arXiv subjects

Gil Refael

Publications and source records attributed to Gil Refael.

At least 109 records · Page 6Linked to original sources

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↗

arXiv2016

Topological Polaritons in a Quantum Spin Hall Cavity

We study the topological structure of matter-light excitations, so called polaritons, in a quantum spin Hall insulator coupled to photonic cavity modes. We identify a topological invariant in the presence of time reversal (TR) symmetry, and demonstrate the existence of a TR-invariant topological phase. We find protected helical edge states with energies below the lower polariton branch and characteristic uncoupled excitonic states, both detectable by optical techniques. Applying a Zeeman field allows us to relate the topological index to the double coverage of the Bloch sphere by the polaritonic pseudospin.

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arXiv2016

Persistent Hall response in a quantum quench

Out-of-equilibrium systems can host phenomena that transcend the usual restrictions of equilibrium systems. Here we unveil how out-of-equilibrium states, prepared via a quantum quench, can exhibit a non-zero Hall-type response that persists at long times, and even when the instantaneous Hamiltonian is time reversal symmetric; both these features starkly contrast with equilibrium Hall currents. Interestingly, the persistent Hall effect arises from processes beyond those captured by linear response, and is a signature of the novel dynamics in out-of-equilibrium systems. We propose quenches in two-band Dirac systems as natural venues to realize persistent Hall currents, which exist when either mirror or time-reversal symmetry are broken (before or after the quench). Its long time persistence, as well as sensitivity to symmetry breaking, allow it to be used as a sensitive diagnostic of the complex out-equilibrium dynamics readily controlled and probed in cold-atomic optical lattice experiments.

cond-mat.quant-gas↗

arXiv2015

Lighting up topological insulators: large surface photocurrents from magnetic superlattices

The gapless surface states of topological insulators (TI) can potentially be used to detect and harvest low-frequency infrared light. Nonetheless, it was shown that significant surface photocurrents due to light with frequency below the bulk gap are rather hard to produce. Here we demonstrate that a periodic magnetic pattern added to the surface dramatically enhances surface photocurrents in TI's. Moreover, the sensitivity of this set-up to the wavelength of the incident light can be optimized by tuning the geometry of the magnetic pattern. The ability to produce substantial photocurrents on TI surfaces from mid-range and far-infrared light could be used in photovoltaic applications, as well as for detection of micrometer wavelength radiation. For light of wavelength greater than 15$μ$m we estimate that at room temperature, a detector based on the effect we describe can have a specific detectivity as high as 10$^7$ cm$\sqrt{\text{Hz}}$/W (i.e. 10$^9$ Jones). The device can therefore operate at much larger wavelengths than existing infrared detectors, while maintaining a comparable figure of merit.er wavelength radiation.

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arXiv2015

Topological Quantum Infidelity

Can topological quantum entanglement between anyons in one topological medium "stray" into a different, topologically distinct medium? In other words, can quantum information encoded non-locally in the combined state of non-Abelian anyons be shared between two distinct topological media? We consider a setup with two p-wave superconductors of opposite chirality and demonstrate that such scenario is indeed possible. The information encoded in the fermionic parity of two Majorana zero modes, originally within the same superconducting domain, can be shared between the domains or moved entirely from one domain to another provided that vortices can tunnel between them in a controlled fashion.

cond-mat.str-el↗

arXiv2015

Linear magnetoresistance in metals: guiding center diffusion in a smooth random potential

We predict that guiding center (GC) diffusion yields a linear and non-saturating (transverse) magnetoresistance in 3D metals. Our theory is semi-classical and applies in the regime where the transport time is much greater than the cyclotron period, and for weak disorder potentials which are slowly varying on a length scale much greater than the cyclotron radius. Under these conditions, orbits with small momenta along magnetic field $B$ are squeezed and dominate the transverse conductivity. When disorder potentials are stronger than the Debye frequency, linear magnetoresistance is predicted to survive up to room temperature and beyond. We argue that magnetoresistance from GC diffusion explains the recently observed giant linear magnetoresistance in 3D Dirac materials.

