What is topological quantum matter?

What is topological quantum matter?

In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition.

What is topological matter?

What is topological matter? Systems, the theory of which employs topological spaces and corresponding nontrivial invariants that have measurable physical consequences. Diverse topological spaces (usually metric spaces) and invariants applicable, e.g. topological insulators, superconductors and semi-metals → fiber.

What is topology in condensed matter physics?

The idea behind topological systems is simple: if there exists a quantity, which cannot change in an insulating system where all the particles are localized, then the system must become conducting and obtain propagating particles when the quantity (called a “topological invariant”) finally changes.

What is Z2 topological order?

Z2 topological order and first-order quantum phase transitions in systems with combinatorial gauge symmetry. We find that the Z2 topological phase remains stable, while the paramagnetic phase is replaced by a ferromagnetic phase. The topological-ferromagnetic quantum phase transition is also of first-order.

Is Quantum a matter?

Quantum matter refers to materials which need to be described by quantum mechanics. The study of quantum matter falls into the field of condensed matter physics—a fundamental branch of physics—which is the study of the structure and behaviour of solid and fluid matter.

What is a topological superconductor?

Topological superconductors (TSCs) are a peculiar class of superconductors where the nontrivial topology of bulk leads to the emergence of Majorana bound states (MBSs) within the bulk superconducting gap1,2,3,4,5.

What is kitaev chain?

The Kitaev chain is a one dimensional model based on a lattice of N spinless fermions. It is characterized by three parameters: the chemical potential μ, the hopping amplitude t, and the p-wave superconducting pairing constant Δ. The Kitaev Hamiltonian, written in a set of standard fermionic operators , is [1, 2]

Is topological sort unique?

In general, the topological sort is not unique. For example, if we have v0 < v1, and v2 < v3, any one of the orderings v1v2v3v4, v3v4v1v2, v1v3v2v4 is a topological sort.

Do we live in a quantum world?

Based on these two insights, Bohr argued that a quantum theory can never explain classical physics. Some physicists argue that we just haven’t worked hard enough, and that we do fundamentally live in a quantum world, and that we can reproduce classical physics from purely quantum rules.

What is a topological insulator superconductor?

Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions.

What is particle hole symmetry?

Particle-hole symmetries then arise for gapful or gapless free-fermion systems at half filling, as the concatenation of particle-hole conjugation with one or another involution that reverses the sign of the first-quantized Hamiltonian. …

How are the topological states of quantum matter described?

Topological states of quantum matter are generally described by topological field theories. Readers may already be familiar with Maxwell’s field theory describing the electromagnetic fields and Einstein’s field theory describing the gravitational fields. These field theories depend on the geometry of the underlying space.

Are there any topological effects in particle physics?

However, there are only a few topological effects that have been experimentally tested in particle physics. Topological states of quantum matter now offer a new laboratory to test some of the most profound ideas in mathematics and physics.

How are the edge states of condensed matter topologically protected?

In this precise sense, the helical edge states are topologically protected by TR symmetry. The QSH state can be generalized to a 3D topological insulator 12, 13, 14, where the surface state consists of a single 2D Dirac cone.

Can a QAH effect occur in a topological insulator?

Recently, the QAH effect has been proposed to occur in TR-invariant topological insulators with magnetic doping 11, 16, 17, 18. This is not accidental, but instead highlights the deep relationship between these two states of matter.