Self-consistent Born Approximation Research Articles

Singlet Polaron Theory of Low-Energy Optical Excitations in NiPS_{3}.

We develop a theory that explains the low-energy optical excitations near 1.5eV observed by optical experiments in NiPS_{3}. Using abinitio methods, we construct a two-band Hubbard model for two effective Ni orbitals. The dominant effective hopping corresponds to third-nearest neighbors. This model exhibits triplet-singlet excitations of energy near 2 times the Hund exchange. We derive an effective model for the movement of two singlets in an antiferromagnetic background, that we solve using a generalized self-consistent Born approximation, disentangling the nature of these novel excitations, which move coherently as "singlet polarons".

Exciton interacting with a moiré lattice: Polarons, strings, and optical probing of spin correlations

The ability to create and stack different atomically thin transition metal dichacogenide (TMD) layers on top of each other has opened up a rich playground for exploring new and interesting two-dimensional (2D) quantum phases. As a consequence of this remarkable development, there is presently a need for new sensors to probe these 2D layers, since conventional techniques for bulk materials such as x-ray and neutron scattering are inefficient. Here, we develop a general theory for how an exciton in a TMD monolayer couples to spin and charge correlations in an adjacent moiré lattice created by a TMD bilayer. Virtual tunneling of charge carriers, assumed for concreteness to be holes, between the moiré lattice and the monolayer combined with the presence of bound hole-exciton states, i.e., trions, give rise to an effective interaction between the moiré holes and the exciton. In addition to the Umklapp scattering, we show that this interaction is spin-dependent and therefore couples the exciton to the spin correlations of the moiré holes, which may be in- as well as out-of-plane. We then use our theory to examine two specific examples where the moiré holes form in-plane ferromagnetic or antiferromagnetic order. In both cases, the exciton creates spin waves in the moiré lattice, which we analyze by using a self-consistent Born approximation that includes such processes to infinite order. We show that the competition between magnetic order and exciton motion leads to the formation of a well-defined quasiparticle consisting of the exciton surrounded by a cloud of magnetic frustration in the moiré lattice sites below. For the antiferromagnet, we furthermore demonstrate the presence of the elusive geometric string excitations and discuss how they can be observed via their smoking gun energy dependence on the spin-spin coupling, which can be tuned by varying the twist angle of the moiré bilayer. All these phenomena have clear signatures in the exciton spectrum, and as such our results illustrate that excitons are promising quantum probes providing optical access to the spin correlations of new phases predicted to exist in TMD materials. Published by the American Physical Society 2024

Finite-Temperature Hole-Magnon Dynamics in an Antiferromagnet.

Employing the numerically accurate multiple Davydov Ansatz in combination with the thermo-field dynamics approach, we delve into the interplay of the finite-temperature dynamics of holes and magnons in an antiferromagnet, which allows for scrutinizing previous predictions from the self-consistent Born approximation while offering, for the first time, accurate finite-temperature computation of detailed magnon dynamics as a response and a facilitator to the hole motion. The study also uncovers a pronounced temperature dependence of the magnon and hole populations, pointing to the feasibility of potential thermal manipulation and control of hole dynamics. Our methodology can be applied not only to the calculation of steady-state angular-resolved photoemission spectra but also to the simulation of femtosecond terahertz pump-probe and other nonlinear signals for the characterization of antiferromagnetic materials.

Influence of ab initio derived site-dependent hopping parameters on electronic transport in graphene nanoribbons.

