Momentum-resolved Spectral Function Research Articles

Angle-resolved photoemission spectroscopy with an in situ tunable magnetic field.

Angle-resolved photoemission spectroscopy (ARPES) is a powerful tool for probing the momentum-resolved single-particle spectral function of materials. Historically, in situ magnetic fields have been carefully avoided as they are detrimental to the control of photoelectron trajectory during the photoelectron detection process. However, magnetic field is an important experimental knob for both probing and tuning symmetry-breaking phases and electronic topology in quantum materials. In this paper, we introduce an easily implementable method for realizing an in situ tunable magnetic field at the sample position in an ARPES experiment and analyze magnetic-field-induced artifacts in the ARPES data. Specifically, we identified and quantified three distinct extrinsic effects of a magnetic field: constant energy contour rotation, emission angle contraction, and momentum broadening. We examined these effects in three prototypical quantum materials, i.e., a topological insulator (Bi2Se3), an iron-based superconductor (LiFeAs), and a cuprate superconductor (Pb-Bi2Sr2CuO6+x), and demonstrate the feasibility of ARPES measurements in the presence of a controllable magnetic field. Our studies lay the foundation for the future development of the technique and interpretation of ARPES measurements of field-tunable quantum phases.

Thermal evolution of the single-particle spectral function in the half-filled Hubbard model and pseudogap

In the half-filled one-orbital Hubbard model on a square lattice, we find pseudogap-like features in the form of two-peak structures associated with the momentum-resolved spectral function. These features exist within the temperature window ${T}_{N}\ensuremath{\lesssim}T\ensuremath{\lesssim}{T}^{*}$, where ${T}_{N}$ is the N\'eel temperature and ${T}^{*}$ is the temperature below which there exists a well-formed dip in the density of state. Inside the window ${T}_{N}\ensuremath{\lesssim}T\ensuremath{\lesssim}{T}^{*}$, the peak-to-peak separation in the two-peak structure of the momentum-resolved spectral function grows on moving away from the point ($\ensuremath{\pi}/2,\ensuremath{\pi}/2$) along the normal state Fermi surface toward $(\ensuremath{\pi},0)$, a behavior with remarkable similarities to what is observed in the $d$-wave state and pseudogap phase of high-${T}_{c}$ cuprates. We unveil these features by using a parallelized cluster-based Monte Carlo method for simulating the magnetic order parameter fields on a superlattice. The method enables us to access the momentum-resolved single-particle spectral function corresponding to a lattice size of $\ensuremath{\approx}240 \ifmmode\times\else\texttimes\fi{}$ 240 with an almost negligible finite-size effect.

Fermi arcs and pseudogap phase in a minimal microscopic model of d -wave superconductivity

We show conclusively that a pseudogap state can arise at $T > T_c$, for reasonable pairing interaction strength, from order parameter fluctuations in a two dimensional minimal model of $d$-wave superconductivity. The occurrence of the pseudogap requires neither strong correlation nor the presence of competing order. We study a model with attractive nearest neighbor interaction and establish our result using a combination of cluster based Monte Carlo for the order parameter field and a twisted-boundary scheme to compute the momentum-resolved spectral function. Apart from a dip in the density of states that characterizes the pseudogap, the momentum and frequency resolution on our effective lattice size $\sim 160 \times 160$ allows two major conclusions: (i)~at $T < T_c$, despite the presence of thermal phase fluctuations the superconductor has only nodal Fermi points while all non nodal points on the normal state Fermi surface show a two peak spectral function with a dip at $\omega =0$, and (ii)~for $T > T_c$ the Fermi points develops into arcs, characterized by a single quasiparticle peak, and the arcs connect up to recover the normal state Fermi surface at a temperature $T^* > T_c$. We show the variation of $T_c$ and $T^*$ with coupling strength and provide detailed spectral results at a coupling where $T^* \sim 1.5T_c$.

Photoinduced Dirac-cone flattening in BaNiS2

Using a real-time implementation of the self-consistent $GW$ method, we theoretically investigate the photo-induced changes in the electronic structure of the quasi two-dimensional semi-metal BaNiS$_2$. This material features four Dirac cones in the unit cell and our simulation of the time- and momentum-resolved nonequilibrium spectral function reveals a flattening of the Dirac bands after a photo-doping pulse with a 1.5 eV laser. The simulation results are consistent with the recently reported experimental data on photo-doped BaNiS$_2$ and ZrSiSe, another Dirac semi-metal. A detailed analysis of the numerical data allows us to attribute the nonequilibrium modifications of the Dirac bands to (i) an increased effective temperature after the photo-excitation, which affects the screening properties of the system, and (ii) to nontrivial band shifts in the photo-doped state, which are mainly induced by the Fock term.

