Quantum pump effect in one-dimensional systems of Dirac fermions

Arrachea, Liliana; Naón, Carlos M.; Salvay, Mariano J.

doi:10.1103/physrevb.76.165401

Cited by 19 publications

(19 citation statements)

References 61 publications

(50 reference statements)

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“…Eqs. (27)(28) imply that for the pure pumping case with ω 0 = 0, I . Thus the backscattering correction to the conductance given by −I bs,dc /V bias = −qI bs,dc /ω 0 is proportional to U bias .…”

Section: Single Impuritymentioning

confidence: 99%

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Charge transport in a Tomonaga-Luttinger liquid: Effects of pumping and bias

Agarwal

Sen

2007

Phys. Rev. B

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We study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, point-like impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K − 1 for spinless electrons, where K is the interaction parameter. For K < 1/2, the current grows large for special values of the bias. For non-interacting electrons with K = 1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons.

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Section: Single Impuritymentioning

confidence: 99%

“…(27)(28) and (29)(30) all reverse sign if we change ω 0 → −ω 0 and x p → −x p for all p. This is a natural consequence of parity reversal, i.e., interchange of left and right.…”

Section: Several Impuritiesmentioning

confidence: 99%

Charge transport in a Tomonaga-Luttinger liquid: Effects of pumping and bias

Agarwal

Sen

2007

Phys. Rev. B

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“…Now let us go back to equation (14). Performing the integral and defining the dimensionless frequency ω a = Ω|a|/v associated with the separation between barriers, I bs can be expressed as was predicted for a two-barrier quantum pump in a linear setup [29], in an annular setup [24,25] and also obtained within Floquet scattering matrix formalism [28]. The proportionality I bs ∝ sin[ 2k F a ] exclude the possibility of pure pumping with a single impurity (a = 0) in a quantum wire.…”

Section: The Additional Termmentioning

confidence: 99%

“…In recent years there have been experimental observations of the quantum pumping effect, including the periodic deformation of the walls of quantum dots [19][20][21][22] and the induction of currents by applying surface acoustic waves in carbon nanotubes [23]. The pumping current was studied in one-dimensional systems of non-interacting electrons with different geometries like wires or rings [24][25][26][27][28], quantum dots [29][30][31] and in a quasi one-dimensional graphene ribbon [32,33]. In the context of Luttinger liquids, the pumping current was computed for infinite length at zero and finite temperature [34,35], where a power (exponential)-law dependence with the frequency, the spatial separation between the impurities and the temperature was found in different energy regimes with exponents which are functions of the electron-electron interactions.…”

Section: Introductionmentioning

confidence: 99%

Pumping current of a Luttinger liquid with finite length

2012

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We study transport properties in a Tomonaga-Luttinger liquid in the presence of two timedependent point like weak impurities, taking into account finite-length effects. By employing analytical methods and performing a perturbation theory, we compute the backscattering pumping current (I bs ) in different regimes which can be established in relation to the oscillatory frequency of the impurities and to the frequency related to the length and the renormalized velocity (by the electron-electron interactions) of the charge density modes. We investigate the role played by the spatial position of the impurity potentials. We also show how the previous infinite length results for I bs are modified by the finite size of the system.

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“…We take b = 0.1, and use Eqs. (28)(29) to compute the averaged current as a function of φ 0 = 2πτ /T . In Fig.…”

Section: Charge Pumping On a Finite Ringmentioning

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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Quantum pump effect in one-dimensional systems of Dirac fermions

Cited by 19 publications

References 61 publications

Charge transport in a Tomonaga-Luttinger liquid: Effects of pumping and bias

Charge transport in a Tomonaga-Luttinger liquid: Effects of pumping and bias

Pumping current of a Luttinger liquid with finite length

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

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