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A TeV spectral break in the total flux of cosmic-ray electrons and positrons(CREs) at which the spectral power index softens from $\sim 3$ to $\sim 4$ hasbeen observed by H.E.S.S. and recently confirmed by DAMPE with a highsignificance of $6.6~\sigma$. Such an observation is apparently inconsistentwith the data from other experiments such as Fermi-LAT, AMS-02 and CALET. Weperform a global analysis to the latest CRE data including Fermi-LAT, AMS-02,CALET, DAMPE and H.E.S.S. with energy scale uncertainties taken into account toimprove the consistency between the data sets. The fit result strongly favorsthe existence of the break at $\sim 1$ TeV with an even higher statisticalsignificance of $13.3~\sigma$. In view of the tentative CRE break, we revisit anumber of models of nearby sources, such as a single generic Pulsar Wind Nebula(PWN), known multiple PWNe from the ATNF catalog, and their combinations witheither an additional Dark Matter (DM) component or a Supernova Remnant (SNR).We show that the CRE break at $\sim 1$ TeV, together with the known CR positronexcess points towards the possibility that the nearby sources should be highlycharge asymmetric. Among the models under consideration, the one with a PWNplus SNR is most favored by the current data. The favoured distance and age ofthe PWN and SNR sources are both within $0.6$ kpc and around $10^{5}$ yrrespectively. Possible candidate sources include PSR J0954-5430, Vela andMonogem ring, etc. We find that for the models under consideration, theadditional DM component is either unnecessary, or predicts too much photons intension with the H.E.S.S. data of $\gamma$-rays from the direction of theGalactic Center. We also show that the current measurement of the anisotropiesin the arrival direction of the CRE can be useful in determining the propertyof the sources.

Implications of a possible TeV break in the cosmic-ray electron and positron flux