Single-particle Spectral Function Research Articles

Spectral properties of the two-impurity Anderson model with varying distance and various interactions

We present an approximation for the treatment of two interacting magnetic impurities immersed into a noninteracting metallic host. The scheme is based on direct perturbation theory with respect to the hybridization between the impurity and band electrons. This two-impurity enhanced noncrossing approximation can fully incorporate the indirect interactions between the impurities that are mediated by the conduction electrons as well as additional arbitrary direct interaction matrix elements. We qualify the approximation by investigating the uncoupled case and conclude that the two-impurity approximation is equally accurate as its single-impurity counterpart. The physical properties of the two-impurity Anderson model are first investigated in some limiting cases. In a regime where each of the uncoupled two impurities would exhibit a pronounced Kondo effect, we ignore the indirect coupling via the conduction band and only incorporate direct interactions. For a ferromagnetic direct exchange coupling, the system displays a behavior similar to a spin-one Kondo effect, while an antiferromagnetic coupling competes with the Kondo effect and produces a pseudogap in the many-body Kondo resonance of the single-particle spectral function. Interestingly, a direct one-particle hopping also produces a pseudogap, but additionally pronounced side peaks emerge. This gap is characteristically different from the case with antiferromagnetic coupling since it emerges as a consequence of distinct Kondo effects for the bonding and antibonding orbital, i.e., it reflects a splitting of even and odd parity states. For the general case of only indirect coupling via the conduction band, the results show signatures of all the previously discussed limiting cases as a function of the impurity-impurity distance. Oscillatory behavior in physical quantities is to be expected due to the generated Ruderman-Kittel-Kasuya-Yosida interaction. We are led to the conclusion that the well-known Doniach scenario captures essential aspects of this model, but the details, especially at small distances, are more complicated.

Dispersions, weights, and widths of the single-particle spectral function in the normal phase of a Fermi gas

The dispersions, weights, and widths of the peaks of the single-particle spectral function in the presence of pair correlations, for a Fermi gas with either attractive or repulsive short-range inter-particle interaction, are determined in the normal phase over a wide range of wave vectors, with a twofold purpose. The first one is to determine how these dispersions identify both an energy scale known as the pseudo-gap near the Fermi wave vector, as well as an additional energy scale related to the contact C at large wave vectors. The second one is to differentiate the behaviors of the repulsive gas from the attractive one in terms of crossing versus avoided crossing of the dispersions near the Fermi wave vector. An analogy will also be drawn between the occurrence of the pseudo-gap physics in a Fermi gas subject to pair fluctuations and the persistence of local spin waves in the normal phase of magnetic materials.

Probing Anisotropic Superfluidity in Atomic Fermi Gases with Rashba Spin-Orbit Coupling

Motivated by the prospect of realizing a Fermi gas with a synthetic non-Abelian gauge field, we investigate theoretically a strongly interacting Fermi gas in the presence of a Rashba spin-orbit coupling. As the twofold spin degeneracy is lifted by spin-orbit interaction, bound pairs with mixed singlet and triplet components emerge, leading to an anisotropic superfluid. We calculate the relevant physical quantities, such as the momentum distribution, the single-particle spectral function, and the spin structure factor, that characterize the system.

Momentum-resolved optical lattice modulation spectroscopy for bosons in optical lattices

We propose an experimental method of optical lattice modulation spectroscopy for studying the spectral function of ultracold bosons in an optical lattice. We show that different features of the single-particle spectral function in different quantum phases can be obtained by measuring the change in momentum distribution after the modulation. In the Mott phase, this gives information about the momentum-dependent gap to particle-hole excitations as well as their spectral weight. In the superfluid phase, one can obtain the spectrum of the gapless Bogoliubov quasiparticles as well as the gapped amplitude fluctuations. The distinct evolution of the response with modulation frequency in the two phases can be used to identify these phases and the quantum phase transition separating them.

