A clinical trial involving 30 healthy adults demonstrated that L-theanine supplementation for four weeks significantly improved executive function and verbal fluency. 
The same study found that l-theanine reduced the time it took for participants to fall asleep and enhanced subjective sleep quality. Additionally, in a later study, L-theanine effectively countered caffeine-induced insomnia. 
Calm state of mind
L-theanine increases the intensity of alpha waves, low-frequency brain waves associated with states of calm alertness. 
Attention and reaction time
A study of 18 university students found that L-theanine improved attention and reaction time in students prone to performance anxiety 
 Miodownik C;Maayan R;Ratner Y;Lerner V;Pintov L;Mar M;Weizman A;Ritsner MS; “Serum Levels of Brain-Derived Neurotrophic Factor and Cortisol to Sulfate of Dehydroepiandrosterone Molar Ratio Associated with Clinical Response to L-Theanine as Augmentation of Antipsychotic Therapy in Schizophrenia and Schizoaffective Disorder Patients.” Clinical Neuropharmacology, U.S. National Library of Medicine, pubmed.ncbi.nlm.nih.gov/21617527/. Accessed 14 Nov. 2023
 Administration of L-Theanine Induced Upregulation of Hippocampal BDNF ..., www.researchgate.net/figure/Administration-of-L-theanine-induced-upregulation-of-hippocampal-BDNF-Though-TrkB-and_fig3_249315928. Accessed 14 Nov. 2023.
 LR;, Rao TP;Ozeki M;Juneja. “In Search of a Safe Natural Sleep Aid.” Journal of the American College of Nutrition, U.S. National Library of Medicine, pubmed.ncbi.nlm.nih.gov/25759004/. Accessed 14 Nov. 2023
 Hidese S;Ogawa S;Ota M;Ishida I;Yasukawa Z;Ozeki M;Kunugi H; “Effects of L-Theanine Administration on Stress-Related Symptoms and Cognitive Functions in Healthy Adults: A Randomized Controlled Trial.” Nutrients, U.S. National Library of Medicine, pubmed.ncbi.nlm.nih.gov/31623400/. Accessed 14 Nov. 2023.
 Yoshitake Baba, et al. “Theanine Maintains Sleep Quality in Healthy Young Women by Suppressing the Increase in Caffeine-Induced Wakefulness after Sleep Onset.” Food & Function, Royal Society of Chemistry, 17 July 2023, pubs.rsc.org/en/content/articlehtml/2023/fo/d3fo01247f.