Coulomb blockade in metallic islands and quantum dots

Transcription

1 Coulomb blockade in metallic islands and quantum dots Charging energy and chemical potential of a metallic island Coulomb blockade and single-electron transistors Quantum dots and the constant interaction model Finite bias and Coulomb diamonds Excited states: transport spectroscopy Calculating the current

2 Different types of quantum dots Metallic island Gated 2-DEG

3 Different types of quantum dots Carbon nanotube InAs InP InAs InP InAs Semiconducting nanowire Single molecule quantum dot

4 Metallic island Continuous density of states: E k B T,... Energy required to add one electron: E C k B T µ S µ D e 2 C Σ α G V G

5 Quantum dot: quantized levels E C 1 C 1 L " 1 L nm dot 30 nm dot 10 nm dot 2 = e CΣ >> Δε EC > Δε E C / E C < Δε Δε Single electron transistor (SET) limit: no energy quantization effects Quantum dot limit: Quantum effects important Constant interaction model peak spacing: e g V g = µ = E C + " N " N 1

6 Finite bias voltage Small width of resonance: k B T,E C Current only when at least one µ N is between µ L and µ R Metallic island In general µ N / e X i i V i, i = C i C With C L = C R,V L = V R = V/2 µ N is independent of V and the diamonds are straight µ N in general Coulomb diamonds (zero current areas)

7 Finite bias voltage Stability diagram: differential conductance on color scale as a function of gate and bias voltages di(v,v g ) dv

8 Finite bias voltage Quantum dot: even diamonds are larger because of spin degeneracy " 4,5 " 2,3 " 1,2

9 Finite bias voltage Carbon nanotube quantum dots: four-fold patter because of additional orbital degeneracy Leturcq, et. al. (2009)

10 Finite bias voltage What are all these other lines?

11 Finite bias voltage: excited states Can also tunnel through excited states increased current conductance peak Tunnel spectroscopy of quantum dot levels Energy needed to add electron N to the ground state, provided that the dot is in the N-1 electron ground state. Energy needed to add electron N to the excited state i, provided that the dot is in the N-1 electron excited state j state.

12 Finite bias voltage: excited states Tunneling can lead to occupation of excited states, also with energies larger than k B T Current-induced heating. To calculate the current, we have to calculate the quantum dot state in nonequilibrium! Energy needed to add electron N to the ground state, provided that the dot is in the N-1 electron ground state. Energy needed to add electron N to the excited state i, provided that the dot is in the N-1 electron excited state j state.

13 Calculating the current Single electron tunneling k B T,E C Available electron in the lead? Rate of electrons tunneling into state i from lead L, R: L,R X f(µ ij N µ L,R ) P (j) j Tunnel rate Probability of state j being occupied Rate of tunneling out to lead L, R, leaving the dot in state i: Current: I = L X ijn n f(µ ij N µ L,R ) I = L,R X h io 1 f(µ ji N µ L,R ) j h i 1 f(µ ji N µ L,R ) P (j) P (j) Need occupations! From thermal equilibrium (small V), or from solving rate (or master) equation

14 Freaky diamonds and their usefulness Spectroscopy of vibrational modes in OPV5 molecule Measuring lifetimes of vibrations in suspended CNTs

15 Freaky diamonds and their usefulness Single-molecule magnet in a transport junction? Can we see the peas in the peapod?

16 Freaky diamonds and their usefulness Engineered Majorana fermions in a nanowire?