Thermodynamic signatures of the polaron-molecule transition in a Fermi gas

We consider the highly spin-imbalanced limit of a two-component Fermi gas, where there is a small density of $\downarrow$ impurities attractively interacting with a sea of $\uparrow$ fermions. In the single-impurity limit at zero temperature, there exists the so-called polaron-molecule transition, where the impurity sharply changes its character by binding a $\uparrow$ fermion at sufficiently strong attraction. Using a recently developed variational approach, we calculate the thermodynamic properties of the impurity, and we show that the transition becomes a smooth crossover at finite temperature due to the thermal occupation of excited states in the impurity spectral function. However, remnants of the single-impurity transition are apparent in the momentum-resolved spectral function, which can in principle be probed with Raman spectroscopy. We furthermore show that the Tan contact exhibits a characteristic non-monotonic dependence on temperature that provides a signature of the zero-temperature polaron-molecule transition. For a finite impurity density, we argue that descriptions purely based on the behavior of the Fermi polaron are invalid near the polaron-molecule transition, since correlations between impurities cannot be ignored. In particular, we show that the spin-imbalanced system undergoes phase separation at low temperatures due to the strong attraction between $\uparrow\downarrow$ molecules induced by the Fermi sea. Thus, we find that the impurity spectrum and the induced impurity-impurity interactions are key to understanding the phase diagram of the spin-imbalanced Fermi gas.

Resonant laser excitation and time-domain imaging of chiral topological polariton edge states

We investigate the dynamics of chiral edge states in topological polariton systems under laser driving. Using a model system comprised of topolgically trivial excitons and photons with a chiral coupling proposed by Karzig et al. [Phys. Rev. X 5, 031001 (2015)], we investigate the real-time dynamics of a lattice version of this model driven by a laser pulse. By analyzing the time- and momentum-resolved spectral function, measured by time- and angle-resolved photoluminescence in analogy with time- and angle-resolved photoemission spectroscopy in electronic systems, we find that polaritonic states in a ribbon geometry are selectively excited via their resonance with the pump laser photon frequency. This selective excitation mechanism is independent of the necessity of strong laser pumping and polariton condensation. Our work highlights the potential of time-resolved spectroscopy as a complementary tool to real-space imaging for the investigation of topological edge state engineering in devices.

From Trivial Kondo Insulator Ce_{3}Pt_{3}Bi_{4} to Topological Nodal-Line Semimetal Ce_{3}Pd_{3}Bi_{4}.

Using the density functional theory combined with dynamical mean-field theory, we have performed systematic study of the electronic structure and its band topology properties of Ce_{3}Pt_{3}Bi_{4} and Ce_{3}Pd_{3}Bi_{4}. At high temperatures (∼290 K), the electronic structures of both compounds resemble the open-core 4f density functional calculation results. For Ce_{3}Pt_{3}Bi_{4}, clear hybridization gap can be observed below 72K, and its coherent momentum-resolved spectral function below 18K exhibits an topologically trivial indirect gap of ∼6 meV and resembles density functional band structure with itinerant 4f state. For Ce_{3}Pd_{3}Bi_{4}, no clear hybridization gap can be observed down to 4K, and its momentum-resolved spectral function resembles electron-doped open-core 4f density functional calculations. The band nodal points of Ce_{3}Pd_{3}Bi_{4} at 4K are protected by the gliding-mirror symmetry and form ringlike structure. Therefore, the Ce_{3}Pt_{3}Bi_{4} compound is topologically trivial Kondo insulator while the Ce_{3}Pd_{3}Bi_{4} compound is topological nodal-line semimetal.

Two-particle spectral function for disordered s -wave superconductors: Local maps and collective modes

We make the first testable predictions for the local two-particle spectral function of a disordered s-wave superconductor, probed by scanning Josephson spectroscopy (sjs), providing complementary information to scanning tunneling spectroscopy (sts). We show that sjs provides a direct map of the local superconducting order parameter that is found to be anticorrelated with the gap map obtained by sts. Furthermore, this anticorrelation increases with disorder. For the momentum resolved spectral function, we find the Higgs mode shows a non-dispersive subgap feature at low momenta, spectrally separated from phase modes, for all disorder strengths. The amplitude-phase mixing remains small at low momenta even when disorder is large. Remarkably, even for large disorder and high momenta, the amplitude-phase mixing oscillates rapidly in frequency and hence do not affect significantly the purity of the Higgs and phase dominated response functions.

