A Unified Description of Superconductivity: Electron Density Dynamic's Response to Phonons at the Brillouin Zone Boundary Driven Real Space Electron-Hole Pairing Characterized by CP Symmetry
It is argued that electron density dynamic's response to phonons at the Brillouin zone boundary is the key factor in the superconductivity mechanism of MgB2 as well as of all superconducting compounds leading to a real space electron-hole pairing characterized by CP symmetry (Charge and Parity symmetries) that enables a unified description of superconductivity phenomenon.First principle calculation of the electron density difference is determined by subtracting the electron density of the crystal distorted by longitudinal acoustical phonons at the Brillouin zone boundary from that of the perfect crystal.The origin of this electron density dynamic's response to this kind of distortion that leads to in real space electron hole pairing caracterized by CP symmetry is discussed in terms of local polarizabilities and delocalized transfer of charge caused by phonon-distortion driven dynamical change of orbital hybridization. This approach also provides clear and quick guidelines in the search for a new superconductors.
We investigate the physical effects of translational symmetry breaking in Fe-based high-temperature superconductors due to alternating anion positions. In the representative parent compounds, including the newly discovered Fe-vacancy-ordered $\mathrm{K_{0.8}Fe_{1.6}Se_2}$, an unusual change of orbital character is found across the one-Fe Brillouin zone upon unfolding the first-principles band structure and Fermi surfaces, suggesting that covering a larger one-Fe Brillouin zone is necessary in experiments. Most significantly, the electron pockets (critical to the magnetism and superconductivity…
Motivated by the studies of the superconducting pairing states in the iron-based superconductors, we analyze the effects of Brillouin zone folding procedure from a space group symmetry perspective for a general class of materials with the $P4/nmm$ space group. The Brillouin zone folding amounts to working with an effective one-Fe unit cell, instead of the crystallographic two-Fe unit cell. We show that the folding procedure can be justified by the validity of a glide reflection symmetry throughout the crystallographic Brillouin zone and by the existence of a minimal double degeneracy along the…
Based on angle resolved photoemission spectra measured on different systems at different dopings, momenta and photon energies, we show that the anomalously large spectral linewidth in the $(π,0)$ region of optimal doped and underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ has significant contributions from the bilayer splitting, and that the scattering rate in this region is considerably smaller than previously estimated. This new picture of the electronic excitation near $(π,0)$ puts additional experimental constraints on various microscopic theories and data analysis.
We performed a high-resolution angle-resolved photoemission spectroscopy study on superconducting (SC) Tl$_{0.63}$K$_{0.37}$Fe$_{1.78}$Se$_2$ ($T_c=29$ K) in the whole Brillouin zone (BZ). In addition to a nearly isotropic $\sim$ 8.2 meV 2-dimensional (2D) SC gap ($2Δ/k_BT_c\sim7$) on quasi-2D electron Fermi surfaces (FSs) located around M$(π,0,0)$-A$(π,0,π)$, we observe a $\sim 6.2$ meV isotropic SC gap ($2Δ/k_BT_c\sim5$) on the Z-centered electron FS that rules out any d-wave pairing symmetry and rather favors an s-wave symmetry. All isotropic SC gap amplitudes can be fit by a single gap fun…
We analyze the weak-coupling instabilities that may arise when multiple high-order Van Hove points are present inside the Brillouin zone. The model we consider is inspired by twisted bilayer graphene, although the analysis should be more generally applicable. We employ a parquet renormalization group analysis to identify the leading weak-coupling instabilities, supplemented with a Ginzburg-Landau treatment to resolve any degeneracies. Hence we identify the leading instabilities that can occur from weak repulsion with the power-law divergent density of states. Five correlated phases are uncover…
We improve the linear tetrahedron method to overcome systematic errors due to overestimations (underestimations) in integrals for convex (concave) functions, respectively. Our method is applicable to various types of calculations such as the total energy, the harge (spin) density, response functions, and the phonon frequency, in contrast with the Blöchl correction, which is applicable to only the first two. We demonstrate the ability of our method by calculating phonons in MgB$_2$ and fcc lithium.
