arXiv subjects

A. Sherman

Publications and source records attributed to A. Sherman.

At least 37 records · Page 2Linked to original sources

arXiv2013

Magnetic response of Pr$_{1-x}$LaCe$_x$CuO$_4$ in comparison with hole-doped cuprates

The origin of differences in the magnetic responses of Pr$_{1-x}$LaCe$_x$CuO$_4$ with $x=0.11-0.12$ and moderately doped $p$-type cuprates is investigated using the t-J model, the Mori projection operator technique and dispersions of charge carriers derived from photoemission experiments. These differences are related to the proximity of the former crystal to the boundary of the antiferromagnetic phase and to the remoteness of $p$-type compounds from it. This leads to different nesting vectors of the low-frequency equi-energy contours of carrier dispersions in these crystals. The strong nesting with the antiferromagnetic momentum as the nesting vector produces the commensurate low-frequency response and the coexistence of two spin-excitation branches in Pr$_{1-x}$LaCe$_x$CuO$_4$, while incommensurate nesting vectors in $p$-type crystals lead to the incommensurate low-frequency response and the hourglass dispersion of susceptibility maxima.

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arXiv2013

Strongly correlated electron system in the magnetic field

The energy spectrum of the two-dimensional t-J model in a perpendicular magnetic field is investigated. The density of states at the Fermi level as a function of the inverse magnetic field $\frac{1}{B}$ reveals oscillations in the range of hole concentrations $0.08<x<0.18$. In the used approximation zero-field Fermi surfaces are large for these $x$, and oscillation frequencies conform with such Fermi surfaces. However, the amplitude of these oscillations is modulated with a frequency which is smaller by an order of magnitude. The appearance of this modulation is related to van Hove singularities in the Landau subbands, which traverse the Fermi level with changing $B$. The singularities are connected with bending the Landau subbands due to strong electron correlations. The frequency of the modulation is of the same order of magnitude as the quantum oscillation frequency observed in underdoped cuprates.

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arXiv2012

Mechanisms of the magnetic incommensurability in p-type cuprate perovskites

We use the t-J model and Mori projection operator formalism for calculating the magnetic susceptibility of p-type cuprates in the superconducting and pseudogap phases. The lack of extended tails in the peaks of the hole spectral function was shown to provide an incommensurate low-frequency response with hole dispersions derived from photoemission. The theory reproduces the hourglass dispersion of the susceptibility maxima with the upper branch reflecting the dispersion of localized spin excitations and the lower branch being due to incommensurate maxima of their damping. The intensive resonance peak appears when the hourglass waist falls below the bottom of the electron-hole continuum. In the pseudogap phase, the Fermi arcs lead to a quasi-elastic incommensurate response for low temperatures. This result explains the lack of the superconducting gap in the susceptibility of phase-separated underdoped lanthanum cuprates. It may also explain the strengthening of the quasi-elastic response by magnetic fields and impurities. The theory accounts for the magnetic stripe reorientation from the axial to diagonal direction at low hole concentrations.

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arXiv2012

Excitations and spin correlations near the interface of two three-dimensional Heisenberg antiferromagnets

Magnetic excitations and spin correlations near the interface of two spin-$\frac12$ Heisenberg antiferromagnets are considered using the spin-wave approximation. When the interaction between boundary spins differs essentially from exchange constants inside the antiferromagnets, quasi-two-dimensional spin waves appear in the near-boundary region. They eject bulk magnons from this region, thereby dividing the antiferromagnets into areas with different magnetic excitations. The decreased dimensionality of the near-boundary modes leads to amplified nearest-neighbor spin correlations in the interface area.

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arXiv2012

Magnetic response of optimally doped Pr$_{1-x}$LaCe$_x$CuO$_4$

The magnetic susceptibility of the optimally doped Pr$_{1-x}$LaCe$_x$CuO$_4$ 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.

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arXiv2011

Magnetic susceptibility in the pseudogap phase of cuprate perovskites

We calculate the magnetic susceptibility in the pseudogap phase of cuprates using the two-dimensional $t-J$ model and the Mori projection operator technique. In this phase, the Fermi arcs lead to a quasi-elastic incommensurate magnetic response for low temperatures. The theory accounts for the reorientation of the susceptibility maxima from the axial to the diagonal direction occurring at small hole concentrations in La$_{2-x}$Sr$_x$CuO$_4$. A small cusp of the hole dispersion near the Fermi level, which is connected with the spin-polaron band, affords the growth of the maxima with decreasing frequency. As in the superconducting phase, the susceptibility maxima have an hourglass dispersion. The assumption of the phase separation into regions of superconducting and pseudogap phases in underdoped cuprates explains the lack of the superconducting gap in their susceptibility. The observed rapid change of widths of the susceptibility maxima with frequency is related to the contribution of the pseudogap phase. This contribution may also explain the strengthening of the quasi-elastic response by modest magnetic fields and by small impurity concentrations.

