Emergence of new exotic states at interfaces with superconductors

Chair

Professor Laura Greene, University of Illinois, USA

Majorana-Fermions

Professor Liang Fu, Massachusetts Institute of Technology, USA

Majorana fermions in nanowires

Professor Leo Kouwenhoven, Delft University of Technology, The Netherlands

Abstract

We recently reported our experiment on "Signatures of Majorana fermions in Hybrid Superconductor-Semiconductor Nanowire Devices". Since then the data has been reproduced and extended by others and also by ourselves. Theoretical analyses have pointed at both alternative explanations as well as strengthening the Majorana interpretation. Also new experimental checks have been proposed including the ultimatecheck in terms of a minimal scheme for braiding to demonstrate non-Abelian statistics. I will give an overview and an outlook. Backgroundinformation and published work can be found at kouwenhovenlab.tudelft.nl.

Majorana fermions in quantum spin Hall insulators

Professor Carlo Beenakker, Leiden University, The Netherlands

Abstract

Topological insulators in proximity to a superconductor have been predicted to support Majorana zero- modes: midgap states with identical creation and annihilation operators and non-Abelian braiding statistics, that are presently under intense scrutiny. The conducting edge of a quantum spin Hall insulator (a quantum well with an inverted band gap) seems like an ideal system to search for these elusive particles in a transport experiment: Only a single mode propagates in each direction along the edge, unaffected by disorder since backscattering of these helical modes is forbidden by time-reversal symmetry. We discuss the prospects for the detection of Majoranas as a short-term application, and braiding as a longer term perspective.

Topological edge and surface states of superfluid 3He

Professor James Sauls, Northwestern University, USA

Abstract

I discuss the relationship between broken symmetries of the ground state and the topological nature of the Fermionic states confined near surfaces, domain walls and topological defects for the superfluid phases of 3He. The Fermionic spectrum of confined (2D) 3He-A are chiral edge states (Weyl Fermions). The negative energy states are are related to the ground-state angular momentum, Lz = (N/2) ℏ, of superfluid 3He-A for N/2 Cooper pairs. The power law suppression of the angular momentum, Lz (T)=(N /2) ℏ [1−βT2] for 0 ≤ T ≪ Tc, in the fully gapped 2D chiral A-phase reflects the thermal excitation of the Weyl branch of Fermions. I discuss the sensitivity of the edge current and ground-state angular momentum to topology and geometry of the confining boundaries. The B-phase of superfluid 3He, described by the Balian-Werthamer state, is the realization of a 3D time-reversal invariant (TRI) topological superfluid with an isotropic energy gap separating the ground-state and bulk continuum states. The surface states are Majorana Fermions with their spins polarized transverse to their direction of propagation, p||, and the surface normal. The negative energy states give rise to a ground-state helical spin current confined on the surface. Superfluid flow through a channel of confined 3He-B breaks SO(2)Lz+Sz rotational  symmetry and time-reversal (T). However, the Bogoliubov-Nambu Hamiltonian remains invariant under the combined symmetry, Uz(π) × T, where Uz(π) is a π rotation about the surface normal. As a result confined 3He-B in the presence of a superflow remains a topological phase with a gapless spectrum of Majorana modes on the surface. Thermal excitation of the Doppler shifted Majorana branches leads to a power law (∼T3) suppression of the superfluid mass current for 0 < T ≲ 0.5 Tc, providing a direct signature of the Majorana branches of surface excitations in the fully gapped 3D topological superfluid, 3He-B.

Chair

Professor James Annett, University of Bristol, UK

Probing odd-triplet contributions to the proximity effect by scanning tunneling spectroscopy

Professor Elke Scheer, Universität Konstanz, Germany

Abstract

In this talk we will address the superconducting proximity effect between a superconductor (S) and a normal metal (N) linked by a spin-active interface. With the help of a low-temperature scanning tunneling microscope [1,2] we study the local density of states of trilayer systems consisting of aluminium, the ferromagnetic insulator (FI) EuS, and the noble metal silver for varying thickness of the FI. In several recent studies it has been shown that EuS acts as ferromagnetic insulator with well-defined magnetic properties down to very low thicknesses [3]. For very thin FI with d¬FI = 2 nm we find a strong enhancement of the induced minigap at the normal side. For intermediate thickness we observe pronounced subgap structures that vary from contact to contact. For dFI = 10 nm the spectra are in agreement with the diffusive theory for S/N structures (without FI) as confirmed in earlier studies [2]. We discuss our findings in the light of recent theories of odd-triplet contributions created by the spin-active interface [4,5].

