DMMMTS · Detection and manipulation of Majorana modes in topological superconductors

Detection and manipulation of Majorana modes in topological superconductors

The main objectives of the research project are related to exploring the properties of topological superconductors. Topological superconductors are fascinating states of matter that support Majorana fermions, enigmatic charge neutral particles that are their own anti-particles. Majorana fermions are carried by topological defects such as vortices within the superconductor, or are localized on the edges of the superconductor. A vortex carrying a Majorana zero mode satisfies a new type of quantum statistics, known as non-abelian statistics. Predicting manifestations of Majorana fermions, exploring their unique statistics and harnessing them towards universal quantum computation are some of the main objectives of this project. We proposed a device dubbed the Majorana-Transmon qubit as reported in Nature Communications [E. Ginossar and E. Grosfeld, Nat. Commun. 5, 4772 (2014)]. The proposed design incorporates Majorana quasi-particles into current qubit architectures and exploits their properties to protect quantum information. We derived the electromagnetic properties of the proposed device, and discovered two remarkable properties: First, we uncovered the presence of a protected doublet that does not couple easily to the electromagnetic environment, thus protecting the qubit from decoherence; the doublet can nevertheless be manipulated via transitions to higher states forming an effective lambda system. Second, we demonstrated how the device can measure the presence of the Majorana quasi-particles by detecting parity interference phenomena in the microwave absorption spectrum. In a follow up paper we described protocols to initialize the qubit, manipulate it, and perform readout [K. Yavilberg, E. Ginossar, E. Grosfeld, Phys. Rev. B 92, 075143 (2015)]. Another main direction was to find measurable observables that can indicate the presence of Majorana edge states or neutral edge states in general. Since such excitations carry heat but no charge, we set to explore thermoelectric effects. To make direct contact with state of the art experiments we proposed a method to detect neutral edge states in the quantum Hall regime. My theory paper predicting this result [G. Viola, S. Das, E. Grosfeld and A. Stern, Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime, Phys. Rev. Lett. 109, 146801 (2012)] was quickly followed by an experimental paper confirming the presence of the predicted effect [I. Gurman, R. Sabo, M. Heiblum, V. Umansky & D. Mahalu, Nature Communications 3, 1289 (2012)]. Another direction was to explore signatures of the coupling of Majorana fermions to a fermion lead. We have explored a Majorana-Cooper-Pair-Box and found a modified relaxation resistance and mesoscopic capacitance compared to a regular Cooper-Pair-Box [A. Golub and E. Grosfeld, Phys. Rev. B 86, 241105(R) (2012)], shedding light on the behavior of Majorana fermions in mesoscopic geometries. We have developed a DMRG code [S. Moukouri and E. Grosfeld, Phys. Rev. B 90, 035112 (2014)] and tDMRG code adapted to finding the properties of interfaces between topological materials and critical systems which we used to discover a subtle parity transfer effect reported in an online preprint [Non-Abelian fermion parity interferometry of Majorana bound states in a Fermi sea, arXiv:1609.04627]. This effect demonstrates that the Majorana quasi-particles retain their unique quantum statistics even when they propagate inside a critical systems, away from their parent superconductor. We have found a way to calculate the adiabatic abelian phase associated with a vortex exchange in p-wave superconductors [D. Ariad, B. Seradjeh, E. Grosfeld, Phys. Rev. B 92, 035136 (2015)]. Through this effort we also extended the field theoretical description of p-wave superconductors to include a novel Chern-Simons type term, giving rise to this exchange phase. This sheds light on the behavior of vortices, which are the carriers of Majorana fermions, in topological superconductors. The results of the research are updated regularly online: http://physics.bgu.ac.il/~grosfeld.

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