d-Mon: A Transmon with Strong Anharmonicity Based on Planar c-Axis Tunneling Junction between d-Wave and s-Wave Superconductors.

We propose a novel qubit architecture based on a planar c-axis Josephson junction between a thin flake d-wave superconductor, such as a high-T_{c} cuprate Bi_{2}Sr_{2}CaCu_{2}O_{8+x}, and a conventional s-wave superconductor. When operated in the transmon regime the device-that we call "d mon"-becomes insensitive to offset charge fluctuations and, importantly, exhibits at the same time energy level spectrum with strong anharmonicity that is widely tunable through the device geometry and applied magnetic flux. Crucially, unlike previous qubit designs based on d-wave superconductors the proposed device operates in a regime where quasiparticles are fully gapped and can be therefore expected to achieve long coherence times.

Transitions in the Learnability of Global Charges from Local Measurements.

We consider monitored quantum systems with a global conserved charge, and ask how efficiently an observer ("eavesdropper") can learn the global charge of such systems from local projective measurements. We find phase transitions as a function of the measurement rate, depending on how much information about the quantum dynamics the eavesdropper has access to. For random unitary circuits with U(1) symmetry, we present an optimal classical classifier to reconstruct the global charge from local measurement outcomes only. We demonstrate the existence of phase transitions in the performance of this classifier in the thermodynamic limit. We also study numerically improved classifiers by including some knowledge about the unitary gates pattern.

Field Theory of Charge Sharpening in Symmetric Monitored Quantum Circuits.

Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the nonequilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. By taking a continuous-time, weak-measurement limit, we construct a controlled replica field theory description of these phases and their intervening charge-sharpening transition in one spatial dimension. We find that the charge fuzzy phase is a critical phase with continuously evolving critical exponents that terminates in a modified Kosterlitz-Thouless transition to the short-range correlated charge-sharp phase. We numerically corroborate these scaling predictions also hold for discrete-time projective-measurement circuit models using large-scale matrix-product state simulations, and discuss generalizations to higher dimensions.

Dynamical topological phase realized in a trapped-ion quantum simulator.

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in almost isolated systems. Here achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work indicates that these capabilities can enable dynamical phases and critical phenomena that show topologically robust methods to create, protect and manipulate quantum entanglement that self-correct against large classes of errors. However, so far, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders1-5. In this work, we demonstrate an emergent dynamical symmetry-protected topological phase6, in a quasiperiodically driven array of ten 171Yb+ hyperfine qubits in Quantinuum's System Model H1 trapped-ion quantum processor7. This phase shows edge qubits that are dynamically protected from control errors, cross-talk and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. This property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders8,9 that would enable error-resilient manipulation of quantum information.

Quantum Hall Network Models as Floquet Topological Insulators.

Network models for equilibrium integer quantum Hall (IQH) transitions are described by unitary scattering matrices that can also be viewed as representing nonequilibrium Floquet systems. The resulting Floquet bands have zero Chern number, and are instead characterized by a chiral Floquet winding number. This begs the question, How can a model without Chern number describe IQH systems? We resolve this puzzle by showing that nonzero Chern number is recovered from the network model via the energy dependence of network model scattering parameters. This relationship shows that, despite their topologically distinct origins, IQH and chiral Floquet topology-changing transitions share identical universal scaling properties.

Quantum Hall effect based on Weyl orbits in Cd3As2.

