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Topological Superconductors and
Anyon/Majorana platforms based on spin-orbit systems

Chasing an emergent "particle that is its own anti-particle".....

FUNDING SUPPORT : Anyon/Majorana research at HasanLab is supported by Princeton University funds,
and external grant awards including the U.S. DOE (Quantum Information Science, QIS program under National Quantum Initiative/NQI)
and Betty & Gordon Moore Foundation (California)

Video introduction (Princeton/IAS workshop)
Platform for emergent Dirac, Majorana & Weyl fermions
(@ California Institute of Technology)

Scientific American : "The Strange Topology That Is Reshaping Physics"

Sir Nevill Mott Lecture (London)

Anyons have been theoretically considered for their unusual quantum exchange properties (Wilczek 1982; Arovas-Schrieffer-Wilczek 1984). Exotic anyons (non-Abelian) have been theoretically proposed in the context of FQHE and topological superconductors
[See, Moore-Read 1991; Read-Green 2000; Kitaev 2001].
Under suitable conditions they can arise in strong spin-orbit coupled superconductors by Moore-Read-Green-Kitaev. Read-Green PRB 2000
Ivanov 2001
We are working on strong spin-orbit coupled superconductors (natural and artificial) in search of such anyonic quasiparticles based on various platforms.

Quantum Matter Summer School at IAS/Princeton Reading List

New Topological States of Matter: emergent Dirac, Majorana & Weyl fermions
(Colloquium at CalTech)

Kavli Institute KITP (UC Santa Barbara) talk on topological superconductivity and Majorana platform

New Topological States of Matter: Platform for emergent Dirac, Majorana & Weyl fermions
(Colloquium at UC-Berkeley)

New Topological States of Matter (Inst. for Adv. Study Distinguished Lecture at HKUST)
Pedagogical Lecture Series

One of the early reviews on "Topological Superconductors":
“Topo. Insulators (and Superconductors)"
Hasan & Kane, Rev. of Mod. Phys. 82, 3045 (2010)

Another review :
Topo. Insulators, Topo. Superconductors and Weyl Semimetals
Hasan, Xu and Bian, Phys. Scr. T164 014001 (2015)

STM Review article:
Probing topological matter with scanning tunnelling microscopy
Nature Reviews Physics 3, 249-263 (2021)

RVB (Anderson) model is an early example of topological phase
P.W. Anderson on topological matter research (NSF news)

Some superconductors are based on Bi2Se3 materials: "Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator (Bi2Se3) class with spin-polarized single-Dirac-cone on the surface" (Submitted 2008)

Field-free platform for Majorana-like zero modes in superconductors with a topological surface state

S. S. Zhang, J.-X. Yin, G. Dai, L. Zhao, T.-R. Chang, N. Shumiya, K. Jiang, H. Zheng, G. Bian, D. Multer, M. Litskevich, G. Chang, I. Belopolski, T. Cochran, X. Wu, D. Wu, J. Luo, G. Chen, H. Lin, F.-C. Chou, X. Wang, C. Jin, R. Sankar, Z. Wang, and M. Z. Hasan
Phys. Rev. B 101, 100507 (2020)

Spin-orbital ground states of superconducting doped topological insulators: A Majorana platform
L. Wray, S. Xu, Y. Xia, D. Qian, A. Fedorov, H. Lin, A. Bansil, Liang Fu, Y. Hor, R. J. Cava, and M. Z. Hasan
Phys. Rev. B 83, 224516 (2011)

Chiral Majorana Fermion Modes on the Surface of Superconducting Topological Insulators

Ching-Kai Chiu, Guang Bian, Hao Zheng, Jia-Xin Yin, Songtian S. Zhang, D. S. Sanchez, I. Belopolski, Su-Yang Xu and M. Zahid Hasan
Europhysics Letters 123, 47005 (2018)

Topological Dirac surface states and superconducting pairing correlations in PbTaSe2 (Topological Superconductor Candidate)

T.-R. Chang, P.-J. Chen, G. Bian, S.-M. Huang, H. Zheng, T. Neupert, R. Sankar, S.-Y. Xu, I. Belopolski, G. Chang, B. Wang, F. Chou, A. Bansil, H.-T. Jeng, H. Lin, and M. Z. Hasan
Phys. Rev. B 93, 245130 (2016)

Superconducting properties in single crystals of the topological nodal semimetal PbTaSe2

C.-L. Zhang, Z. Yuan, G. Bian, S.-Y. Xu, X. Zhang, M. Z. Hasan, and S. Jia
Phys. Rev. B 93, 054520 (2016)