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arXiv2011

Magnetic incommensurability in $p$-type cuprate perovskites

For the superconducting phase with a d-wave order parameter and zero temperature the magnetic susceptibility of the t-J model is calculated using the Mori projection operator technique. Conditions for the appearance of an incommensurate magnetic response below the resonance frequency are identified. A fast decay of the tails of the hole coherent peaks and a weak intensity of the hole incoherent continuum near the Fermi level are enough to produce an incommensurate response using different hole dispersions established for $p$-type cuprates, in which such response was observed. In this case, the nesting of the itinerant-electron theory or the charge modulation of the stripe theory is unnecessary for the incommensurability. The theory reproduces the hourglass dispersion of the susceptibility maxima with their location in the momentum space similar to that observed experimentally. The upper branch of the dispersion stems from the excitations of localized spins, while the lower one is due to the incommensurate maxima of their damping. The narrow and intensive resonance peak arises if the frequency of these excitations at the antiferromagnetic momentum lies below the edge of the two-fermion continuum; otherwise the maximum is broad and less intensive.

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arXiv2010

The spin-1 two-dimensional J1-J2 Heisenberg antiferromagnet on a triangular lattice

The spin-1 Heisenberg antiferromagnet on a triangular lattice with the nearest- and next-nearest-neighbor couplings, $J_1=(1-p)J$ and $J_2=pJ$, $J>0$, is studied in the entire range of the parameter $p$. Mori's projection operator technique is used as a method which retains the rotation symmetry of spin components and does not anticipate any magnetic ordering. For zero temperature four second-order phase transitions are observed. At $p\approx 0.038$ the ground state is transformed from the long-range ordered $120^\circ$ spin structure into a state with short-range ordering, which in its turn is changed to a long-range ordered state with the ordering vector ${\bf Q^\prime}=\left(0,-\frac{2π}{\sqrt{3}}\right)$ at $p\approx 0.2$. For $p\approx 0.5$ a new transition to a state with a short-range order occurs. This state has a large correlation length which continuously grows with $p$ until the establishment of a long-range order happens at $p \approx 0.65$. In the range $0.5<p<0.96$, the ordering vector is incommensurate. With growing $p$ it moves along the line ${\bf Q'-Q}_1$ to the point ${\bf Q}_1=\left(0,-\frac{4π}{3\sqrt{3}}\right)$ which is reached at $p\approx 0.96$. The obtained state with a long-range order can be conceived as three interpenetrating sublattices with the $120^\circ$ spin structure on each of them.

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arXiv2010

The t-J model on a semi-infinite lattice

The hole spectral function of the t-J model on a two-dimensional semi-infinite lattice is calculated using the spin-wave and noncrossing approximations. In the case of small hole concentration and strong correlations, $t\gg J$, several near-boundary site rows appear to be depleted of holes. The reason for this depletion is a deformation of the magnon cloud, which surrounds the hole, near the boundary. The hole depletion in the boundary region leads to a more complicated spectral function in the boundary row in comparison with its bulk shape.

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arXiv2009

Near-Boundary and Bulk Regions of a Semi-Infinite Two-Dimensional Heisenberg Antiferromagnet

Using the spin-wave approximation elementary excitations of a semi-infinite two-dimensional $S=\frac12$ Heisenberg antiferromagnet are considered. The spectrum consists of bulk modes -- standing spin waves and a quasi-one-dimensional mode of boundary spin waves. These latter excitations eject bulk modes from two boundary rows of sites, thereby dividing the antiferromagnet into two regions with different dominant excitations. As a result absolute values of nearest-neighbor spin correlations on the edge exceed the bulk value.

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arXiv2009

Spin correlations near the surface of a three-dimensional Heisenberg antiferromagnet

Nearest-neighbor spin correlations are considered near the surface of a semi-infinite spin-$\frac12$ Heisenberg antiferromagnet on a simple cubic lattice. In the spin-wave approximation, the excitation spectrum of this model involves bulk modes -- standing spin waves and a quasi-two-dimensional mode of surface spin waves. These latter excitations eject the bulk excitations from the surface region thus dividing the antiferromagnet into two parts with different excitations. As a result absolute values of the spin correlations near the surface exceed the bulk value. In the surface region, the pattern of spin correlations resembles the comb structure recently obtained for the two-dimensional case.

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arXiv2009

Excitations near the boundary between a metal and a Mott insulator

A heterostructure of a semi-infinite metal and a Mott insulator is considered. It is supposed that both materials have an identical lattice spacing and hopping integrals and differ in the Hubbard repulsion which is negligible in the metal and exceeds the critical value for the Mott transition in the insulator. At half-filling and for low temperatures the insulator has the long-range antiferromagnetic order. Its low-lying elementary excitations are standing spin waves and a spin-wave mode which is localized near the interface and has a two-dimensional dispersion. This mode ejects bulk modes from the boundary region. The antiferromagnetic ordering of the insulator induces an antiferromagnetic order in the metal where the magnetization decays exponentially with distance from the interface. This decay is characterized by the correlation length equal to 5-6 lattice spacings.

