Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session A9: Majorana Fermions and Superconductivity |
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Sponsoring Units: DCMP Chair: Christian Platt, Stanford University Room: 006D |
Monday, March 2, 2015 8:00AM - 8:12AM |
A9.00001: Topological Shiba chain in a spin-orbit coupled superconductor Philip Brydon, Hoi-Yin Hui, Jay Sau The impurity band formed from a chain of classical spins embedded in a superconductor can be topological, depending on the magnetic texture of the spins. Previous proposals require a helical texture [1] which is, however, unstable towards a ferromagnetic or antiferromagnetic configuration [2]. We show that including surface spin-orbit coupling permits a topological state for a ferromagnetic alignment of the spins [3]. By deriving an effective tight-binding model for the impurity band and hence evaluating the $Z_2$ topological invariant, we show that a topologically non-trivial state is generically present in this model.\\[4pt] [1] T.-P. Choy, J. M. Edge, A. R. Akhmerov, and C. W. J. Beenakker, Phys. Rev. B {\bf 84}, 195442 (2011).\\[0pt] [2] Y. Kim, M. Cheng, B. Bauer, R. M. Lutchyn, and S. Das Sarma, Phys. Rev. B {\bf 90}, 060401(R) (2014).\\[0pt] [3] P. M. R. Brydon, H.-Y. Hui, and J. D. Sau, arXiv:1407.6345. [Preview Abstract] |
Monday, March 2, 2015 8:12AM - 8:24AM |
A9.00002: Zero-bias peak splitting in InSb nanowires Jun Chen, Peng Yu, Mo\"Ira Hocevar, S\'ebastien Plissard, Diana Car, Erik Bakkers, Sergey Frolov Zero-bias conductance peak(ZBP) has been reported as a signature of Majorana fermions in InSb nanowires. Other features like ZBP phase diagram in chemical potential vs magnetic field and peak splitting are proposed as additional evidences of Majorana fermions. We make superconductor-InSb nanowire hybrid devices with the aim of exploring these features and beyond. By means of high-k HfOx as the dielectric layer, we obtain large gate-tunability of chemical potential, which may enable us to map out ZBP phase diagram. Here we report observation of ZBP at finite magnetic field. Such peak is tunable with gates underneath the superconductor. In particular, it splits and merges again as a function of the center gate. We study such splitting in the context of a pair of coupled Majorana bound states. [Preview Abstract] |
Monday, March 2, 2015 8:24AM - 8:36AM |
A9.00003: Electrostatic effects in Majorana hybrid structures Piyapong Sitthison, Tudor Stanescu We study the electrostatic effects that emerge in proximity-coupled semiconductor- superconductor (SM-SC) structures due to the charge transfer induced by the work function difference between the two materials. The effects are described theoretically using a tight-binding model of the heterostructure solved within a self-consistent Poisson-Schrodinger scheme. We find that these effects are responsible for i) generating an effective Rashba-type spin-orbit coupling and ii) modifying the spatial dependence of the low-energy wave functions near the SM-SC interface. This change in the wave-function amplitude at the interface strongly affects the proximity-induced superconducting gap. Both effects have critical consequences on the stability of the Majorana-hosting topological superconducting phase that is predicted to emerge in this type of structures. For a thin-film geometry, we determine the dependence of the effective spin-orbit coupling and induced superconducting gap on the film thickness and on the strength of the SM-SC coupling. [Preview Abstract] |
Monday, March 2, 2015 8:36AM - 8:48AM |
A9.00004: Majorana bound states on a self-organizing helicalmagnetic wire on the surface of a superconductor with spin-orbit coupling Morten Holm Christensen, Jens Paaske, Brian M. Andersen Recent STM experiments [1] have observed zero-energy modes consistent with Majorana bound statesat the ends of ferromagnetically aligned Fe-chains grown on the surface of lead. We consider a chain of magnetic moments on top of an s-wave superconductor with spin-orbit coupling and study their magnetic ordering self-consistently. In the absence of spin-orbit coupling we find that a topologically non-trivial helical state appears for sufficiently high values of the chemical potential, in agreement with Ref. [2], while including spin-orbit coupling and imposing ferromagnetic order we find a non-trivial phase with Majorana bound states in agreement with Ref. [3]. We report numerical results for the general case, with non-zero spin-orbit coupling and self-organized magnetic order, allowing the moments to minimize the free energy. A range of different magnetic orders are identified and topologically non-trivial regions are found to prevail in a large parameter region. [1] Yazdani et. al Science, , 6209 (2014) [2] I. Reis et. al, Phys. Rev. B. 90, (085124) 2014 [3] Brydon et. al, arXiv:1407.6345 (2014) [Preview Abstract] |
