$\mathbf{Q}=0$ collective modes originating from the low-lying Hg-O band in superconducting HgBa${}_{2}$CuO${}_{4+\ensuremath{\delta}}$

$Q = 0$ collective modes originating from the low-lying Hg-O band in superconducting HgBa $_{2}$ CuO $_{4 + δ}$

Tanmoy Das

Phys. Rev. B 86, 054518 – Published 27 August 2012

Abstract

Motivated by the recent discovery of two $Q \sim 0$ collective modes [Y. Li et al., Nature (London) 468, 283 (2010); Y. Li et al., Nat. Phys. 8, 404 (2012)] in single-layer HgBa $_{2}$ CuO $_{4 + δ}$ , which are often taken as evidence of the orbital-current origin of a pseudogap, I examine an alternative and assumption-free scenario constrained by first-principles calculations. I find that in addition to the common CuO $_{2}$ band, a hybridized Hg-O state is present in the vicinity of the Fermi level and that it contributes to the low-energy ground state of this system. I calculate the spin-excitation spectrum based on the random-phase approximation in the superconducting state using a two-band model and show that a collective mode in the multiorbital channel arises at $Q = 0$ . This mode splits in energy yet remains at $Q \sim 0$ as a pseudogap develops breaking both translational and time-reversal symmetries. The observations of the dynamical mode and static moment in the pseudogap state are in good accord with experimental observations. Detection of Hg-O band via optical study, or magnetic moment in the Hg-O layer will be tests of this calculation.

Received 19 June 2012

DOI:https://doi.org/10.1103/PhysRevB.86.054518

Authors & Affiliations

Tanmoy Das

Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Vol. 86, Iss. 5 — 1 August 2012

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Figure 1
(a) Crystal structure and tight-binding hopping parameters of the Hg1201 system. (b) Noninteracting tight-binding FS (red, solid line) plotted on top of the first-principles result (Refs. 18, 19, 20). (c) Corresponding dispersion plotted along high-symmetry directions in solid colors and compared with ab initio dispersions.Reuse & Permissions
Figure 2
Imaginary part of the BCS-RPA susceptibility in the paramagnetic state plotted along the diagonal direction as a function of excitation energy. (a) The intra-atomic component for the CuO $_{2}$ band reveals a strong peak in the $Q_{2} \sim (π, π)$ region. Although in the bare level, this component does not contain any other intensity except at $Q_{2}$ , its RPA value involves weak features near $Q_{1} \sim 0$ due to mixing with other terms within the tensor form of the RPA denominator (discussed in the text). (b) The interatomic RPA susceptibility between the CuO $_{2}$ and Hg-O bands shows intensity at $Q_{1}$ . The zone periodicity of the intensity between $Q_{1}$ and $Q_{2}$ even in the paramagnetic state strongly suggests that the $Q_{1}$ mode is unstable to a (fluctuating) magnetic ground state with a modulation of $Q_{2}$ . (c) The total RPA susceptibility yields strong intensity at both $Q$ vectors of different origins in agreement with experimental data (Ref. 11).Reuse & Permissions
Figure 3
(a) Single-particle spectral-weight map in the SDW state. The gap opening occurs in CuO $_{2}$ at $E_{F}$ at the antinodal region while the smaller magnetic gap in the Hg-O state commences above $E_{F}$ . Inset: As superconductivity is turned on in the CuO $_{2}$ state, the corresponding gap size increases, and for these particular gap values, the upper CuO $_{2}$ magnetic band and lower Hg-O magnetic band become close to each other. (b) The details of the energy level and the corresponding spin-excitation transitions are illustrated in the paramagnetic and magnetic states. At $Q_{2}$ , the magnetic transition across $E_{F}$ also involves a momentum transfer, as expected, which is not explicitly illustrated in this schematic diagram.Reuse & Permissions
Figure 4
(a), (b) Theoretical spin-excitation spectra in the coexistence of the SDW and SC ground state, plotted along the diagonal and the (100) directions, respectively. The symbols give the corresponding experimental data for Hg1201 near optimal doping (Ref. 11). The splitting of the $Q_{1}$ mode in the pseudogap state is more evident in (b). (c), (d) Intensity plots of the same experimental results near $Q_{1}$ and $Q_{2}$ , respectively. It is evident from the experimental data that despite the presence of a tail of the weakly dispersing branch in (c), the strong intensity is concentrated near $Q_{1}$ as in our theoretical spectra in (b). (e) The same theoretical result plotted at $Q_{1}$ and $Q_{2}$ , demonstrating the relative intensities of the corresponding peaks. Here, the two split modes at $Q_{1}$ with equivalent intensities are clearly visible.Reuse & Permissions

Physical Review B

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$Q = 0$ collective modes originating from the low-lying Hg-O band in superconducting HgBa $_{2}$ CuO $_{4 + δ}$

Tanmoy Das

Phys. Rev. B 86, 054518 – Published 27 August 2012

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Physical Review B

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Q=0 collective modes originating from the low-lying Hg-O band in superconducting HgBa2CuO4+δ

Tanmoy Das

Phys. Rev. B 86, 054518 – Published 27 August 2012

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$Q = 0$ collective modes originating from the low-lying Hg-O band in superconducting HgBa $_{2}$ CuO $_{4 + δ}$