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arXiv2008

Fluctuating charge density waves in the Hubbard model

The charge susceptibility of the two-dimensional repulsive Hubbard model is investigated using the diagram technique developed for the case of strong correlations. In this technique, a power series in the hopping constant is used. It is shown that once the Fermi level crosses one of the Hubbard subbands a sharp peak appears in the momentum dependence of the static susceptibility. With further departure from half-filling the peak transforms to a ridge around the $Γ$ point. In the considered range $0\leq|1-\bar{n}|\alt 0.2$ of the electron filling $\bar{n}$ the static susceptibility is finite which points to the absence of the long-range charge ordering. However, for $|1-\bar{n}|\approx 0.12$ the susceptibility maxima are located halfway between the center and the boundaries of the Brillouin zone. In this case an interaction of carriers with tetragonal distortions can stabilize the charge density wave with the wavelength of four lattice spacings, as observed experimentally in the low-temperature tetragonal phase of lanthanum cuprates. In the range of parameters inherent in cuprate perovskites the character of the susceptibility evolution with $\bar{n}$ depends only weakly on the ratio of the nearest-neighbor hopping constant to the Hubbard repulsion and on details of the initial band structure. The location of the susceptibility maxima in the Brillouin zone is mainly determined by the value of $\bar{n}$.

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arXiv2006

Quasiparticle states of the Hubbard model near the Fermi level

The spectra of the t-U and t-t'-U Hubbard models are investigated in the one-loop approximation for different values of the electron filling. It is shown that the four-band structure which is inherent in the case of half-filling and low temperatures persists also for some excess or deficiency of electrons. Besides, with some departure from half-filling an additional narrow band of quasiparticle states arises near the Fermi level. The dispersion of the band, its bandwidth and the variation with filling are close to those of the spin-polaron band of the t-J model. For moderate doping spectral intensities in the new band and in one of the inner bands of the four-band structure decrease as the Fermi level is approached which leads to the appearance of a pseudogap in the spectrum.

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arXiv2006

Evolution of the spectrum of the Hubbard model with filling

The diagram technique for the one-band Hubbard model is formulated for the case of moderate to strong Hubbard repulsion. The expansion in powers of the hopping constant is expressed in terms of site cumulants of electron creation and annihilation operators. For Green's function an equation of the Larkin type is derived and solved in a one-loop approximation for the case of two dimensions and nearest-neighbor hopping. With decreasing the electron concentration in addition to the four bands observed at half-filling a narrow band arises near the Fermi level. The dispersion of the new band, its bandwidth and the variation with filling are close to those of the spin-polaron band in the t-J model.

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arXiv2006

One-loop approximation for the Hubbard model

The diagram technique for the one-band Hubbard model is formulated for the case of moderate to strong Hubbard repulsion. The expansion in powers of the hopping constant is expressed in terms of site cumulants of electron creation and annihilation operators. For Green's function an equation of the Larkin type is derived and solved in a one-loop approximation for the case of two dimensions, nearest-neighbor hopping and half-filling. The obtained four-band structure of the spectrum and the shapes of the spectral function are close to those observed in Monte Carlo calculations. It is shown that the maxima forming the bands are of a dissimilar origin in different regions of the Brillouin zone.

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arXiv2005

Incommensurate spin dynamics in underdoped cuprate perovskites

The incommensurate magnetic response observed in normal-state cuprate perovskites is interpreted based on the projection operator formalism and the t-J model of Cu-O planes. In agreement with experiment the calculated dispersion of maxima in the susceptibility has the shape of two parabolas with upward and downward branches which converge at the antiferromagnetic wave vector. The maxima are located at the momenta $({1/2},{1/2}\pmδ)$, $({1/2}\pmδ,{1/2})$ and at $({1/2}\pmδ,{1/2}\pmδ)$, $({1/2}\pmδ,{1/2}\mpδ)$ in the lower and upper parabolas, respectively. The upper parabola reflects the dispersion of magnetic excitations of the localized Cu spins, while the lower parabola arises due to a dip in the spin-excitation damping at the antiferromagnetic wave vector. For moderate doping this dip stems from the weakness of the interaction between the spin excitations and holes near the hot spots. The frequency dependence of the susceptibility is shown to depend strongly on the hole bandwidth and damping and varies from the shape observed in YBa$_2$Cu$_3$O$_{7-y}$ to that inherent in La$_{2-x}$Sr$_x$CuO$_4$.

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arXiv2005

Incommensurate magnetic response in cuprate perovskites

The incommensurate magnetic response of the normal-state cuprate perovskites is interpreted based on Mori's memory function approach and the t-J model of Cu-O planes. In agreement with experiment the calculated dispersion of the susceptibility maxima has the shape of two parabolas with upward and downward branches which converge at the antiferromagnetic wave vector. The maxima are located at $({1/2},{1/2}\pmδ)$, $({1/2}\pmδ,{1/2})$ and at $({1/2}\pmδ,{1/2}\pmδ)$, $({1/2}\pmδ,{1/2}\mpδ)$ in the lower and upper parabolas, respectively. The upper parabola reflects the dispersion of magnetic excitations of the localized Cu spins, while the lower parabola arises due to a dip in the spin-excitation damping at the antiferromagnetic wave vector. For moderate doping this dip stems from the weakness of the interaction between the spin excitations and holes near the hot spots.

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