Quantized Adiabatic Charge Transport in a Carbon Nanotube

Talyanskii, V. I.; Novikov, Dmitry S.; Simons, Benjamin D.; Levitov, L. S.

doi:10.1103/physrevlett.87.276802

Cited by 58 publications

(84 citation statements)

References 29 publications

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“…The phenomenon of charge pumping and rectification by time-dependent potentials applied to certain points in a system has been extensively studied both theoretically and experimentally [32,33,34,35,36,37,38]. The idea of charge pumping is that periodically oscillating potentials can transfer a net charge per cycle between two leads which are at the same chemical potential.…”

Section: Introductionmentioning

confidence: 99%

Nonadiabatic charge pumping in a one-dimensional system of noninteracting electrons by an oscillating potential

Agarwal

Sen

2007

Phys. Rev. B

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Using a tight-binding model, we study one-parameter charge pumping in a one-dimensional system of non-interacting electrons. An oscillating potential is applied at one site while a static potential is applied in a different region. Using Floquet scattering theory, we calculate the current up to second order in the oscillation amplitude and exactly in the oscillation frequency. For low frequency, the charge pumped per cycle is proportional to the frequency and therefore vanishes in the adiabatic limit. If the static potential has a bound state, we find that such a state has a significant effect on the pumped charge if the oscillating potential can excite the bound state into the continuum states or vice versa. Finally, we use the equation of motion for the density matrix to numerically compute the pumped current for any value of the amplitude and frequency. The numerical results confirm the unusual effect of a bound state.

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Section: Introductionmentioning

confidence: 99%

Nonadiabatic charge pumping in a one-dimensional system of noninteracting electrons by an oscillating potential

Agarwal

Sen

2007

Phys. Rev. B

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“…The idea that oscillating potentials applied to certain points in a one-dimensional system can pump a net charge between two reservoirs at the same chemical potential has been studied extensively for many years, both theoretically and experimentally [43][44][45][46][47][48][49]. For the case of non-interacting electrons, theoretical studies of this phenomenon have used adiabatic scattering theory [9][10][11][12][13][14][15][16][17], Floquet scattering theory [21][22][23], the nonequilibrium Green function formalism [24][25][26][27], and the equation of motion approach [36,37].…”

Section: Introductionmentioning

confidence: 99%

Nonadiabatic charge pumping by oscillating potentials in one dimension: Results for infinite system and finite ring

Soori

Sen

2010

Phys. Rev. B

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We study charge pumping when a combination of static potentials and potentials oscillating with a time period T is applied in a one-dimensional system of non-interacting electrons. We consider both an infinite system using the Dirac equation in the continuum approximation, and a periodic ring with a finite number of sites using the tight-binding model. The infinite system is taken to be coupled to reservoirs on the two sides which are at the same chemical potential and temperature. We consider a model in which oscillating potentials help the electrons to access a transmission resonance produced by the static potentials, and show that non-adiabatic pumping violates the simple sin φ rule which is obeyed by adiabatic two-site pumping. For the ring, we do not introduce any reservoirs, and we present a method for calculating the current averaged over an infinite time using the time evolution operator U (T ) assuming a purely Hamiltonian evolution. We analytically show that the averaged current is zero if the Hamiltonian is real and time reversal invariant. Numerical studies indicate another interesting result, namely, that the integrated current is zero for any time-dependence of the potential if it is applied to only one site. Finally we study the effects of pumping at two sites on a ring at resonant and non-resonant frequencies, and show that the pumped current has different dependences on the pumping amplitude in the two cases.

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“…To calculate excitation gaps we generalize the Pokrovsky-Talapov theory [6] for the case of the four coupled fermion modes. In the absence of interactions, Bragg diffraction on the potential opens minigaps at integer density (1), |m| = 1, 2, ... [7]. Interactions profoundly change the spectrum, yielding a devil's staircase of incompressible states at rational m = p/q.…”

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confidence: 99%

“…If detected, e.g. in a Thouless pump setup [7], corresponding minigaps would provide a direct probe of interactions, with a possibility to map the devil's staircase by pumping at fractions of the base frequency.One-dimensional interacting electrons are conventionally described by the Tomonaga -Luttinger liquid [2]. This hydrodynamic approach is valid in a small momentum shell near the Fermi points, with excitations extended over the whole system.…”

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confidence: 99%

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Devil’s Staircase of Incompressible Electron States in a Nanotube

Novikov

2005

Phys. Rev. Lett.

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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. Here we suggest that an external periodic potential can be a probe of both crystallization and Luttinger correlations. We show that incompressible electron states arise when the electron number densityρ (relative to halffilling) is commensurate with the potential period λ ext :In Eq. (1), m is the number of the NT electrons of each of the four polarizations [5] per period. To calculate excitation gaps we generalize the Pokrovsky-Talapov theory [6] for the case of the four coupled fermion modes. In the absence of interactions, Bragg diffraction on the potential opens minigaps at integer density (1), |m| = 1, 2, ... [7]. Interactions profoundly change the spectrum, yielding a devil's staircase of incompressible states at rational m = p/q. In such a state, the NT electron system is locked by the potential into a qλ ext -periodic structure. If detected, e.g. in a Thouless pump setup [7], corresponding minigaps would provide a direct probe of interactions, with a possibility to map the devil's staircase by pumping at fractions of the base frequency.One-dimensional interacting electrons are conventionally described by the Tomonaga -Luttinger liquid [2]. This hydrodynamic approach is valid in a small momentum shell near the Fermi points, with excitations extended over the whole system. Adequate description of crystallization and commensurability requires including the curvature of the electronic dispersion that becomes important at low density. The curvature can yield crystallization or commensuration by coupling charge and spin modes and by introducing a length scale into an otherwise scale-invariant Gaussian theory. In this work we treat both electron interactions and the curvature of the dispersion non-perturbatively by making use of the relativistic Dirac spectrum of a half-filled nanotube. Curvature is controlled by the Dirac gap and is bosonized exactly by virtue of the massive Thirring -sine-Gordon duality. [8,9] This enables us to study incompressible states both in the limit of a narrow-gap Luttinger liquid and in that of the locked Wigner crystal.Our course of action is to introduce the bosonized description for the NT electrons, develop the phase soliton method and find excitation gaps from the renormalized sine-Gordon action, draw the phase diagram in the semiclassical limit, and comment on the experimental means to detect incompressible states.The model.-Nanotube electrons in the forward scattering approximation [10] are described by the four flav...

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Quantized Adiabatic Charge Transport in a Carbon Nanotube

Cited by 58 publications

References 29 publications

Nonadiabatic charge pumping in a one-dimensional system of noninteracting electrons by an oscillating potential

Nonadiabatic charge pumping in a one-dimensional system of noninteracting electrons by an oscillating potential

Nonadiabatic charge pumping by oscillating potentials in one dimension: Results for infinite system and finite ring

Devil’s Staircase of Incompressible Electron States in a Nanotube

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