arXiv subjects

Ady Stern

Publications and source records attributed to Ady Stern.

At least 73 records · Page 4Linked to original sources

arXiv2021

Imaging Hydrodynamic Electrons Flowing Without Landauer-Sharvin Resistance

Electrical resistance usually originates from lattice imperfections. However, even a perfect lattice has a fundamental resistance limit, given by the Landauer conductance caused by a finite number of propagating electron modes. This resistance, shown by Sharvin to appear at the contacts of electronic devices, sets the ultimate conductance limit of non-interacting electrons. Recent years have seen growing evidence of hydrodynamic electronic phenomena, prompting recent theories to ask whether an electronic fluid can radically break the fundamental Landauer-Sharvin limit. Here, we use single-electron transistor imaging of electronic flow in high-mobility graphene Corbino disk devices to answer this question. First, by imaging ballistic flows at liquid-helium temperatures, we observe a Landauer-Sharvin resistance that does not appear at the contacts but is instead distributed throughout the bulk. This underpins the phase-space origin of this resistance - as emerging from spatial gradients in the number of conduction modes. At elevated temperatures, by identifying and accounting for electron-phonon scattering, we reveal the details of the purely hydrodynamic flow. Strikingly, we find that electron hydrodynamics eliminates the bulk Landuer-Sharvin resistance. Finally, by imaging spiraling magneto-hydrodynamic Corbino flows, we reveal the key emergent length scale predicted by hydrodynamic theories - the Gurzhi length. These observations demonstrate that electronic fluids can dramatically transcend the fundamental limitations of ballistic electrons, with important implications for fundamental science and future technologies

cond-mat.mes-hall↗

arXiv2021

Chiral Magic-Angle Twisted Bilayer Graphene in a Magnetic Field: Landau Level Correspondence, Exact Wavefunctions and Fractional Chern Insulators

We show that the flat bands in the chiral model of magic-angle twisted bilayer graphene remain exactly flat in the presence of a perpendicular magnetic field. This is shown by an exact mapping between the model and the lowest Landau level wavefunctions at an effective magnetic field, in which the external field is either augmented or reduced by one flux quantum per unit cell. When the external field reaches one flux quantum per unit cell, the model exhibits a topological phase transition. These findings allow us to analyze a Jain-series of Fractional Chern Insulators states in the exactly flat band, and to point out an unconventional dependence of the energy gap on the magnetic field.

cond-mat.str-el↗

arXiv2021

Bulk Anyons as Edge Symmetries: Boundary Phase Diagrams of Topologically Ordered States

We study effectively one-dimensional systems that emerge at the edge of a two-dimensional topologically ordered state, or at the boundary between two topologically ordered states. We argue that anyons of the bulk are associated with emergent symmetries of the edge, which play a crucial role in the structure of its phase diagram. Using this symmetry principle, transitions between distinct gapped phases at the boundaries of Abelian states can be understood in terms of symmetry breaking transitions or transitions between symmetry protected topological phases. Yet more exotic phenomena occur when the bulk hosts non-Abelian anyons. To demonstrate these principles, we explore the phase diagrams of the edges of a single and a double layer of the toric code, as well as those of domain walls in a single and double-layer Kitaev spin liquid (KSL). In the case of the KSL, we find that the presence of a non-Abelian anyon in the bulk enforces Kramers-Wannier self-duality as a symmetry of the effective boundary theory. These examples illustrate a number of surprising phenomena, such as spontaneous duality-breaking, two-sector phase transitions, and unfreezing of marginal operators at a transition between different gapless phases.

