Disparate Quantum Corrections to Conduction in Carbon Nanotube Bundles

Abstract

Quantum interference effects such as weak localization (WL) and universal conductance fluctuations (UCF) normally yield consistent electronic phase-coherence lengths in homogeneous conductors. Here we show that in individual carbon nanotube bundles exfoliated from highly conductive solution-spun fibers, different probes, including the field scales and magnitudes of WL and UCF and nonlocal magnetoconductance, lead to strikingly disparate estimates of coherence lengths. WL magnetoconductance measured in a perpendicular magnetic field yields a phase-coherence length of approximately 50 nm. In contrast, UCF amplitudes are comparable to e squared over h even for an 8 micrometer long segment, and nonlocal magnetoconductance persists across a 4 micrometer separation of electrodes, revealing phase-coherent transport over micrometer length scales within a single bundle. The coexistence of short- and long-range coherence implies that locally diffusive electrons remain partially phase-correlated among nanotubes within the same bundle. These findings challenge the conventional single-scale picture of mesoscopic coherence and establish carbon nanotube bundles as a model platform for emergent, network-level quantum transport.

Figures (4)

• Figure 1: (a) Schematic illustration of the exfoliation process from a macroscopic CNT fiber ($\sim$20 $\upmu$m in diameter) to an individual CNT bundle ($\sim$10 nm in diameter) on a Si/SiO$_2$ substrate. A detailed characterization of the fiber’s hierarchical structure is reported in Ref. Yu2025. (b) Temperature dependence of the four-terminal conductance for an 8-$\upmu$m CNT-bundle segment, compared with the CNT-fiber data reproduced from Ref. Yu2025. Both samples show metallic behavior at high temperatures and a moderate upturn in resistance below $\sim$50 K, consistent with quantum corrections arising from weak localization and Altshuler–Aronov interactions.
• Figure 2: (a) Schematic diagram of the local four-terminal measurement configuration used for CNT-bundle devices on Si/SiO$_2$ substrates. (b) Magnetoconductance, expressed in units of $e^2/h =$ 3.874 $\times$ 10$^{-5}$ S, of an $L=8\,\upmu$m CNT-bundle segment measured at several temperatures for perpendicular magnetic-field orientations. A pronounced positive low-field magnetoconductance reflects the suppression of weak localization, while reproducible aperiodic fluctuations correspond to universal conductance fluctuations.
• Figure 3: Magnetoconductance $\Delta G$ for the 8 $\upmu$m CNT-bundle segment measured at different temperatures (2–40 K), plotted as a function of magnetic field $B$. Each panel shows the experimental data (dots) together with the quasi-1D weak localization fit (black dashed curve) using Eq. (1). The extracted phase-coherence length $L_{\phi,\mathrm{1D}}$ is indicated in each panel. Panels (a), (c), (e), (g), and (i) correspond to measurements with the magnetic field parallel to the bundle axis, while panels (b), (d), (f), (h), and (j) correspond to the field perpendicular to the bundle axis.
• Figure 4: (a) Schematic diagrams of the nonlocal measurement configurations used for CNT-bundle devices on Si/SiO$_2$ substrates. (b) Nonlocal magnetoconductance of a CNT-bundle device with $L_{\text{NL}}=4\,\upmu$m separation between current and voltage leads. The positive low-field response at 2 K diminishes with temperature, indicating micrometer-scale phase coherence across the bundle network.