arXiv subjects

Yuval Oreg

Publications and source records attributed to Yuval Oreg.

At least 91 records · Page 5Linked to original sources

arXiv2018

Concomitant opening of a topological bulk-gap with an emerging Majorana edge-state

Majorana 'zero-modes' are expected to be immune to decoherence. The primary method for their characterization in a 1D topological superconductor, is measuring the tunneling current into the edge of the superconductor. Presently, the hallmark of a localized Majorana edge-state is an emergent quantized zero-bias conductance peak (ZBCP). However, such a conductance peak can also result from other mechanisms; e.g., crossing (and sticking) of two branches of a standard Andreev bound state, or a soft potential at the edge of the superconductor. Since the emergence of a 'Majorana-ZBCP' must be accompanied by an opening of a topological gap in the bulk, we performed two simultaneous tunneling measurements: one in the bulk and another at the edge of the 1D superconductor. Measurements were performed with an InAs nanowire in-situ coated with epitaxial aluminum. For particular gate-tuning of the chemical potential in the wire and a Zeeman field parallel to the wire, we observed a closing of the superconducting bulk-gap followed by its reopening concomitant with the appearance of a ZBCP at the edge. We note that a ZBCP could also be observed with different tuning parameters without an observed reopening of the bulk-gap. This demonstrates the importance of simultaneous probing of the bulk and edge when searching for a Majorana edge-state.

cond-mat.mes-hall↗

arXiv2018

Spin liquids from Majorana Zero Modes in a Cooper Box

We propose a path for constructing diverse interacting spin systems from topological nanowires in Cooper Boxes. The wires are grouped into a three-wire building block called an 'hexon', consisting of six Majorana zero modes. In the presence of a strong charging energy, the hexon becomes a Cooper box equivalent to two spin-$1/2$ degrees of freedom. By considering arrays of hexons and controlling the distances between the various wires, one can tune the Hamiltonian governing the low-energy spins, thus providing a route for controllably constructing interacting spin systems in one- and two-dimensions. We explicitly present realizations of the one-dimensional spin-$1/2$ XXZ chain, as well as the transverse field Ising model. We propose an experiment capable of revealing the nature of critical points in such effective spin systems by applying a local gate voltage and measuring the induced charge at a distance. To demonstrate the applicability of this approach to two-dimensions, we provide a scheme for realizing the topologically ordered Yao-Kivelson spin-liquid model, which has a collective Majorana edge mode, similar to the B-phase of Kitaev's honeycomb model.

cond-mat.mes-hall↗

arXiv2018

Thermal conductivity in 1d: disorder-induced transition from anomalous to normal scaling

It is well known that the contribution of harmonic phonons to the thermal conductivity of 1D systems diverges with the harmonic chain length $L$ (explicitly, increases with $L$ as a power-law with a positive power). Furthermore, within various one-dimensional models containing disorder it was shown that this divergence persists, with the thermal conductivity scaling as $\sqrt{L}$ under certain boundary conditions, where $L$ is the length of the harmonic chain. Here we show that when the chain is weakly coupled to the heat reservoirs and there is strong disorder this scaling can be violated. We find a weaker power-law dependence on $L$, and show that for sufficiently strong disorder the thermal conductivity stops being anomalous -- despite both density-of-states and the diverging localization length scaling anomalously. Surprisingly, in this strong disorder regime two anomalously scaling quantities cancel each other to recover Fourier's law of heat transport.

cond-mat.dis-nn↗

arXiv2017

Theory of Disorder-Induced Half-Integer Thermal Hall Conductance

Electrons that are confined to a single Landau level in a two dimensional electron gas realize the effects of strong electron-electron repulsion in its purest form. The kinetic energy of individual electrons is completely quenched and all physical properties are dictated solely by many-body effects. A remarkable consequence is the emergence of new quasiparticles with fractional charge and exotic quantum statistics of which the most exciting ones are non-Abelian quasiparticles. A non-integer quantized thermal Hall conductance $κ_{xy}$ (in units of temperature times the universal constant $π^2 k_B^2 /3 h$; $h$ is the Planck constant and $k_B$ the Boltzmann constant) necessitates the existence of such quasiparticles. It has been predicted, and verified numerically, that such states are realized in the clean half-filled first Landau level of electrons with Coulomb repulsion, with $κ_{xy}$ being either $3/2$ or $7/2$. Excitingly, a recent experiment has indeed observed a half-integer value, which was measured, however, to be $κ_{xy}=5/2$. We resolve this contradiction within a picture where smooth disorder results in the formation of mesoscopic puddles with locally $κ_{xy}=3/2$ or $7/2$. Interactions between these puddles generate a coherent macroscopic state, which is reflected in an extended plateau with quantized $κ_{xy}=5/2$. The topological properties of quasiparticles at large distances are determined by the macroscopic phase, and not by the microscopic puddle where they reside. In principle, the same mechanism might also allow non-Abelian quasiparticles to emerge from a system comprised of microscopic Abelian puddles.