cond-mat.str-el↗

arXiv2021

Delocalization Transition of Disordered Axion Insulator

The axion insulator is a higher-order topological insulator protected by inversion symmetry. We show that under quenched disorder respecting inversion symmetry {\it on average}, the topology of the axion insulator stays robust, and an intermediate metallic phase in which states are delocalized is unavoidable at the transition from an axion insulator to a trivial insulator. We derive this conclusion from general arguments, from classical percolation theory, and from the numerical study of a 3D quantum network model simulating a disordered axion insulator through a layer construction. We find the localization length critical exponent near the delocalization transition to be $ν=1.42\pm 0.12$. We further show that this delocalization transition is stable even to weak breaking of the average inversion symmetry, up to a critical strength. We also quantitatively map our quantum network model to an effective Hamiltonian and we find its low energy k$\cdot$p expansion.

cond-mat.mes-hall↗

arXiv2021

Engineered platforms for topological superconductivity and Majorana zero modes

Among the major approaches that are being pursued for realizing quantum bits, the Majorana-based platform has been the most recent to be launched. It attempts to realize qubits which store quantum information in a topologically-protected manner. The quantum information is protected by its nonlocal storage in localized and well-separated Majorana zero modes, and manipulated by exploiting their nonabelian quantum exchange properties. Realizing these topological qubits is experimentally challenging, requiring superconductivity, helical electrons (created by spin-orbit coupling) and breaking of time reversal symmetry to all cooperate in an uncomfortable alliance. Over the past decade, several candidate material systems for realizing Majorana-based topological qubits have been explored, and there is accumulating, though still debated, evidence that zero modes are indeed being realized. This paper reviews the basic physical principles on which these approaches are based, the material systems that are being developed, and the current state of the field. We highlight both the progress made and the challenges that still need to be overcome.

cond-mat.mes-hall↗

arXiv2021

Novel method distinguishing between competing topological orders

Quantum Hall states - the progenitors of the growing family of topological insulators -- are rich source of exotic quantum phases. The nature of these states is reflected in the gapless edge modes, which in turn can be classified as integer - carrying electrons, fractional - carrying fractional charges; and neutral - carrying excitations with zero net charge but a well-defined amount of heat. The latter two may obey anyonic statistics, which can be abelian or non-abelian. The most-studied putative non-abelian state is the spin-polarized filling factor ν=5/2, whose charge e/4 quasiparticles are accompanied by neutral modes. This filling, however, permits different possible topological orders, which can be abelian or non-abelian. While numerical calculations favor the non-abelian anti-Pfaffian (A-Pf) order to have the lowest energy, recent thermal conductance measurements suggested the experimentally realized order to be the particle-hole Pfaffian (PH-Pf) order. It has been suggested that lack of thermal equilibration among the different edge modes of the A-Pf order can account for this discrepancy. The identification of the topological order is crucial for the interpretation of braiding (interference) operations, better understanding of the thermal equilibration process, and the reliability of the numerical studies. We developed a new method that helps identifying the topological order of the ν=5/2 state. By creating an interface between the two 2D half-planes, one hosting the ν=5/2 state and the other an integer ν=3 state, the interface supported a fractional ν=1/2 charge mode with 1/2 quantum conductance and a neutral Majorana mode. The presence of the Majorana mode, probed by measuring noise, propagating in the opposite direction to the charge mode, asserted the presence of the PH-Pf order but not that of the A-Pf order.

cond-mat.mes-hall↗

arXiv2020

Temperature enhancement of thermal Hall conductance quantization

The quest for non-Abelian quasiparticles has inspired decades of experimental and theoretical efforts, where the scarcity of direct probes poses a key challenge. Among their clearest signatures is a thermal Hall conductance with quantized half-integer value in natural units $ π^2 k_B^2 T /3 h$ ($T$ is temperature, $h$ the Planck constant, $k_B$ the Boltzmann constant). Such a value was indeed recently observed in a quantum-Hall system and a magnetic insulator. We show that a non-topological "thermal metal" phase that forms due to quenched disorder may disguise as a non-Abelian phase by well approximating the trademark quantized thermal Hall response. Remarkably, the quantization here improves with temperature, in contrast to fully gapped systems. We provide numerical evidence for this effect and discuss its possible implications for the aforementioned experiments.

