We propose a new Rashba-free mechanism to realize topological superconductivity with electron-phonon interaction. In the presence of a magnetic field, electron-phonon interaction with small momentum transfer is found to favor spin-triplet Cooper pairing. This process facilitates the formation of chiral topological superconductivity even when Rashba spin-orbital coupling is absent. As a proof of concept, we propose an experimentally feasible heterostructure to systematically study the entangled relationship among forward-phonon scatterings, Rashba spin-orbital couplings, pairing symmetries, and superconducting topology. Our theory sheds light on the important role of electron-phonon coupled materials in the pursuit of non-Abelian Majorana quasiparticles.
The disclosure of spinon superconductivity and superconductivity mediated by spin-waves in hole-doped Bi2212 cuprate raises the question about the origin of the superconductivity in other cuprates and specially in an electron-doped NCCO cuprate.
We study the effect of buckling and breathing phonons, relevant for cuprate superconductors, on the d-wave superconductivity in the two-dimensional Hubbard model by employing dynamical cluster Monte Carlo calculations. The interplay of electronic correlations and the electron-phonon interaction produces two competing effects, an enhancement of the effective d-wave pairing interaction, which favors d-wave superconductivity, and a strong renormalization of the single-particle propagator, which suppress superconductivity. Due to the later effect we find that buckling and breathing phonons suppres…
We study the superconductivity of strongly coupled electron-phonon systems where the geometry of the lattice frustrates the charge order by the sign-problem-free Quantum Monte Carlo(QMC) method. The results suggest that with charge order frustrated, the superconductivity can benefit from strong electron-phonon interaction in a wide range of coupling strengths.
Squeezing of phonons due to the non-linear coupling to electrons is a way to enhance superconductivity as theoretically studied in a recent work [Kennes et al. Nature Physics 13, 479 (2017)]. We study quadratic electron-phonon interaction in the presence of phonon pumping and an additional external squeezing. Interference between these two driving sources induces a phase-sensitive enhancement of electron-electron attraction, which we find as a generic mechanism to enhance any boson-mediated interactions. The strongest enhancement of superconductivity is shown to be on the boundary with the dyn…
We propose that unconventional superconductivity in hydrated sodium cobaltate $Na_xCoO_2$ results from an interplay of electronic correlations and electron-phonon interactions. On the basis of the $t-V$ model plus phonons we found evidences for a) unconventional superconductivity, b) realistic values of $T_c$ and c) the dome shape existing near $x \sim 0.35$. This picture is obtained for $V$ close to the critical Coulomb repulsion $V_c$ which separates the uniform Fermi liquid from $\sqrt{3} \times \sqrt{3}$ CDW ordered phase.
We suggest that the phonon dispersion in cuprates becomes strongly anisotropic due to interaction with spin waves; moreover the phonon dispersion becomes singular along $|k_x|=|k_y|$ directions. This would allow more electrons to form Cooper pairs and increase temperature of the superconducting transition. The interaction of phonons with spin waves is more important than the interaction of phonons with free electrons, because spin waves do not have the Fermi surface constrain.
We investigate the interaction between the electrons of a two-dimensional metal and the acoustic phonons of an underlying piezoelectric substrate. Fundamental inequalities can be obtained from general energy arguments. As a result, phonon mediated attraction can be proven to never overcome electron Coulomb repulsion, at least for long phonon wavelengths. We study the influence of these phonons on the possible pairing instabilities of a two-dimensional electron gas such as graphene.
