Antiferromagnetic Brillouin Zone Research Articles

Why is the antinodal quasiparticle in the electron-doped cuprate Pr1.3−xLa0.7CexCuO4 immune to the antiferromagnetic band-folding effect?

A recent ARPES measurement on electron-doped cuprate Pr1.3−xLa0.7CexCuO4 finds that the antiferromagnetic (AFM) band-folding gap along the boundary of the antiferromagnetic Brillouin zone (AFBZ) exhibits dramatic momentum dependence. In particular, it vanishes in a finite region around the antinodal point, in which a single broadened peak emerges at the unrenormalized quasiparticle energy. Such an observation is argued to be inconsistent with the AFM band-folding picture, which predicts a constant band splitting along the AFBZ boundary. On the other hand, it is claimed that the experimental results are consistent with the prediction of the cluster dynamical mean-field theory (CDMFT) simulation on the Hubbard model, in which the obserevd spectral gap is interpreted as an s-wave pseudogap between the Hubbard bands and the in-gap states. Here we show that the observed momentum dependence of the spectral gap along the AFBZ boundary is indeed consistent with the AFM band-folding picture, provided that we assume the existence of a strongly momentum-dependent quasiparticle scattering rate. More specifically, we show that the quasiparticle scattering rate acts to reduce the spectral gap induced by the AFM band-folding effect. The new quasiparticle poles corresponding to the AF-split bands can even be totally eliminated when the scattering rate exceeds the bare band-folding gap, leaving the system with a single pole at the unrenormalized quasiparticle energy. We predict that the AFM band-folding gap should close in a square root fashion as we move toward along the AFBZ boundary. Our results illustrate that the quasiparticle scattering rate can play a much more profound role than simply broadening the quasiparticle peak in the quasiparticle dynamics of strongly correlated electron systems.

Symmetry-Protected Line Nodes in Non-symmorphic Magnetic Space Groups: Applications to UCoGe and UPd2Al3

We present the group-thoretical classification of gap functions in superconductors coexisting with some magnetic order in non-symmorphic magnetic space groups. Based on the weak-coupling BCS theory, we show that UCoGe-type ferromagnetic superconductors must have horizontal line nodes on either $k_z=0$ or $\pm\pi/c$ plane. Moreover, it is likely that additional Weyl point nodes exist at the axial point. On the other hand, in UPd$_2$Al$_3$-type antiferromagnetic superconductors, gap functions with $A_g$ symmetry possess horizontal line nodes in antiferromagnetic Brillouin zone boundary perpendicular to $c$-axis. In other words, the conventional fully-gapped $s$-wave superconductivity is forbidden in this type of antiferromagnetic superconductors, irrelevant to the pairing mechanism, as long as the Fermi surface crosses a zone boundary. UCoGe and UPd$_2$Al$_3$ are candidates for unconventional superconductors possessing hidden symmetry-protected line nodes, peculiar to non-symmorphic magnetic space groups.

Magnetic Response of Pr<sub>1-<i>x</i></sub>LaCe<i><sub>x</sub></i>CuO<sub>4</sub> in Comparison with Hole-Doped Cuprates

The magnetic susceptibility of the optimally doped Pr1-xLaCexCuO4in the superconducting state is calculated using thet-Jmodel of Cu-O planes, the Mori projection operator technique, and the dispersion of electron bands derived from photoemission experiments. The electron band folding across the antiferromagnetic Brillouin zone border, which is inherent in the crystal, leads to a commensurate low-frequency response. The same band folding causes the appearance of a supplementary spin-excitation branch, which coexists with usual spin excitations. This coexistence can explain two maxima observed in the frequency dependence of the susceptibility. The two nested spin-excitation branches lead to a comb of closely spaced peaks in momentum cuts, which presumably are not resolved in experiment, being seen as a broad commensurate peak up to 100 meV. Reasons for differences in magnetic responses of electron- and hole-doped cuprates are discussed.

