Open Positions

If you are interested in working within this project, please contact one of the principal investigators.

Figure 1

Superconducting order is induced in the surface of a strong topological insulator (STI) gapping out the protected surface states with the Dirac dispersion. Magnetic field B is then applied to induce Abrikosov vortices in the SC order parameter. Each vortex hosts an unpaired Majorana zero mode.

Superconducting order is induced in the surface of a strong topological insulator (STI) gapping out the protected surface states with the Dirac dispersion. Magnetic field B is then applied to induce Abrikosov vortices in the SC order parameter. Each vortex hosts an unpaired Majorana zero mode.

Figure 2

Proposed realization of an interaction-enabled crystalline topological phase in two dimensions, as envisioned in Ref. [3]. Red and blue circles represent vortices and antivortices respectively in Fu-Kane model at neutrality. Dashed lines denote hopping terms while solid lines represent interactions. In the interaction dominated regime the system is in a topological phase with bulk excitation gap and gapless edge modes protected by the combination of time-reversal and C4 rotation symmetry. The existence of this phase fundamentally depends on interactions.

Proposed realization of an interaction-enabled crystalline topological phase in two dimensions, as envisioned in Ref. [3]. Red and blue circles represent vortices and antivortices respectively in Fu-Kane model at neutrality. Dashed lines denote hopping terms while solid lines represent interactions. In the interaction dominated regime the system is in a topological phase with bulk excitation gap and gapless edge modes protected by the combination of time-reversal and C4 rotation symmetry. The existence of this phase fundamentally depends on interactions.

Strongly interacting topological phases of quantum matter

Systems of strongly interacting particles, fermions or bosons, can give rise to topological phases that are not accessible to non-interacting systems. For instance all non-interacting phases of bosons are topologically trivial but interactions can bring about various non-trivial phases such as the bosonic fractional quantum Hall states. Many interaction-enabled topological phases have been discussed theoretically but, aside from the well known fractional quantum Hall states, few experimental realizations exists.

This project focuses on theoretical analyses of natural or artificially engineered structures in which interactions between particles dominate over their kinetic energy and can at the same time give rise to topologically non-trivial phases. One such structure consists of a topological insulator interfaced with an ordinary superconductor (see Figure 1).  According to Fu and Kane [1] vortices in such an interface host Majorana zero modes. Furthermore, in the presence of a vortex lattice there exists a regime in which hopping between the adjacent Majorana fermions is strongly suppressed, the so called "neutrality point" [2]. Close to the neutrality point the kinetic energy of the Majorana fermions is quenched and the low-energy physics is controlled by fermion interactions. Depending on the details of the vortex lattice geometry various interesting one- and two-dimensional models can arise. In some cases they form interaction-enabled topological phases (see Figure 2 for an example) that fundamentally cannot exist in weakly interacting systems [3,4].

More generally, this collaboration is aimed at exploring the interplay between strong interactions and topology in systems that can be potentially realized in a laboratory. These include

- Magnetic and superconducting phases in surfaces of three-dimensional topological insulators

- Interaction effects in systems with flat bands that exhibit non-trivial topology

- Emergence and stability of Majorana fermions in heterostructures involving topological

  insulators in reduced dimensions (wires, 2D films)

- Realistic physical systems that can host exotic particles such as parafermions and   

   Fibonacci anyons

 

References

[1] L. Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008).

[2] C.-K. Chiu, D.I. Pikulin, and M. Franz, Phys. Rev. B. 91, 165402 (2015).

[3] M.F. Lapa, J.C.Y. Teo and T.L. Hughes, Phys. Rev. B 93, 115131 (2016).

[4] C.-K. Chiu, D.I. Pikulin, and M. Franz, Phys. Rev. B 92, 241115 (2015).

[5] A. Rahmani, Xiaoyu Zhu, M. Franz, and I. Affleck, Phys. Rev. Lett. 115, 166401 (2015).

Principal Investigators

M. Franz (UBC) franz@physics.ubc.ca

J.H.  Bardarson (MPI-PKS) jensba@pks.mpg.de

D. Manske (MPI-FKF) d.manske@fkf.mpg.de

Ian Affleck (UBC)

A. Schnyder (MPI-FKF)

 
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