Extremely Correlated Fermi-Liquid Description of Normal-State ARPES in Cuprates

The normal-state single particle spectral function of the high temperature superconducting cuprates, measured by the angle-resolved photoelectron spectroscopy (ARPES), has been considered both anomalous and crucial to understand. Here, we report an unprecedented success of the new extremely correlated Fermi liquid theory by one of us [B. S. Shastry, Phys. Rev. Lett. 107, 056403 (2011)] to describe both laser and conventional synchrotron ARPES data (nodal cut at optimal doping) on Bi(2)Sr(2)CaCu(2)O(8+δ) and synchrotron data on La(1.85)Sr(0.15)CuO(4). It fits all data sets with the same physical parameter values, satisfies the particle sum rule and successfully addresses two widely discussed kink anomalies in the dispersion.

Quasiparticles, plasmarons, and quantum spectral function in bilayer graphene

We theoretically study the many-body effects of electron electron interaction on the single particle spectral function of doped bilayer graphene. Using random phase approximation, we calculate the real and imaginary part of the self-energy and hence the spectral function. The spectral function near the Fermi surface shows the usual quasiparticle peak, establishing doped bilayer graphene, in contrast to the unstable neutral system, to be a Fermi liquid. Away from the Fermi surface, an additional broad plasmaron peak is visible in the spectral function. From the low energy behaviour of the self-energy we calculate the quasiparticle residue and the effective mass of the quasiparticles as a function of carrier density. We present results for both the on-shell and the off-shell approximation for the quasiparticle renormalization.

Monte Carlo study of thermal fluctuations and Fermi-arc formation ind-wave superconductors

From the perspective of thermal fluctuations, we investigate the pseudogap phenomena in underdoped high-temperature curpate superconductors. We present a local update Monte Carlo procedure based on the Green's function method to sample the fluctuating pairing field. The Chebyshev polynomial method is applied to calculate the single-particle spectral function directly and efficiently. The evolution of Fermi arcs as a function of temperature is studied by examining the spectral function at Fermi energy as well as the loss of spectral weight. Our results signify the importance of the vortexlike phase fluctuations on the formation of Fermi arcs.

Generalized phonon-assisted Zener tunneling in indirect semiconductors with non-uniform electric fields: A rigorous approach

A general framework to calculate the Zener current in an indirect semiconductor with an externally applied potential is provided. Assuming a parabolic valence and conduction band dispersion, the semiconductor is in equilibrium in the presence of the external field as long as the electron-phonon interaction is absent. The linear response to the electron-phonon interaction results in a non-equilibrium system. The Zener tunneling current is calculated from the number of electrons making the transition from valence to conduction band per unit time. A convenient expression based on the single particle spectral functions is provided, enabling the evaluation of the Zener tunneling current under any three-dimensional potential profile. For a one-dimensional potential profile an analytical expression is obtained for the current in a bulk semiconductor, a semiconductor under uniform field, and a semiconductor under a non-uniform field using the WKB (Wentzel–Kramers–Brillouin) approximation. The obtained results agree with the Kane result in the low field limit. A numerical example for abrupt p-n diodes with different doping concentrations is given, from which it can be seen that the uniform field model is a better approximation than the WKB model, but a direct numerical treatment is required for low bias conditions.

Holographic non-Fermi-liquid fixed points

Techniques arising from string theory can be used to study assemblies of strongly interacting fermions. Via this 'holographic duality', various strongly coupled many-body systems are solved using an auxiliary theory of gravity. Simple holographic realizations of finite density exhibit single-particle spectral functions with sharp Fermi surfaces, of a form distinct from those of the Landau theory. The self-energy is given by a correlation function in an infrared (IR) fixed-point theory that is represented by a two-dimensional anti de Sitter space (AdS(2)) region in the dual gravitational description. Here, we describe in detail the gravity calculation of this IR correlation function.

Dynamic charge correlations near the Peierls transition

The quantum phase transition between a repulsive Luttinger liquid and an insulating Peierls state is studied in the framework of the one-dimensional spinless Holstein model. We focus on the adiabatic regime but include the full quantum dynamics of the phonons. Using continuous-time quantum Monte Carlo simulations, we track in particular the dynamic charge structure factor and the single-particle spectrum across the transition. With increasing electron-phonon coupling, the dynamic charge structure factor reveals the emergence of a charge gap, and a clear signature of phonon softening at the zone boundary. The single-particle spectral function evolves continuously across the transition. Hybridization of the charge and phonon modes of the Luttinger liquid description leads to two modes, one of which corresponds to the coherent polaron band. This band acquires a gap upon entering the Peierls phase, whereas the other mode constitutes the incoherent, high-energy spectrum with backfolded shadow bands. Coherent polaronic motion is a direct consequence of quantum lattice fluctuations. In the strong-coupling regime, the spectrum is described by the static, mean-field limit. Importantly, whereas finite electron density in general leads to screening of polaron effects, the latter reappear at half filling due to charge ordering and lattice dimerization.

