Efimov-Type Discrete Scale Invariance at the Multicritical Point of a Two-Dimensional Disordered Class D Topological Superconductor
Abstract
The interplay between disorder, topology, and many-body interactions in two-dimensional superconducting systems continues to reveal unexpected critical phenomena beyond the reach of conventional universality theory. We propose and characterize a novel universality class — the Discrete Scale Invariance Multicritical Point (DSI-MCP) — emerging from Efimov-type discrete scale invariance at the tricritical point of a two-dimensional disordered Class D topological superconductor. Using a two-loop renormalization group analysis within the replica framework, we demonstrate that when disorder and three-body couplings simultaneously exceed their critical thresholds, the renormalization group flow bypasses the conventional tricritical point and spirals into a new stable fixed point with complex eigenvalues. The imaginary component of these eigenvalues — absent at any conventional critical point with real scaling exponents — encodes log-periodic scaling and generates an infinite geometric tower of bound states, establishing the condensed matter analogue of the atomic Efimov effect. The DSI-MCP is distinguished from the tricritical point of Pan et al. by three independent criteria: a localization exponent that is fixed by symmetry and independent of the dimensional regularization parameter, a two-parameter multicritical threshold requiring simultaneous supercriticality in both disorder and three-body coupling, and the presence of log-periodic oscillations in the correlation length that are strictly forbidden at any conventional critical point. We further identify a competition between the DSI mechanism and Quantum Griffiths Singularity physics, governed by the statistical character of the disorder distribution, and construct a unified phase diagram delineating three experimentally distinguishable regimes: activated scaling, log-periodic power-law modulation, and a coexistence corridor exhibiting a doubled oscillation frequency with no precedent in the existing literature on disordered topological systems. All predictions are parameter-free once the operating point in coupling space is specified, and are directly accessible to STM spectroscopy, mesoscopic transport, and cold-atom platforms simulating Class D symmetry. These findings establish the DSI-MCP as a new entry in the classification of critical phenomena in disordered topological matter, bridging Efimov physics, quantum Griffiths singularities, and multicritical disorder-driven phase transitions into a unified theoretical framework.
Keywords
Citation Information
@article{vaitheeswarangnanaraj2026,
title={Efimov-Type Discrete Scale Invariance at the Multicritical Point of a Two-Dimensional Disordered Class D Topological Superconductor},
author={Vaitheeswaran Gnanaraj and Balakrishanan Vellaikannan and P Balamanikandan},
journal={Research Square},
year={2026},
doi={https://doi.org/10.21203/rs.3.rs-9455979/v1}
}
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