temperature is found to be relatively high, because 2D electrons are more capable of moving with the atoms, on top of other features of this system to enhance the electron-phonon interaction. This system may also shed light on the nature of superconductivity in cuprates.
The properties of the d-wave superconducting state in the two-dimensional system have been studied. It has been assumed, that the pairing mechanism is based on the electron-phonon and the electron-electron-phonon interactions. The obtained results have shown the energy gap amplitude ($Δ_{tot}$) crossover, from the BCS to non-BCS behavior, as the value of the electron-electron-phonon potential increases. The model has been tested for the ${\rm La_{2-x}Sr_{x}CuO_{4}}$ and ${\rm Bi_{2}Sr_{2}CaCu_{2}O_{8+δ}}$ high-$T_{C}$ superconductors. It has been shown, that the dependence of the $2Δ^{(0)}_{to…
We study the contribution of the Higgs amplitude mode on the nonlinear optical response of superconductors beyond the BCS approximation by taking into account the retardation effect in the phonon-mediated attractive interaction. To evaluate the vertex correction in nonlinear optical susceptibilities that contains the effect of collective modes, we propose an efficient scheme which we call the "dotted DMFT" based on the nonequilibrium dynamical mean-field theory (nonequilibrium DMFT) to go around the difficulty of solving the Bethe-Salpeter equation and analytical continuation. The vertex corre…
In this paper, we reexamine the results of isotope effect experiments of the conventional monoatomic superconductor (Hg). It is shown clearly that the isotopic coefficients of mercury can be largely deviated from $α=0.5$, the standard value suggested by the phonon-mediated BCS pairing theory. According to the reported experimental results of various mercury isotopes, a giant isotope effect ($α=2.896$) is numerically found in the data. This study indicates that the validity of the conventional BCS theory cannot be verified by the isotope effect.
Pseudogap phase in superconductors continues to be an outstanding puzzle that differentiates unconventional superconductors from the conventional ones (BCS-superconductors). Employing high resolution photoemission spectroscopy on a highly dense conventional superconductor, MgB2, we discover an interesting scenario. While the spectral evolution close to the Fermi energy is commensurate to BCS descriptions as expected, the spectra in the wider energy range reveal emergence of a pseudogap much above the superconducting transition temperature indicating apparent departure from the BCS scenario. Th…
The effective attractive interaction between electrons, mediated by electron-phonon coupling, is a well-established mechanism of conventional superconductivity. In metals exhibiting a Fermi surface, the critical temperature of superconductivity is exponentially smaller than the characteristic phonon energy. Therefore such superconductors are found only at temperatures below a few Kelvin. Systems with flat energy bands have been suggested to cure the problem and provide a route to room-temperature superconductivity, but previous studies are limited to only BCS models with an effective attractiv…
According to the BCS model the probability of filling of pair electron states vk2 as a function of kinetic energy is smeared i.e. is not a step function. This means that part of energy of connection through virtual phonons is consumed to increase the kinetic energy in an electron system at the transition to the superconducting state. In this work a modified mechanism of vk2 formation is proposed which takes into account the dynamics of fluctuations near the phase transition. The estimations of superconducting gap and isotopic effect for a matrial with parameters of high-temperature superconduc…
The nature of superconductivity in the dilute semiconductor SrTiO$_3$ has remained an open question for more than 50 years. The extremely low carrier densities ($10^{18}$ - $10^{20}$ cm$^{-3}$) at which superconductivity occurs suggests an unconventional origin of superconductivity outside of the adiabatic limit on which the Bardeen-Cooper-Schrieffer (BCS) and Migdal-Eliashberg (ME) theories are based. We take advantage of a newly developed method for engineering band alignments at oxide interfaces and access the electronic structure of Nb-doped SrTiO$_3$ using high resolution tunneling spectr…
The current search for room-temperature superconductivity is inspired by the unique properties of the electron-phonon interaction in metal superhydrides. Encouraged by the recently found highest-$T_C$ superconductor fcc-$LaH_{10}$, here we discover several superhydrides of another lanthanide - neodymium. We identify three novel metallic Nd-H phases at pressure range from 85 to 135 GPa: $I4/mmm$-$NdH_4$, $C2/c$-$NdH_7$, $P6_3/mmc$-$NdH_9$, synthesized by laser-heating metal samples in NH3BH3 media for in situ generation of hydrogen. A lower trihydride $Fm\bar{3}m$-$NdH_3$ is found at pressures …
A theory of superconductivity is presented where the effect of anharmonicity, as entailed in the acoustic, or optical, phonon damping, is explicitly considered in the pairing mechanism. The gap equation is solved including diffusive Akhiezer damping for longitudinal acoustic phonons or Klemens damping for optical phonons, with a damping coefficient which, in either case, can be directly related to the Gruneisen parameter and hence to the anharmonic coefficients in the interatomic potential. The results show that the increase of anharmonicity has a strikingly non-monotonic effect on the critica…
