arXiv subjects

Jason Alicea

Publications and source records attributed to Jason Alicea.

At least 73 records · Page 4Linked to original sources

arXiv2017

Approximating the Sachdev-Ye-Kitaev model with Majorana wires

The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. We use random matrix theory and numerics to show that our setup emulates the SYK model (up to corrections that we quantify) and discuss experimental signatures.

cond-mat.dis-nn↗

arXiv2016

Tunable spin-orbit coupling and symmetry-protected edge states in graphene/WS$_2$

We demonstrate clear weak anti-localization (WAL) effect arising from induced Rashba spin-orbit coupling (SOC) in WS$_2$-covered single-layer and bilayer graphene devices. Contrary to the uncovered region of a shared single-layer graphene flake, WAL in WS$_2$-covered graphene occurs over a wide range of carrier densities on both electron and hole sides. At high carrier densities, we estimate the Rashba SOC relaxation rate to be $\sim 0.2 \rm{ps}^{-1}$ and show that it can be tuned by transverse electric fields. In addition to the Rashba SOC, we also predict the existence of a `valley-Zeeman' SOC from first-principles calculations. The interplay between these two SOC's can open a non-topological but interesting gap in graphene; in particular, zigzag boundaries host four sub-gap edge states protected by time-reversal and crystalline symmetries. The graphene/WS$_2$ system provides a possible platform for these novel edge states.

cond-mat.mes-hall↗

arXiv2016

Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade

Interfacing s-wave superconductors and quantum spin Hall edges produces time-reversal-invariant topological superconductivity of a type that can not arise in strictly 1D systems. With the aim of establishing sharp fingerprints of this novel phase, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as leads. We determine scaling forms for the conductance through a grounded superconductor and show that the results depend sensitively on the interaction strength in the leads, the size of the superconducting region, and the presence or absence of time-reversal-breaking perturbations. We also study transport across a floating superconducting island isolated by magnetic barriers. Here we predict e-periodic Coulomb-blockade peaks, as recently observed in nanowire devices [Albrecht et al., Nature 531, 206 (2016)], with the added feature that the island can support fractional charge tunable via the relative orientation of the barrier magnetizations. As an interesting corollary, when the magnetic barriers arise from strong interactions at the edge that spontaneously break time-reversal symmetry, the Coulomb-blockade periodicity changes from e to e/2. These findings suggest several future experiments that probe unique characteristics of topological superconductivity at the quantum spin Hall edge.

cond-mat.mes-hall↗

arXiv2016

Ising Anyons in Frustration-Free Majorana-Dimer Models

Dimer models have long been a fruitful playground for understanding topological physics. Here we introduce a new class - termed Majorana-dimer models - wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological $p_x - ip_y$ superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the $\text{Ising} \times (p_x-ip_y)$ theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion.

cond-mat.str-el↗

arXiv2016

Approaching a topological phase transition in Majorana nanowires

Recent experiments have produced mounting evidence of Majorana zero modes in nanowire-superconductor hybrids. Signatures of an expected topological phase transition accompanying the onset of these modes nevertheless remain elusive. We investigate a fundamental question concerning this issue: Do well-formed Majorana modes necessarily entail a sharp phase transition in these setups? Assuming reasonable parameters, we argue that finite-size effects can dramatically smooth this putative transition into a crossover, even in systems large enough to support well-localized Majorana modes. We propose overcoming such finite-size effects by examining the behavior of low-lying excited states through tunneling spectroscopy. In particular, the excited-state energies exhibit characteristic field and density dependence, and scaling with system size, that expose an approaching topological phase transition. We suggest several experiments for extracting the predicted behavior. As a useful byproduct, the protocols also allow one to measure the wire's spin-orbit coupling directly in its superconducting environment.

cond-mat.mes-hall↗

arXiv2016

Bosonic Analogue of Dirac Composite Fermi Liquid

We introduce a particle-hole-symmetric metallic state of bosons in a magnetic field at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding $2π$ Berry flux protected by particle-hole and discrete rotation symmetries. We also construct an alternative particle-hole symmetric state---distinct in the presence of inversion symmetry---without Berry flux. As in the Dirac composite Fermi liquid introduced by Son, breaking particle-hole symmetry recovers the familiar Chern-Simons theory. We discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as signatures in experiments and simulations.

cond-mat.str-el↗

arXiv2016

Milestones toward Majorana-based quantum computing

We introduce a scheme for preparation, manipulation, and readout of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate-control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current; (2) validation of a prototype topological qubit; and (3) demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topological-qubit coherence times. These pre-braiding experiments can be adapted to other manipulation and readout schemes as well.

