Such aircraft do exist. For example, the Pipistrel Velis Electro trainer. And more recently, the Rhyxeon RX4E became the first electric aircraft to be type-certified for commercial passenger operations.
It's likely that we'll see many more electric fan aircraft in the coming years/decades, whether powered by batteries and/or hydrogen fuel cells, or hybrids with both conventional turbofan and electric propulsion in order to improve efficiency and environmental performance.
