Quantum transport in carbon nanotubes

Abstract

Carbon nanotubes are a versatile material in which many aspects of condensed matter physics come together. Recent discoveries have uncovered new phenomena that completely change our understanding of transport in these devices, especially the role of the spin and valley degrees of freedom. This review describes the modern understanding of transport through nanotube devices. Unlike in conventional semiconductors, electrons in nanotubes have two angular momentum quantum numbers, arising from spin and valley freedom. The interplay between the two is the focus of this review. The energy levels associated with each degree of freedom, and the spin-orbit coupling between them, are explained, together with their consequences for transport measurements through nanotube quantum dots. In double quantum dots, the combination of quantum numbers modifies the selection rules of Pauli blockade. This can be exploited to read out spin and valley qubits and to measure the decay of these states through coupling to nuclear spins and phonons. A second unique property of carbon nanotubes is that the combination of valley freedom and electron-electron interactions in one dimension strongly modifies their transport behavior. Interaction between electrons inside and outside a quantum dot is manifested in SU(4) Kondo behavior and level renormalization. Interaction within a dot leads to Wigner molecules and more complex correlated states. This review takes an experimental perspective informed by recent advances in theory. As well as the well-understood overall picture, open questions for the field are also clearly stated. These advances position nanotubes as a leading system for the study of spin and valley physics in one dimension where electronic disorder and hyperfine interaction can both be reduced to a low level.

SU(2)–SU(4) Kondo Crossover and Emergent Electric Polarization in a Triangular Triple Quantum Dot

“…6,29 In fact, the possibility of the SU(4) Kondo effect is indicated by the observation of both spin SU(2) and valley SU(2) Kondo effects in a magnetic field. Note that valley mixing normally lowers the SU(4) symmetry and hinders a direct detection of the SU(4) Kondo effect.…”

“…In reality, Γ E+ ≃ Γ E− ≫ Γ A is a plausible condition, by analogy with the valley degeneracy of a carbon nanotube relevant to a metallic contact. 29 The SU(2)-SU(4) crossover in the Kondo effect can be demonstrated by introducing a deviation from the C 3 symmetry of the TTQD system, which can be characterized by a finite value of |Γ E+ − Γ E− |.…”

Lifting the Franck-Condon blockade in driven quantum dots

“…Transport through CNT quantum dots has extensively been studied theoretically and experimentally. 13,14 Nanoelectromechanics is a growing field of research with various experiments investigating the interplay between the mechanical and the quantized electronic degree of freedom in suspended CNTs. 12,[15][16][17] A general feature of interacting systems composed of electrons and quantized mechanical vibrations ("vibrons") is the suppression of conductance, in certain parameter regimes, for strong coupling between the two degrees of freedom.…”

Antisymmetric Spin–Orbit Coupling Effect on Kondo-Induced Electric Polarization in a Triangular Triple Quantum Dot

“…The Kondo physics has been extensively studied in a wide range of fields from d-or f -electron impurities embedded in bulk materials 2, 3) to artificial atomic systems with metallic lead contacts such as quantum dot (QD) or magnetic molecular devices. [4][5][6][7][8][9] In particular, much attention has been paid to rich Kondo phenomena associated with coupled spin clusters or fabricated quantum devices, for instance, the transport properties between leads through a double 4,6,[10][11][12][13][14][15] or triple QD. [16][17][18][19][20] As a different context, several theoretical studies have recently investigated the Kondo effect for a single impurity in two-dimensional electron gas with the Rashba spin-orbit (SO) coupling.…”