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Results for “Eliashberg theory”

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory

Migdal-Eliashberg theory describes the properties of the normal and superconducting states of electron-phonon-mediated superconductors based on a perturbative treatment of the electron-phonon interactions. It is necessary to include both electron and phonon self-energies self-consistently in Migdal-Eliashberg theory in order to match numerically exact results from determinantal quantum Monte Carlo in the adiabatic limit. Here in this work we provide a method to obtain the real-axis solutions of the Migdal-Eliashberg equations with electron and phonon self-energies calculated self-consistently. Our method avoids the typical challenge of computing cumbersome singular integrals on the real axis and is numerically stable and exhibits fast convergence. Analyzing the resulting real-frequency spectra and self-energies of the two-dimensional Holstein model, we find that self-consistently including the lowest-order correction to the phonon self-energy significantly affects the solution of the Migdal-Eliashberg equations. The calculation captures the broadness of the spectral function, renormalization of the phonon dispersion, enhanced effective electron-phonon coupling strength, minimal increase in the electron effective mass, and the enhancement of superconductivity which manifests as a superconducting ground state despite strong competition with charge-density-wave order. We discuss surprising differences in two common definitions of the electron-phonon coupling strength derived from the electron mass and the density of states, quantities which are accessible through experiments such as angle-resolved photoemission spectroscopy and electron tunneling. An approximate upper bound on 2Δ/T c for conventional superconductors mediated by retarded electron-phonon interactions is proposed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Machine learning of superconducting critical temperature from Eliashberg theory

Abstract The Eliashberg theory of superconductivity accounts for the fundamental physics of conventional superconductors, including the retardation of the interaction and the Coulomb pseudopotential, to predict the critical temperature T c . McMillan, Allen, and Dynes derived approximate closed-form expressions for the critical temperature within this theory, which depends on the electron–phonon spectral function α 2 F ( ω ). Here we show that modern machine-learning techniques can substantially improve these formulae, accounting for more general shapes of the α 2 F function. Using symbolic regression and the SISSO framework, together with a database of artificially generated α 2 F functions and numerical solutions of the Eliashberg equations, we derive a formula for T c that performs as well as Allen–Dynes for low- T c superconductors and substantially better for higher- T c ones. This corrects the systematic underestimation of T c while reproducing the physical constraints originally outlined by Allen and Dynes. This equation should replace the Allen–Dynes formula for the prediction of higher-temperature superconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Eliashberg theory of phonon-mediated superconductivity — When it is valid and how it breaks down

We analyze the validity of Eliashberg theory of phonon-mediated superconductivity in 2D systems in light of recent extensive Monte-Carlo studies of the Holstein model. Conventional wisdom says that Eliashberg theory is applicable as long as vertex corrections remain small. For small ratio of the phonon energy Ω 0 and the Fermi energy E F , this condition is supposed to hold even when the dimensionless electron–phonon coupling λ is larger than one, i.e., in the strong coupling regime. A comparison between various quantities computed in the Migdal approximation and those computed by Quantum Monte Carlo prove that this belief is wrong, and we identify analytically some of the ways in which this breakdown occurs for various ‘‘normal state’’ properties at λ = λ cr , where λ cr = O(1). Here, the breakdown occurs at temperatures high enough that neither superconducting nor charge–density wave correlations extend over any significant range of distances, so it cannot be associated with the onset of an instability toward any of the relevant ordered ground-states — rather it is associated with the local physics of classical bipolaron formation. Still, we show that certain properties, including the superconducting Tc and the superconducting gap structure below T c , can be accurately inferred from the strong-coupling limit of Eliashberg theory at λ ≤ λ cr .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Isotope effect and critical magnetic fields of superconducting YH 6 : A Migdal-Eliashberg theory approach

The emergence of near-ambient temperature superconductivity under pressure in metal hydride systems has motivated a desire to further understand such remarkable properties, specifically critical magnetic fields. Here, YH 6 is suggested to be a departure from conventional superconductivity, due to apparent anomalous behavior. Using density functional calculations in conjunction with Migdal-Eliashberg theory we show that in YH 6 the critical temperature and the isotope effect under pressure, as well as the high critical fields, are consistent with strong-coupling conventional superconductivity, a property anticipated to extend to other related systems. Furthermore, strong-coupling corrections occur to the expected BCS values for the isotope effect coefficient (α), Ginzburg-Landau parameter [κ 1 ⁡(T)], London penetration depth [λ L (T)], electromagnetic coherence length [ξ⁡(T)], and the energy gap (Δ 0 ).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Superconducting properties of MoTe 2 from ab initio anisotropic Migdal-Eliashberg theory

