In-gap Excitations Research Articles

Effects of the on-site energy on the electronic response of Sr3(Ir1−xMnx)2O7

We investigated the doping and temperature evolutions of the optical response of Sr3(Ir1−xMnx)2O7 single crystals with 0 ≤ x ≤ 0.36 by utilizing infrared spectroscopy. Substitution of 3d transition metal Mn ions into Sr3Ir2O7 is expected to induce an insulator-to-metal transition via the decrease in the magnitude of the spin–orbit coupling and the hole doping. In sharp contrast, our data reveal the resilience of the spin–orbit coupling and the incoherent character of the charge transport. Upon Mn substitution, an incoherent in-gap excitation at about 0.25 eV appeared with the decrease in the strength of the optical transitions between the effective total angular momentum Jeff bands of the Ir ions. The resonance energies of the optical transitions between the Jeff bands which are directly proportional to the magnitude of the spin–orbit coupling hardly varied. In addition to these evolutions of the low-energy response, Mn substitution led to the emergence of a distinct high-energy optical excitation at about 1.2 eV which is larger than the resonance energies of the optical transitions between the Jeff bands. This observation indicates that the Mn 3d states are located away from the Ir 5d states in energy and that the large difference in the on-site energies of the transition metal ions is responsible for the incoherent charge transport and the robustness of the spin–orbit coupling. The effect of Mn substitution was also registered in the temperature dependence of the electronic response. The anomaly in the optical response of the parent compound observed at the antiferromagnetic transition temperature is notably suppressed in the Mn-doped compounds despite the persistence of the long-range antiferromagnetic ordering. The suppression of the spin-charge coupling could be related to charge disproportionation of the Ir ions.

In-gap band in the one-dimensional two-orbital Kanamori-Hubbard model with interorbital Coulomb interaction

We study the electronic spectral properties at zero temperature of the one-dimensional (1D) version of the degenerate two-orbital Kanamori Hubbard model (KHM), one of the well established frameworks to study transition metal compounds, using state-of-the-art numerical techniques based on the Density Matrix Renormalization Group. While the system is Mott insulating for the half-filled case, as expected for an interacting 1D system, we find interesting and rich structures in the single-particle density of states (DOS) for the hole-doped system. In particular, we find the existence of in-gap states which are pulled down to lower energies from the upper Hubbard band (UHB) with increasing the inter-orbital Coulomb interaction $V$. We analyze the composition of the DOS by projecting it onto different local excitations and we observe that for large dopings these in-gap excitations are formed mainly by inter-orbital holon-doublon (HD) states and their energies follow approximately the HD states in the atomic limit. We observe that the Hund interaction $J$ increases the width of the in-gap band, as expected from the two-particle fluctuations in the Hamiltonian. The observation of a finite density of states within the gap between the Hubbard bands for this extended 1D model indicates that these systems present a rich excitation spectra which could help us understand the microscopic physics behind multi-orbital compounds.

Dynamical topological excitations in parafermion chains

Topological excitations in many-body systems are one of the paradigmatic cornerstones of modern condensed matter physics. In particular, parafermions are elusive fractional excitations potentially emerging in fractional quantum Hall-superconductor junctions, and represent one of the major milestones in fractional quantum matter. Here, by using a combination of tensor network and kernel polynomial techniques, we demonstrate the emergence of zero modes and finite energy excitations in many-body parafermion chains. We show the appearance of zero energy modes in the many-body spectral function at the edge of a topological parafermion chain, their relation with the topological degeneracy of the system, and we compare their physics with the Majorana bound states of topological superconductors. We demonstrate the robustness of parafermion topological modes with respect to a variety of perturbations, and we show how weakly coupled parafermion chains give rise to in-gap excitations. Our results exemplify the versatility of tensor network methods for studying dynamical excitations of interacting parafermion chains, and highlight the robustness of topological modes in parafermion models.

Solitonic in-gap modes in a superconductor-quantum antiferromagnet interface

Bound states at interfaces between superconductors and other materials are a powerful tool to characterize the nature of the involved systems, and to engineer elusive quantum excitations. In-gap excitations of conventional s-wave superconductors occur, for instance, at magnetic impurities with net magnetic moment breaking time-reversal symmetry. Here we show that interfaces between a superconductor and a quantum antiferromagnet can host robust in-gap excitations, without breaking time-reversal symmetry. We illustrate this phenomenon in a one-dimensional model system with an interface between a conventional s-wave superconductor and a one-dimensional Mott insulator described by a standard Hubbard model. This genuine many-body problem is solved exactly by employing a combination of kernel polynomial and tensor network techniques. We unveil the nature of such zero modes by showing that they can be adiabatically connected to solitonic solutions between a superconductor and a classical antiferromagnet. Our results put forward a new class of in-gap excitations between superconductors and a disordered quantum spin phase can be relevant for a wider range of heterostructures.