Graphene Nano Ribbons (GNRs) have been studied extensively due to their potential applications in electrical transport, optical devices, etc. The Tight Binding (TB) model is a common method used to theoretically study the properties of GNRs. However, the hopping parameters of two-dimensional graphene (2DG) are often used as the hopping parameters of the TB model of GNRs, which may lead to inaccuracies in the prediction of GNRs. In this work, we calculated the site-dependent hopping parameters from density functional theory and construction of Wannier orbitals for use in a realistic TB model. It has been found that due to the edge effect, the hopping parameters of edge C atoms are markedly different from the bulk part, which is prominently observed in narrow GNRs. Compared to graphene, the change of hopping parameter of edge C atoms of zigzag GNRs (ZGNRs) and armchair GNRs (AGNRs) is as high as 0.11 and 0.08 eV, respectively. Moreover, we investigated the impact of the calculated site-dependent (SD) hopping parameters on the electronic transport properties of GNRs in the absence and presence of the perpendicular electric field and dilute charged impurities using the Green function approach, Landauer-Büttiker formalism and self-consistent Born approximation. We find an electron-hole asymmetry in the electronic structure and transport properties of ZGNRs with SD hopping parameters. Furthermore, AGNRs with SD hopping energies show a band gap regardless of their width, while AGNRs with 2DG hopping parameters exhibit metallic or semiconductor phases depending on their width. In addition, electric field-induced 4-ZGNR with SD hopping parameters undergoes a metallic to n-doped semiconducting phase transition whereas for 4-ZGNR with 2DG hopping parameters and 8-AGNRs with 2DG or SD hopping parameters, the application of an electric field opens the band gap in both conduction and valence bands simultaneously. Our findings provide evidence for the electron-hole symmetry breaking in ZGNR with SD hopping parameters and make ZGNRs a suitable candidate in valleytronic devices.

Interlayer Conductivity of Quasi-Two-Dimensional Layered Conductors in a Magnetic Field at Yamaji Angles

The behavior of the interlayer magnetoresistance Rzz is analyzed in quasi-two-dimensional layered metals ina magnetic field tilted at Yamaji angles at which the minimum of the interlayer conductivity is observed. Thecases of the Lorentzian line shape of Landau levels and of the shape corresponding to the self-consistent Bornapproximation are studied. At high fields, the behavior Rzz B3/2 is theoretically predicted, which agrees wellwith experimental data.

Spectrum of the Hole Excitation in Spin-Orbit Mott Insulator Na2IrO3

We study the motion of a hole with internal degrees of freedom, introduced to the zigzag magnetic ground state of Na2IrO3, by using the self-consistent Born approximation. We find that the low-, intermediate-, and high-energy spectra are primarily attributed to the singlet, triplet, and quintet hole contributions, respectively. The spectral functions exhibit distinct features such as the electron-like dispersion of low-energy states near the Γ point, the maximum M-point intensity of mid-energy states, and the hole-like dispersion of high-energy states. These features are robust and almost insensitive to the exchange model and Hund’s coupling, and are in qualitative agreement with the angular-resolved photoemission spectra observed in Na2IrO3. Our results reveal that the interference between internal degrees of freedom in different sublattices plays an important role in inducing the complex dispersions.

Born approximation study of the strong disorder in magnetized surface states of a topological insulator

In this study we investigate the effect of random point disorder on the surface states of a topological insulator with out-of-plane magnetization. We consider the disorder within a high order Born approximation. The Born series converges to the one branch of the self-consistent Born approximation (SCBA) solution at low disorder. As the disorder strength increases, the Born series converges to another SCBA solution with the finite density of states within the magnetization induced gap. Further increase of the disorder strength leads to a divergence of the Born series, showing the limits of the applicability of the Born approximation. We find that the convergence properties of this Born series are closely related to the properties of the logistic map, which is known as a prototypical model of chaos. We also calculate the longitudinal and Hall conductivities within the Kubo formulas at zero temperature with the vertex corrections for the velocity operator. Vertex corrections are important for describing transport properties in the strong disorder regime. In the case of strong disorder, the longitudinal conductivity is weakly dependent on the disorder strength, while the Hall conductivity decreases with increasing disorder.

