Interband Coulomb Research Articles

Incommensurate charge density wave in multiband intermetallic systems exhibiting competing orders

The appearance of an incommensurate charge density wave vector $\textbf{Q} = (Q_x,Q_y)$ on multiband intermetallic systems presenting commensurate charge density wave (CDW) and superconductivity (SC) orders is investigated. We consider a two-band model in a square lattice, where the bands have distinct effective masses. The incommensurate CDW (inCDW) and CDW phases arise from an interband Coulomb repulsive interaction, while the SC emerges due to a local intraband attractive interaction. For simplicity, all the interactions, the order parameters and hybridization between bands are considered $\textbf{k}$-independent. The multiband systems that we are interested are intermetallic systems with a $d$-band coexisting with a large $c$-band, for which a mean-field approach has proved suitable. We obtain the eigenvalues and eigenvectors of the Hamiltonian numerically and minimize the free energy density with respect to the diverse parameters of the model by means of the Hellmann-Feynman theorem. We investigate the system in real as well as momentum space and we find an inCDW phase with wave vector $\textbf{Q} = (\pi, Q_y) = (Q_x, \pi)$. Our numerical results show that the arising of an inCDW state depends on parameters, such as the magnitude of the inCDW and CDW interactions, band filling, hybridization and the relative depth of the bands. In general, inCDW tends to emerge at low temperatures, away from half-filling. We also show that, whether the CDW ordering is commensurate or incommensurate, large values of the relative depth between bands may suppress it. We discuss how each parameter of the model affects the emergence of an inCDW phase.

Ab initio quantum approach to electron-hole exchange for semiconductors hosting Wannier excitons

We propose a quantum approach to ``electron-hole exchange,'' better named electron-hole pair exchange, that makes use of the second quantization formalism to describe the problem in terms of Bloch-state electron operators. This approach renders transparent the fact that such singular effect comes from interband Coulomb processes. We first show that, due to the sign change when turning from valence-electron destruction operator to hole creation operator, the interband Coulomb interaction only acts on spin-singlet electron-hole pairs, just like the interband electron-photon interaction, thereby making these spin-singlet pairs optically bright. We then show that, when written in terms of reciprocal lattice vectors ${\mathbf{G}}_{m}$, the singularity of the interband Coulomb scattering in the small wave-vector transfer limit entirely comes from the ${\mathbf{G}}_{m}=\mathbf{0}$ term, which renders its singular behavior easy to calculate. Comparison with the usual real-space formulation in which the singularity appears through a sum of ``long-range processes'' over all ${\mathbf{R}}_{\ensuremath{\ell}}\ensuremath{\ne}\mathbf{0}$ lattice vectors once more proves that periodic systems are easier to handle in terms of reciprocal vectors ${\mathbf{G}}_{m}$ than in terms of lattice vectors ${\mathbf{R}}_{\ensuremath{\ell}}$. Well-accepted consequences of the electron-hole exchange on excitons and polaritons are reconsidered and refuted for different major reasons.

Interplay between charge density wave and superconductivity in multiband systems with interband Coulomb interaction

In this work we study the competition or coexistence between charge density wave (CDW) and superconductivity (SC) in a two-band model system in a square lattice. One of the bands has a net attractive interaction ($J_d$) that is responsible for SC. The model includes on-site Coulomb repulsion between quasi-particles in different bands ($U_{dc}$) and the hybridization ($V$) between them. We are interested in describing inter-metallic systems with a $d$-band of moderately correlated electrons, for which a mean-field approximation is adequate, coexisting with a large $sp$-band. For simplicity, all interactions and the hybridization $V$ are considered site-independent. We obtain the eigenvalues of the Hamiltonian numerically and minimize the free energy density with respect to the relevant parameters to obtain the phase diagrams as function of $J_d$, $U_{dc}$, $V$, composition ($n_{\mathrm{tot}}$) and the relative depth of the bands ($\epsilon_{d0}$). We consider two types of superconducting ground states coexisting with the CDW. One is a homogeneous ground state and the other is a pair density wave where the SC order parameter has the same spatial modulation of the CDW. Our results show that the CDW and SC orders compete, but depending on the parameters of the model these phases may coexist. The model reproduces most of the experimental features of high dimensionality ($d>1$) metals with competing CDW and SC states, including the existence of first and second-order phase transitions in their phase diagrams.

