import org.openqa.selenium.By;
import org.openqa.selenium.JavascriptExecutor;
import org.openqa.selenium.WebDriver;
import org.openqa.selenium.WebElement;
import org.openqa.selenium.chrome.ChromeDriver;
import org.openqa.selenium.chrome.ChromeOptions;

public class shadow_DOM {

    static WebDriver driver;
    public static void main(String[] args)
    {
        System.setProperty("webdriver.chrome.driver", "C:\Utility\BrowserDrivers\chromedriver.exe");
        ChromeOptions options = new ChromeOptions();
        options.addArguments("start-maximized");
        //options.addArguments("disable-infobars");
        options.addArguments("--disable-extensions");
        driver = new ChromeDriver(options);
        driver.get("chrome://downloads/");
        WebElement root1 = driver.findElement(By.tagName("downloads-manager"));
        WebElement shadow_root1 = expand_shadow_element(root1);

        WebElement root2 = shadow_root1.findElement(By.cssSelector("downloads-toolbar#toolbar"));
        WebElement shadow_root2 = expand_shadow_element(root2);

        WebElement root3 = shadow_root2.findElement(By.cssSelector("cr-toolbar#toolbar"));
        WebElement shadow_root3 = expand_shadow_element(root3);

        WebElement root4 = shadow_root3.findElement(By.cssSelector("cr-toolbar-search-field#search"));
        WebElement shadow_root4 = expand_shadow_element(root4);

        WebElement search_term = shadow_root4.findElement(By.cssSelector("div#searchTerm input#searchInput"));
        String js = "arguments[0].setAttribute('value','pdf')";
        ((JavascriptExecutor) driver).executeScript(js, search_term);

        WebElement search_button = shadow_root4.findElement(By.cssSelector("paper-icon-button#icon"));
        search_button.click();

        System.out.println("Search Button Clicked");
    }

    public static WebElement expand_shadow_element(WebElement element)
    {
        WebElement shadow_root = (WebElement)((JavascriptExecutor)driver).executeScript("return arguments[0].shadowRoot", element);
        return shadow_root;
    }

}

Search Button Clicked