Ya. M. Blanter

Shot Noise in Mesoscopic Conductors

Abstract Theoretical and experimental work concerned with dynamic fluctuations has developed into a very active and fascinating subfield of mesoscopic physics. We present a review of this development focusing on shot noise in small electric conductors. Shot noise is a consequence of the quantization of charge. It can be used to obtain information on a system which is not available through conductance measurements. In particular, shot noise experiments can determine the charge and statistics of the quasiparticles relevant for transport, and reveal information on the potential profile and internal energy scales of mesoscopic systems. Shot noise is generally more sensitive to the effects of electron–electron interactions than the average conductance. We present a discussion based on the conceptually transparent scattering approach and on the classical Langevin and Boltzmann–Langevin methods; in addition a discussion of results which cannot be obtained by these methods is provided. We conclude the review by pointing out a number of unsolved problems and an outlook on the likely future development of the field.

Carbon nanotubes as nanoelectromechanical systems

We theoretically study the interplay between electrical and mechanical properties of suspended, doubly clamped carbon nanotubes in which charging effects dominate. In this geometry, the capacitance between the nanotube and the gate(s) depends on the distance between them. This dependence modifies the usual Coulomb models and we show that it needs to be incorporated to capture the physics of the problem correctly. We find that the tube position changes in discrete steps every time an electron tunnels onto it. Edges of Coulomb diamonds acquire a (small) curvature. We also show that bistability in the tube position occurs and that tunneling of an electron onto the tube drastically modifies the quantized eigenmodes of the tube. Experimental verification of these predictions is possible in suspended tubes of sub-micron length.

Topological Confinement in Bilayer Graphene

We study a new type of one-dimensional chiral states that can be created in bilayer graphene (BLG) by electrostatic lateral confinement. These states appear on the domain walls separating insulating regions experiencing the opposite gating polarity. While the states are similar to conventional solitonic zero modes, their properties are defined by the unusual chiral BLG quasiparticles, from which they derive. The number of zero mode branches is fixed by the topological vacuum charge of the insulating BLG state. We discuss how these chiral states can manifest experimentally and emphasize their relevance for valleytronics.

Tunneling in suspended carbon nanotubes assisted by longitudinal phonons.

Current-voltage characteristics of suspended single-wall carbon nanotube quantum dots show a series of steps equally spaced in voltage. The energy scale of this harmonic, low-energy excitation spectrum is consistent with that of the longitudinal low-k phonon mode (stretching mode) in the nanotube. Agreement is found with a Franck-Condon-based model in which the phonon-assisted tunneling process is modeled as a coupling of electronic levels to underdamped quantum harmonic oscillators. A comparison with this model indicates a rather strong electron-phonon coupling factor of order unity.

The theory of electronic topological transitions

Abstract In the present review an attemp to survey all the theory of electronic topological transitions from the very first paper until the recent achievements is made. The presentation is started from the description of possible topological siguularities in electronic spectra of metals. Then the singularities of thermodynamical and transport properties of a metal in the vicinity of ETT, their fluctuations are discussed in details. In purpose to attract the wide reader audience, the transport phenomena including the behaviour of conductivity, thermoelectric power and sound absorption coefficient in the vicinity ETT are discussed in the framework of simple Boltzmann equation approach. The last chapter of the review are devoted to the discussion of the modern problems of ETT theory, application of it to the study of properties of 2D systems, quantum oscillations in magnetic field, generalized topological transitoins. The review is supplied by the extensive and complete bibliography including around 300 references.

Aharonov-Bohm effect and broken valley degeneracy in graphene rings

We analyze theoretically the electronic properties of Aharonov-Bohm rings made of graphene. We show that the combined effect of the ring confinement and applied magnetic flux offers a controllable way to lift the orbital degeneracy originating from the two valleys, even in the absence of intervalley scattering. The phenomenon has observable consequences on the persistent current circulating around the closed graphene ring, as well as on the ring conductance. We explicitly confirm this prediction analytically for a circular ring with a smooth boundary modeled by a space-dependent mass term in the Dirac equation. This model describes rings with zero or weak intervalley scattering so that the valley isospin is a good quantum number. The tunable breaking of the valley degeneracy by the flux allows for the controlled manipulation of valley isospins. We compare our analytical model to another type of ring with strong intervalley scattering. For the latter case, we study a ring of hexagonal form with lattice-terminated zigzag edges numerically. We find for the hexagonal ring that the orbital degeneracy can still be controlled via the flux, similar to the ring with the mass confinement.

Transport in disordered graphene nanoribbons

We study electronic transport in graphene nanoribbons with rough edges. We first consider a model of weak disorder that corresponds to an armchair ribbon whose width randomly changes by a single unit cell size. We find that in this case, the low-temperature conductivity is governed by an effective one-dimensional hopping between segments of distinct band structure. We then provide numerical evidence and qualitative arguments that similar behavior also occurs in the limit of strong uncorrelated boundary disorder.

Rectification of fluctuations in an underdamped ratchet

We investigate analytically the motion of underdamped particles subject to a deterministic periodic potential and a periodic temperature. Despite the fact that an underdamped particle experiences the temperature modulation many times in its escape out of a well and in its motion along the potential, a net directed current linear in the friction constant is found. If both the potential and the temperature modulation are sinusoidal with a phase lag

TRANSITION FROM SUB-POISSONIAN TO SUPER-POISSONIAN SHOT NOISE IN RESONANT QUANTUM WELLS

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INTERACTION CONSTANTS AND DYNAMIC CONDUCTANCE OF A GATED WIRE

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