Optical integral in the cuprates and the question of sum-rule violation

Norman, M. R.; Chubukov, Andrey V.; Heumen, E. van; Kuzmenko, A. B.; Marel, D. van der

doi:10.1103/physrevb.76.220509

Cited by 26 publications

(40 citation statements)

References 37 publications

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“…The generic formalism of the computation of the optical conductivity and the optical integral has been discussed several times in the literature [21][22][23]26,29 and we just list the formulas that we used in our computations. The conductivity σ(Ω) and the optical integral W (ω c ) are given by (see for example Ref.…”

Section: Optical Integral In Normal and Superconducting Statesmentioning

confidence: 99%

“…For the NS, previous works 21, 22 on particular models for the cuprates indicated that the origin of the temperature dependence of W (ω c ) is likely the T dependence of the cutoff term f (ω c ). Specifically, Norman et.…”

Section: Introductionmentioning

confidence: 96%

“…The issue of sum rule attracted substantial interest in the studies of high T c cuprates [5][6][7][8][9][10][11][12][13][14][15][16][17][18][21][22][23][24][25][26] in which pairing is without doubts a strong coupling phenomenon. From a theoretical perspective, the interest in this issue was originally triggered by a similarity between W K and the kinetic energy K = 2 ε k n k .…”

Section: Introductionmentioning

confidence: 99%

“…Theoretical analysis of these results 21,22,25,28,30 added one more degree of complexity to the issue. It is tempting to analyze the temperature dependence of W K and relate it to the observed behavior of the optical integral, and some earlier works 25,28,30 followed this route.…”

Section: Introductionmentioning

confidence: 99%

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Optical integral and sum-rule violation in high-Tcsuperconductors

Maiti

Chubukov

2010

Phys. Rev. B

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The purpose of this work is to investigate the role of the lattice in the optical Kubo sum rule in the cuprates. We compute conductivities, optical integrals W , and ∆W between superconducting and normal states for 2-D systems with lattice dispersion typical of the cuprates for four different models -a dirty BCS model, a single Einstein boson model, a marginal Fermi liquid model, and a collective boson model with a feedback from superconductivity on a collective boson. The goal of the paper is two-fold. First, we analyze the dependence of W on the upper cut-off (ωc) placed on the optical integral because in experiments W is measured up to frequencies of order bandwidth. For a BCS model, the Kubo sum rule is almost fully reproduced at ωc equal to the bandwidth. But for other models only 70%-80% of Kubo sum rule is obtained up to this scale and even less so for ∆W , implying that the Kubo sum rule has to be applied with caution. Second, we analyze the sign of ∆W . In all models we studied ∆W is positive at small ωc, then crosses zero and approaches a negative value at large ωc, i.e. the optical integral in a superconductor is smaller than in a normal state. The point of zero crossing, however, increases with the interaction strength and in a collective boson model becomes comparable to the bandwidth at strong coupling. We argue that this model exhibits the behavior consistent with that in the cuprates.

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Section: Optical Integral In Normal and Superconducting Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optical integral and sum-rule violation in high-Tcsuperconductors

Maiti

Chubukov

2010

Phys. Rev. B

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“…was used to analyze whether the anomalous redistribution of spectral weight below the superconducting transition temperature T c reveals information about the change of the kinetic energy, or more precisely of the optical mass m * , upon entering the superconducting state 6,7 . Finally, fine structures in the optical spectrum were used to determine the mechanism of superconductivity in the cuprates [8][9][10][11] .…”

Section: Introductionmentioning

confidence: 99%

Transfer of optical spectral weight in magnetically ordered superconductors

2010

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We show that, in antiferromagnetic superconductors, the optical spectral weight transferred to low frequencies below the superconducting transition temperature originates from energies that can be much larger than twice the superconducting gap ∆. This contrasts to non-magnetic superconductors, where the optical spectrum is suppressed only for frequencies below 2∆. In particular, we demonstrate that the superfluid condensate of the magnetically ordered superconductor is not only due to states of the magnetically reconstructed Fermi surface, but is enhanced by transfer of spectral weight from the mid infrared peak generated by the spin density wave gap. We apply our results to the iron arsenide superconductors, addressing the decrease of the zero-temperature superfluid density in the doping regime where magnetism coexists with unconventional superconductivity.

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Gordian knot in the pseudo‐gap phase of hole‐underdoped cuprates

Goswami

2013

Physica Status Solidi (b)

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We consider the coexistent d-density wave (DDW) order, at the anti-ferromagnetic (AF) wave vector Q ¼ (p,p), representing the pseudo-gap (PG) state, and d-wave superconductivity (DSC), driven by an assumed attractive interaction, for the two-dimensional (2D) fermion system on a square lattice starting with a mean-field Hamiltonian involving the singlet DDW and the DSC pairings. The two energy gaps, corresponding to PG and DSC, in the excitation spectrum do not merge into one 'quadrature' gap if the normal state dispersion is imperfectly nested. With the pinning of the van Hove singularities (vHSs) of the dispersion close to the chemical potential (m), we show that the PG and DSC are representing two competing orders as the former brings about a depletion of the spectral weight (a contour plot of the spectral weight density for 60 K at the doping level $10% is shown in the abstract figure) available for pairing in the anti-nodal region of momentum space in the coexistent state. The calculation of quasi-particle thermal conductivity a xx in the DDW and normal phases via the Boltzmann equation in the relaxation-time approximation shows that there is a mild discontinuity in a xx at the PG transition temperature T

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Optical integral in the cuprates and the question of sum-rule violation

Cited by 26 publications

References 37 publications

Optical integral and sum-rule violation in high-Tcsuperconductors

Optical integral and sum-rule violation in high-Tcsuperconductors

Transfer of optical spectral weight in magnetically ordered superconductors

Gordian knot in the pseudo‐gap phase of hole‐underdoped cuprates

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