Discovered decades ago, the quantum Hall effect remains one of the most studied phenomena in condensed matter physics and is relevant for research areas such as topological phases, strong electron correlations and quantum computing1-5. The quantized electron transport that is characteristic of the quantum Hall effect typically originates from chiral edge states-ballistic conducting channels that emerge when two-dimensional electron systems are subjected to large magnetic fields2. However, whether the quantum Hall effect can be extended to higher dimensions without simply stacking two-dimensional systems is unknown. Here we report evidence of a new type of quantum Hall effect, based on Weyl orbits in nanostructures of the three-dimensional topological semimetal Cd3As2. The Weyl orbits consist of Fermi arcs (open arc-like surface states) on opposite surfaces of the sample connected by one-dimensional chiral Landau levels along the magnetic field through the bulk6,7. This transport through the bulk results in an additional contribution (compared to stacked two-dimensional systems and which depends on the sample thickness) to the quantum phase of the Weyl orbit. Consequently, chiral states can emerge even in the bulk. To measure these quantum phase shifts and search for the associated chiral modes in the bulk, we conduct transport experiments using wedge-shaped Cd3As2 nanostructures with variable thickness. We find that the quantum Hall transport is strongly modulated by the sample thickness. The dependence of the Landau levels on the magnitude and direction of the magnetic field and on the sample thickness agrees with theoretical predictions based on the modified Lifshitz-Onsager relation for the Weyl orbits. Nanostructures of topological semimetals thus provide a way of exploring quantum Hall physics in three-dimensional materials with enhanced tunability.

Logarithmically Slow Relaxation in Quasiperiodically Driven Random Spin Chains.

We simulate the dynamics of a disordered interacting spin chain subject to a quasiperiodic time-dependent drive, corresponding to a stroboscopic Fibonacci sequence of two distinct Hamiltonians. Exploiting the recursive drive structure, we can efficiently simulate exponentially long times. After an initial transient, the system exhibits a long-lived glassy regime characterized by a logarithmically slow growth of entanglement and decay of correlations analogous to the dynamics at the many-body delocalization transition. Ultimately, at long time scales, which diverge exponentially for weak or rapid drives, the system thermalizes to infinite temperature. The slow relaxation enables metastable dynamical phases, exemplified by a "time quasicrystal" in which spins exhibit persistent oscillations with a distinct quasiperiodic pattern from that of the drive. We show that in contrast with Floquet systems, a high-frequency expansion strictly breaks down above fourth order, and fails to produce an effective static Hamiltonian that would capture the prethermal glassy relaxation.

Scaling Theory of Entanglement at the Many-Body Localization Transition.

We study the universal properties of eigenstate entanglement entropy across the transition between many-body localized (MBL) and thermal phases. We develop an improved real space renormalization group approach that enables numerical simulation of large system sizes and systematic extrapolation to the infinite system size limit. For systems smaller than the correlation length, the average entanglement follows a subthermal volume law, whose coefficient is a universal scaling function. The full distribution of entanglement follows a universal scaling form, and exhibits a bimodal structure that produces universal subleading power-law corrections to the leading volume law. For systems larger than the correlation length, the short interval entanglement exhibits a discontinuous jump at the transition from fully thermal volume law on the thermal side, to pure area law on the MBL side.

Magnetic torque anomaly in the quantum limit of Weyl semimetals.

Electrons in materials with linear dispersion behave as massless Weyl- or Dirac-quasiparticles, and continue to intrigue due to their close resemblance to elusive ultra-relativistic particles as well as their potential for future electronics. Yet the experimental signatures of Weyl-fermions are often subtle and indirect, in particular if they coexist with conventional, massive quasiparticles. Here we show a pronounced anomaly in the magnetic torque of the Weyl semimetal NbAs upon entering the quantum limit state in high magnetic fields. The torque changes sign in the quantum limit, signalling a reversal of the magnetic anisotropy that can be directly attributed to the topological nature of the Weyl electrons. Our results establish that anomalous quantum limit torque measurements provide a direct experimental method to identify and distinguish Weyl and Dirac systems.

Transport evidence for Fermi-arc-mediated chirality transfer in the Dirac semimetal Cd3As2.