cond-mat.mes-hall↗

arXiv2020

Superconducting fractional quantum Hall edges via repulsive interactions

We study proximity coupling between a superconductor and counter-propagating gapless modes arising on the edges of Abelian fractional quantum Hall liquids with filling fraction $ν=1/m$ (with $m$ an odd integer). This setup can be utilized to create non-Abelian parafermion zero-modes if the coupling to the superconductor opens an energy gap in the counter-propagating modes. However, when the coupling to the superconductor is weak an energy gap is opened only in the presence of sufficiently strong attractive interactions between the edge modes, which do not commonly occur in solid state experimental realizations. We therefore investigate the possibility of obtaining a gapped phase by increasing the strength of the proximity coupling to the superconductor. To this end, we use an effective wire construction model for the quantum Hall liquid and employ renormalization group methods to obtain the phase diagram of the system. Surprisingly, at strong proximity coupling we find a gapped phase which is stabilized for sufficiently strong repulsive interactions in the bulk of the quantum Hall fluids. We furthermore identify a duality transformation that maps between the weak coupling and strong coupling regimes, and use it to show that the gapped phases in both regimes are continuously connected through an intermediate proximity coupling regime.

cond-mat.mes-hall↗

arXiv2020

Entropic evidence for a Pomeranchuk effect in magic angle graphene

In the 1950's, Pomeranchuk predicted that, counterintuitively, liquid 3He may solidify upon heating, due to a high excess spin entropy in the solid phase. Here, using both local and global electronic entropy and compressibility measurements, we show that an analogous effect occurs in magic angle twisted bilayer graphene. Near a filling of one electron per moir'e unit cell, we observe a dramatic increase in the electronic entropy to about 1kB per unit cell. This large excess entropy is quenched by an in-plane magnetic field, pointing to its magnetic origin. A sharp drop in the compressibility as a function of the electron density, associated with a reset of the Fermi level back to the vicinity of the Dirac point, marks a clear boundary between two phases. We map this jump as a function of electron density, temperature, and magnetic field. This reveals a phase diagram that is consistent with a Pomeranchuk-like temperature- and field-driven transition from a low-entropy electronic liquid to a high-entropy correlated state with nearly-free magnetic moments. The correlated state features an unusual combination of seemingly contradictory properties, some associated with itinerant electrons, such as the absence of a thermodynamic gap, metallicity, and a Dirac-like compressibility, and others associated with localized moments, such as a large entropy and its disappearance with magnetic field. Moreover, the energy scales characterizing these two sets of properties are very different: whereas the compressibility jump onsets at T~30K, the bandwidth of magnetic excitations is ~3K or smaller. The hybrid nature of the new correlated state and the large separation of energy scales have key implications for the physics of correlated states in twisted bilayer graphene.

cond-mat.mes-hall↗

arXiv2020

Quantum simulations with complex geometries and synthetic gauge fields in a trapped ion chain

In recent years, arrays of atomic ions in a linear RF trap have proven to be a particularly successful platform for quantum simulation. However, a wide range of quantum models and phenomena have, so far, remained beyond the reach of such simulators. In this work we introduce a technique that can substantially extend this reach using an external field gradient along the ion chain and a global, uniform driving field. The technique can be used to generate both static and time-varying synthetic gauge fields in a linear chain of trapped ions, and enables continuous simulation of a variety of coupling geometries and topologies, including periodic boundary conditions and high dimensional Hamiltonians. We describe the technique, derive the corresponding effective Hamiltonian, propose a number of variations, and discuss the possibility of scaling to quantum-advantage sized simulators. Additionally, we suggest several possible implementations and briefly examine two: the Aharonov-Bohm ring and the frustrated triangular ladder.

