*Proc Natl Acad Sci U S A ; 119(42): e2210589119, 2022 Oct 18.*

##### RESUMO

Spin chains proximitized with superconducting condensates have emerged as one of the most promising platforms for the realization of Majorana modes. Here, we craft diluted spin chains atom by atom following a seminal theoretical proposal suggesting indirect coupling mechanisms as a viable route to trigger topological superconductivity. Starting from single adatoms hosting deep Shiba states, we use the highly anisotropic Fermi surface of the substrate to create spin chains characterized by different magnetic configurations along distinct crystallographic directions. By scrutinizing a large set of parameters we reveal the ubiquitous emergence of boundary modes. Although mimicking signatures of Majorana modes, the end modes are identified as topologically trivial Shiba states. Our work demonstrates that zero-energy modes in spin chains proximitized to superconductors are not necessarily a link to Majorana modes while simultaneously identifying other experimental platforms, driving mechanisms, and test protocols for the determination of topologically nontrivial superconducting phases.

*Phys Rev Lett ; 129(6): 066801, 2022 Aug 05.*

##### RESUMO

Spin qubits in silicon and germanium quantum dots are promising platforms for quantum computing, but entangling spin qubits over micrometer distances remains a critical challenge. Current prototypical architectures maximize transversal interactions between qubits and microwave resonators, where the spin state is flipped by nearly resonant photons. However, these interactions cause backaction on the qubit that yields unavoidable residual qubit-qubit couplings and significantly affects the gate fidelity. Strikingly, residual couplings vanish when spin-photon interactions are longitudinal and photons couple to the phase of the qubit. We show that large and tunable spin-photon interactions emerge naturally in state-of-the-art hole spin qubits and that they change from transversal to longitudinal depending on the magnetic field direction. We propose ways to electrically control and measure these interactions, as well as realistic protocols to implement fast high-fidelity two-qubit entangling gates. These protocols work also at high temperatures, paving the way toward the implementation of large-scale quantum processors.

*Nat Nanotechnol ; 17(7): 696-700, 2022 Jul.*

##### RESUMO

Wireless technology relies on the conversion of alternating electromagnetic fields into direct currents, a process known as rectification. Although rectifiers are normally based on semiconductor diodes, quantum mechanical non-reciprocal transport effects that enable a highly controllable rectification were recently discovered1-9. One such effect is magnetochiral anisotropy (MCA)6-9, in which the resistance of a material or a device depends on both the direction of the current flow and an applied magnetic field. However, the size of rectification possible due to MCA is usually extremely small because MCA relies on inversion symmetry breaking that leads to the manifestation of spin-orbit coupling, which is a relativistic effect6-8. In typical materials, the rectification coefficient Î³ due to MCA is usually â£Î³â£ â² 1 A-1 T-1 (refs. 8-12) and the maximum values reported so far are â£Î³â£ ≈ 100 A-1 T-1 in carbon nanotubes13 and ZrTe5 (ref. 14). Here, to overcome this limitation, we artificially break the inversion symmetry via an applied gate voltage in thin topological insulator (TI) nanowire heterostructures and theoretically predict that such a symmetry breaking can lead to a giant MCA effect. Our prediction is confirmed via experiments on thin bulk-insulating (Bi1-xSbx)2Te3 (BST) TI nanowires, in which we observe an MCA consistent with theory and â£Î³â£ ≈ 100,000 A-1 T-1, a very large MCA rectification coefficient in a normal conductor.

*Phys Rev Lett ; 128(3): 037201, 2022 Jan 21.*

##### RESUMO

Magnetic materials in which it is possible to control the topology of their magnetic order in real space or the topology of their magnetic excitations in reciprocal space are highly sought after as platforms for alternative data storage and computing architectures. Here we show that multiferroic insulators, owing to their magnetoelectric coupling, offer a natural and advantageous way to address these two different topologies using laser fields. We demonstrate that via a delicate balance between the energy injection from a high-frequency laser and dissipation, single skyrmions-archetypical topological magnetic textures-can be set into motion with a velocity and propagation direction that can be tuned by the laser field amplitude and polarization, respectively. Moreover, we uncover an ultrafast Floquet magnonic topological phase transition in a laser-driven skyrmion crystal and we propose a new diagnostic tool to reveal it using the magnonic thermal Hall conductivity.

