In our education system, science subjects have been always compartmentalized. Biology, Chemistry and Physics have been taught in isolation with each other, yet insights often comes after you take a step back and look at the big picture.
Condensed matter physics has been on fire recently (Not you, Galaxy Note 7), discoveries have been made here and there. This year, the Nobel prize committee has selected three physicists for their work in the field “for theoretical discoveries of topological phase transitions and topological phases of matter”.
To us, it sounds like a mishmash of alphabets. In order to understand this, we need to look at some old school concepts.
Phase transition (Or, in simple term, change of states)
We are taught in elementary schools that matter has three states, i.e. solid, liquid and gas. The most common example is water, which
is a liquid and can transform into ice or vapor if we cool or heat it enough. The constituent atoms or molecules move randomly with different magnitudes.
In extreme cases, some other exotic states appear. For example, plasma is a hot ionized gas, and quantum condensate, a state where the atoms occupy the lowest energy levels. This study deals with the cold world – what happens if I cool things down enough?
Let’s take a piece of metal and apply a voltage across two opposite ends (say, up and down). You will get a current flowing. Then when you apply a magnetic field at the right angle to the current, you will detect a voltage across the other two opposite ends (left and right). It is called Hall effect, named after the scientist Edwin Herbert Hall in 1879.
When you take an extremely thin metal sheet, and cool it down to near absolute zero, cool thing happens. When you do the same procedures as aforementioned, you will still get a Hall voltage, but the ratio of the current to the Hall voltage is always the same, no matter what material you choose.
The weirder thing is that if you change the magnetic field enough, the ratio will change as well, but only in integer steps. It doubles, triples and so on without taking any values. This quantum hall effect was not unexplained until David Thouless, one of the laureates, provided the answer using a field from Mathematics – topology.
Topology describes things that do not change when you transform it in a continuous manner, be it stretching, twisting or compressing. If one shape can transform to another shape with the said action, they belong to the same topological category. For example, a piece of paper can be folded into a paper crane, or a lump of clay can be molded into a bowl. If you punch a hole into an object, it belongs to another category, like a cup with handle is different from a cup without handle.
So, we can group things under categories of no hole, one hole, two holes etc. It always jump in steps (there is no one and a half hole!).
Linking two unlikely realms together, the scientists managed to explain why quantum hall effect only changes in integer steps, and based on this to explain exotic phase transitions.