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Recently, a novel material with bilayer kagome latticeCa$_{10}$Cr$_7$O$_{28}$ was proposed to be a gapless quantum spin liquid, dueto the lack of long-range magnetic order and the observation of broad diffuseexcitations. Here, we present the ultralow-temperature thermal conductivitymeasurements on single crystals of Ca$_{10}$Cr$_7$O$_{28}$ to detect itslow-lying magnetic excitations. At finite temperatures, with increasing themagnetic fields, the thermal conductivity exhibits a clear dip around 6 T,which may correspond to a crossover in the magnetic ground state. At thezero-temperature limit, no residual linear term is found at any fields,indicating the absence of gapless itinerant fermionic excitations. Therefore,if the spinons do exist, they are either localized or gapped. In the gappedcase, the fitting of our data gives a small gap $\Delta \sim$ 0.27(2) K. Theseresults put strong constraints on the theoretical description of the groundstate in this quantum spin liquid candidate.

Ultralow-temperature heat transport in the quantum spin liquid candidate Ca10Cr7O28 with bilayer kagome lattice