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arXiv2015

Topological Polaritons

The interaction between light and matter can give rise to novel topological states. This principle was recently exemplified in Floquet topological insulators, where \emph{classical} light was used to induce a topological electronic band structure. Here, in contrast, we show that mixing \emph{single} photons with excitons can result in new topological polaritonic states --- or "topolaritons". Taken separately, the underlying photons and excitons are topologically trivial. Combined appropriately, however, they give rise to non-trivial polaritonic bands with chiral edge modes allowing for unidirectional polariton propagation. The main ingredient in our construction is an exciton-photon coupling with a phase that winds in momentum space. We demonstrate how this winding emerges from spin-orbit coupling in the electronic system and an applied Zeeman field. We discuss the requirements for obtaining a sizable topological gap in the polariton spectrum, and propose practical ways to realize topolaritons in semiconductor quantum wells and monolayer transition metal dichalcogenides.

cond-mat.quant-gas↗

arXiv2015

The anomalous Floquet-Anderson insulator as a non-adiabatic quantized charge pump

Periodically driven quantum systems provide a novel and versatile platform for realizing topological phenomena. Among these are analogs of topological insulators and superconductors, attainable in static systems; however, some of these phenomena are unique to the periodically driven case. Here, we show that disordered, periodically driven systems admit an "anomalous" two dimensional phase, whose quasi-energy spectrum consists of chiral edge modes that coexist with a fully localized bulk - an impossibility for static Hamiltonians. This unique situation serves as the basis for a new topologically-protected non-equilibrium transport phenomenon: quantized non-adiabatic charge pumping. We identify the bulk topological invariant that characterizes the new phase (which we call the "anomalous Floquet Anderson Insulator", or AFAI). We provide explicit models which constitute a proof of principle for the existence of the new phase. Finally, we present evidence that the disorder-driven transition from the AFAI to a trivial, fully localized phase is in the same universality class as the quantum Hall plateau transition.

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arXiv2015

Optimal Control of Majorana Zero Modes

Braiding of Majorana zero modes provides a promising platform for quantum information processing, which is topologically protected against errors. Strictly speaking, however, the scheme relies on infinite braiding times as it utilizes the adiabatic limit. Here we show how to minimize nonadiabatic errors for finite braiding times by finding an optimal protocol for the Majorana movement. Interestingly, these protocols are characterized by sharp transitions between Majorana motion at maximal and minimal velocities. We find that these so-called bang-bang protocols can minimize the nonadiabatic transitions of the system by orders of magnitude in comparison with naive protocols.

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arXiv2015

Chiral Bogoliubons in Nonlinear Bosonic Systems

We present a versatile scheme for creating topological Bogoliubov excitations in weakly interacting bosonic systems. Our proposal relies on a background stationary field that consists of a Kagome vortex lattice, which breaks time-reversal symmetry and induces a periodic potential for Bogoliubov excitations. In analogy to the Haldane model, no external magnetic field or net flux is required. We construct a generic model based on the two-dimensional (2D) nonlinear Schrödinger equation and demonstrate the emergence of topological gaps crossed by chiral Bogoliubov edge modes. Our scheme can be realized in a wide variety of physical systems ranging from nonlinear optical systems to exciton-polariton condensates.

cond-mat.quant-gas↗

arXiv2015

`Holographic' treatment of surface disorder on a topological insulator

The effect of surface disorder on electronic systems is particularly interesting for topological phases with surface and edge states. Using exact diagonalization, it has been demonstrated that the surface states of a 3D topological insulator survive strong surface disorder, and simply get pushed to a clean part of the bulk. Here we explore a new method which analytically eliminates the clean bulk, and reduces a $D$-dimensional problem to a Hamiltonian-diagonalization problem within the $(D-1)$-dimensional disordered surface. This dramatic reduction in complexity allows the analysis of significantly bigger systems than is possible with exact diagonalization. We use our method to analyze a 2D topological spin-Hall insulator with non-magnetic and magnetic edge impurities, and we calculate the probability density (or local density of states) of the zero-energy eigenstates as a function of edge-parallel momentum and layer index. Our analysis reveals that the system size needed to reach behavior in the thermodynamic limit increases with disorder. We also compute the edge conductance as a function of disorder strength, and chart a lower bound for the length scale marking the crossover to the thermodynamic limit.

cond-mat.dis-nn↗

arXiv2015

Disorder-induced Floquet Topological Insulators

We investigate the possibility of realizing a disorder-induced topological Floquet spectrum in two-dimensional periodically-driven systems. Such a state would be a dynamical realization of the topological Anderson insulator. We establish that a disorder-induced trivial-to-topological transition indeed occurs, and characterize it by computing the disorder averaged Bott index, suitably defined for the time-dependent system. The presence of edge states in the topological state is confirmed by exact numerical time-evolution of wavepackets on the edge of the system. We consider the optimal driving regime for experimentally observing the Floquet-Anderson topological insulator, and discuss its possible realization in photonic lattices.

