Change search field to type="search".

chrome/browser/resources/file_manager/css/file_manager.css

 /* Copyright (c) 2012 The Chromium Authors. All rights reserved.
  * Use of this source code is governed by a BSD-style license that can be
  * found in the LICENSE file. */
 
 html.col-resize * {
   cursor: col-resize !important;
 }
 
 /* Outer frame of the dialog. */
 body {
@@ skipping 412 matching lines @@
 .dialog-header div[role=button]:hover,
 .dialog-header div[role=button]:active {
   border-color: #ddd;
 }
 
 .dialog-header div[role=button][disabled] {
   background-color: #f1f1f1;
 }
 
 #search-box {
-  background: url('../images/icon_search.png') no-repeat scroll 3px 3px;
+  background: url('../images/icon_search.png') no-repeat scroll 2px 1.5px;
   border: 1px solid #BBB;
   border-radius: 2px;
   display: -webkit-box;
   height: 20px;
   margin-right: 10px;
   padding-left: 22px;
 }
 
 /* button:hover and button[disabled]:hover rules must be override by placing
  * the following four rules after them.
@@ skipping 826 matching lines @@
   100% { opacity: 1; }
 }
 
 :hover > .tooltip {
   -webkit-animation-duration: 800ms;
   -webkit-animation-iteration-count: 1;
   -webkit-animation-name: tooltip-show;
   -webkit-animation-timing-function: linear;
   opacity: 1;
 }