Light quantum control of persisting Higgs modes in iron-based superconductors

The Higgs mechanism, i.e., spontaneous symmetry breaking of the quantum vacuum, is a cross-disciplinary principle, universal for understanding dark energy, antimatter and quantum materials, from superconductivity to magnetism. Unlike one-band superconductors (SCs), a conceptually distinct Higgs amplitude mode can arise in multi-band, unconventional superconductors via strong interband Coulomb interaction, but is yet to be accessed. Here we discover such hybrid Higgs mode and demonstrate its quantum control by light in iron-based high-temperature SCs. Using terahertz (THz) two-pulse coherent spectroscopy, we observe a tunable amplitude mode coherent oscillation of the complex order parameter from coupled lower and upper bands. The nonlinear dependence of the hybrid Higgs mode on the THz driving fields is distinct from any known SC results: we observe a large reversible modulation of resonance strength, yet with a persisting mode frequency. Together with quantum kinetic modeling of a hybrid Higgs mechanism, distinct from charge-density fluctuations and without invoking phonons or disorder, our result provides compelling evidence for a light-controlled coupling between the electron and hole amplitude modes assisted by strong interband quantum entanglement. Such light-control of Higgs hybridization can be extended to probe many-body entanglement and hidden symmetries in other complex systems.

Collective modes in excitonic insulators: Effects of electron-phonon coupling and signatures in the optical response

We consider a two-band spinless model describing an excitonic insulator (EI) on the two-dimensional square lattice with anisotropic hopping parameters and electron-phonon (el-ph) coupling, inspired by the EI candidate Ta$_2$NiSe$_5$. We systematically study the nature of the collective excitations in the ordered phase which originates from the interband Coulomb interaction and the el-ph coupling. When the ordered phase is stabilized only by the Coulomb interaction (pure EI phase), its collective response exhibits a massless phase mode in addition to the amplitude mode. We show that in the BEC regime, the signal of the amplitude mode becomes less prominent and that the anisotropy in the phase mode velocities is relaxed compared to the model bandstructure. Through coupling to the lattice, the phase mode acquires a mass and the signal of the amplitude mode becomes less prominent. Importantly, character of the softening mode at the boundary between the normal semiconductor phase and the ordered phase depends on the parameter condition. In particular, we point out that even for el-ph coupling smaller than the Coulomb interaction the mode that softens to zero at the boundary can have a phonon character. We also discuss how the collective modes can be observed in the optical conductivity. Furthermore, we study the effects of nonlocal interactions on the collective modes and show the possibility of realizing a coexistence of an in-gap mode and an above-gap mode split off from the single amplitude mode in the system with the local interaction only.

Overlooked Transportation Anisotropies in d-Band Correlated Rare-Earth Perovskite Nickelates

Anisotropies in electronic transportations conventionally originate from the nature of low symmetries in crystal structures, and were not anticipated for perovskite oxides, the crystal asymmetricity of which is far below, e.g. van der Waals or topological crystal. Beyond conventional expectations, herein we demonstrate pronounced anisotropies in the inter-band coulomb repulsion dominated electronic transportation behaviors under low-dimensional confinement for the perovskite family of rare-earth nickelates (ReNiO3). From one aspect, imparting bi-axial interfacial strains upon various lattice planes results in extrinsic anisotropies in the abrupt orbital transitions of ReNiO3, and their metal to insulator transition behaviors that elevates the transition temperature beyond the existing merit. From the other aspect, the in-plane orbital entropy associated to the in-plane symmetry of the NiO6 octahedron within ReNiO3 causes intrinsic anisotropies for the gradually orbital transition with temperature to further improve their thermistor transportation properties. The present work unveils the overlooked role of the electronic orbital directionality within low dimensional correlated perovskites that can trigger anisotropic transportation behaviors, in spite of their relatively symmetric crystal structures. Establishing anisotropic transportations integrating the electron correlation and quantum confinement effects will bring in a new freedom for achieving further improvement in transportation properties of multi-functional perovskite oxides.

