arXiv subjects

Andrey V. Chubukov

Publications and source records attributed to Andrey V. Chubukov.

At least 199 records · Page 11Linked to original sources

arXiv1998

On the behavior of a Heisenberg antiferromagnet at very low temperatures

We present an analytical result for the ratio of the physical correlation length in a 2D Heisenberg antiferromagnet on a square lattice, and the one which is actually computed in numerical simulations. This last correlation length is deduced from the second moment of the structure factor at the antiferromagnetic momentum Q. We show that the ratio is very close to one in agreement with previously obtained numerical result of the 1/N expansion.

cond-mat.str-el↗

arXiv1997

Temperature variation of the pseudogap in underdoped cuprates

We consider thermal evolution of the spectral function A(Omega, T) in underdoped cuprates at T >Tc. We find that in the strong coupling limit, the fermionic Green's function near (0,π) behaves as G^{-1} (Omega) ~ \sqrt{Omega} in the whole frequency range relevant to photoemission experiments. The analysis of the pairing problem with this form of G yields a leading edge gap in A(Ω) and a broad maximum at larger frequencies. We find that classical fluctuations predominantly add a frequency independent term to G^{-1} (Omega). This term destroys the leading edge gap at T =T* (k)$which has a maximum value of about 200K near (0,π).

cond-mat.str-el↗

arXiv1997

The dispersion of a single hole in an antiferromagnet

We revisit the problem of the dispersion of a single hole injected into a quantum antiferromagnet. We applied a spin-density-wave formalism extended to a large number of orbitals and obtained an integral equation for the full quasiparticle Green's function in the self-consistent "non-crossing" Born approximation. We found that for $t/J \gg 1$, the bare fermionic dispersion is completely overshadowed by the self-energy corrections. We obtain a broad incoherent continuum which extends over a frequency range of $\sim 6t$ and a narrow region of width $O(JS)$ below the top of the valence band, where the excitations are mostly coherent, though with a small quasiparticle residue $Z \sim J/t$. Furthermore, we argue in this paper that two-magnon Raman scattering as well as neutron scattering experiments strongly suggest that the zone boundary magnons are not free particles since a substantial portion of their spectral weight is transferred into an incoherent background. We modeled this effect by introducing a cutoff $q_c$ in the integration over magnon momenta. We found analytically that for small $q_c$, the strong coupling solution for the Green's function is universal, and both effective masses are equal to $(4JS)^{-1}$. We further computed the full fermionic dispersion for $J/t =0.4$ relevant for $Sr_2CuO_2Cl_2$, and $t^\prime=-0.4J$ and found not only that the masses are both equal to $(2J)^{-1}$, but also that the energies at $(0,0)$ and $(0,π)$ are equal, the energy at $(0,π/2)$ is about half of that at $(0,0)$, and the bandwidth for the coherent excitations is around $3J$. All of these results are in full agreement with the experimental data.

cond-mat.str-el↗

arXiv1997

Theory of the leading edge gap in underdoped cuprates

We present the theory of the leading edge gap in the normal state of underdoped high-$T_c$ materials. The consideration is based on a magnetic scenario for cuprates. We show that as doping decreases, the increasing interaction with paramagnons gives rise to a near destruction of the Fermi liquid and this in turn yields precursors to $d-$wave pairing. We argue that the leading edge gap at $\sim 30 meV$ and a broad maximum in the spectral function at $\sim150 meV$ are byproducts of the same physical phenomenon.

cond-mat.str-el↗

arXiv1997

Resonant Raman Scattering in Antiferromagnets

Two-magnon Raman scattering provides important information about electronic correlations in the insulating parent compounds of high-$T_c$ materials. Recent experiments have shown a strong dependence of the Raman signal in $B_{1g}$ geometry on the frequency of the incoming photon. We present an analytical and numerical study of the Raman intensity in the resonant regime. It has been previously argued by one of us (A.Ch) and D. Frenkel that the most relevant contribution to the Raman vertex at resonance is given by the triple resonance diagram. We derive an expression for the Raman intensity in which we simultaneously include the enhancement due to the triple resonance and a final state interaction. We compute the two-magnon peak height (TMPH) as a function of incident frequency and find two maxima at $ω^{(1)}_{res} \approx 2Δ+ 3J$ and $ω^{(2)}_{res} \approx 2Δ+ 8J$. We argue that the high-frequency maximum is cut only by a quasiparticle damping, while the low-frequency maximum has a finite amplitude even in the absence of damping. We also obtain an evolution of the Raman profile from an asymmetric form around $ω^{(1)}_{res}$ to a symmetric form around $ω^{(2)}_{res}$. We further show that the TMPH depends on the fermionic quasiparticle damping, the next-nearest neighbor hopping term $t^{\prime}$ and the corrections to the interaction vertex between light and the fermionic current. We discuss our results in the context of recent experiments by Blumberg et al. on $Sr_2CuO_2Cl_2$ and $YBa_2Cu_3O_{6.1}$ and Rübhausen et al. on $PrBa_2Cu_3O_7$ and show that the triple resonance theory yields a qualitative and to some extent also quantitative understanding of the experimental data.