The dispersion of charge carriers in a metal is distinctly different from that of free electrons owing to their interactions with the crystal lattice. These interactions may lead to quasiparticles mimicking the massless relativistic dynamics of high-energy particle physics, and they can twist the quantum phase of electrons into topologically non-trivial knots-producing protected surface states with anomalous electromagnetic properties. These effects intertwine in materials known as Weyl semimetals, and in their crystal-symmetry-protected analogues, Dirac semimetals. The latter show a linear electronic dispersion in three dimensions described by two copies of the Weyl equation (a theoretical description of massless relativistic fermions). At the surface of a crystal, the broken translational symmetry creates topological surface states, so-called Fermi arcs, which have no counterparts in high-energy physics or conventional condensed matter systems. Here we present Shubnikov-de Haas oscillations in focused-ion-beam-prepared microstructures of Cd3As2 that are consistent with the theoretically predicted 'Weyl orbits', a kind of cyclotron motion that weaves together Fermi-arc and chiral bulk states. In contrast to conventional cyclotron orbits, this motion is driven by the transfer of chirality from one Weyl node to another, rather than momentum transfer of the Lorentz force. Our observations provide evidence for direct access to the topological properties of charge in a transport experiment, a first step towards their potential application.

Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals.

We re-examine the question of quantum oscillations from surface Fermi arcs and chiral modes in Weyl semimetals. By introducing two tools--semiclassical phase-space quantization and a numerical implementation of a layered construction of Weyl semimetals--we discover several important generalizations to previous conclusions that were implicitly tailored to the special case of identical Fermi arcs on top and bottom surfaces. We show that the phase-space quantization picture fixes an ambiguity in the previously utilized energy-time quantization approach and correctly reproduces the numerically calculated quantum oscillations for generic Weyl semimetals with distinctly curved Fermi arcs on the two surfaces. Based on these methods, we identify a 'magic' magnetic-field angle where quantum oscillations become independent of sample thickness, with striking experimental implications. We also analyze the stability of these quantum oscillations to disorder, and show that the high-field oscillations are expected to persist in samples whose thickness parametrically exceeds the quantum mean free path.

Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals.

In a magnetic field, electrons in metals repeatedly traverse closed magnetic orbits around the Fermi surface. The resulting oscillations in the density of states enable powerful experimental techniques for measuring a metal's Fermi surface structure. On the other hand, the surface states of Weyl semimetals consist of disjoint, open Fermi arcs raising the question of whether they can be observed by standard quantum oscillatory techniques. Here, we find that the open Fermi arcs participate in unusual closed magnetic orbits by traversing the bulk of the sample to connect opposite surfaces. These orbits have anomalous features that are impossible for conventional surface states, and result in quantum oscillations that contain observable signatures of the topological character of the bulk Weyl semimetal. We also apply our predictions to the compounds Cd3As2 and Na3Bi that were recently proposed to be three-dimensional Dirac (doubled Weyl) semimetals, and propose experimental signatures of their possible Fermi arc states.

Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2.

Condensed-matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations as well as the possibility to manipulate them for potential applications. It has recently been proposed that chiral, massless particles known as Weyl fermions can emerge in certain bulk materials or in topological insulator multilayers and give rise to unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry effectively forming a massless Dirac fermion has been predicted to appear as low-energy excitations in a number of materials termed three-dimensional Dirac semimetals. Here we report scanning tunnelling microscopy measurements at sub-kelvin temperatures and high magnetic fields on the II-V semiconductor Cd3As2. We probe this system down to atomic length scales, and show that defects mostly influence the valence band, consistent with the observation of ultrahigh-mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference, we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a magnetic field applied along the axis of the Dirac points, Weyl fermions are the low-energy excitations in Cd3As2.

Edge ferromagnetism from Majorana flat bands: application to split tunneling-conductance peaks in high-Tc cuprate superconductors.

In mean-field descriptions of nodal d-wave superconductors, generic edges exhibit dispersionless Majorana fermion bands at zero energy. These states give rise to an extensive ground-state degeneracy, and are protected by time-reversal symmetry. We argue that the infinite density of states of these flat bands make them inherently unstable to interactions, and show that repulsive interactions lead to edge ferromagnetism which splits the flat bands. This edge ferromagnetism offers an explanation for the observation of the splitting of zero-bias peaks in edge tunneling in high-Tc cuprate superconductors. We argue that this mechanism for splitting is more likely than previously proposed scenarios and describe its experimental consequences.