We study Fe$_{1+y}$Te$_{0.6}$Se$_{0.4}$ multi-band superconductor with $T_c=14$K by polarization-resolved Raman spectroscopy. Deep in the superconducting state, we detect pair-breaking excitation at 45cm$^{-1}$ ($2Δ=5.6$meV) in the $XY$($B_{2g}$) scattering geometry, consistent with twice of the superconducting gap energy (3 meV) revealed by ARPES on the hole-like Fermi pocket with $d_{xz}/d_{yz}$ character. We analyze the superconductivity induced phonon self-energy effects for the $B_{1g}$(Fe) phonon and estimate the electron-phonon coupling constant $λ^Γ\approx 0.026$, which is insufficient…
I present results from an extended Migdal-Eliashberg theory of electron-phonon interactions and superconductivity. The history of the electron-phonon problem is introduced, and then study of the intermediate parameter regime is justified from the energy scales in the cuprate superconductors. The Holstein model is detailed, and limiting cases are examined to demonstrate the need for an extended theory of superconductivity. Results of the extended approximation are shown, including spectral functions and phase diagrams. These are discussed with reference to Hohenberg's theorem, the Bardeen-Coope…
I examine electron-phonon mediated superconductivity in the intermediate coupling and phonon frequency regime of the quasi-2D Holstein model. I use an extended Migdal-Eliashberg theory which includes vertex corrections and spatial fluctuations. I find a d-wave superconducting state that is unique close to half-filling. The order parameter undergoes a transition to s-wave superconductivity on increasing filling. I explain how the inclusion of both vertex corrections and spatial fluctuations is essential for the prediction of a d-wave order parameter. I then discuss the effects of a large Coulom…
The effects of structural quantum criticality on the strong-coupling superconductivity of (Sr$_{1-x}$Ca$_x$)$_3$Rh$_4$Sn$_{13}$ have been investigated via electrical resistivity and specific heat measurements. We demonstrate that the lattice specific heat at low temperatures considerably increases toward the structural quantum critical point (SQCP), $x_{\rm c}\approx0.9$. The superconducting gap increases with $x$ in the exact same fashion as the low-temperature lattice specific heat, clearly indicating that the abundant low-energy phonons cause strong-coupling superconductivity. Despite the e…
This paper has been withdrawn by the authors, because we had probably observed some spurious intensity with x=0.29 sample (Fig.3(b)). This came out after further studies of the detailed x-dependence of the highest energy LO phonon branch in LSCO.
Determinant quantum Monte Carlo (DQMC) simulations are used to study non-linear electron-phonon interactions in a two-dimensional Holstein-like model on a square lattice. We examine the impact of non-linear electron-lattice interactions on superconductivity and on Peierls charge-density-wave (CDW) correlations at finite temperatures and carrier concentrations. We find that the CDW correlations are dramatically suppressed with the inclusion of even a small non-linear interaction. Conversely, the effect of the non-linearity on superconductivity is found to be less dramatic at high temperatures; …
We present a systematic theory of acoustic-phonon-mediated superconductivity, which incorporates Coulomb repulsion, explaining the recent experiment in Bernal bilayer graphene under a large displacement field. The acoustic-phonon mechanism predicts that $s$-wave spin-singlet and $f$-wave spin-triplet pairings are degenerate and dominant. Assuming a spin-polarized valley-unpolarized normal state, we obtain $f$-wave spin-triplet superconductivity with a $T_c\sim 20$ mK near $n_e=-0.6\times 10^{12}$ cm$^{-2}$ for hole doping, in approximate agreement with the experiment. We further predict the ex…
We investigate the competition between acoustic-phonon-mediated superconductivity and the long-range Coulomb interaction in moiréless graphene multilayers, specifically, Bernal bilayer graphene, rhombohedral trilayer graphene, and ABCA-stacked tetralayer graphene. In these graphene multilayers, the acoustic phonons can realize, through electron-phonon coupling, both spin-singlet and spin-triplet pairings, and the intra-sublattice pairings ($s$-wave spin-singlet and $f$-wave spin-triplet) are the dominant channels. Our theory naturally explains the distinct recent experimental findings in Berna…
Strong electron-phonon interactions in cuprates and other high-temperature superconductors have gathered support over the last decade in a large number of experiments. Here I briefly introduce the Froehlich-Coulomb multi-polaron model of high-temperature superconductivity, which includes strong on-site repulsive correlations and the long-range Coulomb and electron-phonon (e-ph) interactions. Our extension of the BCS theory to the strong-coupling regime with the long-range \emph{unscreened} electron-phonon interaction could naturally explain the isotope effects, unconventional thermomagnetic tr…
Motivated by the observation of two distinct superconducting phases in the moiréless ABC-stacked rhombohedral trilayer graphene, we investigate the electron-acoustic-phonon coupling as a possible pairing mechanism. We predict the existence of superconductivity with the highest $T_c\sim 3$K near the Van Hove singularity. Away from the Van Hove singularity, $T_c$ remains finite in a wide range of doping. In our model, the $s$-wave spin-singlet and $f$-wave spin-triplet pairings yield the same $T_c$, while other pairing states have negligible $T_c$. Our theory provides a simple explanation for th…
We report first principles calculations of the electronic structure, phonon dispersions and electron phonon coupling of LaNiPO. These calculations show that this material can be explained as a conventional electron phonon superconductor in contrast to the FeAs based high temperature superconductors.