cond-mat.str-el↗

arXiv1997

Electronic structure of underdoped cuprates

We consider a two-dimensional Fermi liquid coupled to low-energy commensurate spin fluctuations. At small coupling, the hole Fermi surface is large and centered around $Q =(π,π)$. We show that as the coupling increases, the shape of the quasiparticle Fermi surface and the spin-fermion vertex undergo a substantial evolution. At strong couplings, $g \gg ω_0$, where $ω_0$ is the upper cutoff in the spin susceptibility, the hole Fermi surface consists of small pockets centered at $(\pm π/2, \pm π/2)$. Simultaneously, the full spin-fermion vertex is much smaller than the bare one, and scales nearly linearly with $|q-Q|$, where $q$ is the momentum of the susceptibility. At intermediate couplings, there exist both, a large hole Fermi surface centered at $(π,π)$, and four hole pockets, but the quasiparticle residue is small everywhere except for the pieces of the pockets which face the origin of the Brillouin zone. The relevance of these results for recent photoemission experiments in $YBCO$ and $Bi2212$ systems is discussed.

cond-mat.str-el↗

arXiv1997

On the vertex corrections in antiferromagnetic spin fluctuation theories

We argue that recent calculations by Amin and Stamp (PRL 77, 301 (1996); cond-mat/9601086) overestimate the strength of the vertex corrections in the spin-fermion model for cuprates. We clarify the physical origin of the apparent discrepancy between their results and earlier calculations. We also comment on the relative sign of the vertex correction.

cond-mat.str-el↗

arXiv1996

Crossover from $O(3)$ to $O(4)$ behavior in weakly frustrated antiferromagnets

We consider an anisotropic version of the $CP^{1}$ model which describes frustrated quantum antiferromagnets with incommensurate spin correlations. We extend the two-component spinon field, describing lattice spins, to the $M$-component complex vector, and show, in the $1/M$ expansion, that for arbitrary small incommensurability longitudinal and transverse stiffnesses tend to the same value as the system approaches the quantum critical point. For physical spins ($M=2$), this yields $O(4)$ critical behavior. However, if the spin structure is commensurate, the longitudinal stiffness is identically zero. In this case, the critical behavior is the same as in $O(3)$ sigma model. We show how the critical exponents interpolate between $O(3)$ and $O(4)$ values near the transition. We also show that the competition between these two fixed points leads to a confinement-deconfinement transition at a finite temperature.

cond-mat↗

arXiv1995

Raman scattering in a two-layer antiferromagnet

Two--magnon Raman scattering is a useful tool to verify recent suggestions concerning the value of the interplanar exchange constant in antiferromagnetic two--layer systems, such as $YBa_2Cu_3O_{6+x}$. We present a theory for Raman scattering in a two--layer antiferromagnet. We study the spectra for the electronic and magnetic excitations across the charge transfer gap within the one--band Hubbard model and derive the matrix elements for the Raman scattering cross section in a diagrammatic formalism. We analyze the effect of the interlayer exchange coupling $J_2$ for the Raman spectra in $A_{1g}$ and $B_{1g}$ scattering geometries both in the non--resonant regime (when the Loudon--Fleury model is valid), and at resonance. We show that within the Loudon--Fleury approximation, a nonzero $J_2$ gives rise to a finite signal in $A_{1g}$ scattering geometry. Both, in this approximation and at resonance, the intensity in the $A_{1g}$ channel has a peak at {\it small} transferred frequency equal to twice the gap in the spin--wave spectrum. We compare our results with experiments in $YBa_2Cu_3O_{6.1}$ and $Sr_2CuO_2Cl_2$ compounds and argue that the large value of $J_2$ suggested in a number of recent studies is incompatible with Raman experiments in $A_{1g}$ geometry.

