High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin–orbit effects and p-wave superconductivity

Abstract

Disorder is a key factor influencing the behavior of condensed states of matter, however the true extent of its impact is generally difficult to determine due to the prominent roles played by quantum interference, entanglement between spin and orbital degrees of freedom and proximity to quantum critical points. Here we show that the one-particle disorder self-energy --- a direct probe of the renormalization of low-energy excitations due to defects and impurities distributed randomly in a crystal --- can be obtained by means of unbiased spectral expansions of lattice Green's functions in a computationally expedient manner. Our scheme provides a powerful framework to map out the frequency and wavevector dependence of electronic excitations in unprecedented large tight-binding systems, up to $10^{9}$ orbitals, with energy resolution only limited by the mean level spacing. We demonstrate the versatility of our approach in 3 distinct problems: (i) the Gade singularity in honeycomb layers with dilute topological defects; (ii) the rich landscape of impurity resonances in a spin--orbit-coupled ferromagnet; and (iii) the tailoring of emergent $s$-wave and $p$-wave superconducting phases in graphene via atomic defects. These examples reveal rich features in the disorder self-energy $\Sigma_{\textrm{dis}}(\mathbf{k},\omega)$ that are absent from the self-consistent $T$-matrix approach and other common approximation schemes, which include regimes of nontrivial wavevector dependence and anomalous dependence upon the impurity concentration. Our study unravels puzzling, and so far largely inaccessible, manifestations of strong nonperturbative quantum interference effects in quantum materials and disordered phases of matter.

Anomalous Transport Signatures in Weyl Semimetals with Point Defects

“…Additionally, our quantum transport simulations reveal that the spectral convergence rate (which measures how quickly the conductivity curves saturate with decreasing η) is strongly dependent on the precise Fermi level location in the low energy regime. We attribute this effect to a strong energy dependence of the disorder self-energy and related elastic scattering times [47]. Indeed, the dips observed at the resonant energies signal a strong suppression of electron diffusivity.…”

“…[41] would imply that a spectral weight proportional to n v would be drawn out of the continuum and placed exactly at the nodal energy. Generally speaking, such a situation cannot be maintained for sufficiently large defect concentrations and, in fact, coherent multiple-scattering may become important in the quantum regime, even at low concentrations [38,47].…”

Atomistic Theory of Hot-Carrier Relaxation in Large Plasmonic Nanoparticles

“…In recent years, KPM and other spectral methods have been established as promising tools to study quantum-mechanical phenomena in mesoscopic systems. For example, they have been used to extract spectral properties − and transport properties − in multibillion atom lattices. Recently, these methods have also been leveraged to obtain the rate of hot-carrier generation in million-atom plasmonic NPs and were successfully used to explain differences in photocatalytic performance of various Au–Pd nanoarchitectures and Au NP shapes .…”

Fast Fourier-Chebyshev Approach to Real-Space Simulations of the Kubo Formula

“…For noninteracting systems described by the tight-binding approximation, D is the total number of orbitals and thus the computational effort scales only linearly with the system size. This advantageous OðDMÞ scaling has been leveraged to enable unprecedented fully non-perturbative studies of one-particle properties in disordered systems [13][14][15][16][17][18][19][20][21], but open questions remain regarding the possibility to handle two-particle properties (crucial for nonequilibrium studies) in an equally satisfactory fashion. Perhaps the most familiar among these is the electrical conductivity tensor, describing the charge current response to an external electric field [22].T h e longitudinal dc response, σ aa ≔ lim ω→0 σ aa ðωÞ (with a ¼ x, y, z), is only dependent on the electronic states at the Fermi energy (in the T → 0 limit).…”

“…Implementation and benchmark.-In order to assess its baseline performance, FastCheb is implemented within framework of the open-source KITE code [16]. KITE is a high-performance code for spectral simulations of Green's functions and related quantities in real space [18,19],a n d hence is an ideal testbed for this study. The efficiency of our algorithm can be best appreciated in a direct comparison with the standard recursive method.…”