Selenium doesn't provide a way to do this so a workaround seems to be the only way.
Assuming you're in Windows or Linux, your CTRL+T idea should be written as below, however that hack failed for me:
browser.actions().keyDown(protractor.Key.CONTROL).sendKeys('t').perform();
Even attempting to do it on an element:
$$('input').first().sendKeys(protractor.Key.chord(protractor.Key.CONTROL, "t"));
Good news is the following hack does seem to work, feel free to replace location.href
with the url you want to open:
browser.driver.executeScript(function() {
(function(a){
document.body.appendChild(a);
a.setAttribute('href', location.href);
a.dispatchEvent((function(e){
e.initMouseEvent("click", true, true, window, 0, 0, 0, 0, 0, true, false, false, false, 0, null);
return e;
}(document.createEvent('MouseEvents'))))}(document.createElement('a')));
});