Mean-field theory of competing orders in metals with antiferromagnetic exchange interactions

It has long been known that two-dimensional metals with antiferromagnetic exchange interactions have a weak-coupling instability to the superconductivity of spin-singlet, $d$-wave electron pairs. We examine additional possible instabilities in the spin-singlet particle-hole channel and study their interplay with superconductivity. We perform an unrestricted Hartree-Fock-BCS analysis of bond order parameters in a single-band model on the square lattice with nearest-neighbor exchange and repulsion, while neglecting on-site interactions. The dominant particle-hole instability is found to be an incommensurate, bidirectional, bond density wave with wave vectors along the $(1,1)$ and $(1,\ensuremath{-}1)$ directions and an internal $d$-wave symmetry. The magnitude of the ordering wave vector is close to the separation between points on the Fermi surface, which intersect the antiferromagnetic Brillouin zone boundary. The temperature dependence of the superconducting and bond order parameters demonstrates their mutual competition. We also obtain the spatial dependence of the two orders in a vortex lattice induced by an applied magnetic field: ``halos'' of the bond order appear around the cores of the vortices.

Magnetic Response of Optimally Doped Pr1−x LaCe x CuO4

The magnetic susceptibility of the optimally doped Pr1−x LaCe x CuO4 in the superconducting state is calculated using the t-J model of Cu–O planes, Mori’s projection operator technique, and the dispersion of electron bands derived from photoemission experiments. The electron band folding across the antiferromagnetic Brillouin zone border, which is inherent in the crystal, leads to a commensurate low-frequency response. The same band folding causes the appearance of a supplementary spin-excitation branch. The coexistence of the two spin-excitation branches explains two maxima observed in the frequency dependence of the susceptibility. The calculated momentum and frequency dependencies are close to experimental observations. Similarities and differences in the magnetic responses of electron- and hole-doped cuprates are discussed.

Fermi surface reconstruction in hole-dopedt−Jmodels without long-range antiferromagnetic order

We calculate the Fermi surface of electrons in hole-doped, extended $t$-$J$ models on a square lattice in a regime where no long-range antiferromagnetic order is present, and no symmetries are broken. Using the ``spinon-dopon'' formalism of Ribeiro and Wen, we show that short-range antiferromagnetic correlations lead to a reconstruction of the Fermi surface into hole pockets which are not necessarily centered at the antiferromagnetic Brillouin zone boundary. The Brillouin zone area enclosed by the Fermi surface is proportional to the density of dopants away from half-filling, in contrast to the conventional Luttinger theorem, which counts the total electron density. This state realizes a ``fractionalized Fermi liquid'' (FL*), which has been proposed as a possible ground state of the underdoped cuprates; we note connections to recent experiments. We also discuss the quantum phase transition from the FL* state to the Fermi liquid state with long-range antiferromagnetic order.

Dispersion and damping of zone-boundary magnons in the noncentrosymmetric superconductor CePt3Si

Inelastic neutron scattering (INS) is employed to study damped spin-wave excitations in the noncentrosymmetric heavy-fermion superconductor CePt3Si along the antiferromagnetic Brillouin zone boundary in the low-temperature magnetically ordered state. Measurements along the and reciprocal-space directions reveal deviations in the spin-wave dispersion from the previously reported model. The broad asymmetric shape of the peaks in energy signifies strong spin-wave damping by interactions with the particle–hole continuum. Their energy width exhibits no evident anomalies as a function of momentum along the direction which could be attributed to Fermi surface nesting effects, implying the absence of pronounced commensurate nesting vectors at the magnetic zone boundary. In agreement with a previous study, we find no signatures of the superconducting transition in the magnetic excitation spectrum, such as a magnetic resonant mode or a superconducting spin gap, either at the magnetic ordering wavevector or at the zone boundary. However, the low superconducting transition temperature in this material still leaves the possibility of such features being weak and therefore hidden below the incoherent background at energies ≲0.1 meV, precluding their detection by INS.