We develop a theory for light-induced superconductivity in underdoped cuprates in which the competing bond-density wave order is suppressed by driving phonons with light. Close to a bond-density wave instability in a system with a small Fermi surface, such as a fractionalized Fermi liquid, we show that the coupling of electrons to phonons is strongly enhanced at the bond-density wave ordering wavevectors, leading to a strong softening of phonons at these wavevectors. For a model of classical phonons with anharmonic couplings, we show that the combination of strong softening and driving can lea…
In this chapter we review the essentials of conventional electron-phonon superconductivity, as provided through the Migdal-Eliashberg formalism. Signatures of the electron-phonon interaction, as they appear in conventional superconductors, are described in detail. An appendix briefly describes more recent attempts to understand the electron-phonon interaction for all coupling strengths.
Breaking down the traditional perception on phonons which are achiral, the recent discovery of chiral phonon carrying angular momentum provides possible ways to couple electron, photon, spin, magnon and exciton, etc. We theoretically proposed an electron-chiral phonon interaction with two-phonon process, in contrast to conventional electron-phonon interaction, and a kind of effective Hubbard U through exchanging two chiral phonons is proposed. Taking two-dimensional diatomic honeycomb lattice as an example, we found this repulsive Hubbard U mediated by chiral phonons induces unconventional and…
We propose a mew picture for superconductivity in $κ-(BEDT-TTF)_2X$ salts arguing that small-{\bf q} electron-phonon scattering dominates the pairing. We reproduce the distinct X-shaped d-wave gap reported recently by magnetooptic measurements and we argue that the softness of the momentum structure of the gap and the near degeneracy of s- and d-wave gap states may be at the origin of the experimental controversy about the gap symmetry. We show that a magnetic field applied parallel to the planes may induce extended gapless-regions on the FS accounting for the experimental signatures of a Fuld…
The electronic structure, phonons, electron-phonon coupling, and superconductivity are theoretically studied in noncentrosymmetric superconductor ThCoC$_2$ as a function of pressure, in the pressure range 0 - 20 GPa. We found that the electronic band splitting induced by the spin-orbit coupling is enhanced under pressure. In spite of the overall stiffening of the crystal lattice, the electron-phonon coupling constant $λ$ increases with pressure, from 0.583 at 0 GPa to 0.652 at 20 GPa. If the isotropic Eliashberg electron-phonon coupling theory is used to simulate the effect on the critical tem…
We discuss the BCS theory for electrons in graphene with a superimposed electrical unidirectional superlattice potential (SL). New Dirac points emerge together with van Hove singularities (VHS) linking them. We obtain a superconducting transition temperature $ T_c $ for chemical potentials close to the VHS assuming that acoustic phonon coupling should be the dominant mechanism. Pairing of two onsite electrons with one electron close to the $ {\bf K} $ and the other close to the $ -{\bf K} $ point is the most stable pair formation. The resulting order parameter is almost constant over the entir…
We report self-consistent calculations of the gap symmetry for the iron-based high-temperature superconductors using realistic small-q phonon mediated pairing potentials and four-band energy dispersions. When both electron and hole Fermi surface pockets are present, we obtain the nodeless $s_\pm$ state that was first encountered in a spin-fluctuations mechanism picture. Nodal gap structures such as $d_{x^2-y^2}$ and $s_\pm+d_{x^2-y^2}$ and even a p-wave triplet state, are accessible upon doping within our phononic mechanism. Our results resolve the conflict between phase sensitive experiments …
I present the results of first principles calculations of the phonon dispersions and electron-phonon coupling for BaTi$_2$Sb$_2$O. The phonon dispersions show a weak lattice instability near the zone corners that leads to a charge-density wave phase. The calculations of the electron-phonon coupling reveal strong coupling, especially to the in-plane Ti modes. The total coupling is large enough to readily explain the superconductivity in this compound. As the Fermi surfaces are disconnected with different orbital character weights, this compound is likely to host a multiband superconductivity.