Electronic phase separation at LaAlO3/SrTiO3 interfaces tunable by oxygen deficiency

Electronic phase separation is crucial for the fascinating macroscopic properties of the ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ (LAO/STO) paradigm oxide interface, including the coexistence of superconductivity and ferromagnetism. We investigate this phenomenon using angle-resolved photoelectron spectroscopy (ARPES) in the soft-x-ray energy range, where the enhanced probing depth combined with resonant photoexcitation allow us access to fundamental electronic structure characteristics -- momentum-resolved spectral function, dispersions and ordering of energy bands, Fermi surface -- of buried interfaces. Our experiment uses x-ray irradiation of the LAO/STO interface to tune its oxygen deficiency, building up a dichotomic system where mobile weakly correlated $\mathrm{Ti}\phantom{\rule{0.28em}{0ex}}{t}_{2\mathrm{g}}$ electrons coexist with localized strongly correlated $\mathrm{Ti}\phantom{\rule{0.28em}{0ex}}{e}_{\mathrm{g}}$ ones. The ARPES spectra dynamics under x-ray irradiation shows a gradual intensity increase under constant Luttinger count of the Fermi surface. This fact identifies electronic phase separation (EPS) where the mobile electrons accumulate in conducting puddles with fixed electronic structure embedded in an insulating host phase, and allows us to estimate the lateral fraction of these puddles. We discuss the physics of EPS invoking a theoretical picture of oxygen-vacancy clustering, promoted by the magnetism of the localized $\mathrm{Ti}\phantom{\rule{0.28em}{0ex}}{e}_{\mathrm{g}}$ electrons, and repelling of the mobile ${t}_{2\mathrm{g}}$ electrons from these clusters. Our results on the irradiation-tuned EPS elucidate the intrinsic one taking place at the stoichiometric LAO/STO interfaces.

Many-body approach to Luttinger's theorem for the Kondo lattice

A numerical verification of Luttinger's theorem, based on a recently developed many-body approach, is given for the Kondo-lattice model. For a two-dimensional lattice the completely localized spins $(S=1/2)$ are found to contribute to the Fermi sea volume as if they were electrons, which is in agreement with Oshikawa's topological proof of Luttinger's theorem. Underpinning this result we explicitly calculate the momentum-resolved one-particle spectral function showing nearly dispersionless excitations clearly below the Fermi level for different values of the conduction electron filling. Numerical integration over momentum and energy always leads to the correct particle number of the localized spins according to the well-accepted picture of a large Fermi surface. In this paper, a first many-body approach is shown, which is able to reproduce the correct value of Luttinger's theorem for this model.

Spectral function of the Tomonaga-Luttinger model revisited: Power laws and universality

We reinvestigate the momentum-resolved single-particle spectral function of the Tomonaga-Luttinger model. In particular, we focus on the role of the momentum-dependence of the two-particle interaction V(q). Usually, V(q) is assumed to be a constant and integrals are regularized in the ultraviolet `by hand' employing an ad hoc procedure. As the momentum dependence of the interaction is irrelevant in the renormalization group sense this does not affect the universal low-energy properties of the model, e.g. exponents of power laws, if all energy scales are sent to zero. If, however, the momentum k is fixed away from the Fermi momentum k_F, with |k-k_F| setting a nonvanishing energy scale, the details of V(q) start to matter. We provide strong evidence that any curvature of the two-particle interaction at small transferred momentum q destroys power-law scaling of the momentum resolved spectral function as a function of energy. Even for |k-k_F| much smaller than the momentum space range of the interaction the spectral line shape depends on the details of V(q). The significance of our results for universality in the Luttinger liquid sense, for experiments on quasi one-dimensional metals, and for recent attempts to compute the spectral function of one-dimensional correlated systems taking effects of the curvature of the single-particle dispersion into account (nonlinear Luttinger liquid phenomenology) is discussed.

A real space auxiliary field approach to the BCS-BEC crossover

The BCS to BEC crossover in attractive Fermi systems is a prototype of weak to strong coupling evolution in many body physics. While extensive numerical results are available, and several approximate methods have been developed, most of these schemes are unsuccessful in the presence of spatial inhomogeneity. Such situations call for a real space approach that can handle large spatial scales and retain the crucial thermal fluctuations. With this in mind, we present comprehensive results of a real space auxiliary field approach to the BCS to BEC crossover in the attractive Hubbard model in two dimensions. The scheme reproduces the Hartree-Fock-Bogoliubov ground state, and leads to a $T_c$ scale that agrees with quantum Monte Carlo estimates to within a few percent. We provide results on the $T_c$, amplitude and phase fluctuations, density of states, and the momentum resolved spectral function over the entire interaction and temperature window. We suggest how the method generalises successfully to the presence of disorder, trapping, and population imbalance.

Photoinduced states in a Mott insulator.

