Abstracts TS 2020

Topological Nature of High Temperature Superconductivity

Valerii Vinokour

An underlying mechanism of the high temperature superconductivity (HTS) and the nature of the adjacent phases remains the biggest mystery of condensed matter physics. It is believed that the key to understanding of HTS lies in revealing the origin of the enigmatic properties of the pseudogap state that settles in the underdoped region between the superconducting transition temperature Tc and the pseudogap temperature T* > Tc. The experiments indicate that the pseudogap state is a distinct thermodynamic phase that exhibits metallic transport, magnetoelectric effect and the nematicity. We develop a unified theory that offers a quantitative description of the pseudogap phase properties and describes the observed phase diagram. The proposed mechanism of the superconductivity is the emergence of the condensate of dyons, the composite particles carrying both electric and magnetic charge, in our case the Cooper pair bound with the magnetic monopole. In the HTS phase, the dyon condensate coexists with the fundamental Cooper pair condensate and the elevated Tc results from the stabilizing effect of the monopole condensate. We show that in the pseudogap phase charged magnetic monopole condensate realizes the oblique confinement of Cooper pairs. The universality of the HTS phase diagram for different materials reflects the unique topological mechanism responsible for formation of the emerging phases. Our findings provide a topological reason for the high critical temperature in HTS.

One-dimensional moiré charge density wave in the hidden order state of URu2Si2 induced by fracture

Edwin Herrera

URu2Si2 is a heavy fermion system which crystallizes in a tetragonal structure and where superconductivity emerges inside the misterious hidden order phase. The latter consists of a still unknown type of order that appears together with a strong entropy reduction below 17.5 K. URu2Si2 becomes superconducting below 1.5 K. The hidden order phase is characterized by dynamical spin modes at q0=(0 0 1) and q1=(0.6 0 0). These quench into an antiferromagnetic order under pressure (q0=(0 0 1)) and at high magnetic fields (q1=(0.6 0 0)). Here I will show recent Scanning Tunneling Microscopy experiments (STM) at very low temperatures (0.1 K). I will report on the discovery of a charge modulation with a wavevector that is a moiré combination of the atomic lattice periodicity and q1, produced by fracturing the crystal in presence of the dynamical spin mode at q1. Our results suggest that charge interactions are a fundamental ingredient that competes with hidden order in URu2Si2 and advance controlled fracture as powerful means to obtain ground states derived from strong electronic correlations [1]. Furthermore, I will show results at surfaces with large amounts of atomically flat steps showing the U fourfold lattice. There we find a new heavy fermion 2D-electron gas type of surface state with an effective mass 17 times the free electron mass. We discuss lateral quantization of such 2D heavy electrons and the interaction of the surface band with bulk superconductivity.

[1] E. Herrera, et. al., One-dimensional moire charge density wave in the hidden order state of URu2Si2 induced by fracture, arXiv:2003.07881v2 (2020).

Second Order Topological Superconductivity: Majorana and parafermion corner states

Jelena Klinovaja


Recently, a lot of interest has been raised by the generalization of conventional TIs/TSCs to so-called higher order TIs/TSCs. While a conventional d-dimensional TI/TSC exhibits (d − 1)-dimensional gapless boundary modes, a d-dimensional n-th order TI/TSC hosts gapless modes at its (d − n)-dimensional boundaries. In my talk, I will consider a Josephson junction bilayer consisting of two tunnel-coupled two-dimensional electron gas layers with Rashba spin-orbit interaction, proximitized by a top and bottom s-wave superconductor with phase difference φ close to π [1-3]. In the presence of a finite weak in-plane Zeeman field, the bilayer can be driven into a second order topological superconducting phase, hosting two Majorana corner states (MCSs). If φ=π, in a rectangular geometry, these zero-energy bound states are located at two opposite corners determined by the direction of the Zeeman field. If the phase difference φ deviates from π by a critical value, one of the two MCSs gets relocated to an adjacent corner. As the phase difference φ increases further, the system becomes trivially gapped. The obtained MCSs are robust against static and magnetic disorder.

