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The transport and thermodynamic properties of $\beta$-ReO$_{2}$ crystallizingin a nonsymmorphic structure were studied using high-quality single crystals.An extremely large magnetoresistance (XMR) reaching 22,000 $\%$ in a transversemagnetic field of 10 T at 2 K was observed. However, distinguished from othertopological semimetals with low carrier densities that show XMR,$\beta$-ReO$_{2}$ has a high electron carrier density of 1 $\times$ $10^{22}$cm$^{-3}$ as determined by Hall measurements and large Fermi surfaces in theelectronic structure. In addition, a small Fermi surface with a small effectivemass was evidenced by de Haas-van Alphen oscillation measurements. The previousband structure calculations [S. S. Wang, et al., Nat. Commun. 8, 1844 (2017)]showed that two kinds of loops made of Dirac points of hourglass-shapeddispersions exist and are connected to each other by a point to form a stringof alternating loops, called the Dirac loop chain (DLC), which are protected bythe multiple glide symmetries. Our first-principles calculations revealed thecomplex Fermi surfaces with the smallest one corresponding to the observedsmall Fermi surface, which is just located near the DLC. The XMR of$\beta$-ReO$_{2}$ is attributed to the small Fermi surface and thus is likelycaused by the DLC.

Extremely large magnetoresistance in the hourglass Dirac loop chain metal \beta-ReO$_{2}$