Abstract

Graphene and carbon nanotubes are ideal for strain engineering in quantum nanoelectromechanical systems due to their long coherence lengths, mechanical strength, and sensitivity to deformations. Mechanical strain induces scalar ($\Delta \mu_{\varepsilon}$) and vector ($\bm{A}$) potentials, which directly tune the Hamiltonian, providing precise control of the energy, momentum, and quantum state of electrons in these materials. This strain-tunability could be used to completely suppress ballistic transmission in graphene quantum strain transistors (GQSTs), generate large pseudomagnetic fields ($\nabla \times \bm{A}$), or carry quantum information (valleytronics). Thus far, experimental challenges have prevented thorough exploration of quantum transport strain engineering (QTSE). To this end, we have constructed low temperature ($T\sim 1$~K) QTSE instrumentation. Incorporating fabrication methods for ultra-short ($\sim 10$~nm), suspended carbon nanotube and graphene devices, we predict tunable uniaxial strains up to $\approx \text{1--10}\%$ using this instrumentation.

We first determined the impact of ultra-short channel lengths on transport by measuring unstrained nanotube devices. These formed ``two-in-one" quantum transistors with drastically different behaviour for electrons and holes. In a small bandgap nanotube ($\approx 50$~meV) we observed ballistic transport for electrons, and quantum dot (QD) behaviour for holes, while in larger bandgap nanotubes($\approx 300$~meV), we measured asymmetric QD behaviour between electrons and holes. We showed that this transport asymmetry is caused by electron doping in the nanotube contacts, and is greatly enhanced in ultra-short devices. With these contact effects in mind, we developed a realistic applied theoretical model for transport in uniaxially strained ballistic GQSTs. We calculated conductivity for strained ballistic graphene, and found four transport signatures: gate-shifting of the data from the scalar potential, and strong suppression of conductivity, modification of electron-hole conductivity asymmetry, and a rich resonance spectrum from the vector potential. We calculated high on/off ratios $>10^4$ in realistically achievable GQSTs at sufficient strains. Using our strain instrumentation, we measured transport in strained graphene, observing unambiguously the effects of strain-induced vector and scalar potentials. In graphene QDs, we observed gate-shifting of the charge states with strain, consistent with strong, strain-tunable pseudomagnetic fields. In a strained ballistic graphene device, we observed the four expected transport signatures discussed above, and using our model, we found good semi-quantitative agreement between theory and experiment.