Single-particle Excitation Gap Research Articles

Suppression of odd-frequency pairing by phase disorder in a nanowire coupled to Majorana zero modes

Odd-frequency superconductivity is an exotic phase of matter in which Cooper pairing between electrons is entirely dynamical in nature. Majorana zero modes exhibit pure odd-frequency superconducting correlations due to their specific properties. Thus, by tunnel-coupling an array of Majorana zero modes to a spin-polarized wire, it is in principle possible to engineer a bulk one-dimensional odd-frequency spinless $s$-wave superconductor. We here point out that each tunnel coupling element, being dependent on a large number of material-specific parameters, is generically complex with sample variability in both its magnitude and phase. Using this, we demonstrate that, upon averaging over phase-disorder, the induced superconducting, including odd-frequency, correlations in the spin-polarized wire are significantly suppressed. We perform both a rigorous analytical evaluation of the disorder-averaged $T$-matrix in the wire, as well as numerical calculations based on a tight-binding model, and find that the anomalous, i.e. superconducting, part of the $T$-matrix is highly suppressed with phase disorder. We also demonstrate that this suppression is concurrent with the filling of the single-particle excitation gap by smearing the near-zero frequency peaks, due to formation of bound states that satisfy phase-matching conditions between spatially separated Majorana zero modes. Our results convey important constraints on the parameter control needed in practical realizations of Majorana zero mode structures and suggest that the achievement of a bulk 1D odd-$\omega$ superconductivity from MZMs demand full control of the system parameters.

Density-Matrix Embedding Theory Study of the One-Dimensional Hubbard-Holstein Model.

We present a density-matrix embedding theory (DMET) study of the one-dimensional Hubbard–Holstein model, which is paradigmatic for the interplay of electron–electron and electron–phonon interactions. Analyzing the single-particle excitation gap, we find a direct Peierls insulator to Mott insulator phase transition in the adiabatic regime of slow phonons in contrast to a rather large intervening metallic phase in the anti-adiabatic regime of fast phonons. We benchmark the DMET results for both on-site energies and excitation gaps against density-matrix renormalization group (DMRG) results and find good agreement of the resulting phase boundaries. We also compare the full quantum treatment of phonons against the standard Born–Oppenheimer (BO) approximation. The BO approximation gives qualitatively similar results to DMET in the adiabatic regime but fails entirely in the anti-adiabatic regime, where BO predicts a sharp direct transition from Mott to Peierls insulator, whereas DMET correctly shows a large intervening metallic phase. This highlights the importance of quantum fluctuations in the phononic degrees of freedom for metallicity in the one-dimensional Hubbard–Holstein model.

First-order topological phase transition of the Haldane-Hubbard model

We study the interplay of topological band structure and conventional magnetic long-range order in spinful Haldane model with onsite repulsive interaction. Using the dynamical cluster approximation with clusters of up to 24 sites we find evidence of a first order phase transition from a Chern insulator at weak coupling to a topologically trivial antiferromagnetic insulator at strong coupling. These results call into question a previously found intermediate state with coexisting topological character and antiferromagnetic long-range order. Experimentally measurable signatures of the first order transition include hysteretic behavior of the double occupancy, single-particle excitation gap and nearest neighbor spin-spin correlations. This first order transition is contrasted with a continuous phase transition from the conventional band insulator to the antiferromagnetic insulator in the ionic Hubbard model on the honeycomb lattice.

Exciton condensation due to electron-phonon interaction

We show that the coupling to vibrational degrees of freedom can drive a semimetal excitonic-insulator quantum phase transition in an one-dimensional two-band f-c electron system at zero temperature. The insulating state typifies an excitonic condensate accompanied by a finite lattice distortion. Using the projector-based renormalization method we analyze the ground-state and spectral properties of the interacting electron-phonon model at half-filling. In particular we calculate the momentum dependence of the excitonic order parameter function and determine the finite critical interaction strength for the metal-insulator transition to appear. The electron spectral function reveals the strong hybridization of f- and c-electron states and the opening of a single-particle excitation gap. The phonon spectral function indicates that the phonon mode involved in the transition softens (hardens) in the adiabatic (non-adiabatic and extreme anti-adiabatic) phonon frequency regime.

A BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

Motivated by recent experimental and theoretical studies of excitonic insulators, we use the variational cluster approximation to calculate the single-particle Green's function and anomalous Green's function of the Falicov-Kimball model extended by including a finite valence bandwidth. We thus determine the single-particle excitation gap due to the bound-state formation of an electron and a hole. We also evaluate the order parameter of the excitonic insulating state indicating quantum coherence of condensed excitons. We thereby discuss the excitonic insulator that typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate of preformed excitons (strong-coupling regime). A BCS-BEC crossover of the model thus manifests itself as a function of the Coulombic coupling strength.

Variational cluster approach to the extended Falicov-Kimball model: A BCS-BEC crossover in the Excitonic insulators

We study the Coulomb-interaction induced spontaneous symmetry breaking of the excitonic insulator state in the two-dimensional extended Falicov-Kimball model. Using the variational cluster approximation, we evaluate the order parameter, single-particle excitation gap, momentum distribution functions, and anomalous Green's function as a function of U at zero temperature. We find that in the weak-to-intermediate couplinb regime, the Fermi surface is well-defined and the calculated results can be understood in the close correspondence with the BCS theory, whereas in the strong-coupling regime, the Fermi surface is ill-defined and the results are consistent with the picture of BEC.

BCS-BEC crossover in the extended Falicov-Kimball model: Variational cluster approach

We study the spontaneous symmetry breaking of the excitonic insulator state induced by the Coulomb interaction $U$ in the two-dimensional extended Falicov-Kimball model. Using the variational cluster approximation (VCA) and Hartree-Fock approximation (HFA), we evaluate the order parameter, single-particle excitation gap, momentum distribution functions, coherence length of excitons, and single-particle and anomalous excitation spectra, as a function of $U$ at zero temperature. We find that in the weak-to-intermediate coupling regime, the Fermi surface plays an essential role and calculated results can be understood in close correspondence with the BCS theory, whereas in the strong-coupling regime, the Fermi surface plays no role and results are consistent with the picture of BEC. Moreover, we find that HFA works well both in the weak- and strong-coupling regime, and that the difference between the results of VCA and HFA mostly appears in the intermediate-coupling regime. The reason for this is discussed from a viewpoint of the self-energy. We thereby clarify the excitonic insulator state that typifies either a BCS condensate of electron-hole pairs (weak-coupling regime) or a Bose-Einstein condensate of preformed excitons (strong-coupling regime).

Xenon-plasma light ultrahigh-resolution ARPES study of low-energy single-particle excitation gap in (Bi,Pb)2Sr2CuO6

We have performed ultrahigh-resolution angle-resolved photoemission spectroscopy of (Bi,Pb)2Sr2CuO6 by using a newly developed xenon-plasma light source to clarify the origin of the pseudogap (PG). We determined the comprehensive momentum and temperature dependences of the superconducting (SC) gap and the PG, and revealed a smooth evolution of the PG from the SC gap. We also found a linear scaling behavior of the characteristic PG temperature with the SC gap size regardless of the momentum location. These experimental results strongly suggest that the observed PG is caused by the precursor pairing.

Quantum Phase Transition in a 1D Transport Model with Boson-Affected Hopping: Luttinger Liquid versus Charge-Density-Wave Behavior

We solve a very general two-channel fermion-boson model describing charge transport within some background medium by means of a refined pseudosite density-matrix renormalization group technique. Performing a careful finite-size scaling analysis, we determine the ground-state phase diagram and convincingly prove that the model exhibits a metal-insulator quantum phase transition for the half-filled band case. In order to characterize the metallic and insulating regimes we calculate, besides the local particle densities and fermion-boson correlation functions, the kinetic energy, the charge-structure factor, the Luttinger liquid charge exponent, and the single-particle excitation gap for a one-dimensional infinite system.

