arXiv subjects

Ady Stern

Publications and source records attributed to Ady Stern.

At least 91 records · Page 5Linked to original sources

arXiv2019

Visualizing Poiseuille flow of hydrodynamic electrons

Hydrodynamics is a general description for the flow of a fluid, and is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate. While various aspects of electron hydrodynamics were revealed in recent experiments, the fundamental spatial structure of hydrodynamic electrons, the Poiseuille flow profile, has remained elusive. In this work, we provide the first real-space imaging of Poiseuille flow of an electronic fluid, as well as visualization of its evolution from ballistic flow. Utilizing a scanning nanotube single electron transistor, we image the Hall voltage of electronic flow through channels of high-mobility graphene. We find that the profile of the Hall field across the channel is a key physical quantity for distinguishing ballistic from hydrodynamic flow. We image the transition from flat, ballistic field profiles at low temperature into parabolic field profiles at elevated temperatures, which is the hallmark of Poiseuille flow. The curvature of the imaged profiles is qualitatively reproduced by Boltzmann calculations, which allow us to create a 'phase diagram' that characterizes the electron flow regimes. Our results provide long-sought, direct confirmation of Poiseuille flow in the solid state, and enable a new approach for exploring the rich physics of interacting electrons in real space.

cond-mat.mes-hall↗

arXiv2019

Phenomenological theory of heat transport in the fractional quantum Hall effect

The thermal Hall conductance is a universal and topological property which characterizes the fractional quantum Hall (FQH) state. The quantized value of the thermal Hall conductance has only recently been measured experimentally in integer quantum Hall (IQH) and FQH regimes, however, the existing setup is not able to detect if the thermal current is counter-propagating or co-propagating with the charge current. Furthermore, although there is experimental evidence for heat transfer between the edge modes and the bulk, the current theories do not take this dissipation effect in consideration. In this work we construct phenomenological rate equations for the heat currents which include equilibration processes between the edge modes and energy dissipation to an external thermal bath. Solving these equations in the limit where temperature bias is small, we compute the temperature profiles of the edge modes in a FQH state, from which we infer the two terminal thermal conductance of the state as a function of the coupling to the external bath. We show that the two terminal thermal conductance depends on the coupling strength, and can be non-universal when this coupling is very strong. Furthermore, we propose an experimental setup to examine this theory, which may also allow the determination of the sign of the thermal Hall conductance.

cond-mat.str-el↗

arXiv2019

Benefits of weak disorder in one dimensional topological superconductors

Majorana bound states are zero-energy modes localized at the ends of a one-dimensional (1D) topological superconductor. Introducing disorder usually increases the Majorana localization length, until eventually inducing a topological phase transition to a trivial phase. In this work we show that in some cases weak disorder causes the Majorana localization length to decrease, making the topological phase more robust. Increasing the disorder further eventually leads to a change of trend and to a phase transition to a trivial phase. Interestingly the transition occurs at $ξ_0\gg l$, where $l$ is the disorder mean-free path and $ξ_0$ is the localization length in the clean limit. Our results are particularly relevant to a 1D topological superconductors formed in planar Josephson junctions.

cond-mat.mes-hall↗

arXiv2019

Unified description of the classical Hall viscosity

In absence of time-reversal symmetry, viscous electron flow hosts a number of interesting phenomena, of which we focus here on the Hall viscosity. Taking a step beyond the hydrodynamic definition of the Hall viscosity, we derive a generalized relation between Hall viscosity and transverse electric field using a kinetic equation approach. We explore two different geometries where the Hall viscosity is accessible to measurement. For hydrodynamic flow of electrons in a narrow channel, we find that the viscosity may be measured by a local probe of the transverse electric field near the center of the channel. Ballistic flow, on the other hand, is dominated by boundary effects. In a Corbino geometry viscous effects arise not from boundary friction but from the circular flow pattern of the Hall current. In this geometry we introduce a viscous Hall angle which remains well defined throughout the crossover from ballistic to hydrodynamic flow, and captures the bulk viscous response of the fluid.

cond-mat.mes-hall↗

arXiv2019

Splitting the hinge mode of higher-order topological insulators

The surface of a higher order topological insulator (HOTI) comprises a two-dimensional topological insulator (TI) with broken inversion symmetry, whose mass is determined by the microscopic details of the surface such as surface potentials and termination. It hosts a helical mode pinned to selected hinges where the surface gap changes its sign. We study the effect of perturbations that break time-reversal and particle-conservation on this helical mode, such as a Zeeman field and a proximate superconductor. We find that in contrast to the helical modes of inversion symmetric TIs, which are gapped by these couplings, the helical modes at the hinges can remain gapless and spatially split. When this happens, the Zeeman field splits the helical mode into a chiral mode surrounding the magnetized region; and a superconductor results in a helical Majorana mode surrounding the superconducting region. The combination of the two might lead to the gapping of one of the chiral Majorana modes, and leave a single one-dimensional chiral Majorana around the superconducting island. We propose that the different topological states can be measured in electrical transport.

