Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session L05: Topological Superconductivity: TheoryFocus

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Sponsoring Units: DMP Chair: Gregory Fiete, University of Texas at Austin Room: BCEC 108 
Wednesday, March 6, 2019 11:15AM  11:51AM 
L05.00001: Designing topological superconductors Invited Speaker: Liang Fu I will discuss routes to creating topological (and other unconventional) superconductors by tuning the Fermi surface of materials with gating, electric/magnetic field and strain. Candidate systems include 2D materials with spinorbit coupling, with tunable van Hove singularity, or with moire superlattice. 
Wednesday, March 6, 2019 11:51AM  12:03PM 
L05.00002: Extension of symmetrybased indicators and its application Seishiro Ono, Haruki Watanabe The goal of the study of topological phases is to achieve the complete classification of phases for all spatial and internal symmetries. The topological periodic table, the classification table of topological insulators for each internal symmetry class, is a milestone in this line of research. 
Wednesday, March 6, 2019 12:03PM  12:15PM 
L05.00003: Classification of topological crystalline superconducting nodes on highsymmetry line Shuntaro Sumita, Takuya Nomoto, Ken Shiozaki, Youichi Yanase Recent development in exact classification of a superconducting gap has elucidated various unconventional gap structures [18], which have not been predicted by the classification of order parameter based on the point group [9]. One of the important previous results is that all symmetryprotected line nodes are characterized by nontrivial topological numbers [6, 7]. Another intriguing discovery is the gap structures depending on the angular momentum of electrons j_{z} on threefold and sixfold rotationalsymmetric lines [1, 3, 8]. Stimulated by these findings, we classify all crystal symmetryprotected nodes (including such j_{z}dependent nodes) on highsymmetry nfold (n = 2, 3, 4, and 6) axes, by using the combination of group theory and Ktheory [10]. As a result, it is shown that the classification by group theory completely corresponds with the topological classification. Based on the obtained results, we discuss superconducting gap structures in several candidate superconductors. 
Wednesday, March 6, 2019 12:15PM  12:27PM 
L05.00004: WeakPairing Higher Order Topological Superconductors Mao Lin, Yuxuan Wang, Taylor Hughes We consider a new class of superconductors, secondorder topological superconductors (SOTSC), that have gapped, topological surfaces and gapless Majorana modes on lowerdimensional boundaries: corners of a 2D system or hinges for a 3D system. We propose two general scenarios that SOTSC can be realized spontaneously with weakpairing instabilities. First, we show that pwave pairing in a Dirac semimetal in 2D with four mirror symmetric Dirac nodes realizes SOTSC. Second, we show that p+id pairing on an ordinary Fermi surface realizes SOTSC as well. We show that these exotic states can be intrinsically realized in a metallic system with electronic interactions. In the latter case we find that the topological invariants describing the system can be written using simple formulae involving only the lowenergy properties of the Fermi surfaces and superconducting pairing, and we also show it can be induced by proximity effect in a heterostructure of cuprate and superconductor. 
Wednesday, March 6, 2019 12:27PM  12:39PM 
L05.00005: Exotic superconductivity with enhanced energy scales in materials with three band crossings YuPing Lin, Rahul Nandkishore Three band crossings can arise in threedimensional quantum materials with certain space group symmetries. The low energy Hamiltonian supports spin one fermions and a flat band. We study the pairing problem in this setting. We write down a minimal BCS Hamiltonian and decompose it into spinorbit coupled irreducible pairing channels. We then solve the resulting gap equations in channels with zero total angular momentum. We find that in the swave spin singlet channel (and also in an unusual dwave ‘spin quintet’ channel), superconductivity is enormously enhanced, with a possibility for the critical temperature to be linear in interaction strength. Meanwhile, in the pwave spin triplet channel, the superconductivity exhibits features of conventional BCS theory due to the absence of flat band pairing. Three band crossings thus represent an exciting new platform for realizing exotic superconducting states with enhanced energy scales. We also discuss the effects of doping, nonzero temperature, and of retaining additional terms in the k.p expansion of the Hamiltonian. 
Wednesday, March 6, 2019 12:39PM  12:51PM 
L05.00006: Anomalous symmetry protected topological states in interacting fermion systems QingRui Wang, Yang Qi, Zhengcheng Gu The classification and construction of symmetry protected topological(SPT) phases have been intensively studied in interacting systems recently. To our surprise, in interacting fermion systems, there even exists a new class of the socalled anomalous SPT(ASPT) states which are only well defined on the boundary of a trivial fermionic bulk. The physical reason is that certain symmetry action might change the fermion parity locally, but is conserved if we introduce a bulk. We demonstrate the essential idea by considering anomalous topological superconductor with time reversal symmetry $T^2=1$. Finally, we also discuss the classification scheme of anoumalous SPT states for interacting fermions with a total symmetry $G_f=G_b\times\Zf$ and relevant experimental implications. 
Wednesday, March 6, 2019 12:51PM  1:03PM 
L05.00007: Superconducting higherorder semimetals : Secondorder Dirac superconductors and magnetic field induced higherorder topological superconductivity Sayed Ali Akbar Ghorashi, Xiang Hu, Taylor Hughes, Enrico Rossi We identify three dimensional superconductors that exhibit various forms of higher order topology. We show how such superconductors can be obtained through superconducting instabilities induced in higher order quadrupole topological semimetals [1]. In our models the normalstate degrees of freedom consist of two orbitals and spin in an electronic structure that forms a quadrupolar topological semimetal. We consider all possible swave superconducting pairing terms satisfying FermiDirac statistics and obtain six different superconducting models. We find that four of the models have a nonzero residual quadrupolelike topology, and therefore topologically protected Majorana hinge states on the four hinges of the sample. The other two models have no quadrupolar topology yet, in the presence of an external magnetic field, exhibit helical hinge states localized at only two of the four hinges. For these two models we also find that the pair of corners exhibiting hinge states switches upon a change of sign of the magnetic field. 