Anomalous Momentum Dependence of the Superconducting Coherence Peak and Its Relation to the Pseudogap ofLa1.85Sr0.15CuO4

We performed high-resolution angle-resolved photoemission spectroscopy on La1.85Sr0.15CuO4 to study the nature of the single-particle excitation gap. We found that there is a well-defined superconducting coherence peak in the off-nodal region while it is strongly suppressed around the antinode. The momentum dependence of the single-particle excitation gap shows a striking deviation from the dx-y2--wave symmetry with anomalous enhancement around the antinode in both the superconducting and the pseudogap state. The observed close correlation between the superconducting coherence peak and the pseudogap suggests a substantial contribution of the pseudogap to the anomalous behavior of the gap in the superconducting state.

Single-particle excitation gap in La2−xSrxCuO4 studied by high-resolution angle-resolved photoemission

We report angle-resolved photoemission spectroscopy on optimally doped high-Tc superconductor La1.85Sr0.15CuO4 (Tc=37K) to elucidate the character of low-energy excitations in the superconducting state. We find a clear evidence for the emergence of a sharp superconducting quasiparticle peak below Tc together with opening of a superconducting gap at off-nodal region, while no signature of a quasiparticle peak is observed at (π,0). From the comparison of spectral lineshape and energy dispersion between the nodal and the off-nodal region, we conclude that there are two characteristic energy scales (70 and 20meV) in the superconducting state of optimally doped La1.85Sr0.15CuO4.

Low-Energy Charge-Density Excitations inMgB2: Striking Interplay between Single-Particle and Collective Behavior for Large Momenta

A sharp feature in the charge-density excitation spectra of single-crystal MgB2, displaying a remarkable cosinelike, periodic energy dispersion with momentum transfer (q) along the c* axis, has been observed for the first time by high-resolution nonresonant inelastic x-ray scattering (NIXS). Time-dependent density-functional theory calculations show that the physics underlying the NIXS data is strong coupling between single-particle and collective degrees of freedom, mediated by large crystal local-field effects. As a result, the small-q collective mode residing in the single-particle excitation gap of the B pi bands reappears periodically in higher Brillouin zones. The NIXS data thus embody a novel signature of the layered electronic structure of MgB2.

The triplet superconductivity in square lattices and its optimal doping dependence

In this work, we study the p-wave superconductivity in a square lattice within a Hubbard model, in which a second-neighbour correlated hopping Δ t 3 is included. An infinitesimal distortion of the right angles in the square lattice is considered, which leads to second correlated hoppings Δ t 3 ± δ 3 in the x ˆ ± y ˆ directions, respectively. This study is carried out by means of the BCS formalism and we found a triplet superconducting ground state even though V =0. The optimal electron density for the critical temperature and the superconducting gap is analyzed as a function of the parameters of the model. Finally, the single-particle excitation gap is also calculated for different electron densities.

Collective modes in an "ultraquantum crystal." I. Field-induced spin-density-wave phases.

A strongly anisotropic metallic electron gas with quasi-two-dimensional open Fermi surface is unstable with respect to formation of a spin- or charge-density wave when a uniform magnetic field is applied perpendicular to the most conducting plane. In this paper, we study the collective modes of the field-induced density-wave phase. The latter is characterized by two lengths, the spin-density-wave wavelength, and the magnetic length which is much larger, and results from electronic orbital motion under field. As a result, spin-spin correlation functions exhibit structure for wave vectors of the order of the inverse magnetic length. We find that both spin waves and phase fluctuations modes exhibit, besides the trivial Goldstone bosons, a series of rotonlike modes. Those are local minima of the energy dispersion surface along values of the (parallel) momentum which are quantized in terms of the inverse magnetic length. Those modes lie below the single-particle excitation gap at all temperatures; their relative position within the single-particle gap shifts to lower energies as the temperature decreases. Each rotonlike mode may be viewed as a precursor of neighboring phases which are stabilized when the magnetic field varies sufficiently. Within the approximation which neglects coupling between the order-parameter fluctuations and spin fluctuations along the external field axis, spin-wave modes and phase-fluctuation modes are degenerate. The structure of the collective modes proves that field-induced charge- or spin-density waves are quantum crystals with properties distinct from ordinary charge- or spin-density waves, which justifies the generic name of ``ultraquantum crystals.'' The theory applies to Bechgaard salts.