*Proc Natl Acad Sci U S A ; 118(14)2021 Apr 06.*

##### RESUMO

Novel many-body and topological electronic phases can be created in assemblies of interacting spins coupled to a superconductor, such as one-dimensional topological superconductors with Majorana zero modes (MZMs) at their ends. Understanding and controlling interactions between spins and the emergent band structure of the in-gap Yu-Shiba-Rusinov (YSR) states they induce in a superconductor are fundamental for engineering such phases. Here, by precisely positioning magnetic adatoms with a scanning tunneling microscope (STM), we demonstrate both the tunability of exchange interaction between spins and precise control of the hybridization of YSR states they induce on the surface of a bismuth (Bi) thin film that is made superconducting with the proximity effect. In this platform, depending on the separation of spins, the interplay among Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, spin-orbit coupling, and surface magnetic anisotropy stabilizes different types of spin alignments. Using high-resolution STM spectroscopy at millikelvin temperatures, we probe these spin alignments through monitoring the spin-induced YSR states and their energy splitting. Such measurements also reveal a quantum phase transition between the ground states with different electron number parity for a pair of spins in a superconductor tuned by their separation. Experiments on larger assemblies show that spin-spin interactions can be mediated in a superconductor over long distances. Our results show that controlling hybridization of the YSR states in this platform provides the possibility of engineering the band structure of such states for creating topological phases.

*Phys Rev Lett ; 126(1): 016803, 2021 Jan 08.*

##### RESUMO

We establish the quantum fluctuations ΔQ_{B}^{2} of the charge Q_{B} accumulated at the boundary of an insulator as an integral tool to characterize phase transitions where a direct gap closes (and reopens), typically occurring for insulators with topological properties. The power of this characterization lies in its capability to treat different kinds of insulators on equal footing, being applicable to transitions between topological and nontopological band, Anderson, and Mott insulators alike. In the vicinity of the phase transition, we find a universal scaling ΔQ_{B}^{2}(E_{g}) as a function of the gap size E_{g} and determine its generic form in various dimensions. For prototypical phase transitions with a massive Dirac-like bulk spectrum, we demonstrate a scaling with the inverse gap in one dimension and a logarithmic one in two dimensions.

*Phys Rev Lett ; 125(20): 207204, 2020 Nov 13.*

##### RESUMO

We uncover that antiskyrmion crystals provide an experimentally accessible platform to realize a magnonic quadrupole topological insulator, whose hallmark signatures are robust magnonic corner states. Furthermore, we show that tuning an applied magnetic field can trigger the self-assembly of antiskyrmions carrying a fractional topological charge along the sample edges. Crucially, these fractional antiskyrmions restore the symmetries needed to enforce the emergence of the magnonic corner states. Using the machinery of nested Wilson loops, adapted to magnonic systems supported by noncollinear magnetic textures, we demonstrate the quantization of the bulk quadrupole moment, edge dipole moments, and corner charges.

*Phys Rev Lett ; 125(15): 157701, 2020 Oct 09.*

##### RESUMO

We study superconducting quantum interference in a Josephson junction linked via edge states in two-dimensional (2D) insulators. We consider two scenarios in which the 2D insulator is either a topological or a trivial insulator supporting one-dimensional (1D) helical or nonhelical edge states, respectively. In equilibrium, we find that the qualitative dependence of critical supercurrent on the flux through the junction is insensitive to the helical nature of the mediating states and can, therefore, not be used to verify the topological features of the underlying insulator. However, upon applying a finite voltage bias smaller than the superconducting gap to a relatively long junction, the finite-frequency interference pattern in the nonequilibrium transport current is qualitatively different for helical edge states as compared to nonhelical ones.