quant-ph↗

arXiv2020

Ballistic and hydrodynamic magnetotransport in narrow channels

An increasing number of low carrier density materials exhibit a surprisingly large transport mean free path due to inefficient momentum relaxation. Consequently, charge transport in these systems is markedly non-ohmic but rather ballistic or hydrodynamic, features which can be explored by driving current through narrow channels. Using a kinetic equation approach we theoretically investigate how a non-quantizing magnetic field discerns ballistic and hydrodynamic transport, in particular in the spatial dependence of the transverse electric field, $E_y$: We find that $E_y$ is locally enhanced when the flow exhibits a sharp directional anisotropy in the non-equilibrium density. As a consequence, at weak magnetic fields, the curvature of $E_y$ has opposite signs in the ballistic and hydrodynamic regimes. Moreover, we find a robust signature of the onset of non-local correlations in the form of distinctive peaks of the transverse field, which are accessible by local measurements. Our results demonstrate that a purely hydrodynamic approach is insufficient in the Gurzhi regime once a magnetic field is introduced.

cond-mat.mes-hall↗

arXiv2020

$h/e$ Oscillations in Interlayer Transport of Delafossites

Transport of electrons in a bulk metal is usually well captured by their particle-like aspects, while their wave-like nature is commonly harder to observe. Microstructures can be are fully designed to reveal the quantum phase, for example mesoscopic metal rings resembling interferometers. Here we report a new type of phase coherent oscillation of the out-of-plane magnetoresistance in the layered delafossites PdCoO$_2$ and PtCoO$_2$. The oscillation period is equivalent to that determined by the magnetic flux quantum, $h/e$, threading an area defined by the atomic interlayer separation and the sample width. The phase of the electron wave function in these crystals appears remarkably robust over macroscopic length scales exceeding 10$μ$m and persisting up to elevated temperatures of $T$>50K. We show that, while the experimental signal cannot be explained in a standard Aharonov-Bohm analysis, it arises due to periodic field-modulation of the out-of-plane hopping. These results demonstrate extraordinary single-particle quantum coherence lengths in the delafossites, and identify a new form of quantum interference in solids.

cond-mat.mtrl-sci↗

arXiv2019

Cascade of Phase Transitions and Dirac Revivals in Magic Angle Graphene

Twisted bilayer graphene near the magic angle exhibits remarkably rich electron correlation physics, displaying insulating, magnetic, and superconducting phases. Here, using measurements of the local electronic compressibility, we reveal that these phases originate from a high-energy state with an unusual sequence of band populations. As carriers are added to the system, rather than filling all the four spin and valley flavors equally, we find that the population occurs through a sequence of sharp phase transitions, which appear as strong asymmetric jumps of the electronic compressibility near integer fillings of the moire lattice. At each transition, a single spin/valley flavor takes all the carriers from its partially filled peers, "resetting" them back to the vicinity of the charge neutrality point. As a result, the Dirac-like character observed near the charge neutrality reappears after each integer filling. Measurement of the in-plane magnetic field dependence of the chemical potential near filling factor one reveals a large spontaneous magnetization, further substantiating this picture of a cascade of symmetry breakings. The sequence of phase transitions and Dirac revivals is observed at temperatures well above the onset of the superconducting and correlated insulating states. This indicates that the state we reveal here, with its strongly broken electronic flavor symmetry and revived Dirac-like electronic character, is a key player in the physics of magic angle graphene, forming the parent state out of which the more fragile superconducting and correlated insulating ground states emerge.

cond-mat.mes-hall↗

arXiv2019

Theory of robust multi-qubit non-adiabatic gates for trapped-ions

The prevalent approach to executing quantum algorithms on quantum computers is to break-down the algorithms to a concatenation of universal gates, typically single and two-qubit gates. However such a decomposition results in long gate sequences which are exponential in the qubit register size. Furthermore, gate fidelities tend to decrease when acting in larger qubit registers. Thus high-fidelity implementations in large qubit registers is still a prominent challenge. Here we propose and investigate multi-qubit entangling gates for trapped-ions. Our gates couple many qubits at once, allowing to decrease the total number of gates used while retaining a high gate fidelity. Our method employs all of the normal-modes of motion of the ion chain, which allows to operate outside of the adiabatic regime and at rates comparable to the secular ion-trapping frequency. Furthermore we extend our method for generating Hamiltonians which are suitable for quantum analog simulations, such as a nearest-neighbour spin Hamiltonian or the Su-Schrieffer-Heeger Hamiltonian.