[1]C. Debuschewitz, F. Münstermann, V. Kunej, E. Scheer A compact and versatile scanning tunnelling microscope with high energy resolution for use in a 3He Cryostat, J. Low Temp. Phys. 147, 525 (2007) [2]  M. Wolz, C. Debuschewitz, W. Belzig, E. Scheer Evidence for attractive pair interaction in diffusive gold films deduced from studies of the superconducting proximity effect with aluminium, submitted [3] J. Linder, A. Sudbø, T. Yokoyama, R. Grein, M. Eschrig, Phys. Rev. B 81, 214505 (2010) [4] B. Li, N. Roschewsky, B. A. Assaf, M. Eich, M. Epstein-Martin, D. Heiman, M. Münzenberg, and J. S. Moodera, Phys. Rev. Lett. 110, 09700 (2013) [5] A. Cottet, W. Belzig, Phys. Rev. B 72, 180503R (2005); P. Machon, W. Belzig, unpublished.

We gratefully acknowledge financial support from the Kompetenznetzwerk Funktionelle Nanostrukturen of the Baden-Württemberg Stiftung.

Singlet-triplet conversion in superconductor-ferromagnet systems with spin-orbit coupling

Dr Sebastian Bergeret, Centro de Física de Materiale, San Sebastian, Spain

Abstract

It is by now common knowledge that the interaction between conventional superconductivity and ferromagnetism in superconductor-ferromagnet (S/F) hybrids leads to a new type of superconducting correlations in a triplet state. Since the prediction of this intriguing phenomenon in 2001, there has been an increasing experimental activity in the field. That research  focuses mainly on the creation and control of spin-polarized supercurrents and tries to identify the optimal material combination.  To achieve this, however, it is essential to understand the fundamental physics that underpin singlet-triplet conversion. It is commonly believed that singlet-triplet  conversion happens only in the presence of magnetic inhomogeneities. In this talk, I will present a unified model  that shows that the spin-orbit, like magnetic inhomogeneities, can generate  triplet correlations.  Our model provides a full analogy between singlet-triplet conversion and the precession of spins injected into a diffusive metal in the presence of spin-orbit coupling.  In the light of our theory, I will analyze the proximity effect in different hybrid structures and establish a general condition for the creation of the equal-spin triplet component.

Supercurrents in half-metallic ferromagnetic oxides

Professor Jan Aarts, Leiden University, The Netherlands

Abstract

It is by now clear that, by generating so-called odd-frequency triplet Cooper pairs, it is possible to have supercurrents flow through ferromagnets over lengths which are similar to those in normal metals. The mechanism under which triplets are generated is not fully understood as yet, but a spin-active interface between the  superconducting (S) contact and the ferromagnet (F) is a prerequisite, meaning some form of inhomogeneous magnetization or a difference in the scattering of two spin channels. In practice, a single S/F interface does not have the required properties to act as triplet generator in an S/F/S Josephson junction, as shown in experiments involving Co [1]. We show that also for halfmetallic ferromagnetic CrO2 a single interface with a superconductor usually does not lead to triplet supercurrents in an S/F/S junction. However, by inserting an N/F*/N sandwich between S and F (N a normal metal and F* a different ferromagnet, micron-ranged supercurrents can be induced in CrO2. Futhermore, experiments based on Point Contact Andreev Reflection [2] indicate that CrO2 has strong intrinsic spin mixing properties, suggesting that the role of the F* layer is primarily spin rotation.

[1] T. S Khaire, M. A. Khasawneh, W. P. Pratt Jr and N. O. Birge, Phys. Rev. Lett. 104, 137002 (2010).

[2] K.A. Yates, M.S. Anwar, J. Aarts, O. Conde, M. Eschrig, T. Löfwander and L.F. Cohen, EuroPhys. Lett. 103, 67005 (2013).

Triplet supercurrents in ferromagnetic Josephson junctions

Professor Norman Birge, Michigan State University, USA

Abstract

The supercurrent in Josephson junctions containing ferromagnetic materials (called S/F/S junctions) decays and oscillates rapidly with increasing F layer thickness due to the large exchange splitting between the spin-up and spin-down electron bands in F.  In the presence of non-collinear magnetization, Bergeret et al. predicted that spin-triplet pair correlations are generated, which are immune to the exchange field and hence persist over much longer distances in F [1].  Several groups have now observed convincing evidence for such spin-triplet correlations in a variety of S/F and S/F/S systems.  Our own approach is based on Josephson junctions of the form S/F’/F/F’’/S, with non-collinear magnetizations in adjacent ferromagnetic layers [2, 3].  Such structures provide the possibility to control the phase across the junction (0-state or pi-state) by rotating the magnetization of one of the three ferromagnetic layers. We will present our recent progress toward achieving this goal.

We acknowledge support from the US DOE under grant DE-FG02-06ER46341, from IARPA under SPAWAR contract N66001-12-C-2017, and from Northrop Grumman Corporation.