Monday, March 2, 2015 8:48AM - 9:00AM |
A9.00005: Majorana modes and transport across junctions of superconductors and normal metals Diptiman Sen, Manisha Thakurathi, Oindrila Deb We study Majorana modes and transport in one-dimensional systems with junctions of $p$-wave superconductors (SCs) and normal metal (NM) leads. For a system with a SC lying between two NM leads, it is known that there is a Majorana mode at the junction between the SC and each NM. If an impurity is present or the $p$-wave pairing amplitude changes sign at some point in the superconductor, two additional Majorana modes appear near that point. We study the effects of all these modes on the normal and Cooper pair conductances. The main effect is to shift the conductance peaks away from zero bias due to hybridization between the Majoranas; the shift oscillates and also decays exponentially as the length of the SC is increased. Using bosonization and the renormalization group (RG) method, we study the effect of interactions between the electrons on the Majorana modes and the conductances. We then consider a system with a junction of three SC regions connected to NM leads. The junction is parameterized by a scattering matrix. Depending on the relative signs of the pairing amplitudes in the three SCs, there may be one or three Majorana modes at the junction. We study the effect of interactions on these modes using an RG analysis which is valid for weak interactions. [Preview Abstract] |
Monday, March 2, 2015 9:00AM - 9:12AM |
A9.00006: Majorana Correlation as a Signature of a Topological Phase Transition Amit Nag, Jay D. Sau Spin orbit coupled semiconductor nanowires in proximity to ordinary S wave superconductor exhibit a topological phase which supports Majorana fermions at the two ends of the nanowire. A signature of Majorana fermions would be a zero bias conductance peak. Indeed such a peak has been observed in recent experiments but at the same time alternate non topological mechanisms have been suggested to explain appearance of the zero bias peak. Here we demonstrate that the zero bias conductance peak from Majorana fermions must appear in a correlated way between the two ends. We analyze how this peculiarity can be used as a signature of the topological phase transition linked to the appearance of Majorana modes and thus can be used to experimentally distinguish between competing theoretical mechanisms. [Preview Abstract] |
Monday, March 2, 2015 9:12AM - 9:24AM |
A9.00007: Topological Kondo effect in transport through superconducting wire with multiple Majorana end states Oleksiy Kashuba, Carsten Timm The transport through the interface between normal metal and topological superconducting wire can be affected by the interaction of the lead electrons and edge states in the wire. For a minimum of three Majorana fermions at the interface, we find nontrivial renormalization physics. Classification of the tunneling processes by spin-1/2 and spin-3/2 irreducible representations of the SU(2) group allows to identify two different renormalization behaviors associated with the representations. Renormalization triggered by the interaction enhances one group of the tunneling amplitudes and suppresses another one, depending on whether the coupling ferro- or antiferromagnetic. The nontrivial RG processes manifest themselves in distinct temperature dependencies and different spin polarizations of the current through the interface depending on the sign of the interaction. [Preview Abstract] |
Monday, March 2, 2015 9:24AM - 9:36AM |