cond-mat.mes-hall↗

arXiv2017

Observation of half-integer thermal Hall conductance

Topological states of matter are characterized by topological invariant, which are physical quantities whose values are quantized and do not depend on details of the measured system. Of these, the easiest to probe in experiments is the electrical Hall conductance, which is expressed in units of $e^2/h$ ($e$ the electron charge, $h$ the Planck's constant). In the fractional quantum Hall effect (FQHE), fractional quantized values of the electrical Hall conductance attest to topologically ordered states, which are states that carry quasi particles with fractional charge and anyonic statistics. Another topological invariant, which is much harder to measure, is the thermal Hall conductance, expressed in units of $κ_0T=(π^2kB^2/3h)T$ ($kB$ the Boltzmann constant, $T$ the temperature). For the quantized thermal Hall conductance, a fractional value attests that the probed state of matter is non-abelian. Quasi particles in non-abelian states lead to a ground state degeneracy and perform topological unitary transformations among ground states when braided. As such, they may be useful for topological quantum computation. In this paper, we report our measurements of the thermal Hall conductance for several quantum Hall states in the first excited Landau level. Remarkably, we find the thermal Hall conductance of the $ν=5/2$ state to be fractional, and to equal $2.5κ_0T$

cond-mat.mes-hall↗

arXiv2017

Realizing Topological Superconductivity with Superlattices

The realization of topological superconductors (SCs) in one or two dimensions is a highly pursued goal. Prominent proposed realization schemes include semiconductor/superconductor heterostructures and set stringent constraints on the chemical potential of the system. However, the ability to keep the chemical potential in the required range while in the presence of an adjacent SC and its accompanied screening effects, is a great experimental challenge. In this work, we study a SC lattice structure in which the SC is deposited periodically on a one- or two-dimensional sample. We demonstrate that this realization platform overcomes the challenge of controlling the chemical potential in the presence of the superconductor's electrostatic screening. We show how Majorana bound states emerge at the ends of a one-dimensional system proximity coupled to a one-dimensional SC lattice, and move on to present a SC-lattice-based realization of the two-dimensional px+ipy SC, hosting chiral Majorana modes at its edges. In particular, we establish that even when assuming the worst case of absolute screening, in which the chemical potential under the SC is completely unaffected by the external gate potential, the topological phase can be reached by tuning the chemical potential in the area not covered by the SC. Finally, we briefly discuss possible effects of Coulomb blockade on the properties of the system.

cond-mat.mes-hall↗

arXiv2017

Fractional chiral superconductors

Two-dimensional $p_x+ip_y$ topological superconductors host gapless Majorana edge modes, as well as Majorana bound states at the core of $h/2e$ vortices. Here we construct a model realizing the fractional counterpart of this phase: a fractional chiral superconductor. Our model is composed of an array of coupled Rashba wires in the presence of strong interactions, Zeeman field, and proximity coupling to an $s$-wave superconductor. We define the filling factor as $ν=l_{\text{so}}n/4$, where $n$ is the electronic density and $l_{\text{so}}$ is the spin-orbit length. Focusing on filling $ν=1/m$, with $m$ being an odd integer, we obtain a tractable model which allows us to study the properties of the bulk and the edge. Using an $ε$-expansion with $m=2+ε$, we show that the bulk Hamiltonian is gapped and that the edge of the sample hosts a chiral $\mathbb{Z}_{2m}$ parafermion theory with central charge $c=\frac{2m-1}{m+1}$. The tunneling density of states associated with this edge theory exhibits an anomalous energy dependence of the form $ω^{m-1}$. Additionally, we show that $\mathbb{Z}_{2m}$ parafermionic bound states reside at the cores of $h/2e$ vortices. Upon constructing an appropriate Josephson junction in our system, we find that the current-phase relation displays a $4πm$ periodicity, reflecting the underlying non-abelian excitations.

cond-mat.mes-hall↗

arXiv2017

Scalable Designs for Quasiparticle-Poisoning-Protected Topological Quantum Computation with Majorana Zero Modes

We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological $T$-junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.

cond-mat.mes-hall↗

arXiv2017

Reduction of electron repulsion and enhancement of $T_{c}$ in small diffusive superconducting grains