cond-mat.mes-hall↗

arXiv2019

Measuring magnetic fields with magnetic field insensitive transitions

Magnetometry is an important tool prevalent in many applications such as fundamental research, material characterization and biological imaging. Atomic magnetometry conventionally makes use of two quantum states, the energy difference of which depends linearly on the magnetic field due to the Zeeman effect. The magnetic field is evaluated from repeated measurements of the accumulated dynamic phase between the two Zeeman states in a superposition. Here we propose a magnetometry method that employs a superposition of clock states with energies that do not depend, to first-order, on the magnetic field magnitude. Our method makes use of the geometrical dependence of the clock-states wavefunctions on the magnetic field orientation. We propose detailed schemes for measuring both static and time-varying magnetic fields, and analyze the sensitivity of these methods. We show that, similarly to Zeeman-based methods, the smallest measurable signal scales inversely with the system coherence-time, which for clock transitions is typically significantly longer than for magnetically sensitive transitions. Finally, we experimentally demonstrate our method on an ensemble of optically trapped 87Rb atoms.

quant-ph↗

arXiv2018

Selection rules for quasiparticle interference with internal nonsymmorphic symmetries

We study how nonsymmorphic symmetries that commute with lattice translations are reflected in the quasiparticle interference (QPI) maps measured by scanning tunneling microscopy (STM). QPI maps, which result from scattering of Bloch states off impurities, record the interference of incoming and scattered waves as a function of energy and tip's position. Although both the impurity and the tip generically break spatial symmetries, we find that the QPI maps provide universal information on these symmetries. The symmetries impose constraints on the relation between various momentum components of the Bloch functions. These relations result in selection rules on certain momentum transfers in QPI maps. We find that universal information is encoded in the absence of QPI signal, or in the relative intensity of its replications. We show examples for one-dimensional chains and an effective model of the layered compound $\rm ZrSiS$. We discuss the implications of our theory in the analysis of observed QPI of the Weyl semimetal $\rm TaAs$. Our theory is particularly relevant for materials in rod and layer space groups, or when a correlated order parameter, such as antiferromagnetism, enlarges the unit cell.

cond-mat.mes-hall↗

arXiv2018

Probing topological superconductors with emergent gravity

Topological superconductors are characterized by topological invariants that describe the number and nature of their robust boundary modes. These invariants must also have observable consequences in the bulk of the system, akin to the quantized bulk Hall conductivity in the quantum Hall effect, but such consequences are made elusive by the spontaneous breaking of $U(1)$ symmetry in the superconductor. Here we focus on 2+1 dimensional spin-less $p$-wave superconductors and show that emergent gravity serves as a natural bulk probe for their topological invariant. This emergent gravity is due to the same attractive interaction between fermions that leads to superconductivity, and is therefore built into topological superconductors. The bulk response of a topological superconductor to the emergent gravitational field is encoded in a gravitational Chern-Simons term, and is related to the existence of robust boundary modes via energy-momentum conservation, or gravitational anomaly inflow. The gravitational Chern-Simons term implies a universal relation between variations in the superconducting order parameter and the energy-momentum currents and densities that they induce. The spontaneous breaking of $U(1)$ symmetry in the superconductor leads to additional bulk responses, encoded in a gravitational pseudo Chern-Simons term. Although not of topological nature, these carry surprising similarities to the topological responses of the gravitational Chern- Simons term. We show how these two types of responses can be disentangled.

cond-mat.mes-hall↗

arXiv2018

Evolution of the transmission phase through a Coulomb-blockaded Majorana wire

We present a study of the transmission of electrons through a semiconductor quantum wire with strong spin-orbit coupling in proximity to an s-wave superconductor, which is Coulomb-blockaded. Such a system supports Majorana zero modes in the presence of an external magnetic field. Without superconductivity, phase lapses are expected to occur in the transmission phase, and we find that they disappear when a topological superconducting phase is stabilized. We express tunneling through the nanowire with the help of effective matrix elements, which depend on both the fermion parity of the wire and the overlap with Bogoliubov-de-Gennes wave functions. Using a modified scattering matrix formalism, that allows for including electron-electron interactions, we study the transmission phase in different regimes.

cond-mat.mes-hall↗

arXiv2018

Fractional Josephson Vortices and Braiding of Majorana Zero Modes in Planar Superconductor-Semiconductor Heterostructures

We consider the one-dimensional (1D) topological superconductor that may form in a planar superconductor-metal-superconductor Josephson junction in which the metal is is subjected to spin orbit coupling and to an in-plane magnetic field. This 1D topological superconductor has been the subject of recent theoretical and experimental attention. We examine the effect of perpendicular magnetic field and a supercurrent driven across the junction on the position and structure of the Majorana zero modes that are associated with the topological superconductor. In particular, we show that under certain conditions the Josephson vortices fractionalize to half-vortices, each carrying half of the superconducting flux quantum and a single Majorana zero mode. Furthemore, we show that the system allows for a current-controlled braiding of Majorana zero modes.

