Condensed Matter

Theory and Simulation Group

Topological Materials

One way of classifying and understanding different materials is attending to its topological order.
A system has topological order if certain fundamental properties, such as its electron or spin conductivity,
are insensitive to smooth changes in the material parameters. This means that such properties cannot change easily
(unless undergoing a quantum phase transition) and are very robust (against disorder, temperature, etc.). This is important
if we want to detect such properties in an experiment or for practical applications. Predicting and studying systems with a
topological protection is one of the main lines of our theory group.

A topological insulator is a material that behaves as an insulator in its interior or bulk while permitting the movement
of charges (metallic) on its surface. In the bulk of a topological insulator the electronic band structure resembles an
ordinary band insulator, with the Fermi level falling between the conduction and valence bands. On the surface of a
topological insulator there are special states that fall within the bulk energy gap and allow surface metallic conduction.
Carriers in these surface states have their spin locked at a right-angle to their momentum (spin-momentum locking or
topological order). At a given energy the only other available electronic states have opposite spin, so the "U"-turn
scattering is strongly suppressed and conduction on the surface is highly metallic. These states are characterized by
an index (known as Z2 topological invariants) similar to the genus in topology, and are an example of topologically
ordered states.

Apart from topological insulators, within topological materials there also exists the so-called topological
superconductors. In these systems, Majorana bound states appear within the superconducting gap, changing observables
like density of states, Josephson current, etc.

People Involved

**Contact: **Juan Jose Palacios

Elsa Prada

Tobias Stauber

Key References

__Topological superconductors__

*Transport spectroscopy of NS nanowire junctions with Majorana fermions*

E. Prada, P. San-Jose and R. Aguado.

Physical Review B 86, 180503(R) (2012)

*Multiple Andreev reflection and critical current across a topological transition in superconducting nanowire junctions*

P. San-Jose, J. Cayao, E. Prada and R. Aguado.

__Topological insulators__

*Spin-filtered edge states in graphene*

D. Gosalbez-Martinez, D. Soriano, J.J. Palacios, J. Fernandez-Rossier

Solid State Communications 152, 1469 (2013)

*Topologically protected quantum transport in locally exfoliated bismuth at room temperature*

C. Sabater, D. Gosalbez-Martinez, J. Fernandez-Rossier, J.G. Rodrigo, C. Untiedt and J.J. Palacios

Physical Review Letters 110 (17), 176802 (2013)

*Transport through quantum spin Hall insulator/metal junctions in graphene ribbons*

E. Prada and G. Metalidis.

J. Comp. Electronics 12, 63 (2012)

*Band topology and quantum spin Hall effect in bilayer graphene*

E. Prada, P. San-Jose, L. Brey and H. A. Fertig.

Solid State Communications 151, 1075 (2011)