The superconducting properties of small metallic grains has been a topic of active research for half a century now. Early experiments demonstrated a remarkable rise in the critical temperature, $T_{c}$, with reducing grain size in a variety of materials. In two dimensional diffusive superconductors, $T_{c}$ is decreased due to enhanced Coulomb repulsion. We propose that in finite size grains, the diffusive enhancement of the Coulomb repulsion is weakened and leads ultimately to an increase in $T_{c}$ in isolated, disordered two dimensional grains. Our mechanism is superimposed on the possible enhancement in $T_{c}$ due to the change in the density of states of finite size systems.

cond-mat.supr-con↗

arXiv2016

Observed Quantization of Anyonic Heat Flow

The quantum of heat conductance of ballistic one-dimensional (1D) channels, being gQ=k0T with k0=pi^2*2kB^2/3h (T - temperature, kB - Boltzmann's constant, h - Planck's constant), is an important fundamental constant. While the quantization of the electrical conductance of 1D ballistic conductors has long been experimentally established, a demonstration of the quantization of thermal conductance proved to be much harder. It has already been accomplished for weakly interacting systems of phonons, photons, and electronic Fermi-liquids. Theoretically, however, the quantization must also hold in strongly interacting systems, such as the Fractional Quantum Hall effect (FQHE), where electrons fractionalize into anyons and chargeless quasiparticles such as neutral Majorana fermions. Since the bulk in the FQHE is incompressible, it is not expected to contribute significantly to the heat conductance, which is determined by chiral 1D edge modes. The thermal conductance reflects topological properties of the FQH electronic systems to which the electrical conductance gives no access. Here, we present results of extensive measurements of the heat conductance in 'particle-like' (Laughlin's) and 'hole-like' fractional states. We verify the universal value of the quantum of thermal conductance of the charged fractional modes as well as for chargeless neutral modes. We also prove the validity of the theoretical predictions for the more complex (and less studied) 'hole-like' states. Heat transport measurements open a door to ample information, not easily accessible by conductance measurements.

cond-mat.mes-hall↗

arXiv2016

No-go theorem for a time-reversal invariant topological phase in noninteracting systems coupled to conventional superconductors

We prove that a system of non-interacting electrons proximity coupled to a conventional s-wave superconductor cannot realize a time reversal invariant topological phase. This is done by showing that for such a system, in either one or two dimensions, the topological invariant of the corresponding symmetry class (DIII) is always trivial. Our results suggest that the pursuit of Majorana bound states in time-reversal invariant systems should be aimed at interacting systems or at proximity to unconventional superconductors.

cond-mat.mes-hall↗

arXiv2016

Generalized parafermions and non-local Josephson effect in multi-layer systems

We theoretically investigate the effects of backscattering and superconducting proximity terms between the edges of two multi-layer fractional quantum Hall (FQH) systems. While the different layers are strongly interacting, we assume that tunneling between them is absent. Studying the boundaries between regions gapped by the two mechanisms in an $N$-layer system, we find $N$ localized zero-mode operators realizing a generalized parafermionic algebra. We further propose an experiment capable of probing imprints of the generalized parafermionic bound states. This is done by coupling different superconducting contacts to different layers, and examining the periodicity of the Josephson effect as a function of the various relative superconducting phases. Remarkably, even if we apply a phase difference between the superconductors in one layer, we induce a Josephson current at the other layers due to inter-layer interactions. Furthermore, while the Josephson effect is commonly used to probe only charged degrees of freedom, the possibility of independently controlling the superconducting phase differences between the layers allows us to find imprints of the neutral modes of the underlying multi-layer system. In particular, we propose two configurations, one of which is capable of isolating the signal associated with the charge modes, while the other probes the neutral modes.

cond-mat.mes-hall↗

arXiv2016

Interaction-driven topological superconductivity in one dimension

We study one-dimensional topological superconductivity in the presence of time-reversal symmetry. This phase is characterized by having a bulk gap, while supporting a Kramers' pair of zero-energy Majorana bound states at each of its ends. We present a general simple model which is driven into this topological phase in the presence of repulsive electron-electron interactions. We further propose two experimental setups and show that they realize this model at low energies. The first setup is a narrow two-dimensional topological insulator partially covered by a conventional s-wave superconductor, and the second is a semiconductor wire in proximity to an s-wave superconductor. These systems can therefore be used to realize and probe the time-reversal invariant topological superconducting phase. The effect of interactions is studied using both a mean-field approach and a renormalization group analysis.

