Many-body Renormalization Research Articles

Many-body enhancement of high-harmonic generation in monolayer MoS2

Many-body effects play an important role in enhancing and modifying optical absorption and other excited-state properties of solids in the perturbative regime, but their role in high harmonic generation (HHG) and other nonlinear response beyond the perturbative regime is not well-understood. We develop here an ab initio many-body method to study nonperturbative HHG based on the real-time propagation of the non-equilibrium Green’s function with the GW self energy. We calculate the HHG of monolayer MoS2 and obtain good agreement with experiment, including the reproduction of characteristic patterns of monotonic and nonmonotonic harmonic yield in the parallel and perpendicular responses, respectively. Here, we show that many-body effects are especially important to accurately reproduce the spectral features in the perpendicular response, which reflect a complex interplay of electron-hole interactions (or exciton effects) in tandem with the many-body renormalization and Berry curvature of the independent quasiparticle bandstructure.

Band structure of a nonparabolic two-dimensional electron gas system

Using angle-resolved photoelectron spectroscopy (ARPES), we study the band structures of two-dimensional electron gases (2DEGs) formed at Te-doped surfaces of InAs(110), as a result of band bending. The selected surface system is very clean and stable; therefore, ARPES spectra may be registered in short times, with minimal adsorption of residual gases and no photon beam-induced damage. We record a set of data that allows for a detailed analysis of the 2DEG band shapes, their thermal dependencies, and for an assessment of the many-body interactions. We find the electron-phonon interaction extremally weak and the electron-electron interactions hidden in dominant electron-donor interactions. While 2DEG band shapes are observed to be variable in correlation with the 2DEG density, this is tracked down to the variability of the band-bending potential and nonparabolicity of the system, and not to the many-body interactions. Thus, many-body renormalization of the 2DEG bands is not required, and the bands are described well by using the one-electron theoretical frame.

Tuning the Fermi liquid crossover in Sr2RuO4 with uniaxial stress

We perform nuclear magnetic resonance (NMR) measurements of the oxygen-17 Knight shifts for Sr2RuO4, while subjected to uniaxial stress applied along [100] direction. The resulting strain is associated with a strong variation of the temperature and magnetic field dependence of the inferred magnetic response. A quasiparticle description based on density-functional theory calculations, supplemented by many-body renormalizations, is found to reproduce our experimental results, and highlights the key role of a van-Hove singularity. The Fermi-liquid coherence scale is shown to be tunable by strain, and driven to low values as the associated Lifshitz transition is approached.

Origin of the injection-dependent emission blueshift and linewidth broadening of III-nitride light-emitting diodes

III-nitride light-emitting diodes (LEDs) exhibit an injection-dependent emission blueshift and linewidth broadening that is severely detrimental to their color purity. By using first-principles multi-scale modeling that accurately captures the competition between polarization-charge screening, phase-space filling, and many-body plasma renormalization, we explain the current-dependent spectral characteristics of polar III-nitride LEDs fabricated with state-of-the-art quantum wells. Our analysis uncovers a fundamental connection between carrier dynamics and the injection-dependent spectral characteristics of light-emitting materials. For example, polar III-nitride LEDs offer poor control over their injection-dependent color purity due to their poor hole transport and slow carrier-recombination dynamics, which forces them to operate at or near degenerate carrier densities. Designs that accelerate carrier recombination and transport and reduce the carrier density required to operate LEDs at a given current density lessen their injection-dependent wavelength shift and linewidth broadening.

