Although it's been a little more than six years since Apple became the first publicly traded company to breach the trillion-dollar capitalization ceiling, such companies remain few and far between. As of the latest look, only six outfits now boast 13-figure market caps (though Apple is still the largest, at nearly $3.5 trillion).

Then again, it's been a while since the world's been in a position to push a bunch more names up into the next-size tier.

Now it's got such a chance, in the form of the still-maturing artificial intelligence (AI) market. Some are even calling AI the opportunity of a lifetime. And it may well be. Precedence Research predicts the worldwide AI industry is set to grow at an annualized pace of 19% through 2034.

With that as the backdrop, here's a rundown of the next two tickers that could ride the AI wave to a trillion-dollar market cap -- to the extent doing so matters.

1. Taiwan Semiconductor Manufacturing

Taiwan Semiconductor Manufacturing (TSM -2.03%) isn't a household name. But it's unlikely there's not at least one piece of consumer electronics in your household the company didn't have a hand in making.

Taiwan Semiconductor is considered a contract manufacturer. That is to say, it makes many of the microchips that other brands slap their label on. The company's biggest clients include Nvidia, Qualcomm, and Apple, just to name a few. Its customers supply the manufacturer with their chips' designs and specs, and in turn it supplies customers with processors and other technological components. This outsourcing arrangement ultimately tends to be cheaper for brands than building and maintaining their own production facilities. Between this model's cost-effectiveness and the company's sheer production capacity, Taiwan Semiconductor is estimated to make around two-thirds of the world's semiconductors and chips. The underlying dynamic behind this reach isn't likely to change in the foreseeable future either.

That's not to say its customers aren't trying to wean themselves from their reliance on just one company. Competitors are looking for ways to grow their share as well.

Even so, many of these efforts still ultimately rely on Taiwan Semiconductor. Even as Intel is investing tens of billions in its own nascent chip-foundry business, it's still hiring the Taiwanese rival to manufacture the semiconductors it can't yet make on its own. Similarly, looking to avoid another supply chain headache like the one stemming from the COVID-19 pandemic, Apple is heading up the construction of a chip foundry in Arizona. A closer look at the details of these plans, however, reveals these facilities are actually Taiwan Semiconductor's and are being built as a means of better directly serving Apple as a customer.

Whatever the case, the impending entry of next-gen AI solutions is going to require more and better silicon. Precedence Research notes than while the overall AI market is growing at a brisk clip, the AI chip market is set to grow an average yearly rate of about 30% though 2032.

Considering that Taiwan Semiconductor believes it will be able to successfully mass manufacture 2 nm (nanometer) chips by next year -- making these processors up to 15% faster yet while consuming up to 30% less power than today's top-of-the-line alternatives -- it's still the chief beneficiary of this impending market growth.

The company's market cap currently stands at $887 billion, so it's only got a short trip to the trillion-dollar milestone. It wouldn't be crazy to start thinking about when Taiwan Semiconductor might reach a market cap of $2 trillion.

2. Broadcom

And the other name within sight of a 13-figure market cap? That's Broadcom (AVGO 0.29%), which is a $772 billion outfit as of the latest look.

You probably know Broadcom as a telecom and wireless technology company that rose to prominence when computers as well as mobile phones were just becoming commonplace. You may also know it better as Avago. The two companies merged in early 2016, melding both organizations' already-deep product menus.

What you may not know is that one of the biggest bottlenecks that AI data centers are now dealing with isn't the speed of the processors doing the number-crunching but the connections between all of these processors into a single, integrated platform.

Broadcom to the rescue.

Continuing to come up with state-of-the-art connectivity solutions, in May the company unveiled its fifth-generation PCIe ethernet adapters that can easily and more cost-effectively connect existing motherboards (and therefore their processors) to all the others within a data-center network. And earlier this year, Broadcom introduced the world's first vertical-cavity, surface-emitting laser (VCSEL) capable of delivering digital data at an incredible pace of 200 gigabits per second, per lane.

Data centers have been waiting for such a high-speed solution, although the resulting technological leap is so big that they'll also need time to prepare the infrastructure for it. The company believes it will begin making commercial shipments of this fiberoptic technology by the end of this year, helping the AI industry usher in the sort of platforms that have been envisioned but simply can't be achieved with its current technologies.

In the meantime, Broadcom will continue making and marketing more familiar products like at-home Wi-Fi chips, automotive connectivity platforms, cybersecurity tools, conventional microchips, and the like. Between this business and the growing need for next-generation AI data-center hardware, analysts believe this company's revenue will nearly double between now and 2028. Earnings are likely to grow even more.

It technically shouldn't matter, but it does help

A company's market cap is purely a function of its stock's price and the number of shares issued. It's not a mark of profitability, nor of value. Reaching a trillion-dollar valuation doesn't produce a cash bonus for the organization or its shareholders.

In other words, it's just a number.

Nevertheless, from a qualitative perspective, this is a status-based accolade that can help buoy a stock's value. A trillion-dollar market cap will not only garner more investor attention for the company in question, but will ultimately position Broadcom and Taiwan Semiconductor shoulder-to-shoulder with names like Apple and Nvidia. That's not a bad thing.