cond-mat↗

arXiv1995

Fermi surface evolution in underdoped cuprates

We consider a two-dimensional Fermi liquid coupled to low-energy commensurate spin fluctuations. At small coupling, the hole Fermi surface is large and centered around $(π,π)$. We show that as the coupling increases, the shape of the Fermi surface undergoes a substantial evolution, and at strong coupling, the hole Fermi surface consists of small pockets centered at $(\pm π/2, \pm π/2)$. At intermediate couplings, there exists a large hole Fermi surface centered at $(π,π)$ as well as four hole pockets, but the quasiparticle residue is small everywhere except for the pieces of the pockets which face the $Γ$ point. The relevance of these results to recent photoemission experiments in $YBCO$ and $Bi2212$ systems, and their relation to the Luttinger theorem are discussed.

cond-mat↗

arXiv1995

Quasiparticle spectrum in a nearly antiferromagnetic Fermi liquid: shadow and flat bands

We consider a two-dimensional Fermi liquid in the vicinity of a spin-density-wave transition to a phase with commensurate antiferromagnetic long-range order. We assume that near the transition, the Fermi surface is large and crosses the magnetic Brillouin zone boundary. We show that under these conditions, the self-energy corrections to the dynamical spin susceptibility, $χ(q, ω)$, and to the quasiparticle spectral function function, $A(k, ω)$, are divergent near the transition. We identify and sum the series of most singular diagrams, and obtain a solution for $χ(q, ω)$ and an approximate solution for $A(k, ω)$. We show that (i) $A(k)$ at a given, small $ω$ has an extra peak at $k = k_F + π$ (`shadow band'), and (ii) the dispersion near the crossing points is much flatter than for free electrons. The relevance of these results to recent photoemission experiments in $YBCO$ and $Bi2212$ systems is discussed.

cond-mat↗

arXiv1995

Phase Transition, Longitudinal Spin Fluctuations and Scaling in a Two-Layer Antiferromagnet

We consider a two-layer Heisenberg antiferromagnet which can be either in the Néel-ordered or in the disordered phase at $T=0$, depending on the ratio of the intra- and interlayer exchange constants. We reduce the problem to an interacting Bose-gas and study the sublattice magnetization and the transverse susceptibility in the ordered phase, and the spectrum of quasiparticle excitations in both phases. We compare the results with the spin-wave theory and argue that the longitudinal spin fluctuations, which are not included in the spin-wave description, are small at vanishing coupling between the layers, but increase as the system approaches the transition point. We also compute the uniform susceptibility at the critical point to order $O(T^2)$, and show that the corrections to scaling are numerically small, and the linear behavior of $χ_u$ extends to high temperatures. This is consistent with the results of the recent Monte-Carlo simulations by Sandvik and Scalapino.

cond-mat↗

arXiv1995

Resonant two-magnon Raman scattering in parent compounds of high-T$_c$ superconductors.

We propose a theory of two-magnon Raman scattering from the insulating parent compounds of high-T$_c$ superconductors, which contains information not only on magnetism, but also on the electronic properties in these materials. We use spin density wave formalism for the Hubbard model, and study diagrammatically the profile of the two-magnon scattering and its intensity dependence on the incoming photon frequency $ω_i$ both for $ω_i \ll U$ and in the resonant regime, in which the energy of the incident photon is close to the gap between conduction and valence bands. In the nonresonant case, we identify the diagrams which contribute to the conventional Loudon-Fleury Hamiltonian. In the resonant regime, where most of the experiments have been done, we find that the dominant contribution to Raman intensity comes from a different diagram, one which allows for a simultaneous vanishing of all three of its denominators (i.e., a triple resonance). We study this diagram in detail and show that the triple resonance, combined with the spin-density-wave dispersion relation for the carriers, explains the unusual features found in the two-magnon profile and in the two-magnon peak intensity dependence on the incoming photon frequency. In particular, our theory predicts a maximum of the two-magnon peak intensity right at the upper edge of the features in the optical data, which has been one of the key experimental puzzles.

