Engineering topics
Nocera, Alberto
Publications and source records attributed to Nocera, Alberto.
Auger spectroscopy beyond the ultra-short core-hole relaxation time approximation
Abstract We present a time-dependent computational approach to study Auger electron spectroscopy (AES) beyond the ultra-short core-hole relaxation time approximation and, as a test case, we apply it to the paradigmatic example of a one-dimensional Mott insulator represented by a half-filled Hubbard chain. The Auger spectrum is usually calculated by assuming that, after the creation of a core-hole, the system thermalizes almost instantaneously. This leads to a relatively simple analytical expression that uses the ground-state with a core-hole as a reference state and ignores all the transient dynamics related to the screening of the core-hole. In this picture, the response of the system can be associated to the pair spectral function. On the other hand, in our numerical calculations, the core hole is created by a light pulse, allowing one to study the transient dynamics of the system in terms of the pulse duration and in the non-perturbative regime. Time-dependent density matrix renormalization group calculations reveal that the relaxation process involves the creation of a polarization cloud of doublon excitations that have an effect similar to photo-doping. As a consequence, there is a leak of spectral weight to higher energies into what otherwise would be the Mott gap. For longer pulses, these excited states, mostly comprised of doublons, can dominate the spectrum. By changing the duration of the light-pulse, the entire screening process can be resolved in time.
A time-dependent momentum-resolved scattering approach to core-level spectroscopies
While new light sources allow for unprecedented resolution in experiments with X-rays, a theoretical understanding of the scattering cross-section is lacking. In the particular case of strongly correlated electron systems, numerical techniques are quite limited, since conventional approaches rely on calculating a response function (Kramers-Heisenberg formula) that is obtained from a perturbative analysis of scattering processes in the frequency domain. This requires a knowledge of a full set of eigenstates in order to account for all intermediate processes away from equilibrium, limiting the applicability to small tractable systems. In this work, we present an alternative paradigm, recasting the problem in the time domain and explicitly solving the time-dependent Schrödinger equation without the limitations of perturbation theory: a faithful simulation of the scattering processes taking place in actual experiments, including photons and core electrons. We show how this approach can yield the full time and momentum resolved Resonant Inelastic X-Ray Scattering (RIXS) spectrum of strongly interacting many-body systems. We demonstrate the formalism with an application to Mott insulating Hubbard chains using the time-dependent density matrix renormalization group method, which does not require a priory knowledge of the eigenstates and can solve very large systems with dozens of orbitals. This approach can readily be applied to systems out of equilibrium without modification and generalized to other spectroscopies.
Root-N Krylov-space correction vectors for spectral functions with the density matrix renormalization group
In this work, we propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov-space decomposition to compute the correction vectors. Our approach entails the calculation of the root-N (N=2 is the standard square root) of the Hamiltonian propagator using Krylov-space decomposition and repeating this procedure N times to obtain the actual correction vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, whereas achieving better computational performance at large N. We apply our method to spin and charge spectral functions of t-J and Hubbard models in the challenging two-leg ladder geometry and provide evidence that the root-N approach reaches a much improved spectral resolution compared to the conventional correction vector.
Particle-hole asymmetry in the dynamical spin and charge responses of corner-shared 1D cuprates
Although many experiments imply that oxygen orbitals play an essential role in the high-temperature superconducting cuprates, their precise role in collective spin and charge excitations and superconductivity is not yet fully understood. Here, we study the doping-dependent dynamical spin and charge structure factors of single and multi-orbital (pd) models for doped one-dimensional corner-shared spin-chain cuprates using several numerically exact methods. In doing so, we determine the orbital composition of the collective spin and charge excitations of cuprates, with important implications for our understanding of these materials. For example, we observe a particle-hole asymmetry in the orbital-resolved charge excitations, which is directly relevant to resonant inelastic x-ray scattering experiments and not captured by the single-band Hubbard model. Our results imply that one must explicitly include the oxygen degrees of freedom in order to fully understand some experimental observations on cuprate materials.
Spectroscopic signatures of next-nearest-neighbor hopping in the charge and spin dynamics of doped one-dimensional antiferromagnets
In this work, we study the impact of next-nearest-neighbor (nnn) hopping on the low-energy collective excitations of strongly correlated doped antiferromagnetic cuprate spin chains. Specifically, we use exact diagonalization and the density matrix renormalization group method to study the single-particle spectral function, the dynamical spin and charge structure factors, and the Cu L-edge resonant inelastic x-ray scattering (RIXS) intensity of the doped t-t'-J model for a set of t' values. We find evidence for the breakdown of spin-charge separation as |t'| increases and identify its fingerprints in the dynamical response functions. The inclusion of nnn hopping couples the spinon and holon excitations, resulting in the formation of a spin-polaron, where a ferromagnetic spin polarization cloud dresses the doped carrier. The spin-polaron manifests itself as additional spectral weight in the dynamical correlation functions, which appear simultaneously in the spin- and charge-sensitive channels. We also demonstrate that RIXS can provide a unique view of the spin-polaron, due to its sensitivity to both the spin and charge degrees of freedom.