Machine learning the spectral function of a hole in a quantum antiferromagnet

Understanding charge motion in a background of interacting quantum spins is a fundamental problem in quantum many-body physics. The most extensively studied model for this problem is the so-called $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{'}\ensuremath{'}}\text{\ensuremath{-}}J$ model, where the determination of the parameter ${t}^{\ensuremath{'}}$ in the context of cuprate superconductors is challenging. Here we present a theoretical study of the spectral functions of a mobile hole in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{'}\ensuremath{'}}\text{\ensuremath{-}}J$ model using two machine-learning techniques: $K$-nearest neighbor regression (KNN) and a feed-forward neural network (FFNN). We employ the self-consistent Born approximation to generate a dataset of about $1.3\ifmmode\times\else\texttimes\fi{}{10}^{5}$ spectral functions. We show that, for the forward problem, both methods allow for the accurate and efficient prediction of spectral functions, allowing, e.g., rapid searches through parameter space. Furthermore, we find that for the inverse problem (inferring Hamiltonian parameters from spectra), the FFNN can, but the KNN cannot, accurately predict the model parameters using merely the density of states. Our results suggest that it may be possible to use deep-learning methods to predict materials parameters from experimentally measured spectral functions.

Impurity effects on the zeroth pseudo-Landau level in twisted bilayer graphene

We theoretically study the impurity effects on the zeroth pseudo-Landau level (PLL) representation of the flat band in a twisted bilayer graphene (TBG) system. Our research investigates the impact of both short-range and long-range charged impurities on the PLL using the self-consistent Born approximation and random phase approximation. Our findings indicate that short-range impurities have a significant effect on the broadening of the flat band due to impurity scattering. In contrast, the impact of long-range charged impurities on the broadening of the flat band is relatively weak, and the primary impact of the Coulomb interaction is the splitting of the PLL degeneracy when a certain purity condition is satisfied. As a result, spontaneous ferromagnetic flat bands with nonzero Chern numbers emerge. Our work sheds light on the effect of impurities on the quantum Hall plateau transition in TBG systems.

Spin-mediated Mott excitons

Motivated by recent experiments on Mott insulators, in both iridates and ultracold atoms, we theoretically study the effects of magnetic order on the Mott-Hubbard excitons. In particular, we focus on spin-mediated doublon-holon pairing in Hubbard materials. We use several complementary theoretical techniques: Mean-field theory to describe the spin degrees of freedom, the self-consistent Born approximation to characterize individual charge excitations across the Hubbard gap, and the Bethe-Salpeter equation to identify bound states of doublons and holons. The binding energy of the Mott exciton is found to increase with increasing the N\'eel order parameter, whereas the exciton mass decreases. We observe that these trends rely significantly on the retardation of the effective interaction, and require consideration of multiple effects from changing the magnetic order. Our results are consistent with the key qualitative trends observed in recent experiments on iridates. Moreover, the findings could have direct implications on ultracold atom Mott insulators where the Hubbard model is the exact description of the system and the microscopic degrees of freedom can be directly accessed.

Quantum transport in driven systems with vibrations: Floquet nonequilibrium Green's functions and the self-consistent Born approximation

We investigate the effects of alternating voltage on nonequilibrium quantum systems with localized phonon modes. Nonequilibrium Green's functions are utilized, with electron-phonon coupling being considered with the $GD$ approximation (self-consistent Born approximation). Using a Floquet approach, we assume periodicity of the dynamics. This approach allows us to investigate the influence of the driven electronic component on the nonequilibrium occupation of the vibrations. It was found that signatures of inelastic transport gained photon-assisted peaks. A simplistic model was proposed and found to be in good agreement with the full model in certain parameter ranges. Moreover, it was found that driving the alternating current at resonance with vibrational frequencies caused an increase in phonon occupation.