Inelastic light scattering to probe strongly correlated bosons in optical lattices

We have used inelastic light scattering to study correlated phases of an array of one-dimensional interacting Bose gases. In the linear response regime, the observed spectra are proportional to the dynamic structure factor. In particular we have investigated the superfluid to Mott insulator crossover loading the one-dimensional gases in an optical lattice and monitoring the appearance of an energy gap due to finite particle-hole excitation energy. We attribute the low frequency side of the spectra to the presence of some superfluid and normal phase fraction between the Mott insulator regions with different fillings produced in the inhomogeneous systems. In the Mott phase we also investigated excitations to higher excited bands of the optical lattice, the spectra obtained in this case being connected to the single particle spectral function. In one-dimensional systems the effect of thermal fluctuations and interactions is enhanced by the reduced dimensionality showing up in the dynamic structure factor. We measured the dynamic structure factor of an array of one-dimensional bosonic gases pointing out the effect of temperature-induced phase fluctuations in reducing the coherence length of the system.

Localization of correlated fermions in optical lattices with speckle disorder

Strongly correlated fermions in three- and two-dimensional optical lattices with experimentally realistic speckle disorder are investigated. We extend and apply the statistical dynamical mean-field theory, which treats local correlations nonperturbatively, to incorporate on-site and hopping-type randomness on equal footing. Localization due to disorder is detected via the probability distribution function of the local density of states. We obtain a complete paramagnetic ground state phase diagram for experimentally realistic parameters and find a strong suppression of the correlation-induced metal insulator transition due to disorder. Our results indicate that the Anderson-Mott and the Mott insulator are not continuously connected due to the specific character of speckle disorder. Furthermore, we discuss the effect of finite temperature on the single-particle spectral function.

Melting of stripe phases and its signature in the single-particle spectral function

Motivated by the recent experimental data [Phys. Rev. B 79, 100502 (2009)] indicating the existence of a pure stripe charge order over unprecedently wide temperature range in La_{1.8-x}Eu_{0.2}Sr_xCuO_4, we investigate the temperature-induced melting of the metallic stripe phase. In spite of taking into account local dynamic correlations within a real-space dynamical mean-field theory of the Hubbard model, we observe a mean-field like melting of the stripe order irrespective of the choice of the next-nearest neighbor hopping. The temperature dependence of the single-particle spectral function shows the stripe induced formation of a flat band around the antinodal points accompanied by the opening a gap in the nodal direction.

Fermi surface topology of the two-dimensional Kondo lattice model: Dynamical cluster approximation approach

We report the results of extensive dynamical cluster approximation calculations, based on a quantum Monte Carlo solver, for the two-dimensional Kondo lattice model. Our particular cluster implementation renders possible the simulation of spontaneous antiferromagnetic symmetry breaking. By explicitly computing the single-particle spectral function both in the paramagnetic and antiferromagnetic phases, we follow the evolution of the Fermi surface across this magnetic transition. The results, computed for clusters up to 16 orbitals, show clear evidence for the existence of three distinct Fermi surface topologies. The transition from the paramagnetic metallic phase to the antiferromagnetic metal is continuous; Kondo screening does not break down and we observe a back-folding of the paramagnetic heavy fermion band. Within the antiferromagnetic phase and when the ordered moment becomes large the Fermi surface evolves to one which is adiabatically connected to a Fermi surface where the local moments are frozen in an antiferromagnetic order.

Effects of Thermal Phase Fluctuations in a Two-Dimensional Superconductor: An Exact Result for the Spectral Function

We consider the single particle spectral function for a two-dimensional clean superconductor in a regime of strong critical thermal phase fluctuations. In the limit where the maximum of the superconducting gap is much smaller than the Fermi energy we obtain an exact expression for the spectral function integrated over the momentum component perpendicular to the Fermi surface.

