Lifshitz Transitions In Multi-band Hubbard Models for Topological Superconductivity in Complex Quantum Matter

The appearance of unconventional pairing in superconducting cuprates is examined from a microscopic model, taking into account important properties of hole-doped copper oxides. An exchange interaction between fermions and dominantly inter-site bipolarons is considered to be the mechanism which leads to the pairing. Its momentum dependency is connected to the well-established fermion-phonon anomalies in cuprate superconductors. Since charge carriers in these materials are strongly correlated, a screened Coulomb repulsion is added to this exchange term. Any ad hoc assumptions like anisotropy are avoided, but a microscopic explanation of unconventional pairing for coupling strengths that are in accordance with experimental facts is provided. One important outcome is a mathematically rigorous elucidation of the role of Coulomb repulsion in unconventional pairing, which is shown to be concomitant with a strong depletion of superconducting pairs. The theory, applied to the special case of LaSr 214, predicts at optimal doping i) a coherence length of 21Å, which is the same as that obtained from the Ginzburg-Landau critical magnetic field measured for this material, and ii) d-wave pair formation in the pseudogap regime, that is, at temperatures much higher than the superconducting transition temperature.

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“…See ref. [] for more details. In particular, holes in the copper band cannot alone produce superconductivity, see for instance ref.…”

Section: Experimental Foundations Of Our Microscopic Approachmentioning

confidence: 99%

Isotropic Bipolaron–Fermion Exchange Theory and Unconventional Pairing in Cuprate Superconductors

2018

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“…Possible competition between these two mechanisms (superexchange bonds and spin-orbit) or enhancement of entanglement by their joint action is a challenging problem. It adds another aspect to the complexity of quantum matter in high-T c superconductors [40][41][42][43][44], intimately connected with quantum magnetism in strongly correlated transition metal oxides [45]. Here, we analyze the spin-orbital entanglement evolution on a minimal available model, consisting of SU(2)⊗SU(2) symmetric superexchange term [46] and Ising on-site spin-orbit coupling in one dimension.…”

Section: Introductionmentioning

confidence: 99%

Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling

et al. 2020

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Several realistic spin-orbital models for transition metal oxides go beyond the classical expectations and could be understood only by employing the quantum entanglement. Experiments on these materials confirm that spin-orbital entanglement has measurable consequences. Here, we capture the essential features of spin-orbital entanglement in complex quantum matter utilizing 1D spin-orbital model which accommodates SU(2)⊗SU(2) symmetric Kugel-Khomskii superexchange as well as the Ising on-site spin-orbit coupling. Building on the results obtained for full and effective models in the regime of strong spin-orbit coupling, we address the question whether the entanglement found on superexchange bonds always increases when the Ising spin-orbit coupling is added. We show that (i) quantum entanglement is amplified by strong spin-orbit coupling and, surprisingly, (ii) almost classical disentangled states are possible. We complete the latter case by analyzing how the entanglement existing for intermediate values of spin-orbit coupling can disappear for higher values of this coupling.

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“…Because most condensed matter systems do not conform to the full Lorentz symmetry and contain dynamical behavior characterized by Lifshitz transitions [1][2][3][4], tailoring the AdS/CFT program to condensed matter systems such as the cuprates requires a considerable extension. The simplest proffer to engineer such a non-relativistic setup is a Lifshitz geometry characterized by a dynamical critical exponent z [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Quantum Critical Diffusion and Thermodynamics in Lifshitz Holography

Langley,

Phillips

2018

Preprint

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We present the full charge and energy diffusion constants for the Einstein-Maxwell dilaton (EMD) action for Lifshitz spacetime characterized by a dynamical critical exponent z. Therein we compute the fully renormalized static thermodynamic potential explicitly, which confirms the forms of all thermodynamic quantities including the Bekenstein-Hawking entropy and Smarr-like relationship. Our exact computation demonstrates a modification to the Lifshitz Ward identity for the EMD theory. For transport, we target our analysis at finite chemical potential and include axion fields to generate momentum dissipation. While our exact results corroborate anticipated bounds, we are able to demonstrate that the diffusivities are governed by the engineering dimension of the diffusion coefficient, [D] = 2 − z. Consequently, a β-function defined as the derivative of the trace of the diffusion matrix with respect to the effective lattice spacing changes sign precisely at z = 2. At z = 2, the diffusion equation exhibits perfect scale invariance and the corresponding diffusion constant is the pure number 1/d s for both the charge and energy sectors, where d s is the number of spatial dimensions. Further, we find that as z → ∞, the charge diffusion constant vanishes, indicating charge localization. Deviation from universal decoupled transport obtains when either the chemical potential or momentum dissipation are large relative to temperature, an echo of strong thermoelectric interactions.

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Lifshitz Transitions In Multi-band Hubbard Models for Topological Superconductivity in Complex Quantum Matter

Cited by 8 publications

References 123 publications

Isotropic Bipolaron–Fermion Exchange Theory and Unconventional Pairing in Cuprate Superconductors

Isotropic Bipolaron–Fermion Exchange Theory and Unconventional Pairing in Cuprate Superconductors

Evolution of Spin-Orbital Entanglement with Increasing Ising Spin-Orbit Coupling

Quantum Critical Diffusion and Thermodynamics in Lifshitz Holography

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