Holes and magnetic polarons in a triangular lattice antiferromagnet

The intricate interplay between charge motion and magnetic order in geometrically frustrated lattices is central for the properties of many two-dimensional quantum materials. The triangular lattice antiferromagnet is a canonical example of a frustrated system, and here we analyze the dynamics of a hole in such a lattice focusing on observables that have become accessible in a new generation of experiments. Using the $t\ensuremath{-}J$ model, we solve the problem exactly within linear spin wave theory in the limit of strong magnetic interactions, showing that the ground state is described by a coherent state of spin waves. The derivation highlights the crucial role played by the interaction between a static hole and the neighboring spins, which originates in the geometric frustration and has often been omitted in earlier works. Furthermore, we show that the nonequilibrium dynamics after a hole has abruptly been inserted at a lattice site is given by a coherent state with time-dependent oscillatory coefficients. Physically, this describes a burst of magnetic frustration propagating through only two-thirds of the lattice sites, since a destructive interference of spin waves leaves spins parallel to that removed by the hole unperturbed. After the wave has propagated through the lattice, the magnetization relaxes to that of the ground state. We then use our analytical solution to benchmark the widely used self-consistent Born approximation (SCBA) in the limit of strong magnetic interactions, showing that it is very accurate also for a triangular lattice. The magnetic polaron spectrum is analyzed for general magnetic interactions using the SCBA, and we compare our results with those for a square lattice.

Quantum transport of a spin-1 chiral fermion

We theoretically study the quantum transport in a three-dimensional spin-1 chiral fermion system in the presence of impurity scattering. Within the self-consistent Born approximation, we find peak structure of the density of states and significant suppression of electrical conductivity around the zero energy. The zero-energy conductivity depends less on impurity concentration, unlike a Weyl fermion. These properties originate from the flat-band structure of the spin-1 chiral fermion.

Nonequilibrium Hole Dynamics in Antiferromagnets: Damped Strings and Polarons

We develop a nonperturbative theory for hole dynamics in antiferromagnetic spin lattices, as described by the t-J model. This is achieved by generalizing the self-consistent Born approximation to nonequilibrium systems, making it possible to calculate the full time-dependent many-body wave function. Our approach reveals three distinct dynamical regimes, ultimately leading to the formation of magnetic polarons. Following the initial ballistic stage of the hole dynamics, coherent formation of string excitations gives rise to characteristic oscillations in the hole density. Their damping eventually leaves behind magnetic polarons that undergo ballistic motion with a greatly reduced velocity. The developed theory provides a rigorous framework for understanding nonequilibrium physics of defects in quantum magnets and quantitatively explains recent observations from cold-atom quantum simulations in the strong coupling regime.

Disorder-induced phase transitions in double Weyl semimetals

The double Weyl semimetal (DWSM) is a newly proposed topological material that hosts Weyl points with chiral charge n=2. The disorder effect in DWSM is investigated by adopting the tight-binding Hamiltonian. Using the transfer matrix method and the noncommutative Kubo formula, we numerically calculate the localization length and the Hall conductivity in the presence of the on-site nonmagnetic disorder or orbital (spin-flip) disorders, and give the corresponding global phase diagrams. For the on-site nonmagnetic disorder, the system undergoes the DWSM-3D quantum anomalous hall (3D QAH) and normal insulator (NI)-DWSM phase transitions, and evolves into the diffusive metal (DM) phase before being localized by strong disorders, which is consistent with the Weyl semimetal. For \sigma_x orbital disorder, we find that increasing disorder can generate a pair of Weyl nodes at the boundary of the Brillouin zone and induce a 3D QAH-DWSM phase transition. Then we investigate the combined effect of orbital disorders for both disordered 3D QAH phase and DWSM phase. The disorder-induced transitions can be well understood in terms of an effective medium theory based on self-consistent Born approximation.

First-principles quantum treatment of electron–phonon interactions in thin-film nanodevices

Electron–phonon interactions play a crucial role in nano-electronic device performance. As the accurate calculation of these interactions requires huge computational resources, reduction of this burden without losing accuracy poses an important challenge. Here, we investigate the electron–phonon interactions of nano-devices using two first-principles-based methods in numerically efficient manners. The first method is the Lowest Order Approximation (LOA) version of the computationally burdensome self-consistent Born approximation method. The LOA method incorporates the effect of each phonon mode on the electronic current perturbatively. In this work, we theoretically resolve the discrepancy between two conventional approaches of direct LOA calculation. To validate the correct approach, we compared its output with a completely different method (second method) named Special Thermal Displacement (STD) method. The STD method uses non-interacting transport calculation of the displaced atomic configuration of a device. We apply both methods to two thin-film nanodevices: 2D silicon junctionless FET and n-i-n FET. Both methods justify each other by providing similar results and exhibiting important quantum phenomena, such as phonon-assisted subthreshold swing degradation and tunneling.