*Phys Rev Lett ; 125(1): 017701, 2020 Jul 03.*

##### RESUMO

Subgap states in semiconducting-superconducting nanowire hybrid devices are controversially discussed as potential topologically nontrivial quantum states. One source of ambiguity is the lack of an energetically and spatially well defined tunnel spectrometer. Here, we use quantum dots directly integrated into the nanowire during the growth process to perform tunnel spectroscopy of discrete subgap states in a long nanowire segment. In addition to subgap states with a standard magnetic field dependence, we find topologically trivial subgap states that are independent of the external magnetic field, i.e., that are pinned to a constant energy as a function of field. We explain this effect qualitatively and quantitatively by taking into account the strong spin-orbit interaction in the nanowire, which can lead to a decoupling of Andreev bound states from the field due to a spatial spin texture of the confined eigenstates. This result constitutes an important step forward in the research on superconducting subgap states in nanowires, such as Majorana bound states.

*Phys Rev Lett ; 124(18): 187602, 2020 May 08.*

##### RESUMO

Evidence is presented for a first-order magnetic phase transition in a gated two-dimensional semiconductor, monolayer-MoS_{2}. The phase boundary separates a ferromagnetic phase at low electron density and a paramagnetic phase at high electron density. Abrupt changes in the optical response signal an abrupt change in the magnetism. The magnetic order is thereby controlled via the voltage applied to the gate electrode of the device. Accompanying the change in magnetism is a large change in the electron effective mass.

*Phys Rev Lett ; 122(18): 187203, 2019 May 10.*

##### RESUMO

Antiferromagnetic skyrmion crystals are magnetic phases predicted to exist in antiferromagnets with Dzyaloshinskii-Moriya interactions. Their spatially periodic noncollinear magnetic texture gives rise to topological bulk magnon bands characterized by nonzero Chern numbers. We find topologically protected chiral magnonic edge states over a wide range of magnetic fields and Dzyaloshinskii-Moriya interaction values. Moreover, and of particular importance for experimental realizations, edge states appear at the lowest possible energies, namely, within the first bulk magnon gap. Thus, antiferromagnetic skyrmion crystals show great promise as novel platforms for topological magnonics.

*Phys Rev Lett ; 122(12): 126402, 2019 Mar 29.*

##### RESUMO

We 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 Ï close to π. We show that, 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 Ï=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 Ï deviates from π by a critical value, one of the two MCSs gets relocated to an adjacent corner. As the phase difference Ï increases further, the system becomes trivially gapped. The obtained MCSs are robust against static and magnetic disorder. We propose two setups that could realize such a model: one is based on controlling Ï by magnetic flux, the other involves an additional layer of randomly oriented magnetic impurities responsible for the phase shift of π in the proximity-induced superconducting pairing.

*Phys Rev Lett ; 121(19): 196801, 2018 Nov 09.*

##### RESUMO

We propose a tune-free scheme to realize Kramers pairs of Majorana bound states in recently discovered higher-order topological insulators (HOTIs). We show that, by bringing two hinges of a HOTI into the proximity of an s-wave superconductor, the competition between local and crossed Andreev pairing leads to the formation of Majorana Kramers pairs, when the latter pairing dominates over the former. We demonstrate that such a topological superconductivity is stabilized by moderate electron-electron interactions. The proposed setup avoids the application of a magnetic field or local voltage gates, and requires weaker interactions compared with nonhelical nanowires.

*Beilstein J Nanotechnol ; 9: 1263-1271, 2018.*

##### RESUMO

There have recently been several experiments studying induced superconductivity in semiconducting two-dimensional electron gases that are strongly coupled to thin superconducting layers, as well as probing possible topological phases supporting Majorana bound states in such setups. We show that a large band shift is induced in the semiconductor by the superconductor in this geometry, thus making it challenging to realize a topological phase. Additionally, we show that while increasing the thickness of the superconducting layer reduces the magnitude of the band shift, it also leads to a more significant renormalization of the semiconducting material parameters and does not reduce the challenge of tuning into a topological phase.