Motivated by the proposed topological state in Cu$_x$Bi$_2$Se$_3$, we study the possibility of phonon-mediated odd-parity superconductivity in spin-orbit coupled systems with time-reversal and inversion symmetry. For such systems, we show that, in general, pure electron-phonon coupling can never lead to a triplet state with a higher critical temperature than the leading singlet state. The Coulomb pseudopotential, which is the repulsive part of the electron-electron interaction and is typically small in weakly correlated systems, is therefore critical to stabilizing the triplet state. We introd…
We present the numerical solution of the renormalization group (RG) equations derived in Ref. [1], for the problem of superconductivity in the presence of both electron-electron and electron-phonon coupling at zero temperature. We study the instability of a Fermi liquid to a superconductor and the RG flow of the couplings in presence of retardation effects and the crossover from weak to strong coupling. We show that our numerical results provide an ansatz for the analytic solution of the problem in the asymptotic limits of weak and strong coupling.
Taking into account the first localization corrections in the electron-impurity self-energy we study the effect of non-magnetic impurities on unconventional superconductivity (SC) mediated by small-q electron-phonon scattering. We show that when van Hove singularities are close to the Fermi level making the electronic system anisotropic as in the high-$T_c$ oxides, both the d-wave and s-wave states are sensitive to non-magnetic impurities and beyond a critical impurity concentration SC disappears in {\it both gap symmetry channels}. Impurity doping may induce a first order transition from d-wa…
We use a Luttinger-Ward functional approach to study the problem of phonon-mediated superconductivity in electron systems with strong electron-electron interactions (EEIs). Our derivation does not rely on an expansion in skeleton diagrams for the EEI and the resulting theory is therefore nonperturbative in the strength of the latter. We show that one of the building blocks of the theory is the irreducible six-leg vertex related to EEIs. Diagrammatically, this implies five contributions (one of the Fock and four of the Hartree type) to the electronic self-energy, which, to the best of our knowl…
The theory of electron-phonon superconductivity depends on retardation drastically reducing effects of the strong Coulomb repulsion. The standard theory only treats the lowest order diagram, which is an uncontrolled approximation. We study retardation in the Hubbard-Holstein model in a controlled way using perturbation theory and dynamical mean-field theory. We calculate analytically second order results for the pseudopotential $μ^*$ and demonstrate the validity up to intermediate couplings by comparison with non-perturbative results. Retardation effects are still operative, but less efficient…
Temperature dependent Raman scattering studies in polycrystalline MgB2(10<T<300 K)reveal that the E2g phonon does not experience any self energy renormalization effect across the superconducting critical temperature Tc ~ 40 K. In contrast, most of the current theoretical models rely on the role of the E2g phonon in the electron-phonon coupling mechanism of superconductivity in MgB2. According to these models, a hardening of 12% is expected below Tc at the Gamma point of the Brillouim zone. In the presence of our results, those models must be reviewed. The analysis of the temperature dependence…
To study the possible mechanism of superconductivity in Na$_{0.35}$CoO$_2$, we examine the interaction between all the relevant optical phonons (breathing and shear phonons) and $t_{2g}(a_{1g}+e_g')$-electrons of Co-ions, and study the transition temperature for a s-wave superconductivity. The obtained $T_{\rm c}$ is very low when the $e_g'$-valence-bands are far below the Fermi level. However, $T_{\rm c}$ is strongly enhanced when the top of the $e_g'$-valence-bands is close to the Fermi level (say -50meV), thanks to interband hopping of Cooper pairs caused by shear phonons. This ``valence-ba…
The BCS electron-phonon mechanism and the unconventional 'hole mechanism' have been proposed as explanations for the high temperature superconductivity observed in $MgB_2$. It is proposed that a critical test of which theory is correct is the dependence of $T_c$ on hole doping: the hole mechanism predicts that $T_c$ will drop rapidly to zero as holes are added, while the electron-phonon mechanism appears to predict increasing $T_c$ for a substantial range of hole doping. Furthermore, the hole mechanism and electron-phonon mechanism differ qualitatively in their predictions of the effect on $T_…
We consider possible routes to superconductivity in hydrated cobaltates Na_xCoO_2.yH_2O on the basis of the t-J-V model plus phonons on the triangular lattice. We studied the stability conditions for the homogeneous Fermi liquid (HFL) phase against different broken symmetry phases. Besides the sqrt(3)xsqrt(3)-CDW phase, triggered by the nearest-neighbour Coulomb interaction V, we have found that the HFL is unstable, at very low doping, against a bond-ordered phase due to J. We also discuss the occurrence of phase separation at low doping and V. The interplay between the electron-phonon interac…
