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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.


Related in: MedlinePlus

Transient current through ESs.(a) Pulse scheme used to study transient currents through ESs: time TB is fixed, while time TA is varied. (b) Current through the QD as a function of VCG and TA for VSD=−1 mV, VPP=0.9 V, TB=30 ns. All lines are bent due to a parasitic effect of the bias-tee adding a duty-cycle dependent DC-offset to VCG. Dashed lines indicate the peaks due to transport via GS (blue) and ES (red), further investigated in d. (c) Schematic of the transitions occurring during TA for the central peak in b. /N,g› (/N,e›) indicates the ground (excited) state of the dot with N excess electrons. The transition /N,g›→/N+1,g› is not energetically allowed in the range of values used for VSD and VCG during TA, and so /N,g› is an ‘absorbing’ state. At the beginning of each cycle, the dot is initialized in the state with N+1 electrons during TB (not shown). (d) Average number of electrons transmitted per cycle through GS (blue circles) and ES (red circles), as a function of the pulse length TA. Data are extracted from the peaks shown in b, solid lines represent linear and exponential fit to the experimental data (1/γ=78 ns, nsat=0.313).
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f4: Transient current through ESs.(a) Pulse scheme used to study transient currents through ESs: time TB is fixed, while time TA is varied. (b) Current through the QD as a function of VCG and TA for VSD=−1 mV, VPP=0.9 V, TB=30 ns. All lines are bent due to a parasitic effect of the bias-tee adding a duty-cycle dependent DC-offset to VCG. Dashed lines indicate the peaks due to transport via GS (blue) and ES (red), further investigated in d. (c) Schematic of the transitions occurring during TA for the central peak in b. /N,g› (/N,e›) indicates the ground (excited) state of the dot with N excess electrons. The transition /N,g›→/N+1,g› is not energetically allowed in the range of values used for VSD and VCG during TA, and so /N,g› is an ‘absorbing’ state. At the beginning of each cycle, the dot is initialized in the state with N+1 electrons during TB (not shown). (d) Average number of electrons transmitted per cycle through GS (blue circles) and ES (red circles), as a function of the pulse length TA. Data are extracted from the peaks shown in b, solid lines represent linear and exponential fit to the experimental data (1/γ=78 ns, nsat=0.313).

Mentions: A more accurate estimate of the relaxation time of the ESs can be obtained with a different pulse scheme (see Fig. 4a), where TA is varied while keeping TB and VPP fixed252631. Such a measurement is shown in Fig. 4b for the same Coulomb resonance investigated in Fig. 3b–e. The two outermost peaks correspond to transport via the dot GS when this is in resonance with the bias-window during TA (right peak) and TB (left peak). The inner peak results from transport via an ES, as indicated in the scheme sketched in Fig. 4c. For each of these peaks, we estimate the average number of electrons tunnelling through the device per cycle ‹n›=I (TA+TB)/e. Figure 4d shows the number of electrons transmitted via the GS (blue) and via the ES (red) as a function of the pulse length TA. While the first one increases linearly with TA, the second tends to saturate, indicating a transient effect. Fitting this data set with n(TA)=nsat [1-exp(−γ TA)], where nsat is the saturation value for long TA (ref. 25), we extract the characteristic rate of the blocking processes γ=12.8 MHz. As both tunnelling and relaxation lead to the occupation of the GS, γ is approximately given by γ~Γ+1/τ, where τ is the intrinsic relaxation time of the ES and Γ the characteristic tunnelling rate. This in turn gives a lower bound τ>78 ns for the lifetime of the QD ES. By studying further electronic ESs with energies in the range of 1.7–2.5 meV (see Supplementary Fig. S3–S5), we estimate a lower bound for the relaxation time in the range 60–100 ns.


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)

Transient current through ESs.(a) Pulse scheme used to study transient currents through ESs: time TB is fixed, while time TA is varied. (b) Current through the QD as a function of VCG and TA for VSD=−1 mV, VPP=0.9 V, TB=30 ns. All lines are bent due to a parasitic effect of the bias-tee adding a duty-cycle dependent DC-offset to VCG. Dashed lines indicate the peaks due to transport via GS (blue) and ES (red), further investigated in d. (c) Schematic of the transitions occurring during TA for the central peak in b. /N,g› (/N,e›) indicates the ground (excited) state of the dot with N excess electrons. The transition /N,g›→/N+1,g› is not energetically allowed in the range of values used for VSD and VCG during TA, and so /N,g› is an ‘absorbing’ state. At the beginning of each cycle, the dot is initialized in the state with N+1 electrons during TB (not shown). (d) Average number of electrons transmitted per cycle through GS (blue circles) and ES (red circles), as a function of the pulse length TA. Data are extracted from the peaks shown in b, solid lines represent linear and exponential fit to the experimental data (1/γ=78 ns, nsat=0.313).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Transient current through ESs.(a) Pulse scheme used to study transient currents through ESs: time TB is fixed, while time TA is varied. (b) Current through the QD as a function of VCG and TA for VSD=−1 mV, VPP=0.9 V, TB=30 ns. All lines are bent due to a parasitic effect of the bias-tee adding a duty-cycle dependent DC-offset to VCG. Dashed lines indicate the peaks due to transport via GS (blue) and ES (red), further investigated in d. (c) Schematic of the transitions occurring during TA for the central peak in b. /N,g› (/N,e›) indicates the ground (excited) state of the dot with N excess electrons. The transition /N,g›→/N+1,g› is not energetically allowed in the range of values used for VSD and VCG during TA, and so /N,g› is an ‘absorbing’ state. At the beginning of each cycle, the dot is initialized in the state with N+1 electrons during TB (not shown). (d) Average number of electrons transmitted per cycle through GS (blue circles) and ES (red circles), as a function of the pulse length TA. Data are extracted from the peaks shown in b, solid lines represent linear and exponential fit to the experimental data (1/γ=78 ns, nsat=0.313).
Mentions: A more accurate estimate of the relaxation time of the ESs can be obtained with a different pulse scheme (see Fig. 4a), where TA is varied while keeping TB and VPP fixed252631. Such a measurement is shown in Fig. 4b for the same Coulomb resonance investigated in Fig. 3b–e. The two outermost peaks correspond to transport via the dot GS when this is in resonance with the bias-window during TA (right peak) and TB (left peak). The inner peak results from transport via an ES, as indicated in the scheme sketched in Fig. 4c. For each of these peaks, we estimate the average number of electrons tunnelling through the device per cycle ‹n›=I (TA+TB)/e. Figure 4d shows the number of electrons transmitted via the GS (blue) and via the ES (red) as a function of the pulse length TA. While the first one increases linearly with TA, the second tends to saturate, indicating a transient effect. Fitting this data set with n(TA)=nsat [1-exp(−γ TA)], where nsat is the saturation value for long TA (ref. 25), we extract the characteristic rate of the blocking processes γ=12.8 MHz. As both tunnelling and relaxation lead to the occupation of the GS, γ is approximately given by γ~Γ+1/τ, where τ is the intrinsic relaxation time of the ES and Γ the characteristic tunnelling rate. This in turn gives a lower bound τ>78 ns for the lifetime of the QD ES. By studying further electronic ESs with energies in the range of 1.7–2.5 meV (see Supplementary Fig. S3–S5), we estimate a lower bound for the relaxation time in the range 60–100 ns.

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.


Related in: MedlinePlus