Classification of interacting electronic topological insulators in three dimensions.

A fundamental open problem in condensed-matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are six interacting electronic topological insulators that have no noninteracting counterpart. Combined with the previously known band insulators, these produce a total of eight topologically distinct phases. Two of the six interacting topological insulators can be described as Mott insulators in which the electron spins form spin analogs of the topological band insulator. The remaining phases are obtained as combinations of these two "topological paramagnets" and the topological band insulator. We prove that these eight phases form a complete list of all possible interacting topological insulators and discuss their experimental signatures.

Hanbury Brown-Twiss interference of anyons.

We present a study of a Hanbury Brown-Twiss interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate Hanbury Brown-Twiss cross correlations of Abelian Laughlin anyons. The correlations we calculate exhibit partial bunching similar to bosons, indicating a substantial statistical transmutation from the underlying electronic degrees of freedom. We also find qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, indicating that anyons cannot be simply thought of as intermediate between bosons and fermions.

Quantum spin liquids and the metal-insulator transition in doped semiconductors.

We describe a new possible route to the metal-insulator transition in doped semiconductors such as Si:P or Si:B. We explore the possibility that the loss of metallic transport occurs through Mott localization of electrons into a quantum spin liquid state with diffusive charge neutral "spinon" excitations. Such a quantum spin liquid state can appear as an intermediate phase between the metal and the Anderson-Mott insulator. An immediate testable consequence is the presence of metallic thermal conductivity at low temperature in the electrical insulator near the metal-insulator transition. Further, we show that though the transition is second order, the zero temperature residual electrical conductivity will jump as the transition is approached from the metallic side. However, the electrical conductivity will have a nonmonotonic temperature dependence that may complicate the extrapolation to zero temperature. Signatures in other experiments and some comparisons with existing data are made.

Superconducting and ferromagnetic phases in SrTiO3/LaAlO3 oxide interface structures: possibility of finite momentum pairing.

We introduce a model to explain the observed ferromagnetism and superconductivity in LAO/STO oxide interface structures. Because of the polar catastrophe mechanism, 1/2 charge per unit cell is transferred to the interface layer. We argue that this charge localizes and orders ferromagnetically via exchange with the conduction electrons. Ordinarily, this ferromagnetism would destroy superconductivity, but, due to strong spin-orbit coupling near the interface, the magnetism and superconductivity can coexist by forming a Fulde-Ferrell-Larkin-Ovchinikov-type condensate of Cooper pairs at finite momentum, which is surprisingly robust in the presence of strong disorder.

Zero-bias peaks in the tunneling conductance of spin-orbit-coupled superconducting wires with and without Majorana end-states.

One of the simplest proposed experimental probes of a Majorana bound state is a quantized (2e(2)/h) value of zero-bias tunneling conductance. When temperature is somewhat larger than the intrinsic width of the Majorana peak, conductance is no longer quantized, but a zero-bias peak can remain. Such a nonquantized zero-bias peak has been recently reported for semiconducting nanowires with proximity induced superconductivity. In this Letter we analyze the relation of the zero-bias peak to the presence of Majorana end states, by simulating the tunneling conductance for multiband wires with realistic amounts of disorder. We show that this system generically exhibits a (nonquantized) zero-bias peak even when the wire is topologically trivial and does not possess Majorana end states. We make comparisons to recent experiments, and discuss the necessary requirements for confirming the existence of a Majorana state.

Superfluidity and dimerization in a multilayered system of fermionic polar molecules.

We consider a layered system of fermionic molecules with permanent dipole moments aligned perpendicular to the layers by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce interlayer pairing. Because of the competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every other layer. We construct an effective Ising-XY lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high-temperature normal state, at intermediate temperature, we find an unusual dimerized "pseudogap" state with only short-range phase coherence. We propose light-scattering experiments to detect dimerization.