The recent discovery of superconductivity at ~39 K in MgB2, by Nagamatsu et al. establishes this simple binary compound as having the highest bulk superconducting transition temperature, Tc, of any non-copper-oxide material. Much of the initial research has focused on whether MgB2 is a conventional BCS, electron-phonon mediated superconductor, and, if it is, why Tc is so high. Isotope effect measurements, in which the atom masses are manipulated to systematically change the phonon frequencies, are one of the fundamental experimental tests of electron-phonon mediated superconductivity. One woul…
In the paper, the inhomogeneous states with local translational symmetry are under investigation in the framework of the Landau theory. The phonon potential is defined as a compensating field of local representation of the subgroup of translations. The constructed phenomenological Ginzburg-Landau potential takes into account both electromagnetic and electron-phonon interactions explicitly. The suggested phenomenological model does not require doubling of charge to get the correct expression of current density in the Londons equations and is in agreement with the BCS model. A phenomenological d…
Point-contact (PC) spectroscopy measurements on YNi2B2C single crystals in the normal and superconducting (SC) state (T_c=15.4K) for the main crystallographic directions are reported. The PC study reveals the electron-phonon interaction (EPI) function with a dominant maximum around 12meV and a further weak structure (kink or shallow broad maximum) at higher energy at about 50meV. Other phonon maxima at 20, 24 and 32meV specified in the phonon DOS of YNi2B2C by neutron measurements [PRB, V.55, 9058 (1997)] are not resolved in the PC spectra pointing out to the main role of the low energy phonon…
Recent first principles calculations of the phonon dispersion curves in MgB_2 have suggested the presence of anomalies in some of the curves, particularly in the longitudinal acoustical (LA) branch in the Gamma to A direction. Similar behavior has been observed in numerous other superconductors with T_c's higher than those of standard electron-phonon BCS superconductors. Phenomenological calculations of the Gamma->A LA dispersion based on both an acoustical plasmon and a ``resonant polarization'' mechanism are given here to emphasize the importance of these similarities.
In the present paper, the impact of small Fermi energy on the selected parameters of the superconducting state in Ba$_{1-x}$K$_{x}$BiO$_{3}$ (BKBO) is studied at $x \in (0.3, 0.4, 0.5)$. This is done by employing the adiabatic and non-adiabatic Eliashberg equations in context of the available experimental data. It is found that the retardation, strong-coupling and the non-adiabatic effects notably influence superconducting phase in BKBO. In particular, the electron-electron interaction, approximated here by the Coulomb pseudopotential, is argued to be reduced by the non-adiabatic effects that …
The recent report of superconductivity under high pressure at the record transition temperature of Tc=203K in sulfur hydride has been identified as conventional in view of the observation of an isotope effect upon deuteration. Here it is demonstrated that conventional theories of superconductivity in the sense of BCS or Eliashberg formalisms can neither account for the observed values of Tc nor the pressure dependence of the isotope coefficient. The only way out of the dilemma is a multi-band approach of superconductivity where already small interband coupling suffices to achieve the high valu…
In a prior study of the boron isotope effect on the transition temperature ($T_c$) of $R$Ni$_2$B$_2$C ($R$ = Y, Lu) system, a positive isotope effect was observed, e.g., $T_{c}(^{10}B)> T_{c}(^{11}B)$. BCS theory predicts that the superconducting gap at zero temperature ($Δ_0$) is proportional to $T_c$. Therefore, the gap should also show a positive boron isotope effect. On the contrary, in an inelastic light scattering study, we report a negative boron isotope effect on the energy $Ω$ of the gap-like feature in B$_{2g}$ symmetry, e.g., $Ω(^{10}B)< Ω(^{11}B)$. The origin of the effect is discu…
Emergence of superconductivity in a two-band system coupled with breathing and Jahn-Teller phonons is discussed in a weak-coupling limit. With the use of a standard quantum mechanical procedure, the phonon-mediated attraction is derived. From the analysis of the model including such attraction, a BCS-like formula for a superconducting transition temperature $T_{\rm c}$ is obtained. When only the breathing phonon is considered, $T_{\rm c}$ is the same as that of the one-band model. On the other hand, when Jahn-Teller phonons are active, $T_{\rm c}$ is significantly enhanced by the interband att…
In this article in the framework of generalized Frolich model we consider electron-spin-phonon system. A parameter of electron-spin-phonon interaction is found. It is shown its interrelation with experiments on isotope-effect on high temperature superconductors and asymptotic transformation to BCS theory.