We investigate the properties of the metallic state obtained by photodoping carriers into a Mott insulator. In a strongly interacting system, these carriers have a long lifetime, so that they can dissipate their kinetic energy to a phonon bath. In the relaxed state, the scattering rate saturates at a nonzero temperature-independent value, and the momentum-resolved spectral function features broad bands which differ from the well-defined quasiparticle bands of a chemically doped system. Our results indicate that a photodoped Mott insulator behaves as a bad metal, in which strong scattering between doublons and holes inhibits Fermi-liquid behavior down to low temperature.

Momentum-resolved spectral function of ultracold bosons in two-dimensional optical lattices

The excitations of strongly interacting bosons confined in a two-dimensional square lattice are studied. Using a combined Bogoliubov method and the quantum-rotor approach, the Hamiltonian of strongly interacting bosons is mapped onto the $U(1)$-phase action. This allows to calculate the momentum- and energy-resolved one-particle spectral function and its dependence on the presence of the superfluid phase. It is shown that the destruction of the ordered phase leads to the opening of the gap in the excitation spectrum in $\mathbf{k}=\mathbf{0}$. On the other hand, superfluidity manifests itself as a sharp coherence peak resulting from the emergence of the long-range order. Correlation effects lead to the appearance of a smearing of the band structure of incoherent particles although the remnants of the Bogoliubov excitations are still present in the coherent part of the spectrum.

Dynamical cluster approximation within an augmented plane wave framework: Spectral properties of SrVO3

We present a combination of local density approximation (LDA) with the dynamical cluster approximation (LDA+DCA) in the framework of the full-potential linear augmented plane-wave method, and compare our LDA+DCA results for SrVO$_3$ to LDA with the dynamical mean field theory (LDA+DMFT) calculations as well as experimental observations on SrVO$_3$. We find a qualitative agreement of the momentum resolved spectral function with angle-resolved photoemission spectra (ARPES) and former LDA+DMFT results. As a correction to LDA+DMFT, we observe more pronounced coherent peaks below the Fermi level, as indicated by ARPES experiments. In addition, we resolve the spectral functions in the ${\bf K}_{0}=(0,0,0)$ and ${\bf K}_{1}=(\pi,\pi,\pi)$ sectors of DCA, where band insulating and metallic phases coexist. Our approach can be applied to correlated compounds where not only local quantum fluctuations but also spatial fluctuations are important.

Weak-coupling continuous-time quantum Monte Carlo study of the single impurity and periodic Anderson models withs-wave superconducting baths

We apply the unbiased weak-coupling continuous time quantum Monte Carlo (CTQMC) method to review the physics of a single magnetic impurity coupled to s-wave superconducting leads described by the BCS reduced Hamiltonian. As a function of the superconducting gap $\Delta$, we study the signature of the first order transition between the singlet and doublet (local moment) states on various quantities. In particular we concentrate on the Josephson current with 0 to $\pi$ phase shift, the crossing of the Andreev bound states in the single particle spectral function, as well as the local dynamical spin structure factor. Within DMFT, this impurity problem provides a link to the periodic Anderson model with superconducting conduction electrons (BCS-PAM). The first order transition observed in the impurity model is reproduced in the BCS-PAM and is signalized by the crossing of the low energy excitations in the local density of states. The momentum resolved single particle spectral function in the singlet state reveals the coherent, Bloch-like, superposition of Andreev bound states. In the doublet or local moment phase the single particle spectral function is characterized by incoherent quasiparticle excitations.

Momentum-resolved single-particle spectral function for TiOCl from a combination of density functional and variational cluster calculations

We present results for the momentum-resolved single-particle spectral function of the low-dimensional system TiOCl in the insulating state, obtained by a combination of ab initio density functional theory and variational cluster approach calculations. This approach allows to combine a realistic band structure and a thorough treatment of the strong correlations. We show that it is important to include a realistic two-dimensional band structure of TiOCl into the effective strongly correlated models in order to explain the spectral-weight behavior seen in angle-resolved photoemission spectroscopy experiments. In particular, we observe that the effect of the interchain couplings is a considerable redistribution of the spectral weight around the $\ensuremath{\Gamma}$ point from higher to lower binding energies as compared to a purely one-dimensional model treatment. Hence, our results support a description of TiOCl as a two-dimensional compound with strong anisotropy and also set a benchmark on the spectral features of correlated coupled-chain systems.

Quasiparticle Transformation during a Metal-Insulator Transition in Graphene

Here we show, with simultaneous transport and photoemission measurements, that the graphene-terminated SiC(0001) surface undergoes a metal-insulator transition upon dosing with small amounts of atomic hydrogen. We find the room temperature resistance increases by about 4 orders of magnitude, a transition accompanied by anomalies in the momentum-resolved spectral function including a non-Fermi-liquid behavior and a breakdown of the quasiparticle picture. These effects are discussed in terms of a possible transition to a strongly (Anderson) localized ground state.