Andreev states in superconductor / topological insulator hybrid structures
Professor Erhai Zhao, George Mason University, USA
Exotic quasiparticle excitations such as Majorana fermions arise in hybrid structures of topological insulator (TI) and s-wave superconductors (S). Much of the new physics was captured in the elegant model introduced by Fu and Kane for the TI-S interface. And a rich variety of TI-S proximity structures have been investigated experimentally. In this talk, I will present microscopic, self-consistent simulations of the superconducting proximity effect near the TI-S interface for a detailed understanding of the spatial structures of the interfacial bound states. The accuracy of the Fu-Kane model will be assessed. Next, I will demonstrate different regimes of the Andreev bound states spectrum in S-TI-S Josephson junctions, and the related local density of states and the scaling of the supercurrent with the length of the junction. Lastly, I will discuss the nodal structure in the spectrum of TI-S multilayers (superlattices), and present numerical evidence for realizing the analog of the A phase of superfluid helium three, or a Weyl superconductor, in these systems as first pointed out by Meng and Balents.
Broken symmetry by interface exchange-coupling in TI thin film heterostructures
Dr Jagadeesh S Moodera, Massachusetts Institute of Technology,, USA
Inducing an exchange gap locally on the Dirac surface states of a topological insulator (TI) is ideal for observing the predicted unique features such as the quantized topological magnetoelectric effect, half-integer quantized Hall effect, as well as to conﬁne Majorana fermions.[1-3] Our work experimentally demonstrated the proximity-induced interface ferromagnetism in a heterostructure combining a ferromagnetic insulator EuS layer with Bi2Se3, without introducing defects. An exchange gap was observed to be induced on the surface of the TI. Extensive magnetic and magneto-transport (magnetoresistance and anomalous Hall effect) investigation of the heterostructures, including synchrotron interfacial (XAS and XMCD measurements) studies have shown the emergence of a ferromagnetic phase in TI, which is a step forward to unveiling the above exotic properties.
Also, to understand the intrinsic properties of TI it is necessary to correlate structure with the exotic electronic properties as well as interaction with other materials. Molecular beam epitaxy (MBE) ideally allows us to engineer the system whereas using synchrotron and electron diffraction based experimental techniques helps us to investigate with atomic resolution. We will elucidate our studies on well-defined TI films and heterostructure, and the role of imperfections on the symmetry of the material that leads to internal atomic ordering by the decoration of the defects. Charge transport and mobility are seen to relate with film growth strain and relaxation as well as display strong directional dependence on the defect geometry.
Work done in collaboration with Peng Wei, Ferhat Katmis and others.
 X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).  M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).  L. Fu & C. L. Kane, PRL, 100, 096407, (2008).  P. Wei, F. Katmis, B. A. Assaf, H. Steinberg, P. Jarillo-Herrero, D. Heiman, and J. S. Moodera, PRL, 110, 186807 (2013).
Professor Nadya Mason, University of Illinois, USA
Professor Yukio Tanaka, Nagoya University, Japan
Topological superconductor with time reversal symmetry is a hot topic now. Recently, topological superconducting state has been predicted in Cu doped Bi2Se3 (CuxBi2Se3). Point contact spectroscopy has shown a zero bias conductance peak (ZBCP) consistent with the presence of surface edge mode, i.e., surface Andreev bound states (SABSs). We study, i) Tunneling spectroscopy [3,6], ii) Josephson current , iii) Bulk properties  and iv) proximity effect of this system .
i) Tunneling spectroscopy of superconducting topological insulator  We have developed a theory of the tunneling spectroscopy for superconducting topological insulators (STIs), where the SABSs appear as helical Majorana fermions. We have found that the SABSs in the odd-parity STIs have a structural transition in the energy dispersions. The transition [3,4] results in a variety of Majorana fermions, by tuning the chemical potential and the effective mass of the energy band. We further derived an analytical formula of the conductance of the present junction  which is an extension of the conductance formula of unconventional superconductors .
ii) Josephson effect of superconducting topological insulator  We have studied the effect of helical Majorana fermions at the surface of odd-parity STIs on the Josephson current. The Josephson current-phase relation in an STI/s-wave superconductor junction shows robust sin(2ϕ) owing to mirror symmetry, where ϕ denotes the macroscopic phase difference between the two superconductors. The maximum Josephson current in an STI/STI junction exhibits a nonmonotonic temperature dependence depending on the relative spin helicity of the two surface states.
iii) Spin susceptibility 
We have calculated the temperature dependence of the spin susceptibility. We have proposed that the pairing symmetry of a STI can be determined from measurement of the Knight shift by changing the direction of the applied magnetic field.
iv) Proximity effect 
We have self-consistently studied surface states and proximity effect. We demonstrate that, if a topologically trivial bulk s-wave pairing symmetry is realized, parity mixing of pair potential near the surface is anomalously enhanced by surface Dirac fermions, opening an additional surface gap larger than the bulk one. In contrast to classical s-wave superconductors, the resulting surface density of state hosts an extra coherent peak at the induced gap besides a conventional peak at the bulk gap but no such surface parity mixing is induced by Dirac fermions for topological odd-parity superconductors. Our calculation suggests that the simple U-shaped scanning tunneling microscope spectrum does not originate from s-wave superconductivity of CuxBi2Se3.
 L. Fu and E. Berg, Phys. Rev. Lett. 105, 097001 (2010).
S. Sasaki, et. al., Phys. Rev. Lett. 107, 217001 (2011).
 A. Yamakage, K. Yada, M. Sato, and Y. Tanaka, Phys. Rev. B 85, 180509 (2012).
 T. H. Hsieh and L. Fu, Phys. Rev. Lett. 108, 107005 (2012).
A. Yamakage, et.al., Phys. Rev. B 87, 100510(R) (2013).
S. Takami, K. Yada, A. Yamakage, M.Sato and Y. Tanaka, to be submitted in J.Phys.Soc.Jpn.
Y. Tanaka and S. Kashiwaya, Phys. Rev. Lett. 74 3451 (1995)
T. Hashimoto, et.al., J. Phys. Soc. Jpn. 82, 044704 (2013).
T. Mizushima, A. Yamakage, M. Sato and Y. Tanaka, arXiv.1311.2768.
Odd frequency pairing in hybrid structures and multiband superconductors
Professor Alexander Balatsky Los Alamos National Laboratory, USA and Albanova University Center, Sweden
Odd frequency superconductivity proved to be an elusive state that is yet to be observed as a primary pairing state. On the other hand the list of systems and structures where odd frequency can be present as an induced component is growing. I will review various scenarios pointing to emergence of odd frequency pairing due to modifications of the primary conventional pairing. Recently we find that odd frequency component is ubiquitously present in multiband superconductors. We show that odd-frequency superconducting pairing requires only a finite band hybridization, or scattering, and non-identical intraband order parameters, of which only one band needs to be superconducting. From a symmetry analysis we establish a complete reciprocity between parity in band-index and frequency.