Wednesday, March 6, 2019 1:03PM  1:15PM 
L05.00008: Higher Order Topological Phases: A General Principle of Construction Dumitru Calugaru, Vladimir Juricic, Bitan Roy In this talk, we discuss a general principle for constructing higherorder topological (HOT) phases [1]. We argue that if a Ddimensional firstorder or regular topological phase involves m Hermitian matrices that anticommute with additional p1 mutually anticommuting matrices, it is conceivable to realize an n^{th}order HOT phase, where n=1,..., p, with appropriate combinations of discrete symmetrybreaking Wilsonian masses. An n^{th}order HOT phase accommodates zero modes on a surface with codimension n. We exemplify these scenarios for prototypical threedimensional gapless systems, such as a nodalloop semimetal possessing SU(2) spin rotational symmetry, and Dirac semimetals, transforming under (pseudo)spin1/2 or 1 representation. The former system permits an unprecedented realization of a 4^{th}order phase, without any surface zero modes. Our construction can be generalized to HOT insulators and superconductors in any dimension and symmetry class. 
Wednesday, March 6, 2019 1:15PM  1:27PM 
L05.00009: Gauge Theory of the SuperconductorInsulator Transition Valerii Vinokour, Cristina Diamantini, Luca Gammaitoni, Igor Lukyanchuk, Carlo Trugenberger The standard model of particle physics is extraordinarily successful at explaining much of the physical realm. Yet, one of its most profound aspects, the mechanism of confinement, that binds quarks into hadrons and is supposedly mediated by chromoelectric strings in a condensate of magnetic monopoles, is not thoroughly understood and lacks direct experimental evidence. We demonstrate that the infiniteresistance superinsulating state, a mirror analog of superconductivity, emerging at the insulating side of the superconductorinsulator transition (SIT) is a condensed matter realization of the quark confinement. We reveal that the mechanism ensuring the infinite resistance of superinsulators is the binding of Cooper pairs into neutral “mesons” by electric strings and establish a mapping of quarks onto Cooper pairs in superinsulators. We reveal a Cooper pair analog of the asymptotic freedom effect implying that systems smaller than the string scale appear in a quantum metallic state. 
Wednesday, March 6, 2019 1:27PM  1:39PM 
L05.00010: Superconducting vortex from magnetic skyrmions ShuPing Lee, Yi Li

Wednesday, March 6, 2019 1:39PM  1:51PM 
L05.00011: Magnoninduced superconductivity in a topological insulator coupled to ferro and antiferromagnetic insulators Henning Hugdal, Stefan Rex, Flavio Nogueira, Asle Sudbo We study the effective interactions between Dirac fermions on the surface of a threedimensional topological insulator due to the proximity coupling to the magnetic fluctuations in a ferromagnetic or antiferromagnetic insulator. Magnetic fluctuations can mediate attractive interactions between Dirac fermions of both Amperean and BCS type. In the ferromagnetic case, we find pairing between fermions with parallel momenta, socalled Amperean pairing, whenever the effective Lagrangian for the magnetic fluctuations does not contain a quadratic term. If a quadratic term is present, the pairing is instead of BCS type above a certain chemical potential. In the antiferromagnetic case, BCS pairing occurs when the ferromagnetic coupling between magnons on the same sublattice exceeds the antiferromagnetic coupling between magnons on different sublattices. Outside this region in parameter space, we again find that Amperean pairing is realized 
Wednesday, March 6, 2019 1:51PM  2:03PM 
L05.00012: Reproducing topological properties with quasiMajorana states Adriaan Vuik, Bas Nijholt, Anton Akhmerov, Michael Wimmer Andreev bound states in hybrid superconductorsemiconductor devices can have nearzero energy in the topologically trivial regime as long as the confinement potential is sufficiently smooth. We show that in addition to the suppressed coupling between the quasiMajorana states, also the coupling of these states across a tunnel barrier to the outside is exponentially different. As a consequence, quasiMajorana states mimic most of the proposed Majorana signatures: quantized zerobias peaks, the 4π Josephson effect, and the tunneling spectrum in presence of a normal quantum dot. We identify a quantized conductance dip instead of a peak in the open regime as a distinguishing feature of true Majorana states in addition to having a bulk topological transition. Because braiding schemes rely only on the ability to couple to individual Majorana states, the exponential control over coupling strengths allows to also use quasiMajorana states for braiding. 
Wednesday, March 6, 2019 2:03PM  2:15PM 
L05.00013: FuldeFerrellLarkinOvchinnikov phases in Proximitized Josephson junctions ChienTe Wu, Fnu Setiawan, Kathryn Levin FuldeFerrellLarkinOvchinnikov (FFLO) phases, which are notoriously difficult to find in more homogeneous systems, have been observed in proximitized superconductors. Of particular interest are those heterostructures which are associated with topological phases[1,2]. In this talk, we establish the effects of spinorbit coupling and show why these elusive phases are observable in the presence of proximitization. We focus on that FFLO phase which appears inside a substrate (subjected to an inplane magnetic field) and formed in a Josephson junction configuration. To do so, we solve the Bogoliubovde Gennes equations for the full multicomponent system. The substrates consist of (1) a conical Holmium magnet with an effective 1D spinorbit coupling, and (2) a twodimensional electron gas. 
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