A9.00008: Modulation of the phase in SC order parameter in Kitaev chain and its consequences Sho Nakosai, Yukio Tanaka, Naoto Nagaosa Kitaev's superconducting chain model, one dimensional spinless p-wave superconductor, is a prototype of topological superconductors and supports Majorana modes at the ends of the system. There have been intensive researches on the model since the role of topology in condensed mater physics is highlighted, and recently not a few experimental results show the model can be effectively generated in designed systems. Anytime soon, we will arrange it as we like. A simple extension of the model is two-parallel-aligned chains. It possesses four Majorana states in total. When we take into account the modulation of the phase in the superconducting order parameter, however, the degeneracy of the energy levels is resolved. We investigate the physical consequence of it. The phase should change along the chain to reduce the total energy of the system, and the deterministic equation for it is in the form of sine-Gordon equation. The distribution of the supercurrent due to the modulation leaves the degeneracy in the ground states. Then we can regard the system as a flux qubit. In the presence of external magnetic field, these modulations will couple with the spontaneous field associated with the phase modulation, and result in control of states and an unusual Josephson effect. [Preview Abstract] |
Monday, March 2, 2015 9:36AM - 9:48AM |
A9.00009: Topological Superconductivity in Ferromagnetic Metal Chains: Part I Jian Li, Hua Chen, Ilya Drozdov, Ali Yazdani, Bogdan Bernevig, Allan MacDonald Recent experiments have demonstrated superconductivity induced in ferromagnetic atomic chains as a new route to the research of Majorana physics. In this talk we discuss the theory behind these experiments. We will first present a generic picture for how superconductivity is induced in ferromagnetic metal chains through coupling to a superconductor with strong spin-orbit coupling, and explain why this hybrid system is a plausible new platform in searching for topological superconductivity. We will then present a tight-binding model associated with the existing experiments. We reveal a new chain magnetic symmetry that is able to stabilize multiple Majorana end modes in the absence of disorder, resulting in a one-dimensional crystalline topological superconductor. We show phase diagrams in terms of such topological phases and point out their relevance to the existing experiments. In the last part of this talk we will briefly discuss some other directions of research based on the new platform, including braiding Majorana quasi-particles in ferromagnetic chains, as well as realizing topological superconductivity in two-dimensional ferromagnetic thin films. [Preview Abstract] |
Monday, March 2, 2015 9:48AM - 10:00AM |
A9.00010: Impurity-induced bound states in superconductors with spin-orbit coupling Younghyun Kim, Junhua Zhang, E. Rossi, Roman Lutchyn We study the effect of strong spin-orbit coupling on bound states induced by impurities in superconductors. The presence of spin-orbit coupling breaks the $SU(2)$-spin symmetry and causes the superconducting order parameter to have generically both singlet (s-wave) and triplet (p-wave) components. As a result, impurity-induced bound states corresponding to different angular momentum channels hybridize and display a number of qualitatively different features from that of the well-known Yu-Shiba-Rusinov states in conventional s-wave superconductors. In particular, we find that in the presence of spin-orbit coupling the spectrum of the impurity-induced bound states depends on the orientation of the magnetic moment of the impurity. Our predictions can be used to distinguish the symmetry of the order parameter and have implications for the Majorana proposals based on chains of magnetic atoms placed on the surface of superconductors with strong spin-orbit coupling [1].\\[4pt] [1] S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, Ali Yazdani, Science 346, 602 (2014). [Preview Abstract] |
Monday, March 2, 2015 10:00AM - 10:12AM |