cond-mat.supr-con↗

arXiv2018

Evidence of topological superconductivity in planar Josephson junctions

Majorana zero modes are quasiparticle states localized at the boundaries of topological superconductors that are expected to be ideal building blocks for fault-tolerant quantum computing. Several observations of zero-bias conductance peaks measured in tunneling spectroscopy above a critical magnetic field have been reported as experimental indications of Majorana zero modes in superconductor/semiconductor nanowires. On the other hand, two dimensional systems offer the alternative approach to confine Ma jorana channels within planar Josephson junctions, in which the phase difference ϕ between the superconducting leads represents an additional tuning knob predicted to drive the system into the topological phase at lower magnetic fields. Here, we report the observation of phase-dependent zero-bias conductance peaks measured by tunneling spectroscopy at the end of Josephson junctions realized on a InAs/Al heterostructure. Biasing the junction to ϕ ~ π significantly reduces the critical field at which the zero-bias peak appears, with respect to ϕ = 0. The phase and magnetic field dependence of the zero-energy states is consistent with a model of Majorana zero modes in finite-size Josephson junctions. Besides providing experimental evidence of phase-tuned topological superconductivity, our devices are compatible with superconducting quantum electrodynamics architectures and scalable to complex geometries needed for topological quantum computing.

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

Composite Weyl semimetal as a parent state for three dimensional topologically ordered phases

We introduce (3+1) dimensional models of short-range-interacting electrons that form a strongly correlated many-body state whose low-energy excitations are relativistic neutral fermions coupled to an emergent gauge field, $\text{QED}_{4}$. We discuss the properties of this critical state and its instabilities towards exotic phases such as a gapless `composite' Weyl semimetal and fully gapped topologically ordered phases that feature anyonic point-like as well as line-like excitations. These fractionalized phases describe electronic insulators. They may be further enriched by symmetries which results in the formation of non-trivial surface states.

cond-mat.str-el↗

arXiv2018

Coupled Wire Model of Z4 Orbifold Quantum Hall States

We introduce a coupled wire model for a sequence of non-Abelian quantum Hall states that generalize the Z4 parafermion Read Rezayi state. The Z4 orbifold quantum Hall states occur at filling factors ν= 2/(2m-p) for odd integers $m$ and $p$, and have a topological order with a neutral sector characterized by the orbifold conformal field theory with central charge $c=1$ at radius $R=\sqrt{p/2}$. When $p=1$ the state is Abelian. The state with $p=3$ is the $Z_4$ Read Rezayi state, and the series of $p\ge 3$ defines a sequence of non-Abelian states that resembles the Laughlin sequence. Our model is based on clustering of electrons in groups of four, and is formulated as a two fluid model in which each wire exhibits two phases: a weak clustered phase, where charge $e$ electrons coexist with charge $4e$ bosons and a strong clustered phase where the electrons are strongly bound in groups of 4. The transition between these two phases on a wire is mapped to the critical point of the 4 state clock model, which in turn is described by the orbifold conformal field theory. For an array of wires coupled in the presence of a perpendicular magnetic field, strongly clustered wires form a charge $4e$ bosonic Laughlin state with a chiral charge mode at the edge, but no neutral mode and a gap for single electrons. Coupled wires near the critical state form quantum Hall states with a gapless neutral mode described by the orbifold theory. The coupled wire approach allows us to employ the Abelian bosonization technique to fully analyze the physics of single wire, and then to extract most topological properties of the resulting non-Abelian quantum Hall states. These include the list of quasiparticles, their fusion rules, the correspondence between bulk quasiparticles and edge topological sectors, and most of the phases associated with quasiparticles winding one another.

cond-mat.str-el↗

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

Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level

It is well known that there is a particle-hole symmetry for spin-polarized electrons with two-body interactions in a partially filled Landau level, which becomes exact in the limit where the cyclotron energy is large compared to the interaction strength, so one can ignore mixing between Landau levels. This symmetry is explicit in the description of a half-filled Landau level recently introduced by D. T. Son, using Dirac fermions, but it was thought to be absent in the older fermion-Chern- Simons approach, developed by Halperin, Lee, and Read and subsequent authors. We show here, however, that when properly evaluated, the Halperin, Lee, Read (HLR) theory gives results for long-wavelength low-energy physical properties, including the Hall conductance in the presence of impurities and the positions of minima in the magnetoroton spectra for fractional quantized Hall states close to half-filling, that are identical to predictions of the Dirac formulation. In fact, the HLR theory predicts an emergent particle-hole symmetry near half filling, even when the cyclotron energy is finite.

cond-mat.str-el↗

arXiv2017

Triple point fermions in a minimal symmorphic model

Gapless topological phases of matter may host emergent quasiparticle excitations which have no analog in quantum field theory. This is the case of so called triple point fermions (TPF), quasiparticle excitations protected by crystal symmetries, which show fermionic statistics but have an integer (pseudo)spin degree of freedom. TPFs have been predicted in certain three-dimensional non-symmorphic crystals, where they are pinned to high symmetry points of the Brillouin zone. In this work, we introduce a minimal, three-band model which hosts TPFs protected only by the combination of a C4 rotation and an anti-commuting mirror symmetry. Unlike current non-symmorphic realizations, our model allows for TPFs which are anisotropic and can be created or annihilated pairwise. It provides a simple, numerically affordable platform for their study.

cond-mat.mes-hall↗