Molybdenum ditelluride (MoTe 2 ) is attracting considerable interest since it is the archetypal type-II Weyl semimetal and a candidate for topological superconductivity. In this work, we investigate the superconducting phase diagram of two MoTe 2 polymorphs using the ab initio anisotropic Migdal-Eliashberg theory, and we show that the superconducting dome originates from the synergistic contribution of the density of states at the Fermi level and the transverse acoustic Te modes in the 1$\textit{T}’$ phase. We find that the electron and hole pockets carry trivial $\textit{s}$-wave order parameters of slightly different magnitude, reminiscent of a two-gap structure as suggested by recent experiments. We suggest that a possible route for enhancing the superconducting critical temperature, and realizing $s_{+ –}$ pairing, in the $T_d$ phase is to exploit its nontrivial band topology via electron doping.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Charge correlations suppress unconventional pairing in the Holstein model

In a recent work by Schrodi et al. [Phys. Rev. B. 104, L140506 (2021)], the authors find an unconventional superconducting state with a sign-changing order parameter using the Migdal-Eliashberg theory, including the first vertex correction. This unconventional solution arises despite using an isotropic bare electron-phonon coupling in the Hamiltonian. We examine this claim using hybrid quantum Monte Carlo for a single-band Holstein model with a cuprate-like noninteracting band structure and identical parameters to Schrodi et al.. Our Monte Carlo results for these parameters suggest that unconventional pairing correlations do not exceed their noninteracting values at any carrier concentration we have checked. Instead, strong charge-density-wave correlations persist at the lowest accessible temperatures for dilute and nearly half-filled bands. As a result, we present arguments for how vertex-corrected Migdal-Eliashberg calculation schemes can lead to uncontrolled results in the presence of Fermi surface nesting.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Synergetic Ferroelectricity and Superconductivity in Zero-Density Dirac Semimetals near Quantum Criticality

Here, we study superconductivity in a three-dimensional zero-density Dirac semimetal in proximity to a ferroelectric quantum critical point. We find that the interplay of criticality, inversion-symmetry breaking, and Dirac dispersion gives rise to a robust superconducting state at the charge-neutrality point, where no Fermi surface is present. Using Eliashberg theory, we show that the ferroelectric quantum critical point is unstable against the formation of a ferroelectric density wave (FDW), whose fluctuations, in turn, lead to a first-order superconducting transition. Surprisingly, long-range superconducting and FDW orders are found to cooperate with each other, in contrast to the more usual scenario of phase competition. Therefore, we suggest that driving charge neutral Dirac materials, e.g., Pb x Sn 1–x Te, through a ferroelectric quantum critical point may lead to superconductivity intertwined with FDW order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Intrinsic and doping-enhanced superconductivity in monolayer 1 H − TaS 2 : Critical role of charge ordering and spin-orbit coupling

The interplay of superconductivity with charge density wave (CDW) in metallic transition-metal dichalcogenides has been widely debated, and viable strategies manipulating these quantum states in the two-dimensional (2D) limit remain unclear. Using the ab initio anisotropic Migdal-Eliashberg theory, we successfully explain the superconductivity observed in monolayer 1H-TaS 2 by simultaneously determining its precise CDW structure and treating the marked modification of electron-phonon interaction and critical temperature T c by spin-orbit coupling effects. With this paradigm, we further show that electron doping weakens the CDW order leading to increased T c up to 11 K, along with a single-gap to two-gap superconductivity transition due to the suppression of the CDW gap. By contrast, a low hole doping barely affects the CDW but still yields a significantly enhanced superconducting order, implying their good coexistence. Combined with the synergistic behavior of CDW and superconductivity, which cooperate upon TaS 2 thickness reduction causing an unusual rise of T c , our results unravel diversified interactions between the two collective orders in ultrathin TaS 2 , being competition, coexistence or cooperation depending on external stimuli, which provide key clues for controlling correlated states in devices based on 2D CDW superconductors.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Crucial role of thermal fluctuations and vertex corrections for the magnetic pseudogap

