Magento 2: Add invoice Increment ID to Order grid

Question

I am trying to add invoice increment ID to order grid in magento 2 admin like below:

app/code/Payment/Status/view/adminhtml/ui_component/sales_order_grid.xml

<?xml version="1.0" encoding="UTF-8"?>
<listing xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Ui:etc/ui_configuration.xsd">
    <columns name="sales_order_columns">
        <column name="invoice_id" class="Payment\Status\Ui\Component\Listing\Column\Invoice">
            <argument name="data" xsi:type="array">
                <item name="config" xsi:type="array">
                    <item name="filter" xsi:type="string">text</item>
                    <item name="label" xsi:type="string" translate="true">Invoice #</item>
                </item>
            </argument>
        </column>
    </columns>
</listing>

app/code/Payment/Status/Ui/Component/Listing/Column/Invoice.php

<?php
namespace Payment\Status\Ui\Component\Listing\Column;

use \Magento\Sales\Api\OrderRepositoryInterface;
use \Magento\Framework\View\Element\UiComponent\ContextInterface;
use \Magento\Framework\View\Element\UiComponentFactory;
use \Magento\Ui\Component\Listing\Columns\Column;
use \Magento\Framework\Api\SearchCriteriaBuilder;

class Invoice extends Column
{
    protected $_orderRepository;
    protected $_searchCriteria;

    public function __construct(ContextInterface $context, UiComponentFactory $uiComponentFactory, OrderRepositoryInterface $orderRepository, SearchCriteriaBuilder $criteria, array $components = [], array $data = [])
    {
        $this->_orderRepository = $orderRepository;
        $this->_searchCriteria  = $criteria;
        parent::__construct($context, $uiComponentFactory, $components, $data);
    }

    public function prepareDataSource(array $dataSource)
    {
        if (isset($dataSource['data']['items'])) {
            foreach ($dataSource['data']['items'] as & $item) {

                $order  = $this->_orderRepository->get($item["entity_id"]);
                $invoice_ids = array();
                foreach ($order->getInvoiceCollection() as $invoice)
                {
                    $invoice_ids[] = $invoice->getIncrementId();
                }
                if(count($invoice_ids)>0){
                    $invoice_id = implode(', ', $invoice_ids);
                }
                else{
                    $invoice_id = '';
                }

                $item[$this->getData('name')] = $invoice_id;
            }
        }

        return $dataSource;
    }
}

And it showing correctly but filter and sorting not working for that column.

Can you anyone help?