are AWS EFS Mount Targets supported in AWS Local Zones?

I am trying to create an EFS mount target in us-east-1-atl-1a AWS Local Zone using Terraform, but I received following error. I attempted to create it manually using UI, but I don't see an option to select us-east-1-atl-1a as an AZ(See screenshot). Does anyone know if this AWS Local Zone supports EFS mount targets? AWS Local Zone info page doesn't mention EFS at all.

Terraform Error:

│ Error: UnsupportedAvailabilityZone: Mount targets are not supported in subnet's availability zone.
│ {
│   RespMetadata: {
│     StatusCode: 400,
│     RequestID: "23192f37-77e6-421b-b623-4a2b6dfb6217"
│   },
│   ErrorCode: "UnsupportedAvailabilityZone",
│   Message_: "Mount targets are not supported in subnet's availability zone."
│ }
│
│   with aws_efs_mount_target.efs-mounts[0],
│   on efs.tf line 7, in resource "aws_efs_mount_target" "efs-mounts":
│    7: resource "aws_efs_mount_target" "efs-mounts" {
│
╵
╷
│ Error: creating EKS Cluster (d115): UnsupportedAvailabilityZoneException: Cannot create cluster 'd115' because us-east-1-atl-1a, the targeted availability zone, does not currently have sufficient capacity to support the cluster. Retry and choose from these availability zones: us-east-1a, us-east-1b, us-east-1c, us-east-1d, us-east-1f
│ {
│   RespMetadata: {
│     StatusCode: 400,
│     RequestID: "51476966-09d3-4976-b8a1-f381b9c29c17"
│   },
│   ClusterName: "d115",
│   Message_: "Cannot create cluster 'd115' because us-east-1-atl-1a, the targeted availability zone, does not currently have sufficient capacity to support the cluster. Retry and choose from these availability zones: us-east-1a, us-east-1b, us-east-1c, us-east-1d, us-east-1f",
│   ValidZones: [
│     "us-east-1a",
│     "us-east-1b",
│     "us-east-1c",
│     "us-east-1d",
│     "us-east-1f"
│   ]
│ }