We develop a multi-step workflow for the discovery of conventional superconductors, starting with a Bardeen Cooper Schrieffer inspired pre-screening of 1736 materials with high Debye temperature and electronic density of states. Next, we perform electron-phonon coupling calculations for 1058 of them to establish a large and systematic database of BCS superconducting properties. Using the McMillan-Allen-Dynes formula, we identify 105 dynamically stable materials with transition temperatures, Tc>5 K. Additionally, we analyze trends in our dataset and individual materials including MoN, VC, VTe, …
Experimental discovery of near-room-temperature (NRT) superconductivity in highly-compressed H$_3$S, LaH$_1$$_0$ and YH$_6$ restores fundamental interest to electron-phonon pairing mechanism in superconductors. One of prerequisites of phonon-mediated NRT superconductivity in highly-compressed hydrides is strong electron-phonon interaction, which can be quantified by dimensionless ratios of Bardeen-Cooper-Schrieffer (BCS) theory vs $k{_B}T{_c}$/(${\hslash}$$ω{_l}{_n}$), where Tc is the critical temperature and $ω{_l}{_n}$ is the logarithmic phonon frequency (Mitrovic et al. 1984 Phys. Rev. B 29…
Prompted by the recent report on the evidence for superconductivity at ambient temperature and pressure in nanostructures of silver particles embedded into a gold matrix [arXiv:1807.08572], we have exploited first principles materials discovery approaches to predict superconductivity in the 3D bulk crystals and 2D slabs of Ag-Au binary alloys at 1 atm pressure within the phonon-mediated BCS-like pairing mechanism. In calculations, it turns out that, the estimated superconducting transition temperatures of the ensued stable and metastable Ag-Au alloys resulted in Tc as low as one mK. Whereas si…
Most of the proposed models of high-temperature superconductivity (HTSC) are based on the short-range electron-electron correlations or/and on a short-range electron-phonon interaction. However, in the cuprates the screening is poor due to a low carrier density, layered crystal structure, and high ionicity of the lattice. We develop further the bipolaron model of HTSC, which explicitly takes into account the long-range origin of all interactions. The long-range electron-phonon (Froehlich) interaction binds carriers into real space pairs (small bipolarons) with surprisingly low mass but suffici…
Recent advances in time-domain terahertz (THz) spectroscopy have unveiled that resonantly-enhanced strong THz third-harmonic generation (THG) mediated by the collective Higgs amplitude mode occurs in s-wave superconductors, where charge-density fluctuations (CDF) have also been shown to contribute to the nonlinear third-order susceptibility. It has been theoretically proposed that the nonlinear responses of Higgs and CDF exhibit essentially different polarization dependences. Here we experimentally discriminate the two contributions by polarization-resolved intense THz transmission spectroscop…
The discovery of the first high critical temperature (Tc) transition metal diboride superconductor, MgB2 structure alpha-MoB2 under pressure with Tc up to 32 K at 100 GPa, provides new input into some unexplained aspects of electron-phonon coupling in intermetallic compounds. We establish that MoB2 is a phonon-mediated superconductor but has little in common with MgB2 (Tc=40 K at zero pressure). MoB2 is a strongly metallic, three dimensional, multi-Fermi surface material, becoming of additional interest because it displays a frequency separation of Mo and B vibrations that mirrors that of meta…
We have studied the d-wave pairing-instability in the two-dimensional Holstein-Hubbard model at the level of a full fluctuation exchange approximation which treats both Coulomb and electron-phonon (EP) interaction diagrammatically on an equal footing. A generalized numerical renormalization group technique has been developed to solve the resulting self-consistent field equations. The $d$-wave superconducting phase diagram shows an optimal T_c at electron concentration <n> ~ 0.9 for the purely electronic Hubbard system. The EP interaction suppresses the d-wave T_c which drops to zero when the p…
When quasiparticles in a BCS superconductor recombine into Cooper pairs, phonons are emitted within a narrow band of energies above the pairing energy at 2$Δ$. We show that a phonon bandgap restricting the escape of recombination phonons from a superconductor can increase the quasiparticle recombination lifetime by more than an order of magnitude. A phonon bandgap can be realized and matched to the recombination energy with a phononic crystal, a periodically-patterned dielectric membrane. We discuss in detail the non-equilibrium quasiparticle and phonon distributions that arise in a supercondu…
We investigate the dynamics of a phonon-mediated superconductor driven out of equilibrium. The electronic hopping amplitude is ramped down in time, resulting in an increased electronic density of states. The dynamics of the coupled electron-phonon model is investigated by solving Migdal-Eliashberg equations for the double-time Keldysh Green's functions. The increase of the density of states near the Fermi level leads to an enhancement of superconductivity when the system thermalizes to the new state at the same temperature. We provide a time- and momentum-resolved view on this thermalization p…
We report on measurements of the specific heat of the recently discovered superconductor MgB$_2$ in the temperature range between 3 and 220 K. Based on a modified Debye-Einstein model, we have achieved a rather accurate account of the lattice contribution to the specific heat, which allows us to separate the electronic contribution from the total measured specific heat. From our result for the electronic specific heat, we estimate the electron-phonon coupling constant $λ$ to be of the order of 2, significantly enhanced compared to common weak-coupling values $\leq 0.4$. Our data also indicate …
