17 research outputs found
Topological Superconductivity induced by Ferromagnetic Metal Chains
Recent experiments have provided evidence that one-dimensional (1D)
topological superconductivity can be realized experimentally by placing
transition metal atoms that form a ferromagnetic chain on a superconducting
substrate. We address some properties of this type of systems by using a
Slater-Koster tight-binding model. We predict that topological
superconductivity is nearly universal when ferromagnetic transition metal
chains form straight lines on superconducting substrates and that it is
possible for more complex chain structures. The proximity induced
superconducting gap is where is the -wave
pair-potential on the chain, is the spin-orbit splitting energy
induced in the normal chain state bands by hybridization with the
superconducting substrate, and is the exchange-splitting of the
ferromagnetic chain -bands. Because of the topological character of the 1D
superconducting state, Majorana end modes appear within the gaps of finite
length chains. We find, in agreement with experiment, that when the chain and
substrate orbitals are strongly hybridized, Majorana end modes are
substantially reduced in amplitude when separated from the chain end by less
than the coherence length defined by the -wave superconducting gap. We
conclude that Pb is a particularly favorable substrate material for
ferromagnetic chain topological superconductivity because it provides both
strong wave pairing and strong Rashba spin-orbit coupling, but that there
is an opportunity to optimize properties by varying the atomic composition and
structure of the chain. Finally, we note that in the absence of disorder a new
chain magnetic symmetry, one that is also present in the crystalline
topological insulators, can stabilize multiple Majorana modes at the end of a
single chain.Comment: 19 pages, 15 figures; an analysis of Majorana decay length scale has
been added in the revised versio
Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
Majorana fermions are predicted to localize at the edge of a topological
superconductor, a state of matter that can form when a ferromagnetic system is
placed in proximity to a conventional superconductor with strong spin-orbit
interaction. With the goal of realizing a one-dimensional topological
superconductor, we have fabricated ferromagnetic iron (Fe) atomic chains on the
surface of superconducting lead (Pb). Using high-resolution spectroscopic
imaging techniques, we show that the onset of superconductivity, which gaps the
electronic density of states in the bulk of the Fe chains, is accompanied by
the appearance of zero energy end states. This spatially resolved signature
provides strong evidence, corroborated by other observations, for the formation
of a topological phase and edge-bound Majorana fermions in our atomic chains.Comment: 18 pages, 5 figures, and supplementary information. appears in
Science (2014
One-dimensional Topological Edge States of Bismuth Bilayers
The hallmark of a time-reversal symmetry protected topologically insulating
state of matter in two-dimensions (2D) is the existence of chiral edge modes
propagating along the perimeter of the system. To date, evidence for such
electronic modes has come from experiments on semiconducting heterostructures
in the topological phase which showed approximately quantized values of the
overall conductance as well as edge-dominated current flow. However, there have
not been any spectroscopic measurements to demonstrate the one-dimensional (1D)
nature of the edge modes. Among the first systems predicted to be a 2D
topological insulator are bilayers of bismuth (Bi) and there have been recent
experimental indications of possible topological boundary states at their
edges. However, the experiments on such bilayers suffered from irregular
structure of their edges or the coupling of the edge states to substrate's bulk
states. Here we report scanning tunneling microscopy (STM) experiments which
show that a subset of the predicted Bi-bilayers' edge states are decoupled from
states of Bi substrate and provide direct spectroscopic evidence of their 1D
nature. Moreover, by visualizing the quantum interference of edge mode
quasi-particles in confined geometries, we demonstrate their remarkable
coherent propagation along the edge with scattering properties that are
consistent with strong suppression of backscattering as predicted for the
propagating topological edge states.Comment: 15 pages, 5 figures, and supplementary materia
Measurement-induced entanglement and teleportation on a noisy quantum processor
Measurement has a special role in quantum theory: by collapsing the
wavefunction it can enable phenomena such as teleportation and thereby alter
the "arrow of time" that constrains unitary evolution. When integrated in
many-body dynamics, measurements can lead to emergent patterns of quantum
information in space-time that go beyond established paradigms for
characterizing phases, either in or out of equilibrium. On present-day NISQ
processors, the experimental realization of this physics is challenging due to
noise, hardware limitations, and the stochastic nature of quantum measurement.