cond-mat.mes-hall↗

arXiv2016

Electron Attraction Mediated by Coulomb Repulsion

One of the defining properties of electrons is their mutual Coulombic repulsion. In solids, however, this basic property may change. A famous example is that of superconductors, where coupling to lattice vibrations make electrons attract each other and leads to the formation of bound pairs. But what if all degrees of freedom are electronic? Is it still possible to make electrons attractive via their repulsion from other electrons? Such a mechanism, termed 'excitonic', was proposed fifty years ago by W. A. Little, aiming to achieve stronger and more exotic superconductivity, yet despite many experimental efforts, direct evidence for such 'excitonic' attraction is still lacking. Here, we demonstrate this unique attraction by constructing, from the bottom up, the fundamental building block of this mechanism. Our experiments are based on quantum devices made from pristine carbon nanotubes, combined with cryogenic precision manipulation. Using this platform we demonstrate that two electrons can be made to attract using an independent electronic system as the binding glue. Owing to its large tunability, our system offers crucial insights into the underlying physics, such as the dependence of the emergent attraction on the underlying repulsion and the origin of the pairing energy. We also demonstrate transport signatures of 'excitonic' pairing. This experimental demonstration of 'excitonic' pairing paves the way for the design of exotic states of matter.

cond-mat.mes-hall↗

arXiv2016

Signatures of topological Josephson junctions

Quasiparticle poisoning and diabatic transitions may significantly narrow the window for the experimental observation of the $4π$-periodic $dc$ Josephson effect predicted for topological Josephson junctions. Here, we show that switching current measurements provide accessible and robust signatures for topological superconductivity which persist in the presence of quasiparticle poisoning processes. Such measurements provide access to the phase-dependent subgap spectrum and Josephson currents of the topological junction when incorporating it into an asymmetric SQUID together with a conventional Josephson junction with large critical current. We also argue that pump-probe experiments with multiple current pulses can be used to measure the quasiparticle poisoning rates of the topological junction. The proposed signatures are particularly robust, even in the presence of Zeeman fields and spin-orbit coupling, when focusing on short Josephson junctions. Finally, we also consider microwave excitations of short topological Josephson junctions which may complement switching current measurements.

cond-mat.mes-hall↗

arXiv2016

A geometric protocol for a robust Majorana magic gate

A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this manuscript we present a protocol that achieves the missing, so called, $π/8$ 'magic' phase gate. The protocol is based on the manipulation of geometric phases in a universal manner, and does not require fine tuning for distinct physical realizations. The protocol converges exponentially with the number of steps in the geometric path. Furthermore, the magic gate protocol relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to any-phase-gate, where $π/8$ is substituted by any $α$.

cond-mat.mes-hall↗

arXiv2015

Current Correlations in a Majorana Beam Splitter

We study current correlations in a $T$-junction composed of a grounded topological superconductor and of two normal-metal leads which are biased at a voltage $V$. We show that the existence of an isolated Majorana zero mode in the junction dictates a universal behavior for the cross correlation of the currents through the two normal-metal leads of the junction. The cross correlation is negative and approaches zero at high bias voltages as -1/$V$. This behavior is robust in the presence of disorder and multiple transverse channels, and persists at finite temperatures. In contrast, an accidental low-energy Andreev bound state gives rise to nonuniversal behavior of the cross correlation. We employ numerical transport simulations to corroborate our conclusions.

cond-mat.mes-hall↗

arXiv2015

From an array of quantum wires to three-dimensional fractional topological insulators

The coupled-wires approach has been shown to be useful in describing two-dimensional strongly interacting topological phases. In this manuscript we extend this approach to three-dimensions, and construct a model for a fractional strong topological insulator. This topologically ordered phase has an exotic gapless state on the surface, called a fractional Dirac liquid, which cannot be described by the Dirac theory of free fermions. Like in non-interacting strong topological insulators, the surface is protected by the presence of time-reversal symmetry and charge conservation. We show that upon breaking these symmetries, the gapped fractional Dirac liquid presents unique features. In particular, the gapped phase that results from breaking time-reversal symmetry has a halved fractional Hall conductance of the form $σ_{xy}=\frac{1}{2}\frac{e^{2}}{mh}$ if the filling is $ν=1/m$. On the other hand, if the surface is gapped by proximity coupling to an $s$-wave superconductor, we end up with an exotic topological superconductor. To reveal the topological nature of this superconducting phase, we partition the surface into two regions: one with broken time-reversal symmetry and another coupled to a superconductor. We find a fractional Majorana mode, which cannot be described by a free Majorana theory, on the boundary between the two regions. The density of states associated with tunneling into this one-dimensional channel is proportional to $ω^{m-1}$, in analogy to the edge of the corresponding Laughlin state.

cond-mat.mes-hall↗