Robust quantized thermal conductance of Majorana floating edge bands in d-wave superconductors

Abstract

We propose and characterize a different class of Majorana boundary states, i.e., floating Majorana edge bands (FMEBs), which emerge in two-dimensional superconductors that break time-reversal symmetry yet host helical-like transport. In contrast to conventional chiral or helical edge modes, FMEBs form isolated, momentum-separated counterpropagating Majorana modes detached from the bulk continuum. We identify a minimal mechanism for their emergence via anisotropic Wilson masses in a two-band Bogoliubov–de Gennes model, and demonstrate their microscopic realization in a quantum anomalous Hall (QAH) insulator proximitized by a d-wave superconductor. Using nonequilibrium Green's function simulations, we uncover clear transport fingerprints: a quantized total thermal conductance in two-terminal devices, and a robust half-quantized plateau in four-terminal geometries that cleanly distinguishes FMEBs from chiral N=±2 QAH phases. This thermal response remains remarkably stable under finite temperature, moderate long-range disorder, and finite chemical potential. Our findings establish FMEBs as an experimentally accessible route toward helical-like Majorana transport in systems without time-reversal symmetry, with direct implications for topological quantum computation.

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