# My Diploma Thesis: Spin Transport in Mesoscopic Systems

Sometimes people ask me what I'm doing right now, and I tell them "I'm writing my diploma thesis on mesoscopic spin transport", and they know just as much as before. So here I want to explain what that means.

## Mesoscopic systems

A mesoscopic system is one that is larger than a few nanometers, but still small enough that you have to care about quantum effects.

That's not a very precise definition, so I'll try again: Consider a metallic wire. For macroscopic systems (ie the ones that we are used to in day-to-day live) you might know that the electrical resistance of such a wire increases linearly as you increase its length, and decreases linearly if you increase its cross section.

This is very intuitive, because electrical resistance describes how hard it is for an electron to travel through our wire. If the wire is longer, it sees more obstacles, so the resistance is higher. If the wire has a larger cross section, it's easier for the electron to find a way that's not blocked, so the resistance is smaller. That's called Ohm's law.

These relations aren't true anymore for rather small systems. If you have a very thin wire, say 20 nanometers, and increase its diameter by another nanometer, the resistance might not change at all. Then you increase its diameter by another nanometer, the resistance suddenly jumps down by a few percent.

All these systems that are too small for Ohm's law to apply are called mesoscopic. All mesoscopic effects have to be explained with quantum physics, at least at some point.

## Electron Spin

Electrons have something called Spin. Everybody knows that it has a charge, and it acts as if it rotated around its own axis very fast. So it looks like a current which runs in a circle, and that creates a small magnetic field.

If you try to measure the magnetic field of one electron, you will only ever get two possible values, which we call spin up and spin down.

## Spin Optics

In a semiconductor, one can split up a beam of electrons into two beams of spin-up and spin-down electrons, just like in optics with polarized light. That splitting can be influenced by an external voltage, like a classical transistor.

The topic of my diploma thesis is to figure out how such spin polarized electron beams behave in certain semiconductor systems.