Berry connection is conventionally defined as a static gauge field in the Brillouin zone. Here we show that for three-dimensional (3d) time-reversal invariant superconductors, a generalized Berry gauge field behaves as a fluctuating field of a Chern-Simons gauge theory. The gapless nodal lines in the momentum space play the role of Wilson loop observables, while their linking and knot invariants modify the gravitational theta angle. This angle induces a topological gravitomagnetoelectric effect where a temperature gradient induces a rotational energy flow. We also show how topological strings …
The multiband nature of iron-pnictide superconductors is one of the keys to the understanding of their intriguing behavior. The electronic and magnetic properties heavily rely on the multiband interactions between different electron and hole pockets near the Fermi level. At the fundamental level, though many theoretical models were constructed on the basis of the so-called 1-Fe Brillouin zone (BZ) with an emphasis of the basic square lattice of iron atoms, most electronic structure measurements were interpreted in the 2-Fe BZ. Whether the 1-Fe BZ is valid in a real system is still an open ques…
The origin of the high temperature superconductivity in the iron-based superconductors remains elusive after being extensively studied for more than a decade. Determination of the pairing symmetry is essential in understanding the superconductivity mechanism. In the iron-based superconductors that have hole pockets around the Brillouin zone center and electron pockets around the zone corners, the pairing symmetry is generally considered to be s$_\pm$, endowing a sign change in the superconducting gap between the hole and electron pockets. For the iron-based superconductors with only hole pocke…
In the two-dimensional Kondo-Heisenberg lattice model away from half-filled, the local antiferromagnetic exchange coupling can provide the pairing mechanism of quasiparticles via the Kondo screening effect, leading to the heavy fermion superconductivity. We find that the pairing symmetry \textit{strongly} depends on the Fermi surface (FS) structure in the normal metallic state. When $J_{H}/J_{K}$ is very small, the FS is a small hole-like circle around the corner of the Brillouin zone, and the s-wave pairing symmetry has a lower ground state energy. For the intermediate coupling values of $J_{…
We develop a first-principles scheme to calculate adiabatic and non-adiabatic phonon frequencies in the full Brillouin zone. The method relies on the variational properties of a force-constants functional with respect to the first-order perturbation of the electronic charge density and on the localization of the deformation potential in the Wannier function basis. This allows for calculation of phonon dispersion curves free from convergence issues related to Brillouin zone sampling. In addition our approach justify the use of the static screened potential in the calculation of the phonon linew…
The hole-doped ground state of a recently introduced extended "t-U-J" two-orbital Hubbard model for the Fe-based superconductors is studied via exact diagonalization methods on small clusters. Similarly as in the previously studied case of electron doping, A. Nicholson et al., Phys. Rev. Lett. 106 21702 (2011), upon hole doping it is observed that there are several competing pairing symmetries including A_{1g}, B_{1g}, and B_{2g}. However, contrary to the electron-doped case, the ground state of the hole-doped state has pseudocrystal momentum k=(π,π) in the unfolded Brillouin zone. In the two …
We show that a new resonant magnetic excitation at incommensurate momenta, observed recently by inelastic neutron scattering experiments on YBa$_2$Cu$_3$O$_{6.85}$ and YBa$_2$Cu$_3$O$_{6.6}$, is a {\it spin exciton}. Its location in the magnetic Brillouin zone and its frequency are determined by the momentum dependence of the particle-hole continuum. We identify several features that distinguish this novel mode from the previous resonance mode observed near ${\bf Q}=(π,π)$, such as its intensity maximum which occurs in a different part of the magnetic Brillouin zone.
