arXiv subjects
Publications and source records attributed to Manfred Bucher.
Recently it was shown that the ratio of kinetic and potential energy at the perihelion of a Kepler orbit relates to the ellipse eccentricity. Here, a general expression for the that ratio at any position on the orbit is presented.
The rotated stripes are a consequence of the orthorhombic crystal lattice and the isotropy of Coulomb repulsion between pairs of doped holes, residing at oxygen lattice sites. With stripe slanting, the doped-hole pairs come closer to equidistance than without. The slant ratio depends on the orthorhombicity $o$ as $s = \sqrt{o/2}$.
Insights from stripe incommensurabilities and antiferromagnetic stability indicate that the magnetic moments of both host Cu^2+ ions and Cu atoms from electron doping support the thermal Hall effect in cuprates, whereas those of O atoms from hole doping oppose it.
The recent non-calculus proof of Kepler's first law succeeds because of an obscure, but valid property of the ellipse.
Comparison with La$_{2-z-x}$Nd$_z$Sr$_x$CuO$_4$ ($z=0, 0.4$) shows that the retrograde doping dependence of charge order in La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ must be caused by a mechanism transcending the common charge-order generation in the hole-doped lanthanum cuprates. This could be a bond-stretching phonon with comparable momentum, $q \sim 0.24$ r.l.u., as observed in La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_4$.
Hole doping of superconducting cuprates generates lattice defects of O atoms. At and beyond closing of the pseudogap, p =< p*, they form a highly symmetric superlattice. Umklapp processes involving reciprocal lattice vectors associated with both the host lattice and the O superlattice could account for the linear temperature dependence of resistivity.
Doped holes in cuprates reside pairwise at lattice-defect O atoms but at different sites in the two cuprate families. In the Sr-doped lanthanum cuprates, the O atoms occupy anion lattice sites and spread due to Coulomb repulsion (relative to the host lattice). In the oxygenated cuprates, the O atoms occupy interstitial sites, hybridize to ozone complexes, and aggregate to strings or (at high oxygenation) to nematic patches, always with spacing of ~ 3.25a_0. At the closing of the pseudogap at hole doping p*, a highly symmetric configuration of the O atoms appears in each family. In the first family it consists of interlaced superlattices in the CuO_2 plane and each of the bracketing LaO layers, with spacing A_0^{LaO}(p*) = 2A_0^{CuO_2}(p*). In the second family it consists in the completion of a 2D superlattice of ozone complexes, with spacing A_0(p*) ~ 3.25a_0. Both cases are visualized. Implications for the bandstructure and strange-metal phase are considered.
Doping of La_2CuO_4 and La_{1.6}Nd_{0.4}CuO_4 with Sr gives rise to holes that locate pairwise at lattice-site O atoms. Such O atoms reside as lattice defects in the CuO_2 planes if the doping level x is below a watershed value, x < x^, but also the bracketing LaO layers if x > x^. The O atoms form a 2D charge order of incommensurability q^{CuO_2}(x) and q^{LaO}(x). At the doping x* (quantum critical point) that causes the closing of the pseudogap at T=0, q^{CuO_2}(x*) = 2q^{LaO}(x*) holds.
Independent investigations of nuclear quadrupole resonance (NQR) and of stripes in high-$T_c$ cuprates find a small deviation of doped-hole density $h$ from the doping level of $La_{2-x}Sr_xCuO_4$. The value observed with NQR, $ x - h \approx 0.02$, agrees closely with the density of itinerant holes, $\tilde{p}$, responsible for suppression of 3D-AFM, as obtained from stripe incommensurability. The stripe model's assumption that doped holes in $La_{2-x}Sr_xCuO_4$ reside at oxygen sites, and that doped electrons in $Ln_{2-x}Ce_xCuO_4$ ($Ln = Pr, Nd$) reside at copper sites, is (to a large degree) confirmed with NQR. The NQR finding of doped-hole probabilities in oxygen and copper orbitals of $HgBa_2CuO_{4+δ}$ and other oxygen-enriched high-$T_c$ cuprates, $P_p \simeq P_d \simeq 1/2$, as well as of oxygen-doped $YBa_2Cu_3O_{6+y}$, $P_p \simeq 2P_d \simeq 2/3$, is interpreted with the stripe model in terms of excess oxygen atoms in the $CuO_2$ planes and $CuO$ chains.
Charge-order stripes of different types occur when copper oxides are doped with either heterovalent metal, like $La_{2-x}Sr_xCuO_4$, or oxygen, like $YBa_2Cu_3O_{6+y}$. The difference shows up in the doping dependence of their incommensurability: $q_c(x) \propto \sqrt{x-\check{p}}$ but $q_c(y) \approx 0.3$. The square-root dependence in the former compound family results from Coulomb repulsion between doped holes (or electrons), residing pairwise in lattice-site $O$ (or $Cu$) atoms of the $CuO_2$ planes. The almost constant $q_c(y)$ value in the second family results from the aggregation of ozone-like molecules, formed from $O^{2-}$ ions of the host with embedded oxygen atoms, $O_i$, at interstitial sites in the $CuO_2$ planes. The magnetic moments, $\mathbf{m}(O)$, of the lattice-defect $O$ atoms in the first family arrange antiferromagnetically, which gives rise to accompanying magnetization stripes of incommensurability $q_m(x) = q_c(x)/2$. The ozone complexes have a vanishing magnetic moment, $\mathbf{m}=0$, which explains the absence of accompanying magnetization stripes in the second family. Embedding excess oxygen as $O_i$ atoms in $CuO_2$ planes is likewise assumed for $HgBa_2CuO_{4+δ}$ and oxygen-enriched bismuth cuprates. A combination of characteristics from both families is present in oxygen-enriched $La_2CuO_{4+y}$. The validity of determining the hole density in oxygen-enriched cuprates with the universal-dome method is independently confirmed. Besides causing different types of stripes, the two types of lattice-defect oxygen may also cause different types of superconductivity. This could explain the much higher $T_{c,max}$ in oxygen-enriched than $Sr$-doped cuprates, as well as the cusped cooling-curves of X-ray intensity diffracted by stripes in the former family.
