Faculty Bibliography

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.

Transverse NMR relaxation in a macroscopic sample is shown to be extremely sensitive to the structure of mesoscopic magnetic susceptibility variations. Such a sensitivity is proposed as a novel kind of contrast in the NMR measurements. For suspensions of arbitrary-shaped paramagnetic objects, the transverse relaxation is found in the case of a small dephasing effect of an individual object. Strong relaxation rate dependence on the objects' shape agrees with experiments on whole blood. Demonstrated structure sensitivity is a generic effect that arises in NMR relaxation in porous media, biological systems, as well as in kinetics of diffusion limited reactions

The coupling of a semimetallic carbon nanotube to a surface acoustic wave (SAW) is proposed as a vehicle to realize quantized adiabatic charge transport. We demonstrate that electron backscattering from a periodic SAW potential can be used to induce a miniband spectrum at energies near the Fermi level. Within the framework of Luttinger liquid theory, electron interaction is shown to enhance minigaps and thereby improve current quantization.