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Majorana bound states in inhomogeneous nanowires

Ekström, Johan LU (2017) PHYM01 20161
Solid State Physics
Department of Physics
Abstract
Majorana bound states are in condensed matter physics quasiparticle excitations which can be found in so-called topological superconductors. They have lately received much attention since they have been predicted to be partly immune to decoherence and therefore suitable for quantum computation. A nanowire with strong spin orbit coupling and proximity induced superconductivity that is subject to a magnetic field has been shown to host a pair of Majorana bound states living on the opposite ends of the nanowire. One bit of quantum information (a qubit) can be stored in such a pair of Majorana bound states. The quantum information is then protected from decoherence as long as the Majorana bound states are well separated, such that their wave... (More)
Majorana bound states are in condensed matter physics quasiparticle excitations which can be found in so-called topological superconductors. They have lately received much attention since they have been predicted to be partly immune to decoherence and therefore suitable for quantum computation. A nanowire with strong spin orbit coupling and proximity induced superconductivity that is subject to a magnetic field has been shown to host a pair of Majorana bound states living on the opposite ends of the nanowire. One bit of quantum information (a qubit) can be stored in such a pair of Majorana bound states. The quantum information is then protected from decoherence as long as the Majorana bound states are well separated, such that their wave functions do not overlap. In this work we explore the effect of introducing potential barriers in the nanowire. It is shown that for certain parameter settings of the barriers the overlap between the Majorana bound states can be reduced. Furthermore, disorder in the potential is studied. The effect of the disorder is also shown to depend on the parameter settings of the barriers. Finally it is shown that a rotating magnetic field can amplify the spin-orbit coupling in a nanowire. Increasing the spin-orbit coupling results in a decrease in the overlap. (Less)
Popular Abstract
A standard computer of today can easily solve many different mathematical problems. An even more impressive super computer can solve even harder problems and it can also do it much faster than a normal computer. However, some problems like those of optimization and mathematical models for new and better medicines would take more than a life time, even for the best supercomputer to solve. A quantum computer, which uses the effects of the "quantum-world" might be ideal for these kinds of problems and if someone could manage to build one this could revolutionize e.g. the medical industry allowing to produce even better medicines.

One way to realize a quantum computer is to use a very exotic state for electrons, the so-called Majorana bound... (More)
A standard computer of today can easily solve many different mathematical problems. An even more impressive super computer can solve even harder problems and it can also do it much faster than a normal computer. However, some problems like those of optimization and mathematical models for new and better medicines would take more than a life time, even for the best supercomputer to solve. A quantum computer, which uses the effects of the "quantum-world" might be ideal for these kinds of problems and if someone could manage to build one this could revolutionize e.g. the medical industry allowing to produce even better medicines.

One way to realize a quantum computer is to use a very exotic state for electrons, the so-called Majorana bound state. These can be found in a nanowire, a very small, rod-like object, which has a length that is much longer than its diameter. Furthermore the nanowire has to be made superconducting and subjected to a magnetic field for it to host Majorana bound states. In this system two Majorana states "live" on the opposite ends of the nanowire. When the nanowire is long the Majorana states are prevented from overlapping. This could be thought of as two persons being so far apart that they can't communicate with each other. In this situation the Majoranas are ideal for a quantum computer.

A quantum computer should however, be made up by a network of nanowires hosting Majorana states. When making these networks the nanowire will have to be made shorter and due to this it is possible for the Majorana states to start communicating with each other, and the shorter the nanowire is the easier it is for the Majorana states to communicate.

In this project we investigate if it is possible to make it harder for the Majorana states to communicate while still making the nanowire shorter. This is done by first investigating how the Majorana states are affected by changing the potential landscape of the nanowire. Changing the potential landscape of the nanowire means that particles will prefer to be in certain parts of the nanowire compared to others. By making this modification to the nanowire we find that it is in some situations a little harder for the Majorana states to communicate with each other.

The next steps are to find the optimal structure for which the communication between the Majorana states are the smallest. Furthermore, more advanced models should be investigated to verify the found results. Other possibilities to make the communication between the Majoranas should also be searched for. (Less)
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author
Ekström, Johan LU
supervisor
organization
course
PHYM01 20161
year
type
H2 - Master's Degree (Two Years)
subject
language
English
id
8900387
date added to LUP
2017-01-23 16:19:26
date last changed
2017-01-23 16:19:26
@misc{8900387,
  abstract     = {Majorana bound states are in condensed matter physics quasiparticle excitations which can be found in so-called topological superconductors. They have lately received much attention since they have been predicted to be partly immune to decoherence and therefore suitable for quantum computation. A nanowire with strong spin orbit coupling and proximity induced superconductivity that is subject to a magnetic field has been shown to host a pair of Majorana bound states living on the opposite ends of the nanowire. One bit of quantum information (a qubit) can be stored in such a pair of Majorana bound states. The quantum information is then protected from decoherence as long as the Majorana bound states are well separated, such that their wave functions do not overlap. In this work we explore the effect of introducing potential barriers in the nanowire. It is shown that for certain parameter settings of the barriers the overlap between the Majorana bound states can be reduced. Furthermore, disorder in the potential is studied. The effect of the disorder is also shown to depend on the parameter settings of the barriers. Finally it is shown that a rotating magnetic field can amplify the spin-orbit coupling in a nanowire. Increasing the spin-orbit coupling results in a decrease in the overlap.},
  author       = {Ekström, Johan},
  language     = {eng},
  note         = {Student Paper},
  title        = {Majorana bound states in inhomogeneous nanowires},
  year         = {2017},
}