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Recently, much attention has been paid to uncovering the influence ofdissipation on a quantum system, particularly on how the non-Hermitian (NH)terms modify the band topology of topological materials and reshape the profileof the wavefunctions of a system (or the NH skin effect). In this paper, aspecific NH skin effect that induced by local dissipation is studied for chiraledge modes, in which the NH term corresponds to the local imaginary Fermivelocity of the chiral edge modes. By solving the NH Schr\"{o}dinger equationof the non-Hermitian chiral edge modes (nhCEs) with complex Fermi velocity, weuncovered the remarkable complex spectra and the wavefunctions of the nhCEs. Wefind that the complex spectra of these modes is a straight line in thetopological materials, and its chirality can separates the modes with positiveenergy from those with negative energy, in which they are localized atdifferent positions. We also studied the nhCEs at the boundary of 2-dimensional(2D) topological materials, the 2D $p$-wave superconductor and the Qi-Wu-Zhangmodel, in which the general law of nhCEs was verified. We expect that ourfindings will pave the way for researching the transport properties of thechiral edge modes in the non-equilibrium context.

Non-Hermitian Chiral Edge Modes With Complex Fermi Velocity