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In this paper we study the self-adjointness and spectral properties oftwo-dimensional Dirac operators with electrostatic, Lorentz scalar, andanomalous magnetic $\delta$-shell interactions with constant weights that aresupported on a smooth unbounded curve that is straight outside a compact setand whose ends are rays that are not parallel to each other. For all possiblecombinations of interaction strengths we describe the self-adjoint realizationsand compute their essential spectra. Moreover, we prove in different situationsthe existence of geometrically induced discrete eigenvalues.

On two-dimensional Dirac operators with $\delta$-shell interactions supported on unbounded curves with straight ends