Spin–orbit coupling, minimal model and potential Cooper-pairing from repulsion in BiS2-superconductors

We develop the realistic minimal electronic model for recently discovered BiS2 superconductors including the spin–orbit (SO) coupling based on the first-principles band structure calculations. Due to strong SO coupling, characteristic for the Bi-based systems, the tight-binding low-energy model necessarily includes px, py, and pz orbitals. We analyze a potential Cooper-pairing instability from purely repulsive interaction for the moderate electronic correlations using the so-called leading angular harmonics approximation. For small and intermediate doping concentrations we find the dominant instabilities to be -wave, and s±-wave symmetries, respectively. At the same time, in the absence of the sizable spin fluctuations the intra and interband Coulomb repulsions are of the same strength, which yield the strongly anisotropic behavior of the superconducting gaps on the Fermi surface. This agrees with recent angle resolved photoemission spectroscopy findings. In addition, we find that the Fermi surface topology for BiS2 layered systems at large electron doping can resemble the doped iron-based pnictide superconductors with electron and hole Fermi surfaces maintaining sufficient nesting between them. This could provide further boost to increase Tc in these systems.

Evolution of superconducting gaps in Th-substituted Sm1−xThxOFeAs studied by multiple Andreev reflection spectroscopy

Using intrinsic multiple Andreev reflections effect (IMARE) spectroscopy, we studied SnS contacts in the layered oxypnictide superconductors Sm$_{1-x}$Th$_x$OFeAs with various thorium doping and critical temperatures $T_C = 21-54$ K. We observe a scaling between both superconducting gaps and $T_C$. The determined BCS-ratio for the large gap $2\Delta_L/k_BT_C = 5.0-5.7$ and its eigen BCS-ratio (in a hypothetical case of zero interband coupling) $2\Delta_L/k_BT_C^L = 4.1-4.6$ both exceeding the weak-coupling limit 3.52, and for the small gap $2\Delta_S/k_BT_C = 1.2-1.6$ remain nearly constant within all the $T_C$ range studied. The temperature dependences $\Delta_{L,S}(T)$ agree well with a two-band BCS-like Moskalenko and Suhl model. We prove intraband coupling to be stronger than interband coupling, whereas and Coulomb repulsion constants $\mu^{\ast}$ are finite in Sm-based oxypnictides.

Exciton condensation in an extended Falicov-Kimball model in the presence of orbital magnetic fields

We investigate the exciton condensation in the presence of an external, perpendicular magnetic field in a two-dimensional extended spinless Falicov-Kimball model involving itinerant and localized electrons in the half-filled limit, using self-consistent, mean-field approximations. On tuning the orbital magnetic field the excitonic averages are affected in several ways: the external field usually suppresses the excitonic average but we find that it is also possible to enhance excitonic response at some values of the magnetic field. We further examine the effect of Coulomb interaction and the f-electron hopping on the condensation of excitons for some rational values of the applied magnetic fields. The interband Coulomb interaction enhances Δ exponentially and the effect is more pronounced for low hybridization. The strength of excitonic average drops when f-electrons have a dispersion. This trend is independent of the relative sign of the c- and f-electron hopping; although the excitonic response is different for different parity of the c- and f-electrons.

Revealing the role of electrons and phonons in the ultrafast recovery of charge density wave correlations in 1T−TiSe2

Using time- and angle-resolved photoemission spectroscopy with selective near- and mid-infrared photon excitations, we investigate the femtosecond dynamics of the charge density wave (CDW) phase in 1$T$-TiSe$_2$, as well as the dynamics of CDW fluctuations at 240 K. In the CDW phase, we observe the coherent oscillation of the CDW amplitude mode. At 240 K, we single out an ultrafast component in the recovery of the CDW correlations, which we explain as the manifestation of electron-hole correlations. Our momentum-resolved study of femtosecond electron dynamics supports a mechanism for the CDW phase resulting from the cooperation between the interband Coulomb interaction, the mechanism of excitonic insulator phase formation, and electron-phonon coupling.