It is generally believed that in a two-dimensional metal, whose ground state is antiferromagnetically ordered with Q = (π,π), thermal (static) magnetic fluctuations give rise to precursor behavior above TN in which the spectral function of a hot fermion (the one for which k and k + Q are Fermi surface points) contains two peaks, separated by roughly the same energy as in the antiferromagnetically ordered state. The two peaks persist in some range of T > T N and eventually merge into a single peak at zero frequency. This behavior is obtained theoretically by departing from free fermions in a paramagnet and evaluating the dressed fermionic Green's function by summing up infinite series of diagrams with contributions from thermal magnetic fluctuations. We show, following that keeping vertex renormalization diagrams in these series is crucial as other terms only broaden the spectral function of a hot fermion but do not shift its maximum away from zero frequency. As the consequence, the magnetic pseudogap should be treated as an input for theories that neglect vertex corrections, such as, e.g., Eliashberg theory for magnetically mediated superconductivity. We also analyze the potential pseudogap behavior at T = 0. Here, we argue that it may exist, but only at a finite correlation length, and not as a precursor to antiferromagnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Effective theory of superconductivity in strongly coupled amorphous materials

A theory of phonon-mediated superconductivity in strong-coupling amorphous materials is developed based on an effective description of structural disorder and its effect on the vibrational spectrum. The theory accounts for the diffusivelike transport of vibrational excitations due to disorder-induced scattering within the Eliashberg theory of strong-coupling superconductivity. The theory provides a good analytical description of the Eliashberg function $α^2F(ω)$ in comparison with experiments and allows one to disentangle the effects of transverse and longitudinal excitations on the Eliashberg function. In particular, it shows that the transverse excitations play a crucial role in driving an increase or excess in the Eliashberg function at low energy, which is related to the boson peak phenomenon in vibrational spectra of glasses. This low-energy excess, on the one hand, drives an enhancement of the electron-phonon coupling but at the same time reduces the characteristic energy scale $ω_{\text{log}}$ in the Allen-Dynes formula. As a consequence, the nonmonotonicity of $T_c$ as a function of alloying (disorder) in Pb-based systems can be rationalized. Further, the case of Al-based systems, where disorder increases $T_c$ from the start, is also analyzed. General material-design principles for enhancing $T_c$ in amorphous superconductors are presented.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Exact solution of two simple non-equilibrium electron-phonon and electron-electron coupled systems: The atomic limit of the Holstein-Hubbard model and the generalized Hatsugai-Komoto model

One of the challenges in many-body physics is determining the effects of phonons on strongly correlated electrons. The difficulty arises from strong correlations at differing energy scales—for band metals, Migdal-Eliashberg theory accurately determines electron-phonon coupling effects due to the absence of vertex corrections, but strongly correlated electrons require a more complex description, and the standard Migdal-Eliashberg approach does not necessarily apply. In this work, we solve for the atomic limit Green's function of the Holstein-Hubbard model with both time-dependent electron-electron and electron-phonon couplings. Then, we examine the photoemission spectra of this model in and out of equilibrium. Next, we use similar methods to exactly solve an extended version of the Hatsugai-Komoto model and examine its behavior in and out of equilibrium. These calculations lead us to propose using the first moment of the photoemission spectra to signal non-equilibrium changes in electron-electron and electron-phonon couplings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Implications of the electron-phonon coupling in CuPb 9 ( PO 4 ) 6 O for superconductivity: An ab initio study

Here we report ab initio calculations of the electronic and vibrational properties in CuPb 9 (PO 4 ) 6 O, including the electron-phonon coupling strength via strong-coupling Migdal-Eliashberg theory. We verify the presence of appealing flat electronic bands near the Fermi level, a strong hybridization between the Cu 3d and O 2p states, and soft low-energy phonons, which can suggest high-temperature superconducting behavior. However, the electron-phonon coupling strength appears insufficient to overcome the Coulomb repulsion between an electron pair and thus does not support high-temperature superconductivity in CuPb 9 (PO 4 ) 6 O via the conventional electron-phonon Migdal-Eliashberg mechanism. Even neglecting Coulomb repulsion of the electron pair we find this electron-phonon coupling suggests a superconducting transition temperature of less than 2 K.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Electron–phonon physics from first principles using the EPW code

