Entanglement and confinement: A new pairing mechanism in high-T_{C} cuprates

TL;DR

The paper presents RECHP, a confinement-based extension of the RVB framework, to explain the entire phase diagram of high-$T_{C}$ cuprates across electron- and hole-doped families. By introducing long-range entanglement between doped holes and a confinement mechanism, it defines pairing order (PO) and configurational order (CO) and shows how their interplay yields the pseudogap, spin gap, superconducting stripes, and the strange-metal linear-$T$ resistivity. A mean-field treatment of node-hole pockets combined with a 1D-chain entanglement picture yields a gap spectrum $E=\pm\sqrt{\varepsilon_{\varphi}^{2}+\Delta^{2}}$ and connects the entanglement entropy of formation to the pairing strength $\Delta^{\ast}(L)$ via $\Delta^{\ast}(L)=J\,S(L_{eff})$, explaining how confinement grows with chain length. The framework accounts for $T^{\ast}$, $T_{C}$ and their doping dependencies, the appearance of stripe-like current patterns, and observed spin textures, offering a unified explanation for both underdoped and overdoped regimes, as well as electron-doped systems. The predicted Planckian transport and 1D mesoscopic behavior above $T_{C}$ provide experimentally testable signatures of the proposed mechanism.

Abstract

We demonstrate that entanglement and confinement hole pairing (ECHP) is a precise physics of the entanglement framework of the RVB theory of high-Tc cuprates. Our novel strong ECHP mechanism explains the entire phase diagram of both electron and hole-doped cuprates, notably the linearly decreasing T* at the pseudogap, the duality of the spin gap and strange metal phase, the Tc=T* at the optimum doping and the rest of the overdoped regions of the superconducting (SC) dome, the presence of the parallel superconducting stripes in the CuO plane (spin-polarized and spin-unpolarized channels), and the linear-T behavior of the strange metal phase above the overdoped regions of the SC dome. This also explains the experimental spin textures of the cuprates. We refer to our new ECHP model as a resonating entanglement and confinement hole pair (RECHP) theory. Based on RECHP theory, we were able to provide a conceptual and comprehensive qualitative explanation of the entire phase diagram, thus providing the sought-after mechanism responsible for the entire phase diagram of high-Tc cuprates

Figures (8)

• Figure 1: Generic phase diagram for the high $T_{C}$ superconductors. Our theory gives the spin gap and is consistent with $T_{C}=T^{\ast}$ in the overdoped region. [Figure redrawn and edited from Ref. edeger]
• Figure 2: In the figure is shown a "nematic" or random arrangement of electronic "directed" dimers. The Anderson resonating valence bond theory essentially uses nearest neighbor two-qubit singlet entanglement Bell basis $\Psi^{-}$ [Reproduced from Ref. norman]
• Figure 3: The new RECHP theory of cuprates at the pseudogap phase, which resembles "nematic liquid" of extended entangled condensed pair at T*. The short wiggly lines across antiferromagnetic links indicate arbitrary effective length of the link dependent on the hole doping levels. We surmised that longer-chain link is harder to "smectic" order than shorter chain link. This explains the gap between antiferromagnetic phase and the superconducting dome of the phase diagram. We refer to this gap as the spin gap.
• Figure 4: In the CO "smectic" order phase of some materials, the corresponding Bell basis states can be defined as shown. These two sections of entangled hole pairs, namely, the $\Phi$ section and the $\Psi$ section are arranged into alternate sections, periodic "lattice" in $x$- and $y$- directions to form current-carrying condensed pattern of entangled pairs and rivers of charge at their ends. The hole "blob' accounts for the complex dressing of the holes in response to the coupling with the antiferromagnetic background wengweng2weng3danilovmottness.
• Figure 5: Configurational order of antiferromagnetic link showing a synthesis of interacting triplet and singlet entanglement. This gives spin-polarized SR-ARPES results and is deemed to be due to surface distortion in overdoped regions. This is a higher-order entanglement process where triplet entanglements acting as emergent qubits are being entangled as singlet and vice versa. This is presumably dominant in the overdoped region of the phase diagram of some materials.