Realization of a Metallic State in 1T-TaS_{2} with Persisting Long-Range Order of a Charge Density Wave.

Metallization of 1T-TaS_{2} is generally initiated at the domain boundary of a charge density wave (CDW), at the expense of its long-range order. However, we demonstrate in this study that the metallization of 1T-TaS_{2} can be also realized without breaking the long-range CDW order upon surface alkali doping. By using scanning tunneling microscopy, we find the long-range CDW order is always persisting, and the metallization is instead associated with additional in-gap excitations. Interestingly, the in-gap excitation is near the top of the lower Hubbard band, in contrast to a conventional electron-doped Mott insulator where it is beneath the upper Hubbard band. In combination with the numerical calculations, we suggest that the appearance of the in-gap excitations near the lower Hubbard band is mainly due to the effectively reduced on-site Coulomb energy by the adsorbed alkali ions.

Erratum: Broken symmetry of in-gap quasiparticle excitations in superconducting FeSe(001) with high defect density [Phys. Rev. B 98 , 220502(R) (2018)

Erratum: Broken symmetry of in-gap quasiparticle excitations in superconducting FeSe(001) with high defect density [Phys. Rev. B 98 , 220502(R) (2018)

Slow quenches in Chern insulator ribbons

We investigate slow quenches in Chern insulators in ribbon geometry. We consider the Qi-Wu-Zhang model and slowly ramp the parameters (large time of the quench $\ensuremath{\tau}$) from a nontopological (Chern number = 0) to a topological regime (Chern number $\ensuremath{\ne}$ 0). In contrast to the Haldane model considered in [L. Privitera and G. E. Santoro, Phys. Rev. B 93, 241406(R) (2016)], the in-gap state degeneracy point is pinned to an inversion symmetric momentum, which changes the behavior drastically. The density of excitations in the in-gap states scales with the quench time as ${\ensuremath{\tau}}^{\ensuremath{-}1/2}$ as the ramp becomes slow, and the Kibble-Zurek mechanism applies. Despite the slower scaling of the density of in-gap excitations with $\ensuremath{\tau}$, the Hall conductance after the quench deviates from that of the ground state of the final Hamiltonian by an amount that drops as ${\ensuremath{\tau}}^{\ensuremath{-}1}$.

Broken symmetry of in-gap quasiparticle excitations in superconducting FeSe(001) with high defect density

FeSe(001) with a high defect density was studied in the superconductiong phase by means of scanning tunneling spectroscopy at low temperature. Quasiparticle excitations surrounding structural defects are found inside the superconducting gap. This spectral intensity is used for revealing additional scattering channels for the quasiparticle excitations. The related wave vectors are located around the $M$ points of the Brillouin zone and follow ${C}_{2}$ symmetry. We attribute the symmetry and the observed lack of dispersion of the scattering channels to the interaction of Bogoliubov quasiparticles with nematic order.

Low-Energy Excitations in Quantum Spin Liquids Identified by Optical Spectroscopy.

The electrodynamic response of organic spin liquids with highly frustrated triangular lattices has been measured in a wide energy range. While the overall optical spectra of these Mott insulators are governed by transitions between the Hubbard bands, distinct in-gap excitations can be identified at low temperatures and frequencies, which we attribute to the quantum-spin-liquid state. For the strongly correlated β^{'}-EtMe_{3}Sb[Pd(dmit)_{2}]_{2}, we discover enhanced conductivity below 175 cm^{-1}, comparable to the energy of the magnetic coupling J≈250 K. For ω→0, these low-frequency excitations vanish faster than the charge-carrier response subject to Mott-Hubbard correlations, resulting in a dome-shaped band peaked at 100 cm^{-1}. Possible relations to spinons, magnons, and disorder are discussed.

Theory of spin-selective Andreev reflection in the vortex core of a topological superconductor

Majorana zero modes (MZMs) have been predicted to exist in the topological insulator (TI)/superconductor (SC) heterostructure. Recent spin polarized scanning tunneling microscope (STM) experiment$^{1}$ has observed spin-polarization dependence of the zero bias differential tunneling conductance at the center of vortex core, which may be attributed to the spin selective Andreev reflection, a novel property of the MZMs theoretically predicted in 1-dimensional nanowire$^{2}$. Here we consider a helical electron system described by a Rashba spin orbit coupling Hamiltonian on a spherical surface with a s-wave superconducting pairing due to proximity effect. We examine in-gap excitations of a pair of vortices with one at the north pole and the other at the south pole. While the MZM is not a spin eigenstate, the spin wavefunction of the MZM at the center of the vortex core, r = 0, is parallel to the magnetic field, and the local Andreev reflection of the MZM is spin selective, namely occurs only when the STM tip has the spin polarization parallel to the magnetic field, similar to the case in 1-dimensional nanowire2. The total local differential tunneling conductance consists of the normal term proportional to the local density of states and an additional term arising from the Andreev reflection. We also discuss the finite size effect, for which the MZM at the north pole is hybridized with the MZM at the south pole. We apply our theory to examine the recently reported spin-polarized STM experiments and show good agreement with the experiments.

