Short-Range Modulated Electron Lattice and d-Wave Superconductivity in Cuprates: A Phenomenological Ginzburg-Landau Framework

• URL: http://arxiv.org/abs/2512.03368v1
• Date: Wed, 03 Dec 2025 02:02:14 GMT
• Title: Short-Range Modulated Electron Lattice and d-Wave Superconductivity in Cuprates: A Phenomenological Ginzburg-Landau Framework
• Authors: Jaehwahn Kim, Davis A. Rens, Waqas Khalid, Hyunchul Kim,
• Abstract summary: We develop a framework for high-$T_c$ cuprates with a short-range modulation of the electronic charge density couples to a $d$-wave superconducting condensate.<n>The resulting modulated electron lattice (MEL) state is distinct from long-range static charge density wave order.<n>The framework implies correlations between MEL correlation length, superfluid stiffness, disorder, and vortex pinning, and organizes cuprate observations into testable STM/STS predictions.
• Score: 2.7978130585680407
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a phenomenological Ginzburg-Landau (GL) framework for high-$T_c$ cuprates in which a short-range modulation of the electronic charge density couples to a $d$-wave superconducting condensate. The resulting modulated electron lattice (MEL) state is distinct from long-range static charge density wave order: it is short range, partially phase coherent, and linked to superconducting coherence. A preferred wave vector $q^{\ast} \approx 0.3$ reciprocal lattice units along the Cu-O bond direction emerges from the interplay between a momentum-dependent susceptibility and bond-stretching phonons, consistent with neutron and x-ray data on YBa$_2$Cu$_3$O$_{7-δ}$ and related cuprates. The GL free energy contains coupled $d$-wave superconducting and charge sectors with parameters constrained by optimally doped YBa$_2$Cu$_3$O$_{7-δ}$. We identify an MEL enhancement window in doping, temperature, MEL correlation length, and disorder where a coherence linked modulation enhances the superfluid stiffness. Classical Monte Carlo simulations yield an in-plane stiffness enhancement of order ten percent, which we treat as a qualitative prediction to be tested by self-consistent Bogoliubov de Gennes calculations. The MEL framework yields falsifiable experimental signatures. For scanning tunneling spectroscopy in Bi-based cuprates we highlight two predictions: the Fourier-transformed local density of states should exhibit a $q^{\ast} \approx 0.3$ peak whose spectral weight sharpens as superconducting phase coherence develops below $T_c$, in contrast to static charge scenarios, and the local gap magnitude $Δ(r)$ should correlate positively with the local MEL amplitude. The framework implies correlations between MEL correlation length, superfluid stiffness, disorder, and vortex pinning, and organizes cuprate observations into testable STM/STS predictions.

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