One- and two-dimensional topological thermal-diffusion structures exhibit representative localized states, such as interface states and higher-order corner states, respectively. A finite-width ribbon structure lies between these two limiting configurations in terms of both geometric dimensionality and the number of degrees of freedom. However, how the transverse degrees of freedom introduced by the finite width reconstruct the spectral branches and spatial distributions of one-dimensional interface states, as well as how these states differ from higher-order corner states in two-dimensional systems, remains to be clarified.
In this work, the spectral characteristics, edge states, and temperature-field evolution of a Su-Schrieffer-Heeger (SSH) thermal-diffusion ribbon are systematically investigated. Starting from the discrete heat-conduction equation, an SSH-type thermal network is constructed with alternating intracell and intercell couplings along the x direction and uniform interlayer coupling along the y direction. The eigenvalues of the corresponding evolution operator characterize the decay rates of the thermal modes, whereas the eigenvectors describe their spatial temperature distributions.
The results show that, as the number of layers increases, the number of spectral bands increases accordingly, and the continuous spectrum of the two-dimensional periodic system is discretized into multiple branches along the finite-width direction. Because the interlayer coupling is uniform and no SSH-type dimerization is introduced along the ydirection, the geometric boundaries of a uniform ribbon do not support additional topological edge states. When topologically trivial and nontrivial regions are connected to form interfaces along the xdirection, spectrally isolated interface states emerge in both the one-dimensional SSH thermal network and the finite-width SSH ribbon. Their temperature distributions are strongly localized near the topological interfaces, and the transverse layer degrees of freedom split the original one-dimensional interface states into multiple branches with different decay rates and interlayer distributions. These interface-localized states are fundamentally different from higher-order corner states, which require nontrivial coupling configurations and simultaneous localization along both spatial directions.
Time-dependent simulations further demonstrate that the edge states retain their interfacial localization during thermal decay, whereas the bulk states exhibit more extended spatial diffusion. Increasing the interlayer coupling shifts the overall decay-rate spectrum upward and modifies the relative spectral positions of the edge and bulk states, but does not alter the topological-interface origin of the edge states. These results provide a theoretical basis for understanding and controlling localized thermal modes in finite-width topological thermal-diffusion structures.