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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.


Pulsed-gate spectroscopy of ESs.(a) Sketch of the pulse scheme employed in the measurements presented in this figure (duty-cycle 50%). Low and high pulse-level are labelled A and B, respectively. (b) Current through the dot while applying a 100-kHz pulse. Different lines correspond to VPP being varied from 0 to 1.4 V in steps of 50 mV (lines offset by 0.05 pA for clarity). Here and in the following VSD=−1.5 mV. Increasing the amplitude of the pulse, the Coulomb peak splits in two resonances that shift linearly with VPP and whose height is approximately half the one of the original peak (see inset). (c,d) Colour-scale version of the data shown in b. In d the pulse frequency is 800 kHz. (e) Upper panel: same measurement as (b–d), at a higher frequency of 18 MHz. Together with the GS splitting, a number of additional resonances can be seen, corresponding to transient currents through ESs. The level spacing extracted from this measurement coincides with the one given by DC finite-bias measurements (lower panel, same data as in Fig. 2e). The dashed lines are guides to the eye. (f) Schematic of transport via GS, ES and, on the left, of a possible initialization stage. (g) Measurement similar to the ones shown in b, but for a different Coulomb resonance. Here the pulse frequency is 8 MHz, VSD=−1 mV, and VPP is varied from 0 to 2 V in steps of 25 mV (traces offset by 0.02 pA). (h) Same data set as in g and comparison with the corresponding DC measurement, showing excellent agreement between the ESs level spacing extracted from pulsed-gate and finite-bias spectroscopy.
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f3: Pulsed-gate spectroscopy of ESs.(a) Sketch of the pulse scheme employed in the measurements presented in this figure (duty-cycle 50%). Low and high pulse-level are labelled A and B, respectively. (b) Current through the dot while applying a 100-kHz pulse. Different lines correspond to VPP being varied from 0 to 1.4 V in steps of 50 mV (lines offset by 0.05 pA for clarity). Here and in the following VSD=−1.5 mV. Increasing the amplitude of the pulse, the Coulomb peak splits in two resonances that shift linearly with VPP and whose height is approximately half the one of the original peak (see inset). (c,d) Colour-scale version of the data shown in b. In d the pulse frequency is 800 kHz. (e) Upper panel: same measurement as (b–d), at a higher frequency of 18 MHz. Together with the GS splitting, a number of additional resonances can be seen, corresponding to transient currents through ESs. The level spacing extracted from this measurement coincides with the one given by DC finite-bias measurements (lower panel, same data as in Fig. 2e). The dashed lines are guides to the eye. (f) Schematic of transport via GS, ES and, on the left, of a possible initialization stage. (g) Measurement similar to the ones shown in b, but for a different Coulomb resonance. Here the pulse frequency is 8 MHz, VSD=−1 mV, and VPP is varied from 0 to 2 V in steps of 25 mV (traces offset by 0.02 pA). (h) Same data set as in g and comparison with the corresponding DC measurement, showing excellent agreement between the ESs level spacing extracted from pulsed-gate and finite-bias spectroscopy.

Mentions: To investigate the relaxation dynamics of ESs in the graphene QD, we employ a pulsed-excitation scheme similar to the one introduced by Fujisawa et al.252629. The basic idea is to probe transient phenomena in a QD by measuring the averaged DC-current flowing through the system in the presence of a small (fixed) bias voltage VSD and of a square voltage-pulse applied to one of the gates (see Fig. 3a). The crucial requirement is that the rise time of the pulse has to be much shorter than the inverse of the tunnel rates, so that the occupation of the QD cannot follow adiabatically the change of the potential and, when the pulse-level switches from high to low (or vice versa), the system is brought in a state of non-equilibrium. If the frequency of the pulse is low (100 kHz in Fig. 3b), the square-wave modulation of the gate voltage results simply in the splitting of the Coulomb resonance into two peaks30. These peaks stem from the QD ground state (GS) entering the bias-window at two different values of VCG, one for the lower pulse-level (A), and one for the upper one (B). At larger frequencies (800 kHz in Fig. 3d), together with the splitting there is an additional broadening of the peaks. The situation changes dramatically at higher frequencies (from a few to tens of MHz), where a number of additional peaks appear, due to transient transport through QD ESs (see Fig. 3e). Each of these additional resonances corresponds to a situation in which the QD levels are pushed well outside the bias-window in the first half of the pulse, and then brought into a position where transport can occur only through the ESs in the second one, see Fig. 3f. No current can flow in any of these two configurations in the stationary state. However, in the second half of the pulse electrons can tunnel from one lead to the other via the ES, as long as the GS remains unoccupied (see Supplementary Fig. S2). Once the GS gets filled, either because of tunnelling from the leads or relaxation from the ES, transport is blocked. The blockade is released by returning the pulse-level to its initial value. In these conditions, a square-wave modulation of the gate voltage results in a train of short current pulses, which can be resolved in our DC-current measurements only if the frequency of the pulse is higher than the characteristic rate γ of the blocking processes. The lowest frequency at which signatures of transport through ESs emerge provides, therefore, an upper bound for γ.