Signature of pseudogap formation in the density of states of underdoped cuprates

The resonating valence bond spin liquid model for the underdoped cuprates has as an essential element, the emergence of a pseudogap. This energy scale introduces asymmetry in the quasiparticle density of states because it is associated with the antiferromagnetic Brillouin zone. By contrast, superconductivity develops on the Fermi surface and this largely restores the particle-hole symmetry for energies below the superconducting energy-gap scale. In the highly underdoped regime, these two scales can be separately identified in the density of states and also partial density of states for each fixed angle in the Brillouin zone. From the total density of states, we find that the pseudogap energy scale manifests itself differently as a function of doping for positive and negative biases. Furthermore, we find evidence from recent scanning tunneling spectroscopy data for asymmetry in the positive and negative biases of the extracted $\ensuremath{\Delta}(\ensuremath{\theta})$ which is in qualitative agreement with this model. Likewise, the slope of the linear low-energy density of states is nearly constant in the underdoped regime while it increases significantly with overdoping in agreement with the data.

Specific heat of underdoped cuprates: Resonating valence bond description versus Fermi arcs

A recent microscopic model of the pseudogap state, based on the resonating valence bond (RVB) spin liquid, has provided a simple ansatz for the electronic self-energy in which a gap forms on the antiferromagnetic Brillouin zone as the limit of a Mott insulator is approached in the underdoped regime. Here, the ansatz is employed to calculate the electronic specific heat when a superconducting gap is also included. We find qualitative agreement with all experimental observations in the underdoped regime of the cuprates. We explore the relationship of the theory to two other purely phenomenological approaches, the nodal liquid and the Fermi arc model, and provide justification for their use on experimental data in light of this microscopic RVB theory.

Fermi surface and magnetism in the Kondo lattice: A continuum field theory approach

We consider the Fermi surface inside the antiferromagnetic ordered region of a Kondo lattice system in an arbitrary dimension higher than one. We establish the existence of AF S , an antiferromagnetic phase whose Fermi surface is “small,” in the sense that the local moments do not participate in the Fermi-surface formation. This is in contrast to the “large” Fermi surface that is typically assumed for heavy fermion metals. We extend our earlier work to the case that the Fermi surface of the conduction electrons intersects the antiferromagnetic Brillouin zone boundary. Our results provide a new perspective on local quantum criticality. In addition, our results imply that, for the AF S phase, it is important to keep track of the dynamical screening processes; we suggest that this effect is not captured in a recent variational Monte Carlo study of the Kondo lattice.

Disappearance of Antiferromagnetic Spin Excitations in OverdopedLa2−xSrxCuO4

Magnetic excitations for energies up to approximately 100 meV are studied for overdoped La(2-x)Sr(x)CuO(4) with x=0.25 and 0.30, using time-of-flight neutron spectroscopy. Comparison of spectra integrated over the width of an antiferromagnetic Brillouin zone demonstrates that the magnetic scattering at intermediate energies, 20 <or= omega <or= 100 meV, progressively decreases with overdoping. This strongly suggests that the magnetism is not related to Fermi surface nesting, but rather is associated with a decreasing volume fraction of (probably fluctuating) antiferromagnetic bubbles.

