There have been many recent clinical trials conducted by various organizations proving that the combination of L-Theanine and Caffeine increases the ability to focus without the over stimulating effects of Caffeine alone:
A recent study on young adults discovered that "The combination of L-Theanine and Caffeine improves the cognitive performance and increases subjected alertness" 
The Cognitive Neurophysiology Laboratory in New York conducted testing for 4 days on volunteers from the age of 21 and 40 and found that "L-Theanine and Caffeine in combination affect human cognition as evidenced by oscillatory alpha-band activity and attention task performance." 
A study on the cognition and mood of healthy volunteers found that "The L-Theanine and Caffeine combination improved both speed and accuracy of performance of the attention-switching task, and reduced susceptibility to distracting information in the memory task. These results replicate previous evidence with suggests that L-Theanine and caffeine in combination are beneficial for improving performance on cognitively demanding tasks." 
In a detailed study, the researchers concluded that "The results support previous evidence that L-theanine and caffeine in combination can improve attention." 
A literature review from the School of Psychology in Australia stated that "L-theanine may interact with caffeine to enhance performance in terms of attention switching and ability to ignore distraction." 
- International society of sports nutrition position stand: caffeine and performance.
- The effects of l-theanine on alpha-band oscillatory brain activity during a visuo-spatial attention task.
- The combination of l-theanine and caffeine improves cognitive performance and increases subjective alertness.
- L-theanine and caffeine in combination affect human cognition as evidenced by oscillatory alpha-band activity and attention task performance.
- The combined effects of l-theanine and caffeine on cognitive performance and mood.
- L-theanine and caffeine improve task switching but not intersensory attention or subjective alertness.
- Psychological effects of dietary components of tea: caffeine and l-theanine.