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)

Pulsed-gate spectroscopy of ESs.(a) Sketch of the pulse scheme employed in the measurements presented in this figure (duty-cycle 50%). Low and high pulse-level are labelled A and B, respectively. (b) Current through the dot while applying a 100-kHz pulse. Different lines correspond to VPP being varied from 0 to 1.4 V in steps of 50 mV (lines offset by 0.05 pA for clarity). Here and in the following VSD=−1.5 mV. Increasing the amplitude of the pulse, the Coulomb peak splits in two resonances that shift linearly with VPP and whose height is approximately half the one of the original peak (see inset). (c,d) Colour-scale version of the data shown in b. In d the pulse frequency is 800 kHz. (e) Upper panel: same measurement as (b–d), at a higher frequency of 18 MHz. Together with the GS splitting, a number of additional resonances can be seen, corresponding to transient currents through ESs. The level spacing extracted from this measurement coincides with the one given by DC finite-bias measurements (lower panel, same data as in Fig. 2e). The dashed lines are guides to the eye. (f) Schematic of transport via GS, ES and, on the left, of a possible initialization stage. (g) Measurement similar to the ones shown in b, but for a different Coulomb resonance. Here the pulse frequency is 8 MHz, VSD=−1 mV, and VPP is varied from 0 to 2 V in steps of 25 mV (traces offset by 0.02 pA). (h) Same data set as in g and comparison with the corresponding DC measurement, showing excellent agreement between the ESs level spacing extracted from pulsed-gate and finite-bias spectroscopy.
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Related In: Results  -  Collection

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f3: Pulsed-gate spectroscopy of ESs.(a) Sketch of the pulse scheme employed in the measurements presented in this figure (duty-cycle 50%). Low and high pulse-level are labelled A and B, respectively. (b) Current through the dot while applying a 100-kHz pulse. Different lines correspond to VPP being varied from 0 to 1.4 V in steps of 50 mV (lines offset by 0.05 pA for clarity). Here and in the following VSD=−1.5 mV. Increasing the amplitude of the pulse, the Coulomb peak splits in two resonances that shift linearly with VPP and whose height is approximately half the one of the original peak (see inset). (c,d) Colour-scale version of the data shown in b. In d the pulse frequency is 800 kHz. (e) Upper panel: same measurement as (b–d), at a higher frequency of 18 MHz. Together with the GS splitting, a number of additional resonances can be seen, corresponding to transient currents through ESs. The level spacing extracted from this measurement coincides with the one given by DC finite-bias measurements (lower panel, same data as in Fig. 2e). The dashed lines are guides to the eye. (f) Schematic of transport via GS, ES and, on the left, of a possible initialization stage. (g) Measurement similar to the ones shown in b, but for a different Coulomb resonance. Here the pulse frequency is 8 MHz, VSD=−1 mV, and VPP is varied from 0 to 2 V in steps of 25 mV (traces offset by 0.02 pA). (h) Same data set as in g and comparison with the corresponding DC measurement, showing excellent agreement between the ESs level spacing extracted from pulsed-gate and finite-bias spectroscopy.
Mentions: To investigate the relaxation dynamics of ESs in the graphene QD, we employ a pulsed-excitation scheme similar to the one introduced by Fujisawa et al.252629. The basic idea is to probe transient phenomena in a QD by measuring the averaged DC-current flowing through the system in the presence of a small (fixed) bias voltage VSD and of a square voltage-pulse applied to one of the gates (see Fig. 3a). The crucial requirement is that the rise time of the pulse has to be much shorter than the inverse of the tunnel rates, so that the occupation of the QD cannot follow adiabatically the change of the potential and, when the pulse-level switches from high to low (or vice versa), the system is brought in a state of non-equilibrium. If the frequency of the pulse is low (100 kHz in Fig. 3b), the square-wave modulation of the gate voltage results simply in the splitting of the Coulomb resonance into two peaks30. These peaks stem from the QD ground state (GS) entering the bias-window at two different values of VCG, one for the lower pulse-level (A), and one for the upper one (B). At larger frequencies (800 kHz in Fig. 3d), together with the splitting there is an additional broadening of the peaks. The situation changes dramatically at higher frequencies (from a few to tens of MHz), where a number of additional peaks appear, due to transient transport through QD ESs (see Fig. 3e). Each of these additional resonances corresponds to a situation in which the QD levels are pushed well outside the bias-window in the first half of the pulse, and then brought into a position where transport can occur only through the ESs in the second one, see Fig. 3f. No current can flow in any of these two configurations in the stationary state. However, in the second half of the pulse electrons can tunnel from one lead to the other via the ES, as long as the GS remains unoccupied (see Supplementary Fig. S2). Once the GS gets filled, either because of tunnelling from the leads or relaxation from the ES, transport is blocked. The blockade is released by returning the pulse-level to its initial value. In these conditions, a square-wave modulation of the gate voltage results in a train of short current pulses, which can be resolved in our DC-current measurements only if the frequency of the pulse is higher than the characteristic rate γ of the blocking processes. The lowest frequency at which signatures of transport through ESs emerge provides, therefore, an upper bound for γ.

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.