Calculation of Penetration Depth andTcin κ-(ET)2Cu(NCS)2under Pressure

The pressure dependence of the inverse square of the magnetic penetration depth λ -2 in κ-(ET) 2 Cu(NCS) 2 was measured by Larkin et al. [Phys. Rev. B 64 (2001) 144514]. According to the paper, λ -2 behaves differently under low pressure and under high pressure. Under low pressure, the development of λ -2 just below T = T c is rapid compared to the case under high pressure. Moreover, T c in κ-(ET) 2 Cu(NCS) 2 increases under c -axis pressure up to 1 kbar and decreases under higher pressure, while T c decreases monotonically under the hydrostatic pressure, or under the uniaxial pressure parallel to other axes. In order to explain these behaviors, we calculate T c and λ -2 for κ-(ET) 2 Cu(NCS) 2 under pressure. In the calculation we mainly use an effective dimer Hubbard model. In conclusion, the behavior of λ -2 results from three effects: the variation of the bandwidth of quasiparticles, the change of the Fermi surfaces, and the effect of vertex correction. This is a different mechanism from that of λ -2 in cuprates which we observe when the doping varies. Moreover, we explain the increase in T c under the c -axis pressure up to 1 kbar and the decrease in T c over 1 kbar from our calculation. With the increase in the c -axis pressure, two competitive effects with respect to T c appear. One is the approach of the Fermi surface to the antiferromagnetic Brillouin zone boundary, and the other is the suppression of the electron correlation. Under the low c -axis pressure, T c increases since the former effect is dominant. On the other hand, T c decreases since the latter effect is dominant under the high c -axis pressure.

Nonmonotonic d(x(2)-y(2)) superconducting order parameter in Nd2-xCexCuO4.

Low energy polarized electronic Raman scattering of the electron-doped superconductor Nd2-x Ce x CuO4 ( x = 0.15, T(c) = 22 K) has revealed a nonmonotonic d(x(2)-y(2)) superconducting order parameter. It has a maximum gap of 4.4k(B)T(c) at Fermi surface intersections with an antiferromagnetic Brillouin zone (the "hot spots") and a smaller gap of 3.3k(B)T(c) at fermionic Brillouin zone boundaries. The gap enhancement in the vicinity of the hot spots emphasizes the role of antiferromagnetic fluctuations and the similarity in the origin of superconductivity for electron- and hole-doped cuprates.

The effect of quasinesting and a magnon mode on the antiferromagnetic vector for the optical conductivity of a doped two-dimensional antiferromagnet

The optical spectrum of the normal state of a doped two-dimensional antiferromagnet is analyzed in a Kondo lattice model with regard to the complex structure of a spin polaron. The optical properties are determined by sharply anisotropic scattering of spin-polaron excitations by antiferromagnetic fluctuations of a system of localized spins. It is shown that the relaxation of carriers in the infrared range is mainly attributed to the strong coupling between these carriers and the mode of low-frequency spin excitations with the quasimomentum close to the antiferromagnetic vector Q=(π,π). The latter coupling is associated with the fact that the regions of the Fermi surface of the lower polaron band are close to the boundary of the antiferromagnetic Brillouin zone. The calculated optical characteristics are in qualitative agreement with experimental data for the normal state of high-temperature superconductors (HTSCs).

Anomalous electronic structure and pseudogap effects in Nd1.85Ce0.15CuO4.

We report a high-resolution angle-resolved photoemission spectroscopic study of the electron-doped ( n-type) cuprate superconductor Nd1.85Ce0.15CuO4. We observe regions along the Fermi surface where the near- E(F) intensity is suppressed and the spectral features are broad in a manner reminiscent of the high-energy "pseudogap" in the underdoped p-type (hole doped) cuprates. However, instead of occurring near the (pi,0) region, as in the p-type materials, this pseudogap falls near the intersection of the underlying Fermi surface with the antiferromagnetic Brillouin zone boundary.

Quasiparticle bands in plane-chain coupled cuprates

The dispersion spectrum of single hole in a bilayer composed of plane and chain, each described by t-J model, coupled by \(\)-\(\) interactions between them, is calculated in terms of self-consistent Born approximation. It was found that for a weak interlayer coupling the two different quasiparticle bands, plane-like and chain-like bands, show a minimum at (\(\), \(\)) and a maximum at (0, 0) or (\(\), \(\)). In plane-like dispersion we can find an anomalous “flat” region near Fermi surface along the antiferromagnetic Brillouin zone boundary, which favors the formation of the van-Hove singularities. With increasing interlayer coupling, a large modification of the dispersions is carried out, the minimum deviates from (\(\), \(\)) and the energy gap of the two bands decreases and finally disappears when the vertical coupling is larger enough. The shapes of the QP bands are sensitive to the vertical hopping \(\) rather than the vertical exchange energy \(\). As the interlayer coupling increases, the shapes of the two QP bands suggest that the chain-like band approaches to that of quasi-one dimensional model, and the plane-like band undergoes the one layer t - t '-J models' band.