Thermodynamic and spectral properties of adiabatic Peierls chains

We present exact numerical results for the effects of thermal fluctuations on the experimentally relevant thermodynamic and spectral properties of Peierls chains. To this end, a combination of classical Monte Carlo sampling and exact diagonalization is used to study adiabatic half-filled Holstein and Su-Schrieffer-Heeger models. The classical nature of the lattice displacements in combination with parallel tempering permit simulations on large system sizes and a direct calculation of spectral functions in the frequency domain. Most notably, the long-range order and the associated Peierls gap give rise to a distinct low-temperature peak in the specific heat. The closing of the gap and suppression of order by thermal fluctuations involves in-gap excitations in the form of soliton-antisoliton pairs, and is also reflected in the dynamic density and bond structure factors as well as in the optical conductivity. We compare our data to the widely used mean-field approximation, and highlight relations to symmetry-protected topological phases and disorder problems.

Breakdown of the Kondo insulating state inSmB6by introducing Sm vacancies

SmB6 is a proposed topological Kondo insulator where the presence of topological nontriviality can be tuned by variations in the Sm valence. Experimentally, Sm valence can be changed by tuning stoichiometry of SmB6. We show that Raman scattering can detect vacancies lower than 1% of Sm sites in SmB6 crystal by probing the intensity of defect-induced scattering of the acoustic phonon branch at 10~meV. In the electronic Raman spectra of SmB6 at temperatures below 130~K, we observe features developing in A$_{1g}$ and E$_g$ symmetries at 100 and 41~meV which we assign to excitations between hybridized bands, and depressed spectral weight below 20~meV associated with the hybridization gap. With the increased number of Sm vacancies up to 1% we observe an increase of spectral weight below 20~meV showing that the gap is filling in with electronic states. For the sample with the lowest number of vacancies the in-gap exciton excitations with long lifetimes protected by hybridization gap are observed at 16-18~meV in E$_g$ and T$_{2g}$ symmetries. These excitations broaden as a decrease in the lifetime with increasing number of vacancies and are quenched by the presence of in-gap states at concentration of Sm vacancies of about 1%. Based on this study we suggest that only the most stoichiometric SmB6 samples have a bulk gap necessary for topological Kondo insulators.

Photoinduced in-gap excitations in the one-dimensional extended Hubbard model

We investigate the time evolution of optical conductivity in the half-filled one-dimensional extended Hubbard model driven by a transient laser pulse, by using the time-dependent Lanczos method. Photoinduced in-gap excitations exhibit a qualitatively different structure in the spin-density wave (SDW) in comparison to the charge-density-wave (CDW) phase. In the SDW, the origin of a low-energy in-gap excitation is attributed to the even-odd parity of the photoexcited states, while in the CDW an in-gap state is due to confined photogenerated carriers. The signature of the in-gap excitations can be identified as a characteristic oscillation in the time evolution of physical quantities.

Electronic excitations and structure of Li2IrO3 thin films grown on ZrO2:Y (001) substrates

Thin films are a prerequisite for application of the emergent exotic ground states in iridates that result from the interplay of strong spin-orbit coupling and electronic correlations. We report on pulsed laser deposition of Li2IrO3 films on ZrO2:Y (001) single crystalline substrates. X-ray diffraction confirms preferential (001) and (10-1) out-of-plane crystalline orientations with well defined in-plane orientation. Resistivity between 35 and 300 K is dominated by a three-dimensional variable range hopping mechanism. The dielectric function is determined by means of spectroscopic ellipsometry and, complemented by Fourier transform infrared transmission spectroscopy, reveals a small optical gap of ≈300 meV, a splitting of the 5d-t2g manifold, and several in-gap excitations attributed to phonons and possibly magnons.

In-gap quasiparticle excitations induced by non-magnetic Cu impurities in Na(Fe(0.96) Co(0.03)Cu(0.01))As revealed by scanning tunnelling spectroscopy.

