Place the green beans in an even layer at the bottom of the slow cooker.
Arrange the salmon fillets on top of the green beans in a single layer.
In a small bowl, stir together the teriyaki sauce, minced garlic, grated ginger, and sesame oil.
Pour the sauce mixture evenly over the salmon and green beans.
Cover and cook on low for 2 to 3 hours, until the salmon flakes easily with a fork.
Sprinkle sesame seeds over the top just before serving.