cond-mat.mes-hall↗

arXiv2016

Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions

We explicitly derive the duality between a free electronic Dirac cone and quantum electrodynamics in $(2+1)$ dimensions (QED$_3$) with $N = 1$ fermion flavors. The duality proceeds via an exact, non-local mapping from electrons to dual fermions with long-range interactions encoded by an emergent gauge field. This mapping allows us to construct parent Hamiltonians for exotic topological-insulator surface phases, derive the particle-hole-symmetric field theory of a half-filled Landau level, and nontrivially constrain QED$_3$ scaling dimensions. We similarly establish duality between bosonic topological insulator surfaces and $N = 2$ QED$_3$.

cond-mat.str-el↗

arXiv2015

Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators

We show that boundaries of 3D weak topological insulators can become gapped by strong interactions while preserving all symmetries, leading to Abelian surface topological order. The anomalous nature of the weak topological insulators manifests itself in a non-trivial action of symmetries on the quasiparticles; most strikingly, translations change the anyon types in a manner impossible in strictly 2D systems with the same symmetry. As a further consequence, screw dislocations form non-Abelian defects that trap $\mathbb{Z}_4$ parafermion zero modes.

cond-mat.str-el↗

arXiv2015

Topological phases with parafermions: theory and blueprints

We concisely review the recent evolution in the study of parafermions -- exotic emergent excitations that generalize Majorana fermions and similarly underpin a host of novel phenomena. First we illustrate the intimate connection between Z_3-symmetric "spin" chains and one-dimensional parafermion lattice models, highlighting how the latter host a topological phase featuring protected edge zero modes. We then tour several blueprints for the laboratory realization of parafermion zero modes -- focusing on quantum Hall/superconductor hybrids, quantum Hall bilayers, and two-dimensional topological insulators -- and describe striking experimental fingerprints that they provide. Finally, we discuss how coupled parafermion arrays in quantum Hall architectures yield topological phases that potentially furnish hardware for a universal, intrinsically decoherence-free quantum computer.

cond-mat.str-el↗

arXiv2015

Assembling Fibonacci Anyons From a $\mathbb{Z}_3$ Parafermion Lattice Model

Recent concrete proposals suggest it is possible to engineer a two-dimensional bulk phase supporting non-Abelian Fibonacci anyons out of Abelian fractional quantum Hall systems. The low-energy degrees of freedom of such setups can be modeled as $\mathbb{Z}_3$ parafermions "hopping" on a two-dimensional lattice. We use the density matrix renormalization group to study a model of this type interpolating between the decoupled-chain, triangular-lattice, and square-lattice limits. The results show clear evidence of the Fibonacci phase over a wide region of the phase diagram, most notably including the isotropic triangular lattice point. We also study the broader phase diagram of this model and show that elsewhere it supports an Abelian state with semionic excitations.

cond-mat.str-el↗

arXiv2014

Revealing topological superconductivity in extended quantum spin Hall Josephson junctions

Quantum spin Hall-superconductor hybrids are promising sources of topological superconductivity and Majorana modes, particularly given recent progress on HgTe and InAs/GaSb. We propose a new method of revealing topological superconductivity in extended quantum spin Hall Josephson junctions supporting `fractional Josephson currents'. Specifically, we show that as one threads magnetic flux between the superconductors, the critical current traces an interference pattern featuring sharp fingerprints of topological superconductivity---even when noise spoils parity conservation.

cond-mat.supr-con↗

arXiv2014

Composite Dirac liquids: parent states for symmetric surface topological order

We introduce exotic gapless states---`composite Dirac liquids'---that can appear at a strongly interacting surface of a three-dimensional electronic topological insulator. Composite Dirac liquids exhibit a gap to all charge excitations but nevertheless feature a single massless Dirac cone built from emergent electrically neutral fermions. These states thus comprise electrical insulators that, interestingly, retain thermal properties similar to those of the non-interacting topological insulator surface. A variety of novel fully gapped phases naturally descend from composite Dirac liquids. Most remarkably, we show that gapping the neutral fermions via Cooper pairing---which crucially does not violate charge conservation---yields symmetric non-Abelian topologically ordered surface phases captured in several recent works. Other (Abelian) topological orders emerge upon alternatively gapping the neutral Dirac cone with magnetism. We establish a hierarchical relationship between these descendant phases and expose an appealing connection to paired states of composite Fermi liquids arising in the half-filled Landau level of two-dimensional electron gases. To controllably access these states we exploit a quasi-1D deformation of the original electronic Dirac cone that enables us to analytically address the fate of the strongly interacting surface. The algorithm we develop applies quite broadly and further allows the construction of symmetric surface topological orders for recently introduced bosonic topological insulators.

