Thick braneworld in $$f(Q,\mathcal {T})$$ gravity

Abstract In this work, we study a codimension-one thick brane in modified symmetric teleparallel gravity for the specific additive ansatz $$f(Q,\mathcal {T}) = Q + k_{1} Q^{n} + k_{2}\mathcal {T}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>T</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>Q</mml:mi> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>k</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:msup> <mml:mi>Q</mml:mi> <mml:mi>n</mml:mi> </mml:msup> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>k</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mi>T</mml:mi> </mml:mrow> </mml:math> . Using two physically motivated warp factor, we construct the full brane system, derive background solutions, and analyze how nonmetricity corrections and the matter-trace coupling modify brane internal structure and graviton localization. For both warp profiles, we obtain the corresponding Schrödinger-like equation for tensor perturbations, identify conditions for volcano and multi-well effective potentials, and determine when a localized zero mode arises. We discuss the physical implications of our results, such as possible short-range corrections to Newton’s law and resonant Kaluza–Klein modes, and outline observational prospects and directions for future work.