Bismuth perovskites ABiO$_3$ (A = Sr, Ba) host a variety of peculiar phenomena including bond-disproportionated insulating phases and high-temperature superconductivity upon hole doping. While the mechanisms underlying these phenomena are still debat
ed, off-diagonal electron-phonon ($e$-ph) coupling originating from the modulation of the orbital overlaps has emerged as a promising candidate. Here, we employ classical Monte Carlo simulations to study a semiclassical three-orbital model with off-diagonal $e$-ph interactions. We demonstrate the existence of a (bi)polaron correlations that persists in the model at high temperatures and for hole doping away from the bond-disproportionated insulating phase. Using a spatiotemporal regression analysis between various local quantities and the lattice degrees of freedom, we also identify the similarity between heating- and doping-induced melting of a bond-disproportionated insulator at a microscopic level. Our results imply that (bi)polaron physics can be a unifying concept that helps us understand the rich bismuth perovskite phase diagram.
Resonant inelastic X-ray scattering (RIXS) is used increasingly for characterizing low-energy collective excitations in materials. RIXS is a powerful probe, which often requires sophisticated theoretical descriptions to interpret the data. In particu
lar, the need for accurate theories describing the influence of electron-phonon ($e$-p) coupling on RIXS spectra is becoming timely, as instrument resolution improves and this energy regime is rapidly becoming accessible. To date, only rather exploratory theoretical work has been carried out for such problems. We begin to bridge this gap by proposing a versatile variational approximation for calculating RIXS spectra in weakly doped materials, for a variety of models with diverse $e$-p couplings. Here, we illustrate some of its potential by studying the role of electron mobility, which is completely neglected in the widely used local approximation based on Lang-Firsov theory. Assuming that the electron-phonon coupling is of the simplest, Holstein type, we discuss the regimes where the local approximation fails, and demonstrate that its improper use may grossly textit{underestimate} the $e$-p coupling strength.
Using a realistic multi-band model for two holes doped into a CuO$_2$ layer, we devise a method to turn off the magnon-mediated interaction between the holes. This allows us to verify that this interaction is attractive, and therefore could indeed be
(part of) the superconducting glue. We derive its analytical expression and show that it consists of a novel kind of pair-hopping+spin-exchange terms. Its coupling constant is fitted from the ground state energy obtained with variational exact diagonalization, and it faithfully reproduces the effect of the magnon-mediated attraction in the entire Brillouin zone. For realistic parameter values, this effective interaction is borderline strong enough to bind the holes into preformed pairs.
Superconductivity with $T_c approx 15K$ was recently found in doped NdNiO$_2$. The Ni$^{1+}$O$_2$ layers are expected to be Mott insulators so hole doping should produce Ni$^{2+}$ with $S=1$, incompatible with robust superconductivity. We show that t
he NiO$_2$ layers fall inside a ``critical region where the large $pd$ hybridization favors a singlet $^1!A_1$ hole-doped state like in CuO$_2$. However, we find that the superexchange is about one order smaller than in cuprates, thus a magnon ``glue is very unlikely and another mechanism needs to be found.
We revisit the problem of the spectra of two holes in a CuO$_{2}$ layer, modeled as a Cu-d$^{8}$ impurity with full multiplet structure coupled to a full O-2p band as an approximation to the local electronic structure of a hole doped cuprate. Unlike
previous studies that treated the O band as a featureless bath, we describe it with a realistic tight binding model. While our results are in qualitative agreement with previous work, we find considerable quantitative changes when using the proper O-2p band structure. We also find (i) that only the ligand O-2p orbitals play an essential role, within this impurity model; (ii) that the three-orbital Emery model provides an accurate description for the subspace with $^{1}!A_1$ symmetry, which includes the ground-state in the relevant region of the phase diagram; (iii) that this ground-state has only $sim 50%$ overlap with a Zhang-Rice singlet; (iv) that there are other low-energy states, in subspaces with different symmetries, that are absent from the three-orbital Emery model and its one-band descendants. These states play an important role in describing the elementary excitations of doped cuprates.
We present a machine-learning method for predicting sharp transitions in a Hamiltonian phase diagram by extrapolating the properties of quantum systems. The method is based on Gaussian Process regression with a combination of kernels chosen through a
n iterative procedure maximizing the predicting power of the kernels. The method is capable of extrapolating across the transition lines. The calculations within a given phase can be used to predict not only the closest sharp transition, but also a transition removed from the available data by a separate phase. This makes the present method particularly valuable for searching phase transitions in the parts of the parameter space that cannot be probed experimentally or theoretically.
We use the Momentum Average approximation (MA) to study the ground-state properties of strongly bound bipolarons in the double-well electron-phonon (el-ph) coupling model, which describes certain intercalated lattices where the linear term in the el-
ph coupling vanishes due tosymmetry. We show that this model predicts the existence of strongly bound yet lightweight bipolarons in some regions of the parameter space. This provides a novel mechanism for the appearance of such bipolarons, in addition to long-range el-ph coupling and special lattice geometries.
We show that in crystals where light ions are symmetrically intercalated between heavy ions, the electron-phonon coupling for carriers located at the light sites cannot be described by a Holstein model. We introduce the double-well electron-phonon co
upling model to describe the most interesting parameter regime in such systems, and study it in the single carrier limit using the momentum average approximation. For sufficiently strong coupling, a small polaron with a robust phonon cloud appears at low energies. While some of its properties are similar to those of a Holstein polaron, we highlight some crucial differences. These prove that the physics of the double-well electron-phonon coupling model cannot be reproduced with a linear Holstein model.
We use two recently proposed methods to calculate exactly the spectrum of two spin-${1over 2}$ charge carriers moving in a ferromagnetic background, at zero temperature, for three types of models. By comparing the low-energy states in both the one-ca
rrier and the two-carrier sectors, we analyze whether complex models with multiple sublattices can be accurately described by simpler Hamiltonians, such as one-band models. We find that while this is possible in the one-particle sector, the magnon-mediated interactions which are key to properly describe the two-carrier states of the complex model are not reproduced by the simpler models. We argue that this is true not just for ferromagnetic, but also for antiferromagnetic backgrounds. Our results question the ability of simple one-band models to accurately describe the low-energy physics of cuprate layers.
We propose two new methods to calculate exactly the spectrum of two spin-${1over 2}$ charge carriers moving in a ferromagnetic background, at zero temperature. We find that if the spins are located on a different sublattice than that on which the fer
mions move, magnon-mediated effective interactions are very strong and can bind the fermions into low-energy bipolarons with triplet character. This never happens in models where spins and charge carriers share the same lattice, whether they are in the same band or in different bands. This proves that effective one-lattice models do not describe correctly the low-energy part of the two-carrier spectrum of a two-sublattice model, even though they may describe the low-energy single-carrier spectrum appropriately.
