Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory
Abstract
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, quantitiesmore »
- Authors:
-
- Stanford Univ., CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES)
- SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES)
- SLAC National Accelerator Lab., Menlo Park, CA (United States). Stanford Institute for Materials and Energy Science (SIMES); Stanford Univ., CA (United States). Geballe Lab. for Advanced Materials
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1768219
- Grant/Contract Number:
- AC02-76SF00515
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 103; Journal Issue: 2; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Nosarzewski, Benjamin, Schüler, Michael, and Devereaux, Thomas P. Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory. United States: N. p., 2021.
Web. doi:10.1103/physrevb.103.024520.
Nosarzewski, Benjamin, Schüler, Michael, & Devereaux, Thomas P. Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory. United States. https://doi.org/10.1103/physrevb.103.024520
Nosarzewski, Benjamin, Schüler, Michael, and Devereaux, Thomas P. Wed .
"Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory". United States. https://doi.org/10.1103/physrevb.103.024520. https://www.osti.gov/servlets/purl/1768219.
@article{osti_1768219,
title = {Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory},
author = {Nosarzewski, Benjamin and Schüler, Michael and Devereaux, Thomas P.},
abstractNote = {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/Tc for conventional superconductors mediated by retarded electron-phonon interactions is proposed.},
doi = {10.1103/physrevb.103.024520},
journal = {Physical Review B},
number = 2,
volume = 103,
place = {United States},
year = {Wed Jan 20 00:00:00 EST 2021},
month = {Wed Jan 20 00:00:00 EST 2021}
}
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