In the second part of my talk, I will switch from non-interacting systems [4,5], in which one neglects effects of strong electron-electron interactions, to interacting systems and, thus, to exotic fractional phases. I will show that this is indeed possible and explicitly construct a two-dimensional (2D) fractional second-order TSC. I will consider a system of weakly coupled Rashba nanowires in the strong spin-orbit interaction (SOI) regime. The nanowires are arranged into two tunnel-coupled layers proximitized by a top and bottom superconductor such that the superconducting phase difference between them is π. In such a system, strong electron- electron interactions can stabilize a helical topological superconducting phase hosting Kramers partners of Z_2m parafermion edge modes, where m is an odd integer determined by the position of the chemical potential. Furthermore, upon turning on a weak in-plane magnetic field, the system is driven into a second- order topological superconducting phase hosting zero-energy Z_2m parafermion bound states localized at two opposite corners of a rectangular sample.


[1] Y. Volpez, D. Loss, and J. Klinovaja, Phys. Rev. Lett. 122,126402 (2019)

[2] K. Plekhanov, M. Thakurathi, D. Loss, and J. Klinovaja, Phys. Rev. Research 1, 032013(R) (2019)

[3] K. Plekhanov, N. Müller, Y. Volpez, D. M. Kennes, H. Schoeller, D. Loss, and J. Klinovaja, arXiv:2008.03611

[4] K. Laubscher, D. Loss, and J. Klinovaja, Phys. Rev. Research 1, 032017(R) (2019)
[5] K. Laubscher, D. Loss, and J. Klinovaja, Phys. Rev. Research 2, 013330 (2020)

Two-dimensional Topological Superconductivity

Eun-Ah Kim

One could envision different strategies for designing topological superconductivity. One strategy would be to restrict the phase space in the kinetic energy by manipulating the band structure. Another strategy would be to restrict the pairing interaction. I will our proposals following each of these strategies. For the band-structure manipulation, I will discuss the prediction of p-wave superconductivity in p-doped TMD's with intermediate interaction. I will also discuss the competition for the surface state among multiple topological orders in FeSeTe. For the strategy of manipulating pairing interaction, I will discuss our proposal of using a metal-quantum paramagnet heterostructure.

Resonant p-wave oscillations of Josephson current in Nb-Bi2Te2.3Se0.7-Nb topological junctions

Alexander Golubov

Recent proposals of inducing p-wave superconductivity by sandwiching a conventional s- wave superconductor (S) with a topological insulator (TI) triggered a burst of research activity. Topological superconductors harness the inherent electron – hole symmetry of excitations in a superconductor with the helical nature of the electronic states in topological materials, that may lead to Majorana zero energy states. Various theoretical models focused on possible pairing symmetries of the proximity induced superconducting order in topological layers. Several experimental groups already realized S-TI interfaces and S-TI-S junctions, and studied the Josephson current across them. Few papers have reported unusual Shapiro steps consistent with the formation of the p-wave correlations. However, measurements that could provide the definitive evidence of the p-wave superconductivity should be phase-sensitive, to discriminate between the p- and other (s-, d-...) pairings symmetries.
In this work we report a new type of oscillations of the critical Josephson current in magnetic field observed in the Nb-Bi2Te2.3Se0.7-Nb junctions [1,2]. The ultra-short period ∼ 1 Oe of these oscillations and their sharply peaked shape reflect the resonant transmission via Andreev bound states with the ultra-fine ∼ 1 μeV interlevel spacing. We argue that the ultra- fine oscillations revealed in our S-TI-S devices is the direct consequence of the p-wave superconducting order induced at S-TI contacts.

[1] V.S. Stolyarov, D.S. Yakovlev, S.N. Kozlov, O.V. Skryabina, D.S. Lvov, A.I. Gumarov, O.V. Emelyanova, P.S. Dzhumaev, I.V. Shchetinin, R.A. Hovhannisyan, S.V. Egorov, A.M. Kokotin, W.V. Pogosov, V.V. Ryazanov, M.Yu. Kupriyanov, A.A. Golubov, D. Roditchev. COMMUNICATIONS MATERIALS 1:38 (2020)| https://doi.org/10.1038/s43246-020-0037-y | www.nature.com/commsmat.
[2] V.S. Stolyarov, D. Roditchev, V.L Gurtovoy, S.N. Kozlov, D.S. Yakovlev, O.V. Skryabina, V.M. Vinokur, A.A. Golubov, submitted to Nature Physics.

