Characteristic determinant approach to the spectrum of one-dimensional <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi><mml:mtext>-symmetric</mml:mtext><

We obtain a closed-form expression for the energy spectrum of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="script">P</a:mi><a:mi mathvariant="script">T</a:mi><a:mtext>-symmetric</a:mtext></a:mrow></a:math> superlattice systems with complex potentials of periodic sets of two <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>δ</d:mi><d:mspace width="0.28em"/><d:mi>potentials</d:mi></d:mrow></d:math> in the elementary cell. In the presence of periodic gain and loss, we analyzed in detail a diatomic crystal model, varying either the scatterer distances or the potential heights. It is shown that at a certain critical value of the imaginary part of the complex amplitude, topological states depending on the lattice size and the configuration of the unit cell can be pushed out from the given region. This may happen at the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi mathvariant="script">PT</f:mi><f:mtext>-symmetry</f:mtext></f:mrow></f:math> breaking (exceptional) points.