A9.00011: Effect of spin-orbit coupling on the topological phase diagram of a Shiba chain Junhua Zhang, Younghyun Kim, Roman Lutchyn, E. Rossi Recently chains of magnetic adatoms placed on the surface of a superconductor with strong spin-orbit coupling have emerged as very promising systems for the realization of Majorana modes [1]. In a recent work we have found that the presence of spin-orbit coupling can qualitatively modify the spectrum of the impurity-bound states, Yu-Shiba-Rusinov states, induced by a single magnetic impurity placed on a superconductor, when higher angular momentum components of the impurity potential are taken into account [2]. Motivated by these results, we study in detail the effect of spin-orbit coupling on the electronic spectrum of a chain of Yu-Shiba-Rusinov states created by magnetic adatoms placed on the surface of a superconductor. In particular, we study the effect of the spin orbit coupling on the topological phase diagram of a chain of Yu-Shiba-Rusinov states. \\ \noindent [1] S. Nadj-Perge, I. K. Drozdov, J. Li, H. Chen, S. Jeon, J. Seo, A. H. MacDonald, B. A. Bernevig, Ali Yazdani, Science 346, 602 (2014). [2] Younghyun Kim, Junhua Zhang, E. Rossi, and Roman M. Lutchyn, arXiv:1410.4558 (2014). [Preview Abstract] |
Monday, March 2, 2015 10:12AM - 10:24AM |
A9.00012: Topological superconductivity and high Chern numbers in ferromagnetic Shiba lattices Teemu Ojanen, Joel Rontynen, Alex Weststrom, Kim Poyhonen Topological superconductivity was recently observed in a system consisting of a 1D magnetic adatoms on top of a superconducting surface. Anticipating further developments, we show that a 2D array of magnetic atoms support a variant of $p_x+ip_y$ superconductivity and exhibit very complex phase diagram with high Chern numbers. We also present a detailed study of Majorana bound states in 1D chains. [Preview Abstract] |
Monday, March 2, 2015 10:24AM - 10:36AM |
A9.00013: Weak and strong coupling regimes in Majorana hybrid structures John Stenger, Tudor Stanescu We study the proximity-induced low-energy physics that emerges in semiconductor - superconductor hybrid structures in the weak and strong coupling regimes. We find that the proximity-induced gap has a non-monotonic dependence on the effective semiconductor - superconductor coupling strength. To identify the qualitative difference between weak and strong coupled regimes characterized by similar values of the induced gap, we determine the dependence of the differential conductance of a metal - semiconductor - superconductor structure capable of hosting zero-energy Majorana bound states on the heterostructure parameters (semiconductor wire thickness, semiconductor - superconductor coupling strength, etc.) and on applied external fields. We show that an effective low-energy theory can be constructed by properly integrating out the high-energy degrees of freedom (rather than simply ignoring them), which results in a strong renormalization of the low-energy sector. Using this effective theory, we describe the qualitative differences between the Majorana signatures emerging in the weak and strong coupling regimes. [Preview Abstract] |
Monday, March 2, 2015 10:36AM - 10:48AM |
A9.00014: Universal Nonequilibrium Signatures of Majorana Zero Modes in Quench Dynamics Romain Vasseur, Jan Dahlhaus, Joel Moore The quantum evolution after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of ``quantum quench'' to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo) ${\cal L}(t)=\left| \langle\psi(0) | \psi(t)\rangle \right|^2\sim t^{-\alpha}$ for large times after the quench, with a universal critical exponent $\alpha=\frac{1}{4}$ that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels or the presence of bound levels between the lead and the superconductor. As in recent quantum dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy. [Preview Abstract] |
Monday, March 2, 2015 10:48AM - 11:00AM |
A9.00015: New Topological Superconducting phase in Superconductor/2D Topological Insulator/Superconductor Junction Yao Lu, Kam Tuen Law It is well known that a Josephson junction built on top of helical edge states of the topological insulator traps two Majorana fermions when the phase difference between the two superconductors is $\pi $ and the system can be considered as a DIII class topological superconductor. In this work, we show that a narrow strip of two dimensional topological insulator coupled to two superconductors, forming a Josephson junction, can support a new topological phase in the presence of an in plane magnetic field. In this phase, each end of the strip of the topological insulator supports a single Majorana fermion for a wide range of phase difference between the two superconductors. This topological phase can be revealed by Josephson current measurements and tunneling spectroscopy experiments. [Preview Abstract] |
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