EPW is an open-source software for ab initio calculations of electron–phonon interactions and related materials properties. The code combines density functional perturbation theory and maximally localized Wannier functions to efficiently compute electron–phonon coupling matrix elements, and to perform predictive calculations of temperature-dependent properties and phonon-assisted quantum processes in bulk solids and low-dimensional materials. Here, we report on significant developments in the code since 2016, namely: a transport module for the calculation of charge carrier mobility under electric and magnetic fields using the Boltzmann transport equation; a superconductivity module for calculations of phonon-mediated superconductors using the anisotropic multi-band Eliashberg theory; an optics module for calculations of phonon-assisted indirect transitions; a module for the calculation of small and large polarons without supercells; and a module for calculating band structure renormalization and temperature-dependent optical spectra using the special displacement method. For each capability, we outline the methodology and implementation and provide example calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data

Quantum Monte Carlo (QMC) simulations of correlated electron systems provide unbiased information about system behavior at a quantum critical point (QCP) and can verify or disprove the existing theories of non-Fermi liquid (NFL) behavior at a QCP. However, simulations are carried out at a finite temperature, where quantum critical features are masked by finite-temperature effects. Here, we present a theoretical framework within which it is possible to separate thermal and quantum effects and extract the information about NFL physics at T = 0. We demonstrate our method for a specific example of 2D fermions near an Ising ferromagnetic QCP. We show that one can extract from QMC data the zero-temperature form of fermionic self-energy Σ(ω) even though the leading contribution to the self-energy comes from thermal effects. We find that the frequency dependence of Σ(ω) agrees well with the analytic form obtained within the Eliashberg theory of dynamical quantum criticality, and obeys ω 2/3 scaling at low frequencies. Our results open up an avenue for QMC studies of quantum critical metals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Superconductivity and topological aspects of two-dimensional transition-metal monohalides

Two-dimensional (2D) superconducting states have attracted much recent interest, especially when they coexist with nontrivial band topology which affords a promising approach towards Majorana fermions. Using first-principles calculations, we predict van der Waals monolayered transition-metal monohalides MX (M = Zr, Mo; X = F, Cl) as a class of 2D superconductors with remarkable transition temperature (5.9–12.4 K). Anisotropic Migdal-Eliashberg theory reveals that ZrCl have a single superconducting gap Δ ~ 2.14 meV, while MoCl is a two-gap superconductor with Δ ~ 1.96 and 1.37 meV. The Z 2 band topology of 2D MX is further demonstrated that MoF and MoCl are candidates for realizing topological superconductivity. Moreover, the Dirac phonons of ZrCl and MoCl contribute w-shape phononic edge states, which are potential for an edge-enhanced electron-phonon coupling. These findings demonstrate that 2D MX offers an attractive platform for exploring the interplay between superconductivity, nontrivial electronic and phononic topology.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Anisotropy and isotope effect in superconducting solid hydrogen

Elucidating the phase diagram of solid hydrogen is a key objective in condensed matter physics. Several decades ago, it was proposed that at low temperatures and high pressures, solid hydrogen would be a metal with a high superconducting transition temperature. This transition to a metallic state can happen through the closing of the energy gap in the molecular solid or through a transition to an atomic solid. Recent experiments have managed to reach pressures in the range of 400–500 GPa, providing valuable insights. There is strong evidence suggesting that metallization via either of these mechanisms occurs within this pressure range. Computational and experimental studies have identified multiple promising crystal phases, but the limited accuracy of calculations and the limited capabilities of experiments prevent us from determining unequivocally the observed phase or phases. Therefore, it is crucial to investigate the superconducting properties of all the candidate phases. Recently, we reported the superconducting properties of the C2/c-24, Cmca-12, Cmca-4 and I41/amd-2 phases, including anharmonic effects. Here, we report the effects of anisotropy on superconducting properties using Eliashberg theory. Then, we investigate the superconducting properties of deuterium and estimate the size of the isotope effect for each phase. We find that the isotope effect on superconductivity is diminished by anharmonicity in the C2/c-24 and Cmca-12 phases and enlarged in the Cmca-4 and I41/amd-2 phases. Our anharmonic calculations of the C2/c-24 phase of deuterium agree closely with the most recent experiment by Loubeyre et al (2022 Phys. Rev. Lett.29 035501), indicating that the C2/c-24 phase remains the leading candidate in this pressure range, and has a strong anharmonic character. These characteristics can serve to distinguish among crystal phases in experiment. Furthermore, expanding our understanding of superconductivity in pure hydrogen holds significance in the study of high-T c hydrides.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