## What is topological phase transition?

Topological phase transitions represent a new class of quantum critical phenomena. Although they cannot be described within the usual framework of Landau theory, one can still identify a diverging length and time at these transitions, which make them amenable to a scaling approach.

**What is first order and second order phase transition?**

In a liquid the atoms or molecules are disordered in their arrangement, but at the transition, they suddenly become ordered. Thus a first order phase transition is associated with a discontinous jump in the order parameter. The other type of phase transition is a second order phase transition.

### What is topological order physics?

In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states.

**What is a topological superconductor?**

Topological superconductors are a class of superconducting materials characterized by sub-gap zero energy localized modes, known as Majorana boundary states (MBSs). These materials are promising for the development of quantum computing technology.

#### How do you find the topological order on a graph?

In topological sorting, we need to print a vertex before its adjacent vertices. For example, in the given graph, the vertex ‘5’ should be printed before vertex ‘0’, but unlike DFS, the vertex ‘4’ should also be printed before vertex ‘0’. So Topological sorting is different from DFS.

**What is topological material?**

Topological insulators are a new state of quantum matter with a bulk gap and odd number of relativistic Dirac fermions on the surface. The bulk of such materials is insulating but the surface can conduct electric current with well-defined spin texture.

## What are Majorana zero modes?

Majorana zero modes (MZMs) are fermionic states, each of which is an antiparticle of itself. MZMs are required to always appear in pairs (1). Each MZM pair has the degrees of freedom of a single fermion, which is split nonlocally in space into two MZMs.

**What are second order phase transitions?**

Second order phase transitions occur when a new state of reduced symmetry develops continuously from the disordered (high temperature) phase. The ordered phase has a lower symmetry than the Hamiltonianâ€”the phenomenon of spontaneously broken symmetry.