The origin of superconductivity in the iron pnictides remains unclear. One suggestion is that superconductivity in these materials has a magnetic origin, which would imply a sign-reversal s± pairing symmetry. Another suggests it is the result of orbital fluctuations, which would imply a sign-equal s++ pairing symmetry. There is no consensus yet which of these two distinct and contrasting pairing symmetries is the right one in iron pnictide superconductors. Here we explore the nature of the pairing symmetry in the superconducting state of Na(Fe0.97−xCo0.03Cux)As by probing the effect of scattering of Cooper pairs by non-magnetic Cu impurities. Using scanning tunnelling spectroscopy, we identify the in-gap quasiparticle states induced by the Cu impurities, showing signatures of Cooper pair breaking by these non-magnetic impurities–a process that is only consistent with s± pairing. This experiment provides strong evidence for the s± pairing.

Resonant Mode in Rare-earth based Strongly Correlated Semiconductors

An extensive study of the spin dynamics in the strongly correlated semiconductors YbB 12 and SmB 6 , as well as in the series of related electron-doped systems, has been performed by means of inelastic neutron scattering spectroscopy. It was found that rare-earth compounds with a valence instability may develop an exciton-like in-gap excitation, generally similar to the so-called resonant mode initially discovered in HTSC. The results of this work, along with the literature data for a number of high- T c -, heavy-fermion- and pnictide superconductors and some magnetic compounds point to such type of resonant excitations being characteristic for systems with gap-like dynamical response in the presence of competing interactions . The correlation between the temperature evolutions of the resonant mode and of the gap in the excitation spectrum is discussed.

Charge excitations in stripe-ordered La5/3Sr1/3NiO4and La15/8Ba1/8CuO4: Interpretation of the anomalous momentum transfer dependence via fluorescence interferometry

Fluorescence interferometry (FI) makes use of the temporal and spatial coherence of absorption and re-emission process in resonant inelastic x-ray scattering (RIXS), which leads to interference terms in the RIXS cross section of a group of identical, physically equivalent, and interacting atoms. These interferences contain structural information and make RIXS site selective. The basics of FI are derived within the third-order perturbation treatment of indirect RIXS. The final relations for the FI related RIXS cross section were used to interpret the unique momentum-transfer dependence of the in-gap charge excitations observed for 214-type nickelates (La${}_{5/3}$Sr${}_{1/3}$NiO${}_{4}$) and cuprates (La${}_{15/8}$Ba${}_{1/8}$CuO${}_{4}$). By using well-known stripe models, the momentum-transfer dependence of the corresponding indirect RIXS features is traced back to interference terms in the RIXS cross section based on the principles of FI. Thus analyzing the momentum-transfer dependence of the re-emitted radiation yields information about details of the charge stripe structure.

Anomalous S-like dispersion of in-gap single-particle excitations in the pseudogap state of cuprate superconductors

The single-particle excitations which control the opening of the pseudogap in the cuprate superconductors at some temperature ${T}^{\ensuremath{\ast}}$ are considered to derive their specific local spectral features from resonant pairing, whereby charge carriers get momentarily trapped on dynamically deformable molecular Cu-O-Cu clusters. We show how such local excitations evolve into overdamped modes with a characteristic ``S''-like dispersion around the Fermi energy, as one passes below ${T}^{\ensuremath{\ast}}$. This feature should be detectable in a ``momentum distribution curve'' angle-resolved photoemission spectroscopy analysis and help to elucidate the kind of pairing in the cuprates. Our study is based on a generic boson-fermion model for resonant pairing and is an extension of our previous dynamical mean-field theory study [A. Romano and J. Ranninger, Phys. Rev. B 62, 4066 (2000)] of the spectral properties of the pseudogap state.

Power-Law Conductivity inside the Mott Gap: Application toκ−(BEDT−TTF)2Cu2(CN)3

The charge dynamics of spin-liquid states described by U(1) gauge theory coupling to fermionic spinons is discussed in this paper. We find that the gapless spinons give rise to a power-law optical conductivity inside the charge gap. The theory is applied to explain the unusual optical conductivity observed recently in the organic compound kappa-(BEDT-TTF)2Cu2(CN){3}. We also propose an optical experiment to search for the in-gap excitations in the kagome spin-liquid insulator.

Neutron scattering study of spin and lattice dynamics in [formula omitted

The spin dynamics of mixed-valence YbB 12 has been studied by inelastic neutron scattering on a single crystal. In the Kondo-insulating regime, the spectra exhibit a spin-gap structure with two dispersive in-gap excitations at ℏ ω ≈ 15 and 20 meV. The lower mode is associated with short-range correlations near the antiferromagnetic wave vector q 0 = ( 1 2 , 1 2 , 1 2 ) . Its properties are in overall agreement with those expected for a “spin exciton” branch in the hybridization-gap picture, but Lu dilution experiments favor a more local mechanism for the gap formation. The vibrational behavior of Yb ions within the rigid B lattice is reflected into details of the phonon dispersion curves.