quant-ph↗

arXiv2019

An exactly soluble model for a fractionalized Weyl semimetal

We construct an exactly solvable lattice model of a fractional Weyl semimetal (FWS). The low energy theory of this strongly interacting state is that of a Weyl semimetal built out of fractionally charged fermions. We show the existence of a universally quantized and fractional circular photogalvanic effect (CPGE) and a violation of the Wiedemann-Franz law in the system. Together with a spectral gap in the single-particle electronic Green's function they provide strong experimental signatures for this exotic gapless state of matter.

cond-mat.str-el↗

arXiv2019

Flux superperiods and periodicity transitions in quantum Hall interferometers

For strongly screened Coulomb interactions, quantum Hall interferometers can operate in a novel regime: the intrinsic energy gap can be larger than the charging energy, and addition of flux quanta can occur without adding quasi-particles. We show that flux superperiods are possible, and reconcile their appearance with the Byers-Yang theorem. We explain that the observation of anyonic statistical phases is possible by tuning to the transition from a regime with constant chemical potential to a regime with constant particle density, where a flux superperiod changes to a periodicity with one flux quantum at a critical magnetic field strength.

cond-mat.mes-hall↗

arXiv2019

Topological superconductivity in planar Josephson junctions: Narrowing down to the nanowire limit

We theoretically study topological planar Josephson junctions (JJs) formed from spin-orbit-coupled two-dimensional electron gases (2DEGs) proximitized by two superconductors and subjected to an in-plane magnetic field $B_\parallel$. Compared to previous studies of topological superconductivity in these junctions, here we consider the case where the superconducting leads are narrower than the superconducting coherence length. In this limit the system may be viewed as a proximitized multiband wire, with an additional knob being the phase difference $ϕ$ between the superconducting leads. A combination of mirror and time-reversal symmetry may put the system into the class BDI. Breaking this symmetry changes the symmetry class to class D. The class D phase diagram depends strongly on $B_{\parallel}$ and chemical potential, with a weaker dependence on $ϕ$ for JJs with narrower superconducting leads. In contrast, the BDI phase diagram depends strongly on both $B_\parallel$ and $ϕ$. Interestingly, the BDI phase diagram has a "fan"-shaped region with phase boundaries which move away from $ϕ= π$ linearly with $B_\parallel$. The number of distinct phases in the fan increases with increasing chemical potential. We study the dependence of the JJ's critical current on $B_\parallel$, and find that minima in the critical current indicate first-order phase transitions in the junction only when the spin-orbit coupling strength is small. In contrast to the case of a JJ with wide leads, in the narrow case these transitions are not accompanied by a change in the JJ's topological index. Our results, calculated using realistic experimental parameters, provide guidelines for present and future searches for topological superconductivity in JJs with narrow leads, and are particularly relevant to recent experiments [A. Fornieri et al., Nature (London) 569, 89 (2019)].

cond-mat.mes-hall↗

arXiv2019

Comment on "Counter-propagating charge transport in the quantum Hall effect regime"

Laffont et al. [Science 363, 54-57 (2019)] report an upstream current in the nu=2/3 quantum Hall regime, which, they claim, might be due to a counter-propagating charge mode. We show that this observation can also be explained by the expected upstream neutral mode, without the need for an upstream charge mode. Our results agree with the observed data and explain why the upstream current is observed only in the unpolarized nu=2/3 regime.

cond-mat.mes-hall↗