Optical nonlinearities in the excited carrier density of atomically thin transition metal dichalcogenides

In atomically thin semiconductors based on transition metal dichalcogenides, photoexcitation can be used to generate high densities of electron-hole pairs. Due to optical nonlinearities, which originate from Pauli blocking and many-body effects of the excited carriers, the generated carrier density will deviate from a linear increase in pump fluence. In this paper, we describe nonlinear absorption properties and excited carrier dynamics using a theoretical approach that combines results from ab initio electronic-state calculations with a many-body treatment of optical excitation. We determine the validity range of a linear approximation for the excited carrier density vs pump power and identify the role and magnitude of optical nonlinearities at elevated excitation carrier densities for ${\mathrm{MoS}}_{2}, {\mathrm{MoSe}}_{2}, {\mathrm{WS}}_{2}$, and ${\mathrm{WSe}}_{2}$ considering various excitation conditions. For photoexcitation at the bandgap, we find that the use of a linear absorption coefficient of the unexcited system can strongly underestimate the achievable carrier density in ${\mathrm{MoS}}_{2}$ due to many-body renormalizations of the two-particle density of states. The same holds for excitation of the high-energy band continuum in W-based materials.

Many-body Green's function approaches to the doped Fröhlich solid: Exact solutions and anomalous mass enhancement

In polar semiconductors and insulators, the Fr\"ohlich interaction between electrons and long-wavelength longitudinal optical phonons induces a many-body renormalization of the carrier effective masses and the appearence of characteristic phonon sidebands in the spectral function, commonly dubbed 'polaron satellites'. The simplest model that captures these effects is the Fr\"ohlich model, whereby electrons in a parabolic band interact with a dispersionless longitudinal optical phonon. The Fr\"ohlich model has been employed in a number of seminal papers, from early perturbation-theory approaches to modern diagrammatic Monte Carlo calculations. One limitation of this model is that it focuses on undoped systems, thus ignoring carrier screening and Pauli blocking effects that are present in real experiments on doped samples. To overcome this limitation, we here extend the Fr\"ohlich model to the case of doped systems, and we provide exact solutions for the electron spectral function, mass enhancement, and polaron satellites. We perform the analysis using two approaches, namely Dyson's equation with the Fan-Migdal self-energy, and the second-order cumulant expansion. We find that these two approaches provide qualitatively different results. In particular, the Dyson's approach yields better quasiparticle masses and worse satellites, while the cumulant approach provides better satellite structures, at the price of worse quasiparticle masses. Both approaches yield an anomalous enhancement of the electron effective mass at finite doping levels, which in turn leads to a breakdown of the quasiparticle picture in a significant portion of the phase diagram.

Free electron gas in cavity quantum electrodynamics

Cavity modification of material properties and phenomena is a novel research field largely motivated by the advances in strong light-matter interactions. Despite this progress, exact solutions for extended systems strongly coupled to the photon field are not available, and both theory and experiments rely mainly on finite-system models. Therefore, a paradigmatic example of an exactly solvable extended system in a cavity becomes highly desirable. To fill this gap we revisit Sommerfeld's theory of the free electron gas in cavity quantum electrodynamics. We solve this system analytically in the long-wavelength limit for an arbitrary number of noninteracting electrons, and we demonstrate that the electron-photon ground state is a Fermi liquid which contains virtual photons. In contrast to models of finite systems, no ground state exists if the diamagentic ${\mathbf{A}}^{2}$ term is omitted. Further, by performing linear response we show that the cavity field induces plasmon-polariton excitations and modifies the optical and the DC conductivity of the electron gas. Our exact solution allows us to consider the thermodynamic limit for both electrons and photons by constructing an effective quantum field theory. The continuum of modes leads to a many-body renormalization of the electron mass, which modifies the fermionic quasiparticle excitations of the Fermi liquid and the Wigner-Seitz radius of the interacting electron gas. Last, we show how the matter-modified photon field leads to a repulsive Casimir force and how the continuum of modes introduces dissipation into the light-matter system. Several of the presented findings should be experimentally accessible.

Displaced Drude peak and bad metal from the interaction with slow fluctuations.