In conventional superconductors, phonons glue two electrons with opposite spins to form Cooper pairs and condensation of these pairs leads to the superconductivity. Identifying the underlying mechanism of the high temperature superconductivity in cuprates is among the most important problems in physics. Even quarter of a century after the first report of high temperature superconductor by Bednorz and Muller in 1986, there is still no general consensus on the pairing mechanism of superconductivity in these materials. So far, many theories have been developed to explain the exotic properties of …
Insight into why superconductivity in pristine and doped monolayer graphene seems strongly suppressed has been central for the recent years' various creative approaches to realize superconductivity in graphene and graphene-like systems. We provide further insight by studying electron-phonon coupling and superconductivity in doped monolayer graphene and hexagonal boron nitride based on intrinsic phonon modes. Solving the graphene gap equation using a detailed model for the effective attraction based on electron tight binding and phonon force constant models, the various system parameters can be…
We investigate the influence of a d-density wave (DDW) gap on the superconductivity-induced renormalization of phonon frequency and linewidth. The results are discussed with respect to Raman and inelastic neutron scattering experiments. It turns out that the DDW gap can enhance the range of frequencies for $q=0$ phonon softening depending on the underlying band structure. Moreover we show that an anisotropic 'd-wave' pseudogap can also contribute to the q-dependent linewidth broadening of the 340cm$^{-1}$ phonon in YBa$_2$Cu$_3$O$_7$.
Electron-boson coupling plays a key role in superconductivity for many systems. However, in copper-based high-temperature ($T_c$) superconductors, its relation to superconductivity remains controversial despite strong spectroscopic fingerprints. Here we use angle-resolved photoemission spectroscopy to find a striking correlation between the superconducting gap and the bosonic coupling strength near the Brillouin zone boundary in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$. The bosonic coupling strength rapidly increases from the overdoped Fermi-liquid regime to the optimally doped strange metal, concomitant…
Two-dimensional (2D) boron has been predicted to show superconductivity. However, intrinsic 2D carbon and phosphorus have not been reported to be superconductors, which, inspires us to seek superconductivity in their mixture. Here we perform first-principles calculations of the electronic structure, phonon dispersion, and electron-phonon coupling of the metallic phosphorus carbide monolayer, the $β_{0}$-PC. Results show that it is an intrinsic phonon-mediated superconductor, with estimated superconducting temperature $T_{c}$ to be $\sim$13 K. The main contribution to the electron-phonon coupli…
We predict that electron-doped silicene is a good two-dimensional electron-phonon superconductor under biaxial tensile strain by first-principles calculations within rigid band approximation. Superconductivity transition temperature of electron-doped silicene can be increased to be above 10 K by 5% tensile strain. Band structures, phonon dispersive relations, and Eliashberg functions are calculated for detailed analysis. The strong interaction between acoustic phonon modes normal to the silicene plane and the increasing electronic states around the Fermi level induced by tensile strain is main…
K$_3$-picene is a superconducting molecular crystal with critical temperature T$_c=7$K or 18K, depending on preparation conditions. Using density functional theory we show that electron-phonon interaction accounts for T$_c ~ 3-8$ K. The average electron-phonon coupling, calculated by including the phonon energy scale in the electron-phonon scattering, is $λ=0.73$ and $ω_{\rm log}=18.0\,$ meV. Intercalant and intermolecular phonon-modes contribute substantially (40%) to $λ$ as also shown by the isotope exponents of potassium (0.19) and carbon (0.31). The relevance of these modes makes supercond…
We investigate the role of specific phonon mode symmetries for the room temperature superconductivity in atomic hydrogen under large pressure. Using anisotropic Migdal-Eliashberg theory with ab initio input from density functional theory, we show that the $E_u$ phonon modes are the dominant driving force for obtaining such high critical temperatures. When going from 400 to 600 GPa, we find an increased transition temperature, however, the total electron-phonon coupling strength is counterintuitively reduced. Our analysis reveals that this is due to an enhanced contribution to the coupling stre…
The out-of-plane intercalate phonons of superconducting YbC6 have been measured with inelastic x-ray scattering. Model fits to this data, and previously measured out-of-plane intercalate phonons in graphite intercalation compounds (GICs), reveal surprising trends with the superconducting transition temperature. These trends suggest that superconducting GICs should be viewed as electron-doped graphite.