Doping $La_2CuO_{4}$ with alkaline-earth, $Ae= Sr,Ba$ generates holes in $La_{2-y-x}Ln_yAe_xCuO_{4}$ ($Ln =$ $Nd,Eu$). A small fraction of the holes, $\check{p} \le $ $0.02$, suppresses 3D-AFM. The rest resides as double holes at $O$ atoms in the $CuO_2$ planes. The superlattice, formed by the $O$ atoms, gives rise to both charge order stripes and magnetization stripes with incommensurability $q_{c,m}(x) \propto \sqrt{x-\check{p}}$ for $Ae$ doping $x < \hat{x}$, but constant $q_c$ beyond. Antiparallel orientation of magnetic moments $\mathbf{m}(O)$ yields a natural explanation for the coupling of $q_m(x) = \frac{1}{2} q_c(x)$. Doping $Nd_2CuO_{4}$ with $Ce$ generates electrons that reside pairwise in copper atoms. This accounts for the different properties of $n$-doped compounds. When $n$-doped, $q_c(x) \propto \sqrt{x}$. Above a threshold temperature $T'$, electron-hole pairs are thermally generated, but then separate to reside pairwise at $Cu$ and $O$ atoms. This breaks the locking of the incommensurability of charge order and magnetization stripes, $q_m(x) \ne \frac{1}{2} q_c(x)$.
A change of axes and notation would improve an otherwise excellent teaching diagram.
The amount of non-stoichiometric oxygen in La_{2-x}Sr_xCoO_{4+y} is calculated from Sr doping, x, and the measured stripe incommensurability 2delta for x = 1/4 and x = 1/3 based on a linear or square-root dependence of delta(x, y). The results favor the square-root dependence and indicate that the range of excess oxygen extends to x < 0.4 instead of to x < 0.3 as previously thought, coinciding with the low-temperature orthorhombic (LTO) phase.
The longstanding notion of stripe incommensurability being proportional to doping, δ(x) ~ x, in lanthanum transition-metal oxides, La_{2-x}Sr_xTmO_4 (Tm = Cu, Ni, Co), is partly borne out by experiment but also plagued with exceptions. Future neutron-scattering experiments on cobaltates could provide a clear distinction whether a linear or square-root dependence, δ(x) ~ sqrt(x - x_0), is valid.
An analytic expression for the incommensurability of static stripes in La_{2-x}Sr_xNiO_{4+y} is given, depending on the hole density n_h = x + 2y. Apart from geometry factors the formula is the same as for stripes in the related cuprates La_{2-x}Ae_xCuO_4 (Ae = Sr, Ba). Agreement with experimental data from neutron and X-ray diffraction is good. The stability of stripes is interpreted in terms of the separation of hole charges residing at every nu^{th} node of the associated magnetization waves.
The observed faint shadow arcs, shifted unidirectionally from primary Fermi arcs, are caused by lattice distortion from edge dislocations introduced by cleaving the samples.
Dynamics reduces the orthorhombicity of magnetic stripes in La_2CuO_4+y. The measured stripe incommensuration can be used to determine the oxygen content of the sample.
It is proposed that Fermi-surface reconstruction in electron-doped Ln_{2-x}Ce_xCuO_4 (Ln = Pr, Nd) and in hole-doped YBa_2Cu_3O_{6+y} and YBa_2Cu_4O_8 occurs when the Fermi arcs extend into the second Brillouin zone (BZ). The criterion employs the axial component of the Fermi-arc tips, \hat{q} > 0.5, depending on both the position of the Fermi arc's center \dot{Q} and the incommensurabity δ_c of unidirectional (striped) charge-density waves (CDWs). Qualitatively, the concave end-pieces of the Fermi arcs, terminated by Bragg-reflection mirrors due to the CDWs and severed at the boundary of the first BZ by lattice Bragg reflection, are assumed to join and relax to convex loops. Those entities may correspond to the electron pockets attributed to the quantum oscillations observed in these compounds. The criterion also explains why no quantum oscillations are found in the simple hole-doped lanthanum cuprates, La_{2-x}Ae_xCuO_4 (Ae = Sr, Ba), and in the bismuth cuprates Bi_2Sr_{2-x}La_xCuO_{6+y} and Bi_2Sr_2CaCu_2O_{8+y}. The possibility of quantum oscillations in hole-doped, partly substituted La_{2-y-x}Ln_ySr_xCuO_4 (Ln = Nd, Eu; y = 0.4, 0.2) in the high-end doping interval of their pseudogap phase, 0.182 < x < 0.235, is raised. A geometric modification of Bragg-reflection mirrors applies to HgBa_2CuO_{4+y} where CDWs are bidirectional (checkerboard-like).