cond-mat↗

arXiv1995

Quantum-Critical Behavior in a Two-Layer Antiferromagnet

We analyze quantum Monte Carlo data in the vicinity of the quantum transition between a Neel state and a quantum paramagnet in a two-layer, square lattice spin 1/2 Heisenberg antiferromagnet. The real-space correlation function and the universal amplitude ratio of the structure factor and the dynamic susceptibility show clear evidence of quantum critical behavior at low temperatures. The numerical results are in good quantitative agreement with $1/N$ calculations for the $O(N)$ non-linear sigma model. A discrepancy, reported earlier, between the critical properties of the antiferromagnet and the sigma model is resolved. We also discuss the values of prefactors of the dynamic susceptibility and the structure factor in a single layer antiferromagnet at low $T$.

cond-mat↗

arXiv1995

Magnetic Phases of the 2D Hubbard Model at Low Doping

We study the equilibrium spin configuration of the 2D Hubbard model at low doping, when a long-range magnetic order is still present. We use the spin-density-wave formalism and examine the two suggested candidates for a ground state: the planar spiral $(π,Q)$ and $(Q,Q)$ states. In a mean-field theory, each of these two states is a ground state in a certain range of parameters. We however show that both states have negative bosonic modes in a transverse channel which implies that the spiral states are in fact unstable (the $(Q,Q)$ state, in addition, has a negative longitudinal stiffness). We searched for a ground state in a parameter range which on a mean-field level favored the $(π,Q)$ phase, and found that the equilibrium spin configuration is noncoplanar. These findings lead to a novel scenario of spin reorientation upon doping in Hubbard antiferromagnets.

cond-mat↗

arXiv1995

On the confinement of spinons in the $CP^{M-1}$ model

We use the $1/M$ expansion for the $CP^{M-1}$ model to study the long-distance behaviour of the staggered spin susceptibility in the commensurate, two-dimensional quantum antiferromagnet at finite temperature. At $M=\infty$ this model possesses deconfined spin-1/2 bosonic spinons (Schwinger bosons), and the susceptibility has a branch cut along the imaginary $k$ axis. We show that in all three scaling regimes at finite $T$, the interaction between spinons and gauge field fluctuations leads to divergent $1/M$ corrections near the branch cut. We identify the most divergent corrections to the susceptibility at each order in $1/M$ and explicitly show that the full static staggered susceptibility has a number of simple poles rather than a branch cut. We compare our results with the $1/N$ expansion for the $O(N)$ sigma-model.

cond-mat↗

arXiv1994

Crossover and scaling in a nearly antiferromagnetic Fermi liquid in two dimensions

We consider two-dimensional Fermi liquids in the vicinity of a quantum transition to a phase with commensurate, antiferromagnetic long-range order. Depending upon the Fermi surface topology, mean-field spin-density-wave theory predicts two different types of such transitions, with mean-field dynamic critical exponents $z=1$ (when the Fermi surface does not cross the magnetic zone boundary, type $A$) and $z=2$ (when the Fermi surface crosses the magnetic zone boundary, type $B$). The type $A$ system only displays $z=1$ behavior at all energies and its scaling properties are similar (though not identical) to those of an insulating Heisenberg antiferromagnet. Under suitable conditions precisely stated in this paper, the type $B$ system displays a crossover from relaxational behavior at low energies to type $A$ behavior at high energies. A scaling hypothesis is proposed to describe this crossover: we postulate a universal scaling function which determines the entire, temperature-, wavevector-, and frequency-dependent, dynamic, staggered spin susceptibility in terms of 4 measurable, $T=0$, parameters (determining the distance, energy, and order parameter scales, plus one crossover parameter). The scaling function contains the full scaling behavior in all regimes for both type $A$ and $B$ systems. The crossover behavior of the uniform susceptibility and the specific heat is somewhat more complicated and is also discussed. Explicit computation of the crossover functions is carried out in a large $N$ expansion on a mean-field model. Some new results for the critical properties on the ordered side of the transition are also obtained in a spin-density wave formalism. The possible relevance of our results to the doped cuprate compounds is briefly discussed.

cond-mat↗

arXiv1994

Resonant two-magnon Raman scattering in antiferromagnetic insulators

We propose a theory of two-magnon {\it resonant\/} Raman scattering from antiferromagnetic insulators, which contains information both on the magnetism and the carrier properties in the lighly doped phases. We argue that the conventional theory does not work in the resonant regime, in which the energy of the incident photon is close to the gap between the conduction and valence bands. We identify the diagram which gives the dominant contribution to Raman intensity in this regime and show that it can explain the unusual features in the two-magnon profile and in the two-magnon peak intensity dependence on the incoming photon frequency.

cond-mat↗