The rapid growth of Internet services has brought emergent concerns over network energy efficiency. This study aims to improve network energy efficiency using power-down technique. We propose DEER, a fully distributed routing scheme. The main concept of DEER is to dynamically allocate the traffic demands in the nodes so that some links connected to the nodes can be put into sleep mode, thus reducing the energy consumption. The special features of DEER include that it does not need global traffic matrix of the network and that it uses only the local information of link loads, making DEER be able to be implemented in a distributed manner without centralized control. We develop algorithms in DEER to dynamically change the link state (into active or sleep mode) according to link utilization and to balance the loads of links by adjusting the link weights. With the traffic load varying over time, the link state transformation is triggered when any of the pre-defined thresholds is violated. Extensive simulations with the network topology and real traffic traces from the GÉANT network confirm that by involving DEER, up to 50% of the links can be put into sleep while the frequency of chaining the state of a link stays fairly low.