Observation of pseudogap behaviour in a strongly interacting Fermi gas

An ultracold gas of strongly interacting fermions exhibits a pseudogap phase in which pairs of fermions exist above the superfluid transition, but lack the phase coherence of a superfluid. Ultracold atomic Fermi gases present an opportunity to study strongly interacting fermionic systems in a controlled and uncomplicated setting. The ability to tune attractive interactions has led to the discovery of superfluidity in these systems with an extremely high transition temperature with respect to the Fermi temperature1,2 near T/TF=0.2. This superfluidity is the electrically neutral analogue of superconductivity; however, superfluidity in atomic Fermi gases occurs in the limit of strong interactions and defies a conventional Bardeen–Cooper–Schrieffer (BCS) description. For these strong interactions, it is predicted that the onset of pairing and superfluidity can occur at different temperatures3,4,5. Thus, for a range of temperatures, a pseudogap region may exist, in which the system retains some of the characteristics of the superfluid phase—such as a BCS-like dispersion and a partially gapped density of states—but does not exhibit superfluidity. By making two independent measurements—the direct observation of pair condensation in momentum space and a measurement of the single-particle spectral function using an analogue to photoemission spectroscopy6—we directly probe the pseudogap phase. Our measurements reveal a BCS-like dispersion with back-bending near the Fermi wavevector kF, which persists well above the transition temperature for pair condensation.

Pseudogap Pairing in Ultracold Fermi Atoms

The Bose-Einstein condensate to Bardeen-Cooper-Schrieffer crossover in ultracold Fermi gases creates an ideal environment to enrich our knowledge of many-body systems. It is relevant to a wide range of fields from condensed matter to astrophysics. The nature of pairing in strongly interacting Fermi gases can be readily studied. This aids our understanding of related problems in high-Tc superconductors, whose mechanism is still under debate due to the large interaction parameter. Here, we calculate the dynamical properties of a normal, trapped strongly correlated Fermi gas, by developing a quantum cluster expansion. Our calculations for the single-particle spectral function agree with recent rf spectroscopy measurements, and clearly demonstrate pseudogap pairing in the strongly interacting regime.

Spectral signatures of the BCS-BEC crossover in the excitonic insulator phase of the extended Falicov-Kimball model

We explore the spontaneous formation of an excitonic insulator state at the semimetal-semiconductor transition of mixed-valence materials in the framework of the spinless Falicov-Kimball model with direct $f$-$f$ electron hopping. Adapting the projector-based renormalization method, we obtain a set of renormalization differential equations for the extended Falicov-Kimball model parameters and finally derive analytical expressions for the order parameter, as well as for the renormalized $c$- and $f$-electron dispersions, momentum distributions, and wave-vector resolved single-particle spectral functions. Our numerical results proved the valence transition picture, related to the appearance of the excitonic insulator phase, in the case of overlapping $c$ and $f$ bands. Thereby the photoemission spectra show significant differences between the weak-to-intermediate and intermediate-to-strong Coulomb attraction regimes, indicating a BCS-BEC transition of the excitonic condensate.

Dynamical cluster quantum Monte Carlo study of the single-particle spectra of strongly interacting fermion gases

We study the single-particle spectral function of resonantly-interacting fermions in the unitary regime, as described by the three-dimensional attractive Hubbard model in the dilute limit. Our approach, based on the Dynamical Cluster Approximation and the Maximum Entropy Method, shows the emergence of a gap with decreasing temperature, as reported in recent cold-atom photoemission experiments, for coupling values that span the BEC-BCS crossover. By comparing the behavior of the spectral function to that of the imaginary time dynamical pairing susceptibility, we attribute the development of the gap to the formation of local bound atom pairs.

Transport through a vibrating quantum dot: Polaronic effects

We present a Green's function based treatment of the effects of electron-phonon coupling on transport through a molecular quantum dot in the quantum limit. Thereby we combine an incomplete variational Lang-Firsov approach with a perturbative calculation of the electron-phonon self energy in the framework of generalised Matsubara Green functions and a Landauer-type transport description. Calculating the ground-state energy, the dot single-particle spectral function and the linear conductance at finite carrier density, we study the low-temperature transport properties of the vibrating quantum dot sandwiched between metallic leads in the whole electron-phonon coupling strength regime. We discuss corrections to the concept of an anti-adiabatic dot polaron and show how a deformable quantum dot can act as a molecular switch.