Atsevišķu elektronu precīza satveršana kvantu punktos

Transcription

1 Datorzinātnes pielietojumi un tās saiknes ar kvantu fiziku Atsevišķu elektronu precīza satveršana kvantu punktos Pavels Nazarovs

2 What is electron (quantum) pump? Usually by direct current (DC) understand a flow of electrons as a result of applied bias voltage. Δφ I However, in systems of mesoscopic scale DC can be generated even at zero bias. Δφ = A device capable of providing such effect is called a electron (quantum) pump [1]. I f [1] P. W. Brouwer, Phys. Rev. B 58, R1135 (1998).

3 Overview on types of electron pumps Turnstiles (photon-assisted tunneling corrections) Adiabatic pumps (co-tunneling & non-adiabaticity) Surface-acoustic-waves driven pumps (hard to control) Non-adiabatic single-parameter pumps Blumenthal et al. Nature Physics 3, 343 (27) Kaestner et al. Phys. Rev. B 77, (28) Maire et al., Appl. Phys. Lett. 92, (28) Fujiwara et al. Appl.Phys.Lett. 92, 4212 (28) Wright et al. Phys. Rev. B 78, (28) Kaestner et al, Appl. Phys. Lett. 92,19216 (28) Kaestner et al, Appl. Phys. Lett. 94, 1216 (29) Wright et al. Phys. Rev. B 8, (29) Ch. Leichtet et al. Physica E 42, 911 (21) Kashcheyevs et al. Phys. Rev. Lett. 14, (21) Hybrid single-gate pumps, Pekola & Averin (28)

4 How does electron pump look like?

5 How does electron pump work?

6 How does electron pump work? V g Quantized pumping regime can be achieved by changing voltage on the exit gate (V g ). It allows to transport precise number of electrons (1e, 2e or more) per cycle. I 1 e per cycle V g

7 Current dependence on gates voltages L. Fricke, F. Hohls, P. Mirovsky, C. Leicht, B. Kaestner, K. Pierz, H.W. Schumacher, and R. J. Haug, Measurements of two sequential quantized-charge pumps

8 Motivation Practical applications Ampere will be redefined in 212, it can be redefined using electron pump with high accuracy. Closure of metrological I-V-R triangle Fundamental physics Quantum dot precise initialization Multi-particle interaction Source of electrons with specified properties Dynamical quantum dot spectroscopy Density of states sensor

9 Modeling of dynamical quantum dot: collaboration Experimental group Theoretical group Dr. Bernd Kästner group, PTB, Germany Dr. Vyacheslavs Kashcheyevs group, LU, Latvia

10 Modeling of dynamical quantum dot: cascade theory a. Fujiwara et al. APL 28 b. Kaestner et al APL 29 c. Janssen & Hartland 21 d. Robinson & Barnes, PRB 21 L. Fricke, F. Hohls, P. Mirovsky, C. Leicht, B. Kaestner, K. Pierz, H.W. Schumacher, and R. J. Haug, Measurements of two sequential quantized-charge pumps V. Kashcheyevs, B. Kaestner, Universal decay cascade model for dynamical quantum dot initialization, Phys. Rev. Lett. 14, (21).

11 Modeling of dynamical quantum dot: cascade theory I 2.5 Current dependence on second gate voltage in electron pump: experiment (red dots) and theory (blue line) Papers: Ch. Leicht, B. Kaestner, V. Kashcheyevs, et a., Non-adiabatic pumping of single electrons affected by magnetic fields, Physica E 42, 911 (21). V g V. Kashcheyevs, B. Kaestner, Universal decay cascade model for dynamical quantum dot initialization, Phys. Rev. Lett. 14, (21).

12 Modeling of dynamical quantum dot: main concept Current dependence on gate voltages Ch. Leicht, B. Kaestner, V. Kashcheyevs, et a., Non-adiabatic pumping of single electrons affected by magnetic fields, Physica E 42, 911 (21).

13 Modeling of dynamical quantum dot: loading phase Kinetic equation for quantum dot Γ(t) P(- ) = ε(t) Solution of kinetic equation Assumptions Loading phase occurs near maximum of cosine, therefore quadratic approximation for quantum dot s energy level as well as for tunneling rate can be used. ( t) e At e b t be At 2 ( t ) 2 d V Ct t kt 2 2

14 Modeling of dynamical quantum dot: loading phase Solution of kinetic equation Assumptions Loading phase occurs near maximum of cosine, therefore quadratic approximation for quantum dot s energy level as well as for tunneling rate can be used. ( t) e 2 t ( t) V kt 2 2 t 2 V e V 1 V

15 V 1 V V V 2 V e V 1 V

16 Modeling of dynamical quantum dot: main concept V Quantized pumping regime ε(t) V 2*P(t) LnΓ(t) V V e V

17 Modeling of dynamical quantum dot: main concept V Back-tunneling regime V V V e V

18 Modeling of dynamical quantum dot: main concept V On cascade V Cascade border line depends on relative value of τ Fermi and τ On-Off V V e V

19 Modeling of dynamical quantum dot: main concept V Partial loading, touching the Fermi level V V V e V

20 Modeling of dynamical quantum dot: main concept V V

21 Modeling of dynamical quantum dot: complex structure Near loading edge appears complex structure of dynamic quantum dot electrons can be loaded not on ground state, but on exited states.

22 Conclusions More natural approach to describe quantum dot dynamics in terms of new coordinate system with axes V and V ( which represent tunneling rate and energy level position). Cascade border line depends on relative value of τ Fermi and τ On-Off time intervals while quantum dot spends under Fermi level and left barrier being transparent respectively. Exist pumping regimes when electron is being loaded to the exited state, not on the ground state. Complex structure of quantum dot (exited states) becomes noticeable near loading edge and can be used for quantum dot spectroscopy and as density state sensor in the leads.