Flat Bands in Flatlands

Jeanie Lau

In a flat band system, the charge carriers’ energy-momentum relation is very weakly dispersive. The resultant large density of states and the dominance of Coulomb potential energy relative to the kinetic energy often favor the formation of strongly correlated electron states, such as ferromagnetism, nematicity, antiferromagnetism, superconductivity, and charge density waves. The advent of two-dimensional (2D) materials and their heterostructures has ushered in a new era for exploring, tuning and engineering of flat band system. Here I will present our results on transport measurements of high quality few-layer 2D material devices, including intrinsic magnetism and helical edge states in few-layer graphene, and observation of both superconductivity and the Mott-like insulating state in a tBLG device with a twist angle of ~0.93°.

Long range unconventional Josephson effect across a half metallic ferromagnet

Jacobo Santamaria

The Josephson effect results from the coupling of two superconductors across a non- superconducting spacer to yield a quantum coherent state. In ferromagnets, singlet (opposite- spin) Cooper pairs decay over very short distances, and thus Josephson coupling requires a nanometric spacer. This is unless equal-spin triplet pairs are generated which, theoretically, can couple superconductors across much longer distances. Despite many experimental hints of triplet superconductivity, long range triplet Josephson effects have remained elusive. In this talk I will discuss a micron-range Josephson coupling across the half-metallic ferromagnet
La0.7Sr0.3MnO3 combined with the high-temperature superconductor YBa2Cu3O7 in planar junctions. These display the Josephson physics’ hallmarks: critical current oscillations due to flux quantization and quantum phase locking under microwave excitation. The marriage of high- temperature quantum coherent transport and full spin polarization brings unique opportunities for the practical realization of superconducting spintronics, and enables novel strategies for quantum computing.

Topological phases combining superconductivity and magnetism

Mario Cuoco

In this talk I will present different routes to generate and manipulate topological phases due to the interplay between superconductivity and magnetism. The search for new variants of semimetals (SMs) recently highlighted the interplay of Dirac fermions physics and magnetism. Indeed, antiferromagnetic (AFM) SMs can be obtained where both time and inversion are broken while their combination is kept [1,2] or due to chiral- [2] and time-symmetry [2,3] combined with non-symmorphic transformations [2]. Here, we discuss materials, i.e. transition metal oxide systems, that can exhibit AFM-SM phase due to orbitally directional double- exchange effects [4, 2]. In this context, the impact of s-wave spin-singlet pairing on AFM-SMs with Dirac points or nodal loops at the Fermi level [5] is generally shown to convert the semimetal into various types of nodal topological superconductors. The changeover from fully gapped to gapless phases is dictated by symmetry properties of the AFM-superconducting state that set out the occurrence of a large variety of electronic topological transitions [4].
Finally, I will focus on various quantum platforms marked by spin-singlet or spin-triplet pairing interfaced with non-trivial magnetic patterns and discuss the nature of the emerging topological phases [6,7,8]. The coexistence of ferromagnetism or antiferromagnetism with spin-triplet superconductivity is also analysed and discussed with respect to relevant materials cases.

[1] P. Tang, Q. Zhou, G. Xu, and S.-C. Zhang, Nat. Phys. 12, 1100 (2016).
[2] W. Brzezicki and M. Cuoco, Phys. Rev. B 95, 155108 (2017).
[3] S. M. Young and B. J. Wieder, Phys. Rev. Lett. 118, 186401 (2017).
[4] W. Brzezicki, C. Noce, A. Romano, and M. Cuoco, Phys. Rev. Lett. 114, 247002 (2015).
[5] W. Brzezicki and M. Cuoco, Phys. Rev. B 97, 064513 (2018).
[6] M. T. Mercaldo, M. Cuoco, P. Kotetes, Phys. Rev. B 94, 140503(R) (2016).
[7] A. Romano, P. Gentile, C. Noce, I. Vekhter, M. Cuoco, Phys. Rev. Lett. 110, 267002 (2013). 8. P. Kotetes, M. T. Mercaldo, M. Cuoco, Phys. Rev. Lett. 123, 126802 (2019).
[9] M. T. Mercaldo, P. Kotetes, M. Cuoco, Phys. Rev. B 100, 104519 (2019).