[1] F.S. Bergeret, A.F. Volkov, and K.B. Efetov, Phys. Rev. Lett., 86, 4096 (2001). [2] T.S. Khaire, M.A. Khasawneh, W.P. Pratt, Jr., and N.O. Birge, Phys. Rev. Lett. 104, 137002 (2010); C. Klose et al, Phys. Rev. Lett. 108, 127002 (2012). [3] M. Houzet and A.I. Buzdin, Phys. Rev. B 76, 060504(R) (2007).

Andreev states in superconductor / topological insulator hybrid structures

Professor Erhai Zhao, George Mason University, USA

Abstract

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

Abstract

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.[4] 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.

[1] X.-L. Qi and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011). [2] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010). [3] L. Fu & C. L. Kane, PRL, 100, 096407, (2008). [4] P. Wei, F. Katmis, B. A. Assaf, H. Steinberg, P. Jarillo-Herrero, D. Heiman, and J. S. Moodera, PRL, 110, 186807 (2013).

Chair

Professor Nadya Mason, University of Illinois, USA

Professor Yukio Tanaka, Nagoya University, Japan

Abstract

Topological superconductor with time reversal symmetry is a hot topic now. Recently, topological superconducting state has been predicted in Cu doped Bi2Se3 (CuxBi2Se3)[1]. Point contact spectroscopy has shown a zero bias conductance peak (ZBCP) consistent with the presence of surface edge mode[2], i.e., surface Andreev bound states (SABSs)[2]. We study, i) Tunneling spectroscopy [3,6], ii) Josephson current [5], iii) Bulk properties [8] and iv) proximity effect of this system [9].

i) Tunneling spectroscopy of superconducting topological insulator [3] 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 [6] which is an extension of the conductance formula of unconventional superconductors [7].

ii) Josephson effect of  superconducting topological insulator [5] 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 [8]

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 [9]

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.

[1] L. Fu and E. Berg, Phys. Rev. Lett. 105, 097001 (2010).

[2]S. Sasaki, et. al.,  Phys. Rev. Lett. 107, 217001 (2011).

[3] A. Yamakage, K. Yada, M. Sato, and Y. Tanaka, Phys. Rev. B 85, 180509 (2012).

[4] T. H. Hsieh and L. Fu, Phys. Rev. Lett. 108, 107005 (2012).

[5]A. Yamakage,   et.al., Phys. Rev. B 87, 100510(R) (2013).

[6]S. Takami, K. Yada, A. Yamakage, M.Sato and Y. Tanaka, to be submitted in J.Phys.Soc.Jpn.

[7]Y. Tanaka and S. Kashiwaya, Phys. Rev. Lett. 74 3451 (1995)

[8]T. Hashimoto, et.al.,  J. Phys. Soc. Jpn. 82, 044704  (2013).

[9]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

Abstract

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.

Chair

Professor Oded Millo, Racah Institute, Israel

Spin-mixing phenomena in superconductors

Professor Tomas Löfwander, Chalmers University of Technology, Sweden

Superconducting spin filter devices

Professor Mark Blamire, Cambridge University, UK

Abstract

The exchange-splitting of the density of states in a ferromagnetic insulator results an differing tunneling probabilities for the two electron spin directions and so can result in substantial spin polarisation of the tunneling current. Despite this, we showed that superconducting tunnel junctions containing such barriers could show a significant Josephson supercurrent. More recent work has shown that Josephson junctions containing strongly magnetic barriers show a current-phase relationship I = I0 sin(2Ø): i.e. the 2nd harmonic of the conventional form. This behaviour, together with significant asymmetry in the quasiparticle conductance-voltage characteristic, suggests that the triplet pairs mediate the Josephson current in such devices.

Superconducting topological insulators

Professor Yoichi Ando, Osaka University, Japan

Abstract

When a topological insulator becomes a superconductor upon doping, it has a good chance of harboring topological superconductivity. There are two routes for such a possibility. One is that the surface Dirac fermions of topological insulators may obtain superconductivity due to the proximity effect from the bulk and become a spin-non-degenerate 2D topological superconductor. The other is that the bulk superconductivity in a doped topological insulator itself obtains a topological nature due to strong spin-orbit coupling, which could promote odd-parity pairing and make the system a 3D topological superconductor. So far, Cu-doped Bi2Se3 and In-doped SnTe have been found to present zero-bias conductance peaks in point-contact spectroscopy, which suggest the existence of surface Andreev bound states that are a hallmark of unconventional superconductivity. In this talk, I will present latest developments in the experiments on superconducting doped topological insulators.

This work was done in collaboration with S Sasaki, M Kriener, K Segawa, K Yada, Y Tanaka, M Sato, and L Fu.  Y A is supported by JSPS [Grant-in Aid for Scientific Research (S)], MEXT (Innovative Area “Topological Quantum Phenomena” KAKENHI), and AFOSR (AOARD 124038).