Scattering by slowly fluctuating degrees of freedom can cause a transient localization of the current-carrying electrons in metals, driving the system away from normal metallic behavior. We illustrate and characterize this general phenomenon by studying how signatures of localization emerge in the optical conductivity of electrons interacting with slow bosonic fluctuations. The buildup of quantum localization corrections manifests itself in the emergence of a displaced Drude peak (DDP), whose existence strongly alters the low frequency optical response and suppresses the d.c. conductivity. We find that for sufficiently strong interactions, many-body renormalization of the fluctuating field induced at metallic densities enhances electron localization and the ensuing DDP phenomenon in comparison with the well-studied low concentration limit. Our results are compatible with the frequent observation of DDPs in electronic systems where slowly fluctuating degrees of freedom couple significantly to the charge carriers.

Anisotropic fermionic quasiparticles

We have carried out a comprehensive investigation of the quasiparticle properties of a two-dimensional electron gas, interacting via the long-range Coulomb interaction in the presence of bare mass anisotropy (i.e., with an elliptic noninteracting Fermi surface) by calculating the self-energy, the spectral function, the scattering rate, and the effective mass within the leading-order dynamical self-energy approximation. Our theory is exact in the high-density limit. We find anisotropic features of quasiparticle properties that are not captured by the commonly used isotropic approximation where the anisotropic effective mass is replaced by the isotropic averaged density-of-states mass. Some of these interesting results are as follows: (1) The many-body renormalization of the quasiparticle spectrum becomes highly anisotropic as the quasiparticle energy increases away from the Fermi energy; (2) the interaction-induced inelastic-scattering rate features a strong anisotropy, exhibiting an abrupt jump at different injected energies depending on the momentum direction of the injected electron; (3) the effective-mass enhancement is larger (smaller) for the light (heavy) mass, showing that the anisotropy is reduced by interactions. Our results and analysis show that the unjustified neglect of the mass anisotropy can lead to an incorrect description of quasiparticle properties of the anisotropic system and inaccurate estimates of physical quantities of interest although the use of an equivalent isotropic approximation using the density-of-states effective mass as is commonly and uncritically performed in the literature, works as a reasonable approximation in many situations. In addition to the complete random phase approximation theory for the anisotropic quasiparticles, we also provide a theory using the simpler plasmon-pole approximation, commenting on its validity for anisotropic self-energy calculations. We comment also on the interaction effect on the Fermi-surface topology, finding that the elliptic shape of the bare Fermi surface is preserved with suppressed ellipticity in the interacting system to a high degree of accuracy except in the very strongly interacting limit (and for very high bare mass anisotropy). Our theory provides a complete generalization of the existing isotropic many-body theory of interacting electrons to the corresponding anisotropic systems.

Many-body renormalization of the electron effective mass of InSe

The layered semiconductor InSe has a wide range of attractive electronic and optoelectronic properties, in which the effective mass of the charge carriers plays a key role. Here, we study from first principles the many-body renormalization of the electron effective mass in $\ensuremath{\gamma}$-InSe, taking into account the effects of both electron-electron and electron-phonon interactions. Electron-electron interaction, treated within the many-body $GW$ approximation, leads to around 15% of the increase in the in-plane effective mass over the result from density functional theory, and a more than threefold increase in the out-of-plane electron effective mass. The surprisingly large directional anisotropy in the mass renormalization is explained in terms of the symmetries of band-edge wave functions. The mass enhancement induced by electron-phonon interactions, which we find to mainly originate from Fr\"ohlich electron-phonon coupling, is less than 10% at room temperature, indicating weak polaronic effect. After including the many-body renormalization effects, the calculated electron effective masses of InSe are 0.12 and 0.09 in the in-plane and out-of-plane directions, respectively.

Effects of Si concentration on electronic structure and optical gap of Si-doped β-Ga2O3

The electronic structures and the optical gaps of Si-doped β-Ga2O3 with different Si concentration are studied by the generalized gradient approximation combined Hubbard U (GGA + U) method based on the density functional theory. The doping formation energy reveals that Si-doped β-Ga2O3 is mainly realized in the form of substitutional Si rather than interstitial Si, and tends to obtain effective doping under O-poor condition. As substitutional Si concentration increases, the optical gap of Si-doped β-Ga2O3 increases while the bandgap narrows, which are mainly attributed to the Burstein-Moss effect and the many-body renormalization effect. The bandgap widening ΔEBM and the bandgap narrowing ΔEBGN of Si-doped β-Ga2O3 as a function of Si carrier concentration can be described by Pisarkiewicz’s model and Schmid’s empirical expression, respectively.