Equilibrium and nonequilibrium dynamics of a hole in a bilayer antiferromagnet

The dynamics of charge carriers in lattices of quantum spins is a long standing and fundamental problem. Recently, a new generation of quantum simulation experiments based on atoms in optical lattices has emerged that gives unprecedented insights into the detailed spatial and temporal dynamics of this problem, which compliments earlier results from condensed matter experiments. Focusing on observables accessible in these new experiments, we explore here the equilibrium as well as non-equilibrium dynamics of a mobile hole in two coupled antiferromagnetic spin lattices. Using a self-consistent Born approximation, we calculate the spectral properties of the hole in the bilayer and extract the energy bands of the quasiparticles, corresponding to magnetic polarons that are either symmetric or anti-symmetric under layer exchange. These two kinds of polarons are degenerate at certain momenta due to the antiferromagnetic symmetry, and we, furthermore, examine how the momentum of the ground state polaron depends on the interlayer coupling strength. The long time dynamics of a hole initially created in one layer is shown to be characterised by oscillations between the two layers with a frequency given by the energy difference between the symmetric and the anti-symmetric polaron. We finally demonstrate that the expansion velocity of a hole initially created at a given lattice site is governed by the ballistic motion of polarons. It moreover depends non-monotonically on the interlayer coupling, eventually increasing as a quantum phase transition to a disordered state is approached.

Weak quantization of noninteracting topological Anderson insulator

We study the transition between the two-dimensional topological insulator (TI) featuring quantized edge conductance and the trivial Anderson insulator (AI) induced by strong disorder. We discover a distinct scaling behavior of TI near the phase transition where the longitudinal conductance approaches the quantized value by a power law with system size, instead of an exponential law in clean TI. This region is thus called the weak quantization topological insulator (WQTI). By using the self-consistent Born approximation, we associate the emergence of the weak quantization with the imaginary part of the effective self-energy acquiring a finite value at strong disorder. We use our analytical theory, supported by direct numerical simulations, to study the effect of disorder range on the topological Anderson insulator. Interestingly, while this phase is quite generic for uncorrelated or short-range disorder, it is strongly suppressed by long-range disorder, perhaps explaining why it has never been seen in solid state systems.

Electric conductivity of the line-centered honeycomb lattice

The line-centered honeycomb (LCH) lattice has a single-valley Dirac band intersected by a dispersionless flat band at the band center. We investigate in this work the low-energy conductivity of the LCH lattice by considering the short-range impurities and focus on the role of the flat band when it is broken by disorders. Based on the self-consistent Born approximation and real space Kernel Polynomial methods, we showed that the system has a zero-energy conductivity like Graphene but it varies with the disorder strength. The broken flat band due to the disorder effect will contribute to the electron transport and this delocalization effect can lead to the exotic behaviors of conductivity in the low-energy regime as it slightly increases with the disorder strength and decreases with the chemical potential energy of the system. • This work is a careful theoretical analysis on the optical conductivity of a line-centered honeycomb lattice. • We demonstrate that the flat band can lead to several unconventional behaviors of the system conductivity when it is broken by the disorder. • We find that the low-energy conductivity might increase with the disorder strength and decrease with the chemical potential energy, these two features are very contrary to the physics intuition.

Disorder-induced topological phase transition in HgCdTe crystals

Using the self-consistent Born approximation, we study a topological phase transition appearing in bulk HgCdTe crystals induced \emph{uncorrelated} disorder due to both randomly distributed impurities and fluctuations in Cd composition. By following the density-of-states evolution, we clearly demonstrate the topological phase transition, which can be understood in terms of the disorder-renormalized mass of Kane fermions. We find that the presence of heavy-hole band in HgCdTe crystals leads to the topological phase transition at much lower disorder strength than it is expected for conventional 3D topological insulators. Our theoretical results can be also applied to other narrow-gap zinc-blende semiconductors such as InAs, InSb and their ternary alloys InAsSb.