We model the underdoped cuprates using fermions moving in a background with local antiferromagnetic order. The antiferromagnetic order fluctuates in orientation, but not in magnitude, so that there is no long-range antiferromagnetism, but a 'topological' order survives. The normal state is described as a fractionalized Fermi liquid (FL*), with electron-like quasiparticles coupled to the fractionalized excitations of the fluctuating antiferromagnet. The electronic quasiparticles reside near pocket Fermi surfaces enclosing total area x (the dopant density), centered away from the magnetic Brillo…
Low energy polarized electronic Raman scattering of the electron doped superconductor Nd_1.85Ce_0.15CuO_4 (T_c=22 K) has revealed a nonmonotonic d_{x^2-y^2} superconducting order parameter. It has a maximum gap of 4.4 k_BT_c at Fermi surface intersections with antiferromagnetic Brillouin zone (the ``hot spots'') and a smaller gap of 3.3 k_BT_c at fermionic Brillouin zone boundaries. The gap enhancement in the vicinity of the ``hot spots'' emphasizes role of antiferromagnetic fluctuations and similarity in the origin of superconductivity for electron- and hole-doped cuprates.
Charge order has emerged as a generic feature of doped cuprates, leading to important questions about its origin and its relation to superconductivity. Recent experiments on two classes of hole doped cuprates indicate a novel d-wave symmetry for the order. These were motivated by earlier spin fluctuation theoretical studies based on an expansion about hot spots in the Brillouin zone that indicated such order would be competitive with d-wave superconductivity. Here, we reexamine this problem by solving strong coupling equations in the full Brillouin zone. Our results find that bond-oriented ord…
We have analyzed heat capacity and thermal conductivity measurements of Sr2RuO4 in the normal and superconducting state and come to the conclusion that an order parameter with nodal lines on the Fermi surface is required to account for the observed low-temperature behavior. A gapped order parameter is inconsistent with the reported thermodynamic and transport data. Guided by a strongly peaked dynamical susceptibility along the diagonals of the Brillouin zone in neutron scattering data, we suggest a spin-fluctuation mechanism that would favor the pairing state with the gap maxima along the zone…
We identify and investigate the new parameter regime of small charge solitons in one-dimensional arrays of Josephson junctions. We obtain the dispersion relation of the soliton and show that it unexpectedly flattens in the outer region of the Brillouin zone. We demonstrate Lorentz contraction of the soliton in the middle of the Brillouin zone as well as broadening of the soliton in the flat band regime.
The Nielsen-Ninomiya Theorem has set up a ground rule for the minimal number of the topological points in a Brillouin zone. Notably, in the 2D Brillouin zone, chiral symmetry and space-time inversion symmetry can properly define topological invariants as charges characterizing the stability of the nodal points so that the non-zero charges protect these points. Due to the charge neutralization, the Nielsen-Ninomiya Theorem requires at least two stable topological points in the entire Brillouin zone. However, additional crystalline symmetries might duplicate the points. In this regard, for the w…
We develop the symmetry classification of superconducting gap functions in electron bands that do not transform under the crystal point group operations like the pure spin-1/2 states. The Bloch state bases in twofold degenerate bands with spin-orbit coupling are defined across the Brillouin zone in the way which satisfies the symmetry and continuity requirements. These bases are used to construct general multiband pairing Hamiltonians in centrosymmetric crystals. Focusing on single-band pairing, four exceptional cases are identified in which the triplet gap function does not transform under th…
We present a simple theoretical explanation for a transition from d-wave to another superconducting pairing observed in the electron-doped cuprates. The d_{x^2-y^2} pairing potential Delta, which has the maximal magnitude and opposite signs at the hot spots on the Fermi surface, becomes suppressed with the increase of electron doping, because the hot spots approach the Brillouin zone diagonals, where Delta vanishes. Then, the d_{x^2-y^2} pairing is replaced by either singlet s-wave or triplet p-wave pairing. We argue in favor of the latter and discuss experiments to uncover it.
By means of first-principles calculations, we predict two new types of partially hydrogenated graphene systems: C$_{6}$H$_{1}$ and C$_{6}$H$_{5}$, which are shown to be ferromagnetic (FM) semimetal and FM narrow-gap semiconductor, respectively. When properly doped, the Fermi surface of the two systems consists of an electron pocket or six hole patches in the first Brillouin zone with completely spin-polarized charge carries. If superconductivity exists in these systems, the stable pairing symmetries are shown to be $p+ip$ for electron doped case, and anisotropic $p+ip$ for hole doped case. The…