Many-body corrected tight-binding Hamiltonians for an accurate quasiparticle description of topological insulators of the Bi2Se3 family

We generate many-body corrected tight-binding Hamiltonians for topological insulators of the ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ family. To this end, we use ab initio calculated parameters extracted from $GW$ calculations, thus capturing many-body exchange and correlation effects, in contrast to previous tight-binding models. We investigate the effect of many-body renormalizations on the electronic structure of bulk and surface states of semi-infinite systems as well as thin films of these materials. It is shown that the $GW$ self-energy correction brings about profound changes not only in the band-gap values but also in the band dispersion around the inverted gaps with respect to standard density-functional theory (DFT). These changes substantially improve the agreement with experiment. We discuss the strong renormalization effect as being a result of the characteristic overestimation of inverted gaps by standard approximations of DFT (opposite to the underestimation of gaps in topologically trivial materials). In particular, we analyze the consequences that these renormalizations have on the dispersions of the topological surface states and on the surface resonances. For reference, the tight-binding Hamiltonians are provided in the Supplemental Material [30].

Strong Electron-Phonon Coupling and its Influence on the Transport and Optical Properties of Hole-Doped Single-Layer InSe.

We show that hole states in recently discovered single-layer InSe are strongly renormalized by the coupling with acoustic phonons. The coupling is enhanced significantly at moderate hole doping (∼10^{13} cm^{-2}) due to hexagonal warping of the Fermi surface. While the system remains dynamically stable, its electron-phonon spectral function exhibits sharp low-energy resonances, leading to the formation of satellite quasiparticle states near the Fermi energy. Such many-body renormalization is predicted to have two important consequences. First, it significantly suppresses charge carrier mobility reaching ∼1 cm^{2} V^{-1} s^{-1} at 100K in a freestanding sample. Second, it gives rise to unusual temperature-dependent optical excitations in the midinfrared region. Relatively small charge carrier concentrations and realistic temperatures suggest that these excitations may be observed experimentally.

Spectroscopic fingerprints of many-body renormalization in 1T−TiSe2

We have employed high resolution angle resolved photoemission spectroscopy (ARPES) measurements to investigate many-body renormalizations of the single-particle excitations in $1T$-TiSe$_2$. The energy distribution curves of the ARPES data reveal intrinsic peak-dip-hump feature, while the electronic dispersion derived from the momentum distribution curves of the data highlights, for the first time, multiple kink structures. These are canonical signatures of a coupling between the electronic degrees of freedom and some Bosonic mode in the system. We demonstrate this using a model calculation of the single-particle spectral function at the presence of an electron-Boson coupling. From the self-energy analysis of our ARPES data, we discern some of the critical energy scales of the involved Bosonic mode, which are $\sim$15 and 26 meV. Based on a comparison between these energies and the characteristic energy scales of our Raman scattering data, we identify these Bosonic modes as Raman active breathing (${\text{A}}_\text{1g}$) and shear (${\text{E}}_\text{g}$) modes, respectively. Direct observation of the band-renormalization due to electron-phonon coupling increases the possibility that electron-phonon interactions are central to the collective quantum states such as charge density wave (CDW) and superconductivity in the compounds based on $1T$-TiSe$_2$.

Derivation of renormalized Gibbs measures from equilibrium many-body quantum Bose gases

We review our recent result on the rigorous derivation of the renormalized Gibbs measure from the many-body Gibbs state in 1D and 2D. The many-body renormalization is accomplished by simply tuning the chemical potential in the grand-canonical ensemble, which is analogous to the Wick ordering in the classical field theory.

