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arXiv:2412.15981

Identifying and quantifying Su-Schrieffer-Heeger-like interactions with RIXS

Debshikha Banerjee, Jinu Thomas, Alberto Nocera, Steven Johnston

Published Dec 20, 2024• 0 citations
arXivHTMLPDF

Abstract

Su-Schrieffer-Heeger (SSH)-like electron-phonon (e-ph) interactions can drive the formation of light (bi)polarons and several novel states of matter. It is, therefore, prudent to develop experimental protocols for identifying such couplings in real materials and quantifying their strength. Here, we investigate how resonant inelastic x-ray scattering (RIXS) probes e-ph interactions in the one-dimensional half-filled Hubbard-SSH model with onsite phonons. Using the density matrix renormalization group method, we compute the full RIXS response and find that the lattice excitations generated during the scattering process inevitably couple to the system's charge and magnetic sectors, resulting in combined multi-particle excitations that cannot be easily disentangled from one another. While this aspect complicates the interpretation of RIXS experiments, we outline how it can be leveraged to identify and quantify SSH-like interactions in quantum materials.

DOI
10.48550/arxiv.2412.15981

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Su-Schrieffer-Heeger (SSH)-like electron-phonon (e-ph) interactions can drive the formation of light (bi)polarons and several novel states of matter. It is, therefore, prudent to develop experimental protocols for identifying such couplings in real materials and quantifying their strength. Here, we investigate how resonant inelastic x-ray scattering (RIXS) probes e-ph interactions in the one-dimensional half-filled Hubbard-SSH model with onsite phonons. Using the density matrix renormalization group method, we compute the full RIXS response and find that the lattice excitations generated during the scattering process inevitably couple to the system's charge and magnetic sectors, resulting in combined multi-particle excitations that cannot be easily disentangled from one another. While this aspect complicates the interpretation of RIXS experiments, we outline how it can be leveraged to identify and quantify SSH-like interactions in quantum materials.
Su-Schrieffer-Heeger-like (SSH-like) electron-phonon interactions can drive the formation of light (bi)polarons and several novel states of matter. It is, therefore, prudent to develop experimental protocols for identifying such couplings in real materials and quantifying their strength. Here, we investigate how resonant inelastic x-ray scattering (RIXS) probes electron-phonon interactions in the one-dimensional half-filled Hubbard-SSH model with on-site phonons. Using the density matrix renormalization group method, we compute the full RIXS response and find that the lattice excitations generated during the scattering process inevitably couple to the system's charge and magnetic sectors, resulting in combined multiparticle excitations that cannot be easily disentangled from one another. While this aspect complicates the interpretation of RIXS experiments, we outline how it can be leveraged to identify and quantify SSH-like interactions in quantum materials.
An emerging application of resonant inelastic x-ray scattering (RIXS) is the study of lattice excitations and electron-phonon ( e -ph) interactions in quantum materials. Despite the growing importance of this area of research, the community lacks a complete understanding of how the RIXS process excites the lattice and how these excitations encode information about the e -ph interactions. Here, we present a detailed study of the RIXS spectra of the Hubbard-Holstein model defined on extended one-dimensional lattices. Using the density matrix renormalization group method, we compute the RIXS response while treating the electron mobility, many-body interactions, and core-hole interactions on an equal footing. The predicted spectra exhibit notable differences from those obtained using the commonly adopted Lang-Firsov models, with important implications for analyzing past and future experiments. Our results provide a deeper understanding of how RIXS probes e -ph interactions and set the stage for a more realistic analysis of future experiments.
Su-Schrieffer-Heeger (SSH) electron-phonon ($e\ensuremath{-}p\phantom{\rule{0}{0ex}}h$) interactions have been theorized to play critical roles in several novel states of matter, ranging from nontrivial topological states to high-temperature bipolaronic superconductivity. This work compares the superconducting and competing charge and bond correlations of the two-dimensional Holstein and optical (SSH) models. The authors find that near half-filling, light SSH (bi)polarons support superconductivity to larger values of $e\ensuremath{-}p\phantom{\rule{0}{0ex}}h$ coupling compared to the Holstein polaron. These results are essential for identifying and engineering bipolaronic superconductivity in quantum materials.
Abstract We present a method for computing the resonant inelastic x-ray scattering (RIXS) spectra in one-dimensional systems using the density matrix renormalization group (DMRG) method. By using DMRG to address this problem, we shift the computational bottleneck from the memory requirements associated with exact diagonalization (ED) calculations to the computational time associated with the DMRG algorithm. This approach is then used to obtain RIXS spectra on cluster sizes well beyond state-of-the-art ED techniques. Using this new procedure, we compute the low-energy magnetic excitations observed in Cu L-edge RIXS for the challenging corner shared CuO4 chains, both for large multi-orbital clusters and downfolded t-J chains. We are able to directly compare results obtained from both models defined in clusters with identical momentum resolution. In the strong coupling limit, we find that the downfolded t-J model captures the main features of the magnetic excitations probed by RIXS only after a uniform scaling of the spectra is made.
Electron-phonon (e-ph) interactions play a crucial role in determining many properties of materials. In this context, the Su-Schrieffer-Heeger (SSH) model, where atomic motion modulates the electronic hopping, has gained significant attention due to its potential for strong electron pairing in relation to high-Tc superconductivity. Previous studies of the SSH models have addressed many aspects of this problem, but have focused heavily on either dilute or half-filled models with dispersionless (Einstein) phonons. Here, we study the effects of dispersive optical phonons on the lightly doped one-dimensional optical Hubbard-SSH model using the density matrix renormalization group. We observe a significant enhancement in singlet binding driven by phonon dispersion; however, by calculating various correlation functions, we find that the enhanced binding does not translate to increased superconducting correlations but rather robust bond correlations in the studied parameter regime. Nevertheless, the significant impact of phonon dispersion on these correlations highlights the need to go beyond the Einstein phonon limit while modeling realistic quantum materials.
Most nonperturbative numerical studies of electron-phonon interactions focus on model Hamiltonians where the electrons interact with a phonon branch via a single type of microscopic mechanism. Two commonly explored couplings in this context are the Holstein and Su-Schrieffer-Heeger (SSH) interactions, which describe phonons modulating the on-site energy and intersite electron hopping, respectively. Many materials, however, have multiple phonon branches that can each interact with electronic degrees of freedom in different ways. We present here a determinant quantum Monte Carlo study of the half-filled two-dimensional (bond) SSH-Holstein Hamiltonian, where electrons couple to different phonon branches via either the Holstein or SSH mechanism. We map the model's phase diagram and determine the nature of the transitions between charge-density wave, bond-order wave, and antiferromagnetic order.