The stock market dropped on Tuesday, pulling the Nasdaq Composite (^IXIC 0.62%) down 2% at midday. Investors were generally worried about the prospects for an economic slowdown, particularly in light of negative financial reports from some key retailers.

Tesla (TSLA -1.58%) also lost ground, falling 3%. Yet the electric vehicle pioneer's stock has doubled in just the past couple of months, and many investors believe that Tesla's prospects are as strong as ever.

Indeed, reports of potential interest in a lithium producer show the widespread belief that Tesla wants to secure as much lithium as it can now in order to ensure ample battery production capacity as it ramps up its Gigafactory vehicle facilities.

A big rise for Sigma Lithium

One big winner among stocks on Tuesday was Sigma Lithium (SGML -3.99%), whose shares jumped 19%. Reports from Bloomberg suggested that Tesla might be looking at a potential takeover of Sigma, which produces lithium in Brazil.

Sigma has been pursuing multiple strategies as it tries to maximize shareholder value. On one hand, it has looked at a potentially huge boost to its production capacity at its key Brazilian mining property, where the recent discovery of more extensive reserves than originally anticipated led Sigma to think about expansion. At the same time, though, it's apparent that Sigma's largest shareholder, a private equity fund in Brazil, might be looking to cash out after seeing unprecedented interest in Sigma's lithium production.

After having traded for as little as $1 per share less than three years ago, Sigma's stock has now jumped 35-fold. That would suggest Tesla might end up paying a high price to take over the company outright, but with a total market capitalization of $3.6 billion, Sigma isn't so large as to pose a challenge for the financially flush Tesla.

Other lithium stocks are falling

One might expect Tesla's interest in Sigma to have supported the entire lithium stock sector, but that wasn't the case. Most other lithium stocks fell.

One notable decliner was Piedmont Lithium (PLL -0.95%), which lost 2%. Piedmont stock soared in late 2020 when Tesla signed a five-year agreement to purchase lithium ore from the North Carolina-based mining company. Piedmont expected that the Tesla deal would provide 10% to 20% of the total revenue from the North Carolina project. Even with lithium prices having jumped significantly since then, though, the stock has been highly volatile and unable to advance further from early 2021's highs.

Even the largest lithium companies were generally lower. Albemarle (ALB -1.10%) shares were down 4%, while Sociedad Quimica y Minera (SQM 2.09%) lost 3% at midday on Tuesday. Other midsized companies losing ground included 3% losses for Livent (LTHM) as well as for Lithium Americas (LAC).

What will Tesla do?

Tesla's deal with Piedmont shows that the EV pioneer doesn't have to do a full takeover of a lithium producer in order to obtain materials for battery production. Indeed, avoiding such a move keeps Tesla more of a pure play on the vehicle side.

However, vertical integration is often a smart idea, particularly when materials are hard to come by. Some lithium producers, for instance, are working hard to develop their own battery production capacity. By doing so, they can get the benefit of potentially higher margins on value-added products rather than simply selling raw materials.

Tesla hasn't been clear about whether it anticipates building up a stable of wholly owned lithium-producing subsidiaries or simply intends to enter contractual relationships with multiple companies. What the automaker eventually decides, though, will have significant implications for both the EV industry and lithium mining companies.