Theory of Hall Effect and Electrical Transport in High-TcCuprates: Effects of Antiferromagnetic Spin Fluctuations

In the normal state of high-Tc cuprates, the Hall coefficient shows remarkable temperature dependence, and its absolute value is enhanced in comparison with that value simply estimated on the basis of band structure. It has been recognized that this temperature dependence of the Hall coefficient is due to highly anisotropic quasiparticle damping rate on the Fermi surface. In this paper we further take account of the vertex correction to the current vertex arising from quasiparticle interactions. Then the transport current is transformed to a large extent from the quasiparticle velocity, and is no longer proportional to the latter. As a consequence some pieces of the Fermi surface outside of the antiferromagnetic Brillouin zone make negative contribution to the Hall conductivity, even if the curvature of the Fermi surface is hole-like. The Hall coefficient is much larger at low temperatures than the estimate made without the vertex correction. Temperature dependence of the antiferromagnetic spin correlation length is also crucial to cause remarkable temperature dependence of the Hall coefficient. In our treatment the Hall coefficient of the electron-doped cuprates can be negative despite hole-like curvature of the Fermi surface.

Shadow bands of the spin polaron

We discuss the difference between a local spin polaron (in a spin liquid state with only short-range antiferromagnetic (AFM) order) and a spin polaron of infinite radius (if the spin system possesses AFM long-range order) within the scope of the t– J model. The local spin polaron wavefunction is found by a variational ansatz. The shadow bands occur due to the coupling of the local spin polaron to antiferromagnetic spin wave excitations with a wavevector Q=( π, π) . This leads to a dispersion which is symmetric with respect to the antiferromagnetic Brillouin zone (BZ) but has strongly asymmetric spectral weight. The evolution of the spectrum with temperature is discussed.

Spin-polaron damping in the spin-fermion model for cuprate superconductors

A self-consistent, spin rotational invariant Green's function procedure has been developed to calculate the spectral function of carrier excitations in the spin-fermion model for the CuO2 plane. We start from the mean field description of a spin polaron in the Mori-Zwanzig projection method. In order to determine the spin polaron lifetime in the self-consistent Born approximation, the self-energy is expressed by an irreducible Green's function. Both, spin polaron and bare hole spectral functions are calculated. The numerical results show a well pronounced quasiparticle peak near the bottom of the dispersion at (pi/2,pi/2), the absence of the quasiparticle at the Gamma-point, a rather large damping away from the minimum and an asymmetry of the spectral function with respect to the antiferromagnetic Brillouin zone. These findings are in qualitative agreement with photoemission data for undoped cuprates. The direct oxygen-oxygen hopping is responsible for a more isotropic minimum at (pi/2,pi/2).

Consequences of Fermi surface geometry

It is assumed that a Fermi surface exists in the high-Tc superconductors and that the interaction V(r) between electrons may be regarded as static. In the tight-binding context, the matrix element of V(r) between band states contains a term equal to the onsite repulsion U, which seriously suppresses superconductivity, especially for low dimensions and short-range interaction. It is seen how this difficulty can be removed in the context of a BCS-like superconducting state, Πk(uk + vkbk+)/0>, for various Fermi-surface geometries: that for sheets of chains, that for the square geometry appropriate to CuO2 planes, for Fermi surface pockets at the corners of a square antiferromagnetic Brillouin Zone, and for the planar surfaces appropriate to the cubic bismuth-oxide superconductors.