  We obtain exact solutions to the two-dimensional (2D) Dirac equation for the
one-dimensional P\"oschl-Teller potential which contains an asymmetry term. The
eigenfunctions are expressed in terms of Heun confluent functions, while the
eigenvalues are determined via the solutions of a simple transcendental
equation. For the symmetric case, the eigenfunctions of the supercritical
states are expressed as spheroidal wave functions, and approximate analytical
expressions are obtained for the corresponding eigenvalues. A universal
condition for any square integrable symmetric potential is obtained for the
minimum strength of the potential required to hold a bound state of zero
energy. Applications for smooth electron waveguides in 2D Dirac-Weyl systems
are discussed.