Momentum-space imaging of Cooper pairing in a half-Dirac-gas topological superconductor
Su-Yang Xu, Nasser Alidoust, Ilya Belopolski, Anthony Richardella, Chang Liu, Madhab Neupane, Guang Bian, Song-Hsun Huang, Raman Sankar, Chen Fang, Brian Dellabetta, Wenqing Dai, Qi Li, Matthew J. Gilbert, Fangcheng Chou, Nitin Samarth & M. Zahid Hasan
Nature Physics 10, 943 (2014)

Observation of the spin-polarized surface state in a noncentrosymmetric superconductor BiPd
M. Neupane, N. Alidoust, M. Hosen, K. Dimitri, Jian-Xin Zhu, Su-Yang Xu, Nagendra Dhakal, Raman Sankar, Ilya Belopolski, Daniel S. Sanchez, Tay-Rong Chang, Horng-Tay Jeng, Koji Miyamoto, Taichi Okuda, Hsin Lin, Arun Bansil, D. Kaczorowski, F.C. Chou, M. Z. Hasan & T. Durakiewicz
Nature Communications (2016)

Observation of topological order in a superconducting doped topological insulator
L. Andrew Wray, Su-Yang Xu, Yuqi Xia, Yew San Hor, Dong Qian, Alexei V. Fedorov, Hsin Lin, Arun Bansil, Robert J. Cava & M. Zahid Hasan
Nature Physics 6, 855 (2010)


Recently, there has been great interest in finding topologically nontrivial states in materials that are not insulators. A particularly exciting proposal is to realize a topological superconductor. Superconductivity is a collective phenomenon where electrons at the Fermi level cannot exist as single particles but are attracted to each other, forming Cooper pairs. This causes an energy gap, the superconducting gap, in the electronic single-particle spectrum. In a topological insulator, the bulk electronic structure has an insulating band gap whereas the surface shows protected Dirac electron states due to the nontrivial topology. It has been proposed that one can use a similar picture to qualitatively understand a topological superconductor. A topolological superconductor has a superconducting gap in the bulk but show protected metallic states on its boundaries or surfaces. However, unlike a topological insulator where the surface states consist of electrons, the surface states in a topological superconductor are made up of Majorana fermions. A Majorana fermion is a fermionic particle that is its own antiparticle. It was originally proposed in high energy physics as a way to understand neutrinos but has not been conclusively observed as any fundamental particle. On the other hand, it is believed that Majorana fermions arising in condensed matter systems can play a pivital role in building a fault-tolerant quantum computer. Moreover, it has been predicted that certain quantum phase transition associated with a topological superconductor can realize condensed matter supersymmetry. Supersymmetry is a fascinating theory in particle physics under which bosons and fermions can be converted into each other. However, observing supersymmetry in particle physics requires accelerating elementary particles to very high energies, which are probably beyond the capability of the most powerful accelerators currently available such as the large hadron collider, and therefore supersymmetry remains elusive to date. Topological superconductors provide a rare and exciting platform to realize Majorana fermions and supersymmetry physics in similar condensed matter settings. Recently, we have realized a 2D helical topological superconductor in a heterostructure sample constituting of a topological insulator Bi2Se3 film and a s-wave superconductor NbSe2.


Spin and angle resolved photoemission (spin-ARPES) measurements on Bi2Se3/NbSe2 heterostructure demonstrate topological superconductivity and helical Cooper pairing via proximity effect.
Published in S.-Y. Xu, N. Alidoust, I. Belopolski et al., Nature Physics 10, 943 (2014).

  Possible topological superconductivity in CuxBi2Se3

Back in 2010, we were already trying to search for topologically nontrivial states in superconductors. We systematically studied copper-doped bismuth selenide, CuxBi2Se3, which was found to be a superconductor with a transition temperature, Tc ~ 3.8 K. Our critical surface and bulk electronic structure results suggested two possible distinct types of topological superconductivity that can arise in CuxBi2Se3. One scenario (panel c) is that the surface of CuxBi2Se3 realizes a 2D helical topological superconductor via the natural proximity effect between the surface and the bulk of the sample. In this scenario, Majorana fermions are bounded within the magnetic vortices at the surface of the sample under an external magnetic field. The other scenario (panel d) is that the bulk of CuxBi2Se3 is a 3D topological superconductor, where Majorana fermions can flow along the surfaces of the sample in the form of a 2D Majorana surface state, or a 2D Majorana gas. Very recently, we have realized a 2D helical topological superconductor (the scenario one, panel c) in heterostructure samples constituting a topological insulator thin film and an s-wave superconductor NbSe2 substrate.


Observation of topological order in a superconducting doped topological insulator.
Published in L. A. Wray, S.-Y. Xu, Y. Xia, et al., Nature Physics 6, 855 (2010).


Field-free platform for Majorana-like zero mode in superconductors with a topological surface state
Published in Songtian S. Zhang, J.-X. Yin, G. Dai et al., Phys. Rev. B 101, 100507 (2020).


See, recent publications