-
Resonant Tunning Through Quantum Dot Array
-
-
-
Real arrays can be expected to have two main deviations from the ideal Hubbard model. Fitsr, in addition to the intradot Couloumb repulsion there will exist a certain degree of interdot repulsion. Second, individual dots will be invariably “detuned†from each other to some extent. Both these aspects are readily incorporated in our model, and we find that they have a noticeable effect on the two groups of peaks which we identified as the upper and the lower Hubbard bands. Deturning tends to localize the electron states, thus suppresses the conduction peaks. The effects of deturning have been presented in a separate publication. Consider a one-dimensional (1D) array of N coupled dots, indexed from left to right as 1─N, described by the Hamiltonian H,
In Eq (1.1) above, εka and ε in are energy levels in leads and the ith dot of the array, respectively, with an α being the spin index. Ui is the intradot repulsion of the ith dot, while Wi and ti are the interdot repulsions and the interdot coupling between the ith dot and its right neighbor [the (i+1)th dot]. The tunneling matrix element V L (V R ) connects dot 1 (dot N) to the left (right)
ka ka
lead. We assume two spin-degenerate levels on each dot.
The whole array were treated as a single quantum system and calculate its many-body eigenstates by exact diagonalization. The demand on computing power grows factorialy with the number of states. Arrays containing up ten dots (20 states) were studied. Once the eigenstates are known, the conductance is calculated from the relation.
In Eq (1.20), εn,i is the energy of many-body state (n,i), the ith if the n-particle states, Г L(R) are the transition rates between state (n,i) and (n-1,j) by losing or getting one electron through the left (right) lead, and P eq is the occupation probability of state (n,i) at equilibrium,
-
-
-
ABSRACT - [ Total Page(s): 1 ]Abstract coming soon ... Continue reading---
CHAPTER ONE - [ Total Page(s): 4 ]CHAPTER ONERESONANT TUNNELING THROUGH QUANTUM DOT ARRAYS1.1 IntroductionResonant tunneling through Quantum dot arrays is the quantum-mechanical effect of transition through a classically-forbidden energy state.Consider rolling a ball up a hill. If the ball is not given enough velocity, then it will not roll over the hill. This makes sense classically. But in quantum mechanics, objects exhibit wavelike behavior. For a quantum particle moving against a potential hill, the wave function descr ... Continue reading---
CHAPTER THREE - [ Total Page(s): 9 ]The Hamiltonian equation above is a representation of Quantum dot array i.e 1- Darray of N coupled dots index from left to right as 1- N. looking at the energy of a quantum dot confined dots (20 energy states been treated as a single quantum systemFrom the equationεka is the energy levels in leadsεia is the ith dot of the energy Ui is theith inter- dot repulsion and the inter-dot coupling between theith dot and its rightneighbor (the (i+1)th dot)V L and V R are the tunnels matrix element c ... Continue reading---
CHAPTER FOUR - [ Total Page(s): 2 ]CHAPTER FOURDISCUSSION OF RESULTSFrom the matrices gotten in the previous chapter, it is seen that the diagonal four-by-four matrices are proportional to the partition function Z.In Eq. (2), En, is the energy of many-body state (n, i), the ith of the n-particle states, RL ,®ij are the transition rates between state (n,i) and (n-I,j) by losing or getting one electron through the left (right) lead, and peqn,I is the occupation probability of state (n,i) at equilibriumEquation (2) is basically t ... Continue reading---
CHAPTER FIVE - [ Total Page(s): 3 ]CHAPTER FIVECONCLUSION ... Continue reading---
REFRENCES - [ Total Page(s): 1 ]REFERENCESFriedlander, Michael W. 2000 A Thin Cosmic Rain: Particles from Outer Space (Cambridge:Harvard University Press).Watson, Alan 2001 “Ultra High Energy Cosmic Rays: What we Know Now and What the FutureHolds,†in Relativistic Astrophysics: 20th Texas Symposium (AIP Conference Procedings, volume 586, J. C. Wheeler and H. Martel (eds.) American Institure of Physics, pp. 817–826. (The original abstract was different from the published abstract)Anderson, Carl D ... Continue reading---
-
ABSRACT - [ Total Page(s): 1 ]Abstract coming soon ... Continue reading---