Here we address each of these experimental challenges and investigate
measurement-induced quantum information phases on up to 70 superconducting
qubits. By leveraging the interchangeability of space and time, we use a
duality mapping, to avoid mid-circuit measurement and access different
manifestations of the underlying phases -- from entanglement scaling to
measurement-induced teleportation -- in a unified way. We obtain finite-size
signatures of a phase transition with a decoding protocol that correlates the
experimental measurement record with classical simulation data. The phases
display sharply different sensitivity to noise, which we exploit to turn an
inherent hardware limitation into a useful diagnostic. Our work demonstrates an
approach to realize measurement-induced physics at scales that are at the
limits of current NISQ processors
Non-Abelian braiding of graph vertices in a superconducting processor
Indistinguishability of particles is a fundamental principle of quantum
mechanics. For all elementary and quasiparticles observed to date - including
fermions, bosons, and Abelian anyons - this principle guarantees that the
braiding of identical particles leaves the system unchanged. However, in two
spatial dimensions, an intriguing possibility exists: braiding of non-Abelian
anyons causes rotations in a space of topologically degenerate wavefunctions.
Hence, it can change the observables of the system without violating the
principle of indistinguishability. Despite the well developed mathematical
description of non-Abelian anyons and numerous theoretical proposals, the
experimental observation of their exchange statistics has remained elusive for
decades. Controllable many-body quantum states generated on quantum processors
offer another path for exploring these fundamental phenomena. While efforts on
conventional solid-state platforms typically involve Hamiltonian dynamics of
quasi-particles, superconducting quantum processors allow for directly
manipulating the many-body wavefunction via unitary gates. Building on
predictions that stabilizer codes can host projective non-Abelian Ising anyons,
we implement a generalized stabilizer code and unitary protocol to create and
braid them. This allows us to experimentally verify the fusion rules of the
anyons and braid them to realize their statistics. We then study the prospect
of employing the anyons for quantum computation and utilize braiding to create
an entangled state of anyons encoding three logical qubits. Our work provides
new insights about non-Abelian braiding and - through the future inclusion of
error correction to achieve topological protection - could open a path toward
fault-tolerant quantum computing
Studying topological phases of matter in reduced dimensions under the scanning tunneling microscope
Condensed matter physics has experienced a recent boom in the search for topological phases of matter with exploration of material systems that possess topological properties and promise applications in spintronics and quantum computing. Topological systems in reduced dimension are of particular interest as they can possess topologically non-trivial boundary states while potentially being compact in size. 2D and 1D topological systems, however, have been far less experimentally studied as compared to their 3D counterparts. In this thesis direct spectroscopic evidence from Scanning Tunneling Microscopy (STM) experiments for topological edge states will be presented for the two topological phases: (i) a 2D topological insulator (quantum spin Hall) phase realized in a system of Bismuth bilayers and (ii) 1D topological superconductor phase in a synthetic system of ferromagnetic chains on an s-wave superconductor. The end states of the later system are believed to be a realization of Majorana fermions in solid state
<i>In-situ</i> angle-resolved photoemission spectroscopy of copper-oxide thin films synthesized by molecular beam epitaxy
Angle-resolved photoemission spectroscopy (ARPES) is the key momentum-resolved technique for direct probing of the electronic structure of a material. However, since it is highly surface-sensitive, it has been applied to a relatively small set of complex oxides that can be easily cleaved in ultra-high vacuum. Here we describe a new multi-module system at Brookhaven National Laboratory (BNL) in which an oxide molecular beam epitaxy (OMBE) is interconnected with an ARPES and a spectroscopic-imaging scanning tunneling microscopy (SI-STM) module. This new capability largely expands the range of complex-oxide materials and artificial heterostructures accessible to these two most powerful and complementary techniques for studies of electronic structure of materials. We also present the first experimental results obtained using this system — the ARPES studies of electronic band structure of a La2-xSrxCuO4 (LSCO) thin film grown by OMBE