*Phys Rev Lett ; 116(17): 176401, 2016 Apr 29.*

##### RESUMO

We consider periodically driven arrays of weakly coupled wires with conduction and valence bands of Rashba type and study the resulting Floquet states. This nonequilibrium system can be tuned into nontrivial phases such as topological insulators, Weyl semimetals, and dispersionless zero-energy edge mode regimes. In the presence of strong electron-electron interactions, we generalize these regimes to the fractional case, where elementary excitations have fractional charges e/m with m being an odd integer.

*Phys Rev Lett ; 115(23): 237001, 2015 Dec 04.*

##### RESUMO

We study two microscopic models of topological insulators in contact with an s-wave superconductor. In the first model the superconductor and the topological insulator are tunnel coupled via a layer of randomly distributed scalar and of randomly oriented spin impurities. Here, we demonstrate that spin-flip tunneling dominates over the spin-conserving one. In the second model the tunnel coupling is realized by a spatially nonuniform array of single-level quantum dots with randomly oriented spins. We find that the tunnel region forms a π junction where the effective order parameter changes sign. Because of the random spin orientation, effectively both models exhibit time-reversal symmetry. The proposed π junctions support topological superconductivity without magnetic fields and can be used to generate and manipulate Kramers pairs of Majorana fermions by gates.

*Phys Rev Lett ; 112(24): 246403, 2014 Jun 20.*

##### RESUMO

We propose a scheme to induce Z(3) parafermion modes, exotic zero-energy bound states that possess non-Abelian statistics. We consider a minimal setup consisting of a bundle of four tunnel coupled nanowires hosting spinless electrons that interact strongly with each other. The hallmark of our setup is that it relies only on simple one-dimensional wires, a uniform magnetic field, and strong interactions, but does not require the presence of superconductivity or exotic quantum Hall phases.

*Phys Rev Lett ; 112(19): 196803, 2014 May 16.*

##### RESUMO

We theoretically study transport through a semiconducting Rashba nanowire (NW) in the presence of uniform and spatially modulated magnetic fields. The system is fully gapped, and the interplay between the spin orbit interaction and the magnetic fields leads to fractionally charged fermion (FF) bound states of the Jackiw-Rebbi type at each end of the nanowire. We investigate the transport and noise behavior of a N/NW/N system, where the wire is contacted by two normal leads (N), and we look for possible signatures that could help in the experimental detection of such states. We find that the differential conductance and the shot noise exhibit a subgap structure which fully reveals the presence of the FF state. Alternatively, another confirmation of the presence of the FFs is provided by a conductance measurement in an Aharonov-Bohm setup, where the FFs are responsible for oscillations with double period. Our predictions can be tested in InSb/InAs nanowires and are within reach of the present technology.

*Phys Rev Lett ; 111(19): 196401, 2013 Nov 08.*

##### RESUMO

We study anisotropic lattice strips in the presence of a magnetic field in the quantum Hall effect regime. At specific magnetic fields, causing resonant umklapp scattering, the system is gapped in the bulk and supports chiral edge states in close analogy to topological insulators. In electron gases with stripes, these gaps result in plateaus for the Hall conductivity exactly at the known fillings n/m (both positive integers and m odd) for the integer and fractional quantum Hall effect. For double strips, we find topological phase transitions with phases that support midgap edge states with flat dispersion. The topological effects predicted here could be tested directly in optical lattices.

*Phys Rev Lett ; 111(18): 186805, 2013 Nov 01.*

##### RESUMO

We consider quasi-one-dimensional Ruderman-Kittel-Kasuya-Yosida (RKKY) systems in proximity to an s-wave superconductor. We show that a 2k(F) peak in the spin susceptibility of the superconductor in the one-dimensional limit supports helical order of localized magnetic moments via RKKY interaction, where k(F) is the Fermi wave vector. The magnetic helix is equivalent to a uniform magnetic field and very strong spin-orbit interaction (SOI) with an effective SOI length 1/2k(F). We find the conditions to establish such a magnetic state in atomic chains and semiconducting nanowires with magnetic atoms or nuclear spins. Generically, these systems are in a topological phase with Majorana fermions. The inherent self-tuning of the helix to 2k(F) eliminates the need to tune the chemical potential.