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Nearby sources may contribute to cosmic-ray electron (CRE) structures at highenergies. Recently, the first DAMPE results on the CRE flux hinted at a narrowexcess at energy ~1.4 TeV. We show that in general a spectral structure with anarrow width appears in two scenarios: I) "Spectrum broadening" for thecontinuous sources with a delta-function-like injection spectrum. In thisscenario, a finite width can develop after propagation through the Galaxy,which can reveal the distance of the source. Well-motivated sources includemini-spikes and subhalos formed by dark matter (DM) particles $\chi_{s}$ whichannihilate directly into e+e- pairs. II) "Phase-space shrinking" for burst-likesources with a power-law-like injection spectrum. The spectrum afterpropagation can shrink at a cooling-related cutoff energy and form a sharpspectral peak. The peak can be more prominent due to the energy-dependentdiffusion. In this scenario, the width of the excess constrains both the powerindex and the distance of the source. Possible such sources are pulsar windnebulae (PWNe) and supernova remnants (SNRs). We analysis the DAMPE excess andfind that the continuous DM sources should be fairly close within ~0.3 kpc, andthe annihilation cross sections are close to the thermal value. For theburst-like source, the narrow width of the excess suggests that the injectionspectrum must be hard with power index significantly less than two, thedistance is within ~(3-4) kpc, and the age of the source is ~0.16 Myr. In bothscenarios, large anisotropies in the CRE flux are predicted. We identifypossible candidates of mini-spike (PWN) sources in the current Fermi-LAT 3FGL(ATNF) catalog. The diffuse gamma-rays from these sources can be well below theGalactic diffuse gamma-ray backgrounds and less constrained by the Ferm-LATdata, if they are located at the low Galactic latitude regions.

Origins of sharp cosmic-ray electron structures and the DAMPE excess