Geometrically driven effects in curved superconducting nanostructures

Paola Gentile

The most recent advances in nanotechnology have demonstrated the possibility to create flexible semiconductor nanomaterials which are bent into curved, deformable objects ranging from semiconductor nanotubes, to nanohelices, etc. The consequences of the nanowire bending on the electronic quantum properties have been demonstrated to become of particular importance in systems with structure inversion asymmetry, where the interplay between nanoscale deformations and Rashba spin-orbit coupling (RSOC) [1] allows an all-geometrical and electrical control of electronic spin textures and spin transport properties [2,3], including the possibility to induce topological nontrivial phases [4-6]. In the presence of superconducting pairing, inversion symmetry breaking (ISB) makes neither spin nor parity good quantum numbers anymore. The ensuing mixing of even spin-singlet and odd spin- triplet channels leads to a series of novel features, from unconventional surface states to topological phases. Within this framework, we have explored the impact that nanoscale geometry has on superconducting properties of low-dimensional materials, showing that the interplay between RSOC and shape deformations can lead to novel paths for a geometric manipulation of the superconducting state, both for spin-singlet and spin-triplet quantum configurations [7], then significantly affecting the Josephson effect of weak links between Rashba coupled straight superconducting nanowires with geometric misalignment [8] as well as between nanowires of topological superconductors with non-trivial geometric curvature [9].

[1] P. Gentile., M. Cuoco, C. Ortix, SPIN, Vol. 3, No. 2, 1340002 (2013).
[2] Z.-J. Ying, P. Gentile, C. Ortix, M. Cuoco, Phys. Rev. B 94, 081406(R) (2016).
[3] G. Francica, P. Gentile, M. Cuoco, EPL 127, 30001 (2019).
[4] P. Gentile, M. Cuoco, C. Ortix, Phys. Rev. Lett. 115, 256801 (2015).
[5] P. G., V. Benvenuto, C. Ortix, C. Noce, M. Cuoco, Condens. Matter 4 (1), 25 (2019).
[6] S. Pandey, N. Scopigno, P. Gentile, M. Cuoco, C. Ortix, Phys. Rev. B 97, 241103(R) (2018).
[7] Z.-J. Ying, M. Cuoco, C. Ortix, P. Gentile, Physical Review B 96, 100506(R) (2017).
[8] Z.-J. Ying, M. Cuoco, P. Gentile, C. Ortix, 2017 16th International Superconductive Electronics Conference (ISEC), IEEE Xplore (2018).
[9] G. Francica, M. Cuoco, P. Gentile, Phys. Rev. B 101, 094504 (2020).

Angle Bilayer Graphene – Superconductors, Orbital Magnets, Correlated States and beyond

Dimitri Efetov

When twisted close to a magic relative orientation angle near 1 degree, bilayer graphene has flat moire superlattice minibands that have emerged as a rich and highly tunable source of strong correlation physics, notably the appearance of superconductivity close to interaction-induced insulating states. Here we report on the fabrication of bilayer graphene devices with exceptionally uniform twist angles. We show that the reduction in twist angle disorder reveals insulating states at all integer occupancies of the four-fold spin/valley degenerate flat conduction and valence bands, i.e. at moire band filling factors nu = 0, +(-) 1, +(-) 2, +(-) 3, and reveals new superconductivity regions below critical temperatures as high as 3 K close to - 2 filling. In addition we find novel orbital magnetic states with non-zero Chern numbers. Our study shows that symmetry-broken states, interaction driven insulators, and superconducting domes are common across the entire moire flat bands, including near charge neutrality. We further will discuss recent experiments including screened interactions, fragile topology and the first applications of this amazing new materials platform.