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Probing relaxation times in graphene quantum dots.

Volk C, Neumann C, Kazarski S, Fringes S, Engels S, Haupt F, Müller A, Stampfer C - Nat Commun (2013)

Bottom Line: This is mainly due to challenges in device fabrication, in particular concerning the control of carrier confinement and the tunability of the tunnelling barriers, both crucial to experimentally investigate decoherence times.This is achieved by an advanced device design that allows to individually tune the tunnelling barriers down to the low megahertz regime, while monitoring their asymmetry.Measuring transient currents through electronic excited states, we estimate a lower bound for charge relaxation times on the order of 60-100 ns.

View Article: PubMed Central - PubMed

Affiliation: JARA-FIT and II Institute of Physics B, RWTH Aachen, 52074 Aachen, Germany.

ABSTRACT
Graphene quantum dots are attractive candidates for solid-state quantum bits. In fact, the predicted weak spin-orbit and hyperfine interaction promise spin qubits with long coherence times. Graphene quantum dots have been extensively investigated with respect to their excitation spectrum, spin-filling sequence and electron-hole crossover. However, their relaxation dynamics remain largely unexplored. This is mainly due to challenges in device fabrication, in particular concerning the control of carrier confinement and the tunability of the tunnelling barriers, both crucial to experimentally investigate decoherence times. Here we report pulsed-gate transient current spectroscopy and relaxation time measurements of excited states in graphene quantum dots. This is achieved by an advanced device design that allows to individually tune the tunnelling barriers down to the low megahertz regime, while monitoring their asymmetry. Measuring transient currents through electronic excited states, we estimate a lower bound for charge relaxation times on the order of 60-100 ns.

No MeSH data available.


Finite-bias ES spectroscopy and charge sensing.(a) Current through the QD as function of VCG and the source-drain bias VSD in a regime of weak tunnel coupling to the leads; the dashed lines are guides to the eye indicating the edges of the Coulomb diamonds. (b) Line-cut at constant VCG=4.86 V, marked by a line in (a): the stepwise increase of the current is a signature of the discrete QD spectrum; the two well-defined plateaus correspond to the GS and the first ES entering the bias-window. (c) Differential conductance of the QD, dIQD/dVSD. Resonances parallel to both edges of the Coulomb diamonds, indicating transport through ESs, can be clearly seen. (d) Derivative of the charge-detector current ICD with respect to VCG. Regions of high dICD/dVCG correspond to the onset of the transitions with the largest rate, thus providing information on the asymmetry of the tunnelling barriers. Note that this effect can be bias dependent (for example, the diamond centred on VCG≈4.45 V is more strongly coupled to the right lead for VSD>0 and to the left one for VSD<0) and it can be drastically influenced by the onset of transitions through ESs, as indicated by the appearance of kinks as those marked by the arrow. (e,f) Simultaneous measurements of the differential conductance of the dot dIQD/dVSD (e) and of the transconductance of the charge detector dICD/dVSD (f) in a regime of interest for pulsed-gate experiments.
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f2: Finite-bias ES spectroscopy and charge sensing.(a) Current through the QD as function of VCG and the source-drain bias VSD in a regime of weak tunnel coupling to the leads; the dashed lines are guides to the eye indicating the edges of the Coulomb diamonds. (b) Line-cut at constant VCG=4.86 V, marked by a line in (a): the stepwise increase of the current is a signature of the discrete QD spectrum; the two well-defined plateaus correspond to the GS and the first ES entering the bias-window. (c) Differential conductance of the QD, dIQD/dVSD. Resonances parallel to both edges of the Coulomb diamonds, indicating transport through ESs, can be clearly seen. (d) Derivative of the charge-detector current ICD with respect to VCG. Regions of high dICD/dVCG correspond to the onset of the transitions with the largest rate, thus providing information on the asymmetry of the tunnelling barriers. Note that this effect can be bias dependent (for example, the diamond centred on VCG≈4.45 V is more strongly coupled to the right lead for VSD>0 and to the left one for VSD<0) and it can be drastically influenced by the onset of transitions through ESs, as indicated by the appearance of kinks as those marked by the arrow. (e,f) Simultaneous measurements of the differential conductance of the dot dIQD/dVSD (e) and of the transconductance of the charge detector dICD/dVSD (f) in a regime of interest for pulsed-gate experiments.

Mentions: The addition energy of the dot and its ES spectrum are then probed by finite-bias spectroscopy. Figure 2a show the current and the differential conductance through the QD. These Coulomb diamond measurements give an estimate of the addition energy of the QD, Eadd≈10.5 meV. In a simple disc-capacitor model, this corresponds to a QD diameter of 120 nm, in good agreement with the geometric size of our device. Clear signatures of transport through well-defined ESs can be already observed in the current (for example, see Fig. 2b). They become even more evident in the differential conductance (Fig. 2c), from which we extract a level spacing of about Δ=1.5–2.5 meV. This is in agreement with the electronic single-particle level spacing given by  meV, where N, the number of carriers on the dot, is assumed to be on the order of 10–20 (ref. 20).