Influence of strong screening effect on the perpendicular- polarized linear excitonic absorption spectra of semiconducting carbon nanotubes

For incident light polarized perpendicular to the tube axis the multi-band semiconductor Bloch equations (MB-SBEs) that involve various screened interband Coulomb interactions (ICIs) are derived. The calculated E 12 peak is very close to the longitudinal excitonic peak E 22. Compared with the previous theoretical peak positions, the blue-shift of the peak in our results is about 0.5 eV. Then, subsequent detailed analyses show that the screening effect on the diagonal ICIs (D-ICIs) plays a key role in this big blue-shift. The valley-degenerate transverse pair excitations holding the same selection rule further enhance the screening effect on D-ICIs. Specially at q = 0 the dielectric function acting on the D-ICIs enhances two times. In our calculation the strong screening effect contributes 90% of the big blue-shift, while the non-diagonal ICIs (ND-ICIs) contribute to 10% of the blue-shift.

Layer-Confined Excitonic Insulating Phase in Ultrathin Ta2NiSe5 Crystals.

Atomically thin nanosheets, as recently realized using van der Waals layered materials, offer a versatile platform for studying the stability and tunability of the correlated electron phases in the reduced dimension. Here, we investigate a thickness-dependent excitonic insulating (EI) phase on a layered ternary chalcogenide Ta2NiSe5. Using Raman spectroscopy, scanning tunneling spectroscopy, and in-plane transport measurements, we found no significant changes in crystalline and electronic structures as well as disorder strength in ultrathin Ta2NiSe5 crystals with a thickness down to five layers. The transition temperature, Tc, of ultrathin Ta2NiSe5 is reduced from its bulk value by ΔTc/Tc(bulk) ≈ -9%, which strongly contrasts the case of 1T-TiSe2, another excitonic insulator candidate, showing an increase of Tc by ΔTc/Tc(bulk) ≈ +30%. This difference is attributed to the dominance of interband Coulomb interaction over electron-phonon interaction and its zero-ordering wave vector due to the direct band gap structure of Ta2NiSe5. The out-of-plane correlating length of the EI phase is estimated to have monolayer thickness, suggesting that the EI phase in Ta2NiSe5 is highly layer-confined and in the strong coupling limit.

Effects of Coulomb interactions on the superconducting gaps in iron-based superconductors

Recent angle-resolved photoemission spectroscopy measurements of Co-doped LiFeAs report a large and robust superconducting gap on the $\Gamma$-centered hole band that lies 8 meV below the Fermi level. We show that, unlike a conventional superconductor described by BCS theory, a multiband system with strong interband Coulomb interactions can explain these observations. We model LiFeAs with a five-band model in which the shallow hole band is coupled with the other bands by only Coulomb interactions. Using Eliashberg theory, we find reasonable interaction parameters that reproduce the $T_c$ and all five gaps of LiFeAs. The energy independence of the Coulomb interactions then ensures the robustness of the gap induced on the shallow band. Furthermore, due to the repulsive nature of the Coulomb interactions, the gap changes sign between the shallow band and the other hole pockets, corresponding to an unconventional $s_{\pm}$ gap symmetry. Unlike other families of iron-based superconductors, the gap symmetry of LiFeAs has not been ascertained experimentally. The experimental implications of this sign-changing state are discussed.

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

We analyze the stability of excitonic ground states in the two-band Hubbard model with additional electron-phonon and Hund's rule couplings using a combination of mean-field and variational cluster approaches. We show that both the interband Coulomb interaction and the electron-phonon interaction will cooperatively stabilize a charge density wave (CDW) state which typifies an "excitonic" CDW if predominantly triggered by the effective interorbital electron-hole attraction or a "phononic" CDW if mostly caused by the coupling to the lattice degrees of freedom. By contrast, the Hund's rule coupling promotes an excitonic spin density wave. We determine the transition between excitonic charge and spin density waves and comment on a fixation of the phase of the excitonic order parameter that would prevent the formation of a superfluid condensate of excitons. The implications for exciton condensation in several material classes with strongly correlated electrons are discussed.

