Beyond-Quasiparticle Transport with Vertex Correction: Self-Consistent Ladder Formalism for Electron-Phonon Interactions

We present a self-consistent many-body framework for computing phonon-limited electronic transport from first principles, incorporating both beyond-quasiparticle effects and vertex corrections. Using the recently developed first-principles <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>sc</a:mi> <a:mi>G</a:mi> <a:msub> <a:mrow> <a:mi>D</a:mi> </a:mrow> <a:mrow> <a:mn>0</a:mn> </a:mrow> </a:msub> </a:mrow> </a:math> method, we calculate spectral functions with nonperturbative effects such as broadening, satellites, and energy-dependent renormalization. We show that the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mi>sc</c:mi> <c:mi>G</c:mi> <c:msub> <c:mrow> <c:mi>D</c:mi> </c:mrow> <c:mrow> <c:mn>0</c:mn> </c:mrow> </c:msub> </c:mrow> </c:math> spectral functions outperform one-shot <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>G</e:mi> <e:mn>0</e:mn> </e:msub> <e:msub> <e:mi>D</e:mi> <e:mn>0</e:mn> </e:msub> </e:math> and cumulant approximations in model Hamiltonians and real materials, eliminating unphysical spectral kinks and correctly predicting the phonon emission continuum. Building on this, we introduce the self-consistent ladder formalism for transport, which captures vertex corrections due to electron-phonon interactions. This approach unifies and improves upon the two state-of-the-art approaches for first-principles phonon-limited transport: the bubble approximation and the Boltzmann transport equation. Moreover, as a charge-conserving approximation, it enables consistent calculations of the optical conductivity and dielectric function. We validate the developed method against numerically exact results for model Hamiltonians in the dilute polaronic limit and apply it to real materials. Our results show quantitative agreement with the experimental dc conductivities in intrinsic semiconductors Si and ZnO and the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:msub> <g:mrow> <g:mi>SrVO</g:mi> </g:mrow> <g:mrow> <g:mn>3</g:mn> </g:mrow> </g:msub> </g:mrow> </g:math> metal, as well as excellent agreement with the experimental THz optical and dielectric properties of Si and ZnO. This work unifies first-principles and many-body approaches for studying transport, opening new directions for applying many-body theory to materials with strong electron-phonon interactions.