cond-mat.str-el↗

arXiv2014

Stability of zero modes in parafermion chains

One-dimensional topological phases can host localized zero-energy modes that enable high-fidelity storage and manipulation of quantum information. Majorana fermion chains support a classic example of such a phase, having zero modes that guarantee two-fold degeneracy in all eigenstates up to exponentially small finite-size corrections. Chains of `parafermions'---generalized Majorana fermions---also support localized zero modes, but, curiously, only under much more restricted circumstances. We shed light on the enigmatic zero mode stability in parafermion chains by analytically and numerically studying the spectrum and developing an intuitive physical picture in terms of domain-wall dynamics. Specifically, we show that even if the system resides in a gapped topological phase with an exponentially accurate ground-state degeneracy, higher-energy states can exhibit a splitting that scales as a power law with system size---categorically ruling out exact localized zero modes. The transition to power-law behavior is described by critical behavior appearing exclusively within excited states.

cond-mat.str-el↗

arXiv2014

Designer non-Abelian anyon platforms: from Majorana to Fibonacci

The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has evolved from a highly theoretical subject to an active experimental area, particularly following proposals for trapping non-Abelian anyons in `engineered' structures built from well-understood components. In this short overview we briefly tour the impressive progress that has taken place in the quest for the simplest type of non-Abelian anyon---defects binding Majorana zero modes---and then turn to similar strategies for pursuing more exotic excitations. Specifically, we describe how interfacing simple quantum Hall systems with conventional superconductors yields `parafermionic' generalizations of Majorana modes and even Fibonacci anyons---the latter enabling fully fault tolerant universal quantum computation. We structure our treatment in a manner that unifies these topics in a coherent way. The ideas synthesized here spotlight largely uncharted experimental territory in the field of quantum Hall physics that appears ripe for discovery.

cond-mat.str-el↗

arXiv2014

Parafermionic conformal field theory on the lattice

Finding the precise correspondence between lattice operators and the continuum fields that describe their long-distance properties is a largely open problem for strongly interacting critical points. Here we solve this problem essentially completely in the case of the three-state Potts model, which exhibits a phase transition described by a strongly interacting 'parafermion' conformal field theory. Using symmetry arguments, insights from integrability, and extensive simulations, we construct lattice analogues of nearly all the relevant and marginal physical fields governing this transition. This construction includes chiral fields such as the parafermion. Along the way we also clarify the structure of operator product expansions between order and disorder fields, which we confirm numerically. Our results both suggest a systematic methodology for attacking non-free field theories on the lattice and find broader applications in the pursuit of exotic topologically ordered phases of matter.

cond-mat.stat-mech↗

arXiv2014

Classification of spin liquids on the square lattice with strong spin-orbit coupling

Spin liquids represent exotic types of quantum matter that evade conventional symmetry-breaking order even at zero temperature. Exhaustive classifications of spin liquids have been carried out in several systems, particularly in the presence of full SU(2) spin-rotation symmetry. Real magnetic compounds, however, generically break SU(2) spin symmetry as a result of spin-orbit coupling - which in many materials provides an `order one' effect. We generalize previous works by using the projective symmetry group method to classify $Z_2$ spin liquids on the square lattice when SU(2) spin symmetry is maximally lifted. We find that, counterintuitively, the lifting of spin symmetry actually results in vastly more spin liquid phases compared to SU(2)-invariant systems. A generic feature of the SU(2)-broken case is that the spinons naturally undergo $p+ip$ pairing; consequently, many of these $Z_2$ spin liquids feature a topologically nontrivial spinon band structure supporting gapless Majorana edge states. We study in detail several spin-liquid phases with varying numbers of gapless edge states and discuss their topological protection. The edge states are often protected by a combination of time reversal and lattice symmetries and hence resemble recently proposed topological crystalline superconductors.

cond-mat.str-el↗

arXiv2014

Exotic circuit elements from zero-modes in hybrid superconductor/quantum Hall systems

Heterostructures formed by quantum Hall systems and superconductors have recently been shown to support widely coveted Majorana fermion zero-modes and still more exotic `parafermionic' generalizations. Here we establish that probing such zero-modes using quantum Hall edge states yields non-local transport signatures that pave the way towards a variety of novel circuit elements. In particular, we demonstrate quite generally that at low energies the zero-modes convert chirally moving quasiparticles into oppositely charged quasiholes propagating in the same direction---that is, they swap the sign of the chiral edge currents. One may then construct new and potentially useful circuit elements using this `perfect Andreev conversion' process, including superconducting current and voltage mirrors as well as transistors for fractional charge currents. Characterization of these circuit elements should provide striking evidence of the zero-mode physics.

cond-mat.str-el↗