BCS-BEC crossover in a (t 2g ) 4 excitonic magnet
The condensation of spin-orbit-induced excitons in t 2 g 4 electronic systems is attracting considerable attention. At large Hubbard U , antiferromagnetism was proposed to emerge from the Bose-Einstein Condensation (BEC) of triplons ( J eff = 1 ). Furthermore, we show that even at intermediate U regimes, the spin-orbit exciton condensation is possible leading also to staggered magnetic order. The canonical electron-hole excitations (excitons) transform into local triplon excitations at large U , and this BEC strong coupling regime is smoothly connected to the intermediate U excitonic insulator region. We solved the degenerate three-orbital Hubbard model with spin-orbit coupling ( λ ) in one dimension using the density matrix renormalization group, while in two dimensions we use the Hartree-Fock approximation (HFA). Employing these techniques, we provide the full λ versus U phase diagrams for both one- and two-dimensional lattices. Our main result is that at intermediate Hubbard U , increasing λ at fixed U the system transitions from an incommensurate spin-density-wave metal to a Bardeen-Cooper-Schrieffer (BCS) excitonic insulator, with coherence length r coh of O ( a ) and O ( 10 a ) in 1 d and 2 d , respectively, with a being the lattice spacing. Further increasing λ , the system eventually crosses over to the BEC limit (with r coh ≪ a ).
Emergence of superconductivity in doped multiorbital Hubbard chains
Abstract We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our ansatz is an optimized linear superposition of Affleck–Kennedy–Lieb–Tasaki valence-bond states, rendering the combination a valence-bond liquid dubbed orbital resonant valence bond. We show that the undoped (one-electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Anderson’s resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile, leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U / W strengths— W the carrier’s bandwidth—could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.
Theoretical study of the spin and charge dynamics of two-leg ladders as probed by resonant inelastic x-ray scattering
Resonant inelastic x-ray scattering (RIXS) has become an important tool for studying elementary excitations in correlated materials. Here, we present a systematic theoretical investigation of the Cu L-edge RIXS spectra of undoped and doped cuprate two-leg spin-ladders in both the non-spin-conserving (NSC) and spin-conserving (SC) channels. The spectra are rich and host many exotic excitations. In the NSC channel of the undoped case, we identify one-triplon and bound triplet two-triplon excitations in the strong rung coupling limit, as well as confined spinons in the weak rung coupling limit. In the doped case, we observe a quasiparticle excitation formed from a bound charge and spin-1/2 in the strong rung coupling limit. In the SC channel, we also identify several new features, including bound singlet two-triplon excitations and confined spinons in the undoped ladders in the strong and weak rung coupling limits, respectively. Conversely, in the doped case, the SC channel primarily probes both gapless and gapped charge excitations. Finally, we revisit the available data for the ladder compound Sr 14 Cu 24 O 41 in the context of our results.
Block excitonic condensate at n = 3.5 in a spin-orbit coupled t 2 g multiorbital Hubbard model
Theoretical studies recently predicted the condensation of spin-orbit excitons at momentum $q={\pi}$ in ${t}_{2g}^{4}$ spin-orbit coupled three-orbital Hubbard models at electronic density $n=4$. In parallel, experiments involving iridates with noninteger valence states for the Ir ions are starting to attract considerable attention. Using the density matrix renormalization group technique we present evidence for the existence of an excitonic condensate at $n=3.5$ in a one-dimensional Hubbard model with a degenerate ${t}_{2g}$ sector, when in the presence of spin-orbit coupling. At intermediate Hubbard $U$ and spin-orbit ${\lambda}$ couplings, we found an excitonic condensate at the unexpected momentum $q={\pi}/2$ involving ${j}_{\mathrm{eff}}=3/2,m=\pm{}1/2$, and ${j}_{\mathrm{eff}}=1/2,m=\pm{}1/2$ bands in the triplet channel, coexisting with an also unexpected block magnetic order. We also present the entire ${\lambda}$ vs $U$ phase diagram, at a fixed and robust Hund coupling. Interestingly, this new “block excitonic phase” is present even at large values of ${\lambda}$, unlike the $n=4$ excitonic phase discussed before. Our computational study helps to understand and predict the possible magnetic phases of materials with ${d}^{3.5}$ valence and robust spin-orbit coupling.