Probing relaxation times in graphene quantum dots.

Volk C, Neumann C, Kazarski S, Fringes S, Engels S, Haupt F, Müller A, Stampfer C - Nat Commun (2013)

Finite-bias ES spectroscopy and charge sensing.(a) Current through the QD as function of VCG and the source-drain bias VSD in a regime of weak tunnel coupling to the leads; the dashed lines are guides to the eye indicating the edges of the Coulomb diamonds. (b) Line-cut at constant VCG=4.86 V, marked by a line in (a): the stepwise increase of the current is a signature of the discrete QD spectrum; the two well-defined plateaus correspond to the GS and the first ES entering the bias-window. (c) Differential conductance of the QD, dIQD/dVSD. Resonances parallel to both edges of the Coulomb diamonds, indicating transport through ESs, can be clearly seen. (d) Derivative of the charge-detector current ICD with respect to VCG. Regions of high dICD/dVCG correspond to the onset of the transitions with the largest rate, thus providing information on the asymmetry of the tunnelling barriers. Note that this effect can be bias dependent (for example, the diamond centred on VCG≈4.45 V is more strongly coupled to the right lead for VSD>0 and to the left one for VSD<0) and it can be drastically influenced by the onset of transitions through ESs, as indicated by the appearance of kinks as those marked by the arrow. (e,f) Simultaneous measurements of the differential conductance of the dot dIQD/dVSD (e) and of the transconductance of the charge detector dICD/dVSD (f) in a regime of interest for pulsed-gate experiments.
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Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC3644082&req=5

f2: Finite-bias ES spectroscopy and charge sensing.(a) Current through the QD as function of VCG and the source-drain bias VSD in a regime of weak tunnel coupling to the leads; the dashed lines are guides to the eye indicating the edges of the Coulomb diamonds. (b) Line-cut at constant VCG=4.86 V, marked by a line in (a): the stepwise increase of the current is a signature of the discrete QD spectrum; the two well-defined plateaus correspond to the GS and the first ES entering the bias-window. (c) Differential conductance of the QD, dIQD/dVSD. Resonances parallel to both edges of the Coulomb diamonds, indicating transport through ESs, can be clearly seen. (d) Derivative of the charge-detector current ICD with respect to VCG. Regions of high dICD/dVCG correspond to the onset of the transitions with the largest rate, thus providing information on the asymmetry of the tunnelling barriers. Note that this effect can be bias dependent (for example, the diamond centred on VCG≈4.45 V is more strongly coupled to the right lead for VSD>0 and to the left one for VSD<0) and it can be drastically influenced by the onset of transitions through ESs, as indicated by the appearance of kinks as those marked by the arrow. (e,f) Simultaneous measurements of the differential conductance of the dot dIQD/dVSD (e) and of the transconductance of the charge detector dICD/dVSD (f) in a regime of interest for pulsed-gate experiments.
Mentions: The addition energy of the dot and its ES spectrum are then probed by finite-bias spectroscopy. Figure 2a show the current and the differential conductance through the QD. These Coulomb diamond measurements give an estimate of the addition energy of the QD, Eadd≈10.5 meV. In a simple disc-capacitor model, this corresponds to a QD diameter of 120 nm, in good agreement with the geometric size of our device. Clear signatures of transport through well-defined ESs can be already observed in the current (for example, see Fig. 2b). They become even more evident in the differential conductance (Fig. 2c), from which we extract a level spacing of about Δ=1.5–2.5 meV. This is in agreement with the electronic single-particle level spacing given by  meV, where N, the number of carriers on the dot, is assumed to be on the order of 10–20 (ref. 20).

Bottom Line: This is mainly due to challenges in device fabrication, in particular concerning the control of carrier confinement and the tunability of the tunnelling barriers, both crucial to experimentally investigate decoherence times.This is achieved by an advanced device design that allows to individually tune the tunnelling barriers down to the low megahertz regime, while monitoring their asymmetry.Measuring transient currents through electronic excited states, we estimate a lower bound for charge relaxation times on the order of 60-100 ns.

View Article: PubMed Central - PubMed

Affiliation: JARA-FIT and II Institute of Physics B, RWTH Aachen, 52074 Aachen, Germany.

ABSTRACT
Graphene quantum dots are attractive candidates for solid-state quantum bits. In fact, the predicted weak spin-orbit and hyperfine interaction promise spin qubits with long coherence times. Graphene quantum dots have been extensively investigated with respect to their excitation spectrum, spin-filling sequence and electron-hole crossover. However, their relaxation dynamics remain largely unexplored. This is mainly due to challenges in device fabrication, in particular concerning the control of carrier confinement and the tunability of the tunnelling barriers, both crucial to experimentally investigate decoherence times. Here we report pulsed-gate transient current spectroscopy and relaxation time measurements of excited states in graphene quantum dots. This is achieved by an advanced device design that allows to individually tune the tunnelling barriers down to the low megahertz regime, while monitoring their asymmetry. Measuring transient currents through electronic excited states, we estimate a lower bound for charge relaxation times on the order of 60-100 ns.

No MeSH data available.