Publisher's Note: Interband Coulomb coupling in narrow-gap semiconductor nanocrystals:k·ptheory [Phys. Rev. B91, 195314 (2015)

Publisher's Note: Interband Coulomb coupling in narrow-gap semiconductor nanocrystals:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>k</mml:mi><mml:mo>·</mml:mo><mml:mi>p</mml:mi></mml:mrow></mml:math>theory [Phys. Rev. B<b>91</b>, 195314 (2015)

Interband Coulomb coupling in narrow-gap semiconductor nanocrystals:k·ptheory

We derive the matrix elements of Coulomb interaction between states with different numbers of electrons and holes in a semiconductor nanocrystal within the eight-band $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ theory. These matrix elements are responsible for multiple exciton generation which may contribute to the enhancement of the efficiency of solar cells. Our calculations are performed within the multiband envelope function formalism based on the states resulting from diagonalization of the eight-band $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ Hamiltonian. We study in detail and compare two contributions to the interband Coulomb coupling: the mesoscopic one, which involves only the envelope functions and relies on band mixing, and the microscopic one, which relies on the Bloch parts of the wave functions and is nonzero even between single-band states. We show that these two contributions are of a similar order of magnitude. We also study the statistical distribution of the magnitudes of the interband Coulomb matrix elements and show that the overall coupling to remote states decays according to a power law favorable for the convergence of numerical computations.

The influence of the interband Coulomb interaction and the f-electron hopping on excitonic correlations in the extended Falicov-Kimball model

The density matrix renormalization group (DMRG) method is used to examine the effects of the interband Coulomb interaction U between f and d electrons as well as the f-electron hopping on the stability of the excitonic phase in the one-dimensional Falicov-Kimball model (FKM) with local hybridization V. It is found that the interband Coulomb interaction significantly enhances the excitonic average and that this effect is especially strong in the limit of small hybridization, where the interacting excitonic value is enhanced several hundred times in comparison to its non-interacting value. The further increase in Pdf is observed due to the non-zero f-electron hopping, but these changes are considerable only if the d and f bands have opposite parity. In addition, the examination of the interplay between the excitonic effects and the charge density wave (CDW) instability showed that the CDW and excitonic phase coexist up to relatively large values of local hybridization . The ground-state phase diagram of the model in the plane is discussed.

A variational Monte Carlo study of exciton condensation

Exciton condensation in a two-band Hubbard model on a square lattice is studied with variational Monte Carlo method. We show that the phase transition from an excitonic insulator to a band insulator is induced by increasing the interband Coulomb interaction. To examine the character of the exciton condensation, the exciton pair amplitudes both in k-space and in real space are calculated. Using these quantities, we discuss the BCS-BEC crossover within the excitonic insulator phase.

Influence of Coulomb-induced band couplings on linear excitonic absorption spectra of semiconducting carbon nanotubes

Starting from the extended Su-Schrieffer-Heeger model, multiband semiconductor Bloch equations are formulated in momentum space and applied to the analysis of the linear optical response of semiconducting carbon nanotubes (SCNTs). This formalism includes the coupling of electron-hole pair excitations between different valence and conduction bands, originating from the electron-hole Coulomb attraction. The influence of these couplings, which are referred to as nondiagonal interband Coulomb interaction (NDI-CI), on the linear excitonic absorption spectra is investigated and discussed for light fields polarized parallel to the tube direction. The results show that the intervalley NDI-CI leads to a significant increase of the band gap and a decrease of the exciton binding energy that results in a blueshift of the lowest-frequency excitonic absorption peak. The strength of these effects depends on the symmetry of the SCNT. Furthermore, for zigzag SCNTs with higher symmetry other nonintervalley NDI-CI terms also affect the spectral positions of excitonic absorption peaks.

Disorder-driven metal-insulator-transition assisted by interband Coulomb repulsion in a surface transfer doped electron system

The two-dimensional conducting properties of the Si(111) surface doped by the charge surface transfer mechanism have been calculated in the frame of a semiclassical Drude-Boltzmann model considering donor scattering mechanisms. To perform these calculations, the required values of the carrier effective mass were extracted from reported angle-resolved photoemission results. The calculated doping dependence of the surface conductance reproduces experimental results reported and reveals an intricate metallization process driven by disorder and assisted by interband interactions. The system should behave as an insulator even at relatively low doping due to disorder. However, when doping increases, the system achieves to attenuate the inherent localization effects introduced by disorder and to conduct by percolation. The mechanism found by the system to conduct appears to be connected with the increasing of the carrier effective mass observed with doping, which seems to be caused by interband interactions involving the conducting band and deeper ones. This mass enhancement reduces the donor Bohr radius and, consequently, promotes the screening ability of the donor potential by the electron gas.