Strong correlations and d+id superconductivity in twisted bilayer graphene

We compute the phase diagram of twisted bilayer graphene near the magic angle where the occurrence of flat bands enhances the effects of electron-electron interactions and thus unleashes strongly-correlated phenomena. Most importantly, we find a crossover between d+id superconductivity and Mott insulating behavior near half-filling of the lowest electron band when the temperature is increased. This is consistent with recent experiments. Our results are obtained using unbiased many-body renormalization group techniques combined with a mean-field analysis of the effective couplings.

Optical conductivity of overdoped cuprate superconductors: Application to La2−xSrxCuO4

We argue that recent measurements on both the superfluid density and the optical conductivity of high-quality LSCO films can be understood almost entirely within the theory of disordered BCS d-wave superconductors. The large scattering rates deduced from experiments are shown to arise predominantly from weak scatterers, probably the Sr dopants out of the CuO$_2$ plane, and correspond to significant suppression of $T_c$ relative to a pure reference state with the same doping. Our results confirm the "conventional" viewpoint that the overdoped side of the cuprate phase diagram can be viewed as approaching the BCS weak-coupling description of the superconducting state, with significant many-body renormalization of the plasma frequency. They suggest that, while some of the decrease in $T_c$ with overdoping may be due to weakening of the pairing, disorder plays an essential role.

Excitation-induced transition to indirect band gaps in atomically thin transition-metal dichalcogenide semiconductors

Monolayers of transition metal dichalcogenides (TMDCs) exhibit an exceptionally strong Coulomb interaction between charge carriers due to the two-dimensional carrier confinement in connection with weak dielectric screening. High densities of excited charge carriers in the various band-structure valleys cause strong many-body renormalizations that influence both the electronic properties and the optical response of the material. We investigate electronic and optical properties of the typical monolayer TMDCs MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$ in the presence of excited carriers by solving semiconductor Bloch equations on the full Brillouin zone. With increasing carrier density, we systematically find a reduction of the exciton binding energies due to Coulomb screening and Pauli blocking. Together with excitation-induced band-gap shrinkage this leads to redshifts of excitonic resonances up to the dissociation of excitons. As a central result, we predict for all investigated monolayer TMDCs that the $\Sigma$-valley shifts stronger than the K-valley. Two of the materials undergo a transition from direct to indirect band gaps under carrier excitation similar to well-known strain-induced effects. Our findings have strong implications for the filling of conduction-band valleys with excited carriers and are relevant to transport and optical applications as well as the emergence of phonon-driven superconductivity.

Many-body renormalization of Landau levels in graphene due to screened Coulomb interaction

Renormalization of Landau level energies in graphene in strong magnetic field due to Coulomb interaction is studied theoretically, and calculations are compared with two experiments on carrier-density dependent scanning tunneling spectroscopy. An approximate preservation of the square-root dependence of the energies of Landau levels on their numbers and magnetic field in the presence of the interaction is examined. Many-body calculations of the renormalized Fermi velocity with the statically screened interaction taken in the random-phase approximation show good agreement with both experiments. The crucial role of the screening in achieving quantitative agreement is found. The main contribution to the observed rapid logarithmic growth of the renormalized Fermi velocity on approach to the charge neutrality point turned out to be caused not by mere exchange interaction effects, but by weakening of the screening at decreasing carrier density. The importance of a self-consistent treatment of the screening is also demonstrated.

Effect of Structural Relaxation on the Electronic Structure of Graphene on Hexagonal Boron Nitride.

We performed calculations of electronic, optical, and transport properties of graphene on hexagonal boron nitride with realistic moiré patterns. The latter are produced by structural relaxation using a fully atomistic model. This relaxation turns out to be crucially important for electronic properties. We describe experimentally observed features such as additional Dirac points and the "Hofstadter butterfly" structure of energy levels in a magnetic field. We find that the electronic structure is sensitive to many-body renormalization of the local energy gap.