We argue that Raman scattering in $B_{1g}$ symmetry allows one to distinguish between phonon-mediated and magnetically-mediated $d-$wave superconductivity. In spin mediated superconductors, $B_{1g}$ Raman intensity develops a resonance at a frequency $ω_{res} < 2Δ_{max}$, whose origin is similar to a neutron resonance. In phonon-mediated $d-$wave superconductors, such a resonance does not develop. Several extensions of the argument are presented.
We observe a characteristic energy $\hbarω_{c}\approx 2.1$ eV which separates regions of different behavior of the phonon intensities in the Raman spectra of the $R\rm Ba_2Cu_3O_7$ system. A superconductivity-induced drop of phonon intensities is found for the oxygen modes O(4) and O(2)-O(3) only for excitation energies below $\hbarω_c$. This intensity drop indicates an order parameter which affects energies in the vicinity of $\hbarω_c$.
In strontium titanate, the Froehlich electron - LO-phonon interaction dominates the electron response and can also provide superconductivity. Because of high LO-phonon frequencies in SrTiO3, the superconducting system is non-adiabatic. We demonstrate that the dielectric function approach is an adequate theoretical method for superconductivity in SrTiO3 and on the SrTiO3-LaAlO3 interface. The critical temperatures are calculated using realistic material parameters. The obtained critical temperatures are in line with experimental data both for bulk and interface superconductivity. The present me…
Electron pairing by dispersive phonons in altermagnets: re-entrant superconductivity and continuous transition to finite momentum superconducting state
研究交错磁体中色散声子介导的电子配对，发现热声子散射抑制交错磁性，导致超导电性随温度重入，并在低温稳定 FFLO 有限动量超导态，无需 d 波配对。
We report a detailed study of specific heat, electrical resistivity and thermal expansion in combination with inelastic neutron and inelastic X-ray scattering to investigate the origin of superconductivity in the two silicon clathrate superconductors Ba8Si46 and Ba24Si100. Both compounds have a similar structure based on encaged barium atoms in oversized silicon cages. However, the transition temperatures are rather different: 8 K and 1.5 K respectively. By extracting the superconducting properties, phonon density of states, electron-phonon coupling function and phonon anharmonicity from these…
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…
High-resolution photoemission has been used to study the electronic structure of the charge density wave (CDW) and superconducting (SC) dichalcogenide, 2H- NbSe2. From the extracted self-energies, important components of the quasiparticle (QP) interactions have been identified. In contrast to previously studied TaSe2, the CDW transition does not affect the electronic properties significantly. The electron-phonon coupling is identified as a dominant contribution to the QP self-energy and is shown to be very anisotropic (k-dependent) and much stronger than in TaSe2.
The physical properties of the previously reported superconductor IrGe and the Rh1-xIrxGe solid solution are investigated. IrGe has an exceptionally high superconducting transition temperature (Tc = 4.7 K) among the isostructural 1:1 late-metal germanides MGe (M = Rh, Pd, Ir and Pt). Specific-heat measurements reveal that IrGe has an anomalously low Debye temperature, originating from a low-lying phonon, compared to the other MGe phases. A large jump at Tc in the specific-heat data clearly indicates that IrGe is a strong coupling superconductor. In the Rh1-xIrxGe solid solution, a relationship…
Theory of superconductivity generated in one atomic layer thick two dimensional electron gas by a single flat band of high energy longitudinal optical phonons is considered. The polar dielectric $SrTiO_{3}$ (STO) exhibits such an energetic phonon mode and the 2DEG is created both when one unit cell $FeSe$ layer is grown on its $\left( 100\right) $ surface and on the interface with another dielectric like $LaAlO_{3}$ (LAO). We obtain a quantitative description of both systems solving the gap equation for $T_{c}$ without making use of approximations like the Kirzhnits Ansatz for arbitrary chemic…
