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LetL=-Δℍn+V{L=-{\Delta}_{\mathbb{H}^{n}}+V}be a Schrödinger operator on Heisenberg groupsℍn{\mathbb{H}^{n}}, whereΔℍn{{\Delta}_{\mathbb{H}^{n}}}is the sub-Laplacian, the nonnegative potential  V  belongs to the reverse Hölder classB/2{B_{\mathcal{Q}/2}}. Here{\mathcal{Q}}is the homogeneous dimension ofℍn{\mathbb{H}^{n}}. In this article, we introduce the fractional heat semigroups{e-t⁢Lα}t&gt;0{\{e^{-tL^{\alpha}}\}_{t&gt;0}},α&gt;0{\alpha&gt;0}, associated with  L . By the fundamental solution of the heat equation, we estimate the gradient and the time-fractional derivatives of the fractional heat kernelKα,tL⁢(⋅,⋅){K_{\alpha,t}^{L}(\,\cdot\,,\cdot\,)}, respectively. As an application, we characterize the spaceBMOLγ⁢(ℍn){\mathrm{BMO}_{L}^{\gamma}(\mathbb{H}^{n})}via{e-t⁢Lα}t&gt;0{\{e^{-tL^{\alpha}}\}_{t&gt;0}}.

Regularity of fractional heat semigroups associated with Schrödinger operators on Heisenberg groups