Faculty Bibliography

It is shown that a graphene ribbon, a ballistic strip of carbon monolayer, may serve as a quantum wire whose electronic properties can be continuously and reversibly controlled by an externally applied transverse voltage. The electron bands of armchair-edge ribbons undergo dramatic transformations: The Fermi surface fractures, Fermi velocity and effective mass change sign, and excitation gaps are reduced by the transverse field. These effects are manifest in the conductance plateaus, van Hove singularities, thermopower, and activated transport. The control over one-dimensional bands may help enhance effects of electron correlations, and be utilized in device applications.

The energy of Fermi sea perturbed by an external potential is analyzed with the help of an energy anomaly. Using an example of massive Dirac fermions on a circle, we illustrate how the anomaly accounts for the contribution of the deep-lying states. The energy anomaly is a universal function of the applied field and is related to known field-theoretic anomalies. Applied to the transverse polarizability of carbon nanotubes, the anomaly reveals universality and scale invariance of the response dominated by electrons. The electron band transformation in a strong field-effect regime is predicted.

It is shown that a periodic potential applied to a nanotube can lock electrons into incompressible states. Depending on whether electrons are weakly or tightly bound to the potential, excitation gaps open up either due to the Bragg diffraction enhanced by the Tomonaga-Luttinger correlations, or via pinning of the Wigner crystal. Incompressible states can be detected in a Thouless pump setup, in which a slowly moving periodic potential induces quantized current, with a possibility to pump on average a fraction of an electron per cycle as a result of interactions

We address anomalous transport phenomena in arrays of semiconductor nanocrystals (quantum dots): Transient power-law decay of current as a response to a step in large bias voltage applied across the array, as well as memory effects observed after successive applications of the bias voltage. A novel phenomenological model of transport in such systems is proposed, capable of rationalizing both anomalous transport and memory. The model describes electron transport by a stationary Levy process of transmission events and therefore requires no time dependence of system properties. The long tail in the waiting time distribution gives rise to a nonstationary response in the presence of a voltage pulse. Noise measurements agree well with the predicted non-Poissonian fluctuations in current. We briefly discuss possible microscopic mechanisms that could cause the anomalous statistics in transmission.