cond-mat.dis-nn↗

arXiv2015

Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths

External driving is emerging as a promising tool for exploring new phases in quantum systems. The intrinsically non-equilibrium states that result, however, are challenging to describe and control. We study the steady states of a periodically driven one-dimensional electronic system, including the effects of radiative recombination, electron-phonon interactions, and the coupling to an external fermionic reservoir. Using a kinetic equation for the populations of the Floquet eigenstates, we show that the steady-state distribution can be controlled using the momentum and energy relaxation pathways provided by the coupling to phonon and Fermi reservoirs. In order to utilize the latter, we propose to couple the system and reservoir via an energy filter which suppresses photon-assisted tunneling. Importantly, coupling to these reservoirs yields a steady state resembling a band insulator in the Floquet basis. The system exhibits incompressible behavior, while hosting a small density of excitations. We discuss transport signatures, and describe the regimes where insulating behavior is obtained. Our results give promise for realizing Floquet topological insulators.

cond-mat.mes-hall↗

arXiv2015

Shortcuts to nonabelian braiding

Topological quantum information processing relies on adiabatic braiding of nonabelian quasiparticles. Performing the braiding operations in finite time introduces transitions out of the ground-state manifold and deviations from the nonabelian Berry phase. We show that these errors can be eliminated by suitably designed counterdiabatic correction terms in the Hamiltonian. We implement the resulting shortcuts to adiabaticity for simple protocols of nonabelian braiding and show that the error suppression can be substantial even for approximate realizations of the counterdiabatic terms.

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arXiv2014

Topological Polaritons and Excitons in Garden Variety Systems

Topological polaritons (aka topolaritons) present a new frontier for topological behavior in solid-state systems. They combine light and matter, which allows to probe and manipulate them in a variety of ways. They can also be made strongly interacting, due to their excitonic component. So far, however, their realization was deemed rather challenging. Here we present a scheme which allows to realize topolaritons in garden variety zinc-blende quantum wells. Our proposal requires a moderate magnetic field and a potential landscape which can be implemented, e.g., via surface acoustic waves or patterning. We identify indirect excitons in double quantum wells as a particularly appealing alternative for topological states in exciton-based systems. Indirect excitons are robust and long lived (with lifetimes up to milliseconds), and, therefore, provide a flexible platform for the realization, probing, and utilization of topological coupled light-matter states.

cond-mat.quant-gas↗

arXiv2014

Strong disorder renormalization group primer and the superfluid-insulator transition

This brief review introduces the method and application of real-space renormalization group to strongly disordered quantum systems. The focus is on recent applications of the strong disorder renormalization group to the physics of disordered-boson systems and the superfluid-insulator transition in one dimension. The fact that there is also a well understood weak disorder theory for this problem allows to illustrate what aspects of the physics change at strong disorder. In particular the strong disorder RG analysis suggests that the transitions at weak disorder and strong disorder belong to distinct universality classes, but this question remains under debate and is not fully resolved to date. Further applications of the strong disorder renormalization group to higher-dimensional Bose systems and to bosons coupled to dissipation are also briefly reviewed.

cond-mat.dis-nn↗

arXiv2013

Current amplification and relaxation in Dirac systems

We study how electron-electron (e-e) interactions affect the current carried by excited electrons and holes in Dirac systems such as graphene or topological insulators. We find that the current shows distinctly different behavior for e-e collisions involving the electron or the hole. Most surprisingly, for positive Fermi energy, collisions of the electrons can substantially increase the current. This remarkable amplification of the current can be of the order of $\sim 10\%$ per scattering event. It also causes a strong suppression of the overall current relaxation rate of a photoexcited electron-hole pair, with the amplification of the electron current making up for a fast decay of the hole current.

cond-mat.mes-hall↗

arXiv2013

Boosting Majorana zero modes

One-dimensional topological superconductors are known to host Majorana zero modes at domain walls terminating the topological phase. Their nonabelian nature allows for processing quantum information by braiding operations which are insensitive to local perturbations, making Majorana zero modes a promising platform for topological quantum computation. Motivated by the ultimate goal of executing quantum information processing on a finite timescale, we study domain walls moving at a constant velocity. We exploit an effective Lorentz invariance of the Hamiltonian to obtain an exact solution of the associated quasiparticle spectrum and wave functions for arbitrary velocities. Essential features of the solution have a natural interpretation in terms of the familiar relativistic effects of Lorentz contraction and time dilation. We find that the Majorana zero modes remain stable as long as the domain wall moves at subluminal velocities with respect to the effective speed of light of the system. However, the Majorana bound state dissolves into a continuous quasiparticle spectrum once the domain wall propagates at luminal or even superluminal velocities. This relativistic catastrophe implies that there is an upper limit for possible braiding frequencies even in a perfectly clean system with an arbitrarily large topological gap. We also exploit our exact solution to consider domain walls moving past static impurities present in the system.

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