SAN FRANCISCO >> When Goodwin Liu joined the seven-member California Supreme Court in 2011, he became its fourth sitting member of Asian descent. The number is remarkable.

The other state supreme courts in the U.S. combined have a handful of Asian-American justices. And Asian-American representation on other state courts, the federal bench and among the country’s top prosecutors is similarly scant.

Those findings emerged from a new study by Liu and law students at Yale University that provides a portrait of Asian-Americans in the legal profession. The conclusion: They are well-represented among the nation’s attorneys but still missing from some of the highest posts.

“They have a foot in the door in virtually every sector of the legal profession,” Liu said during a recent interview. “The question now is how wide that door’s going to swing open for them.”

For Liu, the study is personal. His parents were doctors who came to the U.S. in the late 1960s from Taiwan. Nothing in his childhood was a conduit for a legal career. His parents encouraged him to study math and science. He didn’t know any attorneys growing up and almost became a doctor.

Liu said the difference for him was mentorship. He had two Asian-American leaders as role models: U.S. Rep. Bob Matsui and former Yale Law School Dean Harold Koh.

Liu became a law professor and associate dean at the University of California, Berkeley, before President Barack Obama nominated him in 2010 for a prestigious federal appeals court seat.

His name was even mentioned as a potential U.S. Supreme Court candidate, but Republicans derailed his nomination to the 9th U.S. Circuit Court of Appeals. They called him a liberal ideologue and took exception to his outspoken opposition to Samuel Alito’s 2006 appointment to the high court.

Liu withdrew his name. Soon afterward, California Gov. Jerry Brown swore him in for a seat on the state Supreme Court.

Liu said the Asian-American representation on the California high court does not carry through to lower courts in the state. As of 2015, only two of 97 appellate court judges were Asian-American. The California Supreme Court now has three Asian-American justices after one of those of Asian descent retired in 2014.

“People may have certain perceptions of what a judge should look like, and Asian-Americans being fairly new to this field are bursting that mold,” Liu said.

Asians are the nation’s fastest-growing racial group and make up more than 5 percent of the population. They make up an even larger percentage of law school students, with a significant number graduating from top institutions.

But Liu said their ranks in leadership positions are disconcerting, seen in some of the numbers the study compiled from research in recent years:

— Three of the 94 U.S. attorneys and four of the country’s nearly 2,500 elected state prosecutors were Asian-American.

— There were 26 active Asian-American judges among more than 850 federal judicial positions. Two percent of almost 10,300 state trial and appellate court judges who were surveyed were Asian-American.

— Asian-Americans were the largest minority group at major law firms but had the highest attrition rates and lowest ratio of partners to associates among all racial groups.

“Now we understand what’s happening,” said Charles Huang, a California prosecutor who co-founded the National Asian Pacific Islander Prosecutors Association. “We don’t know what’s causing it, but we know what the empirical results are.”

The study surveyed more than 600 Asian-American lawyers, and their responses pointed to factors that may serve as barriers.

A relatively small percentage had a parent who was a lawyer. Those who expressed a desire to change their careers said getting a job as a judge or prosecutor was low on the list.

More than 80 percent reported experiencing implicit bias in the workplace. Many respondents said Asian-American attorneys were considered hard-working and responsible, but far fewer said the legal profession associated them with empathy, creativity or assertiveness.

Liu encourages law students to develop their confidence and identity through public speaking and “break from what came” before them, though he warns that the weight of stereotypes might not go away.

Liu said he still struggles with how people might perceive him as an Asian-American judge.

“I think for people who feel like they are going into places that are unfamiliar to them and who defy what perhaps is conventional expectation, you always feel like you’re an impostor,” he said. “There’s always that feeling like, ‘Oh, one day they’re going to find me out.’”