Interband Coulomb Interaction Research Articles

Hosohedral nodal-line superconductivity in hexagonal ABC Dirac semimetals

The recently identified hexagonal non-polar phase of KZnBi, an archetypal topological semimetal, has been found to cohost superconductivity on the surface. We propose that KZnBi can realize an unconventional topological superconductor featuring the hosohedral formation of nodal lines and Bogoliubov Fermi surface emerging under a magnetic field. Our density functional theory (DFT)-based low-energy model shows that the nonsymmorphic band degeneracy of the Dirac bands generically triggers topological nodal line superconductivity fostered by inter-band Coulomb interaction. In particular, the nodal lines of the gap resemble a hexagonal hosohedron with the Schläfli symbol of {2, 6}. Remarkably, the holohedral nodal line superconductor defines the topological phase boundary of the Bogoliubov Fermi surface in the limit where time-reversal symmetry is restored. Our results demonstrate that line nodes readily inflate to the Bogoliubov Fermi surface under an external magnetic field. We provide an experimentally verifiable explanation for the observed superconductivity and suggest a feasible platform for observing topological superconductivity in the hexagonal ABC ternary systems class.

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.

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.

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.

Probing Interband Coulomb Interactions in Semiconductor Nanostructures with 2D Double-Quantum Coherence Spectroscopy

Employing the interband exciton scattering model, we have derived a closed set of equations determining the 2D double-quantum coherence signal sensitive to the interband Coulomb interactions (i.e., many-body Coulomb interactions leading to the couplings between exciton and biexciton bands) in semiconductor nanostructures such as nanocrystals, quantum wires, wells, and carbon nanotubes. Our general analysis of 2D double-quantum coherence resonances has demonstrated that the interband Coulomb interactions lead to new cross-peaks whose appearance can be interpreted as a result of exciton and biexciton state mixing. The presence of the strongly coupled resonant states and weakly coupled background of off-resonant states can significantly simplify cross-peak analysis by eliminating the congested background spectrum. Our simulations of the 2D double-quantum coherence signal in PbSe NCs have validated this approach.

Photoinduced superconductivity in copper oxides with two-component scenario

We investigated the photostimulated superconducting phase trnansition temperature (Tc) in copper oxides with the two-component scenario. In the two-component model the superconductivity is caused by the interband repulsive electron-lattice and Coulomb interaction. The photoexcitation produces a change of the hole doping (p) and as a result the shift ΔTc of Tc of copper oxides. The Tc change is determined by the sign of dTc / dp and can be explained in terms of the phase diagram. The theory is compared with the available experimental data.

Effects of Degenerate Orbitals on the Hubbard Model

Stability of a metallic state in the two-orbital Hubbard model at half-filling is investigated. We clarify how spin and orbital fluctuations are enhanced to stabilize the formation of quasi-particles by combining dynamical mean field theory with the quantum Monte Carlo simulations. These analyses shed some light on the reason why the metallic phase is particularly stable when the intra- and inter-band Coulomb interactions are nearly equal.

Stability of a metallic state in the two-orbital Hubbard model

Electron correlations in the two-orbital Hubbard model at half-filling are investigated by combining dynamical mean field theory with the exact diagonalization method. We systematically study how the interplay of the intra- and inter-band Coulomb interactions, together with the Hund coupling, affects the metal-insulator transition. It is found that if the intra- and inter-band Coulomb interactions are nearly equal, the Fermi-liquid state is stabilized due to orbital fluctuations up to fairly large interactions, while the system is immediately driven to the Mott insulating phase away from this condition. The effects of the isotropic and anisotropic Hund coupling are also addressed.

Superconductivity Driven by the Interband Coulomb Interaction and Implications for the Superconducting Mechanism of MgB2

Superconducting mechanism mediated by interband exchange Coulomb repulsion is examined in an extended two-band Hubbard models with a wide band crossing the Fermi level and coexisting with a narrower band located at moderately lower energy. We apply newly developed path-integral renormalization group method to reliably calculate pairing correlations. The correlation shows marked enhancement at moderate amplitudes of the exchange Coulomb repulsion taken smaller than the on-site repulsion for the narrower band. The pairing symmetry is s-wave while it has unconventional phases with the opposite sign between the order parameters on the two bands, in agreement with the mean-field prediction. Since the band structure of recently discovered superconductor MgB$_2$ shares basic similarities with our model, we propose that the present results provide a relevant clue for the understanding of the superconducting mechanism in MgB$_2$ as well as in this class of multi-band materials with good metallic conduction in the normal state.

Nonequilibrium and many-body Coulomb effects in the relaxation oscillation of a semiconductor laser

A treatment of the dynamics in a semiconductor laser that is based on the coupled Maxwell–semiconductor– Bloch equations is described. It is shown that intraband carrier dynamics and interband Coulomb interactions significantly affect the damping of relaxation oscillations. The specific case of a vertical-cavity surface-emitting laser is treated.