Traversable dark energy wormholes in a quadratic f(R,T) gravity

The main aim of this paper is to explore the Morris–Thorne (MT) static traversable wormhole structures supported by dark energy within the framework of the quadratic [Formula: see text] formalism, where the gravitational Lagrangian is defined by an arbitrary function of the Ricci scalar R as well as the trace of the stress–energy tensor T. To achieve this aim, we consider the function [Formula: see text], where [Formula: see text] and [Formula: see text] denote coupling parameters, together with two different forms of the shape function introduced in the selected metric as well as assume a constant redshift function. We obtained the exact solution to each choice of shape function and investigated wormholes that can emerge depending on the presence of exotic or non-exotic matter. For the selected theoretical setups, we initially examine the general behavior of the corresponding solutions and then discuss, respectively, the throat, flaring out, asymptotically flatness, hydrostatic equilibrium, and energy conditions. We observed that the quadratic component and linear trace term of [Formula: see text] gravity and the hybrid forms of shape functions play an important role in validating the energy conditions for viable wormhole solutions.