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Phase slips occur across all Josephson junctions (JJs) at a rate that increases with the impedance of the junction. In superconducting qubits composed of JJ-array superinductors -- such as fluxonium -- phase slips in the array can lead to decoherence. In particular, phase-slip processes at the individual array junctions can coherently interfere, each with an Aharonov--Casher phase that depends on the offset charges of the array islands. These coherent quantum phase slips (CQPS) perturbatively modify the qubit frequency, and therefore charge noise on the array islands will lead to dephasing. By varying the impedance of the array junctions, we design a set of fluxonium qubits in which the expected phase-slip rate within the JJ-array changes by several orders of magnitude. We characterize the coherence times of these qubits and demonstrate that the scaling of CQPS-induced dephasing rates agrees with our theoretical model. Furthermore, we perform noise spectroscopy of two qubits in regimes dominated by either CQPS or flux noise. We find the noise power spectrum associated with CQPS dephasing appears to be featureless at low frequencies and not $1/f$. Numerical simulations indicate this behavior is consistent with charge noise generated by charge-parity fluctuations within the array. Our findings broadly inform JJ-array-design tradeoffs, relevant for the numerous superconducting qubit designs employing JJ-array superinductors.

Electronic states in quasiperiodic crystals generally preclude a Bloch description, rendering them simultaneously fascinating and enigmatic. Owing to their complexity and relative scarcity, quasiperiodic crystals are underexplored relative to periodic and amorphous structures. Here, we introduce a new type of highly tunable quasiperiodic crystal easily assembled from periodic components. By twisting three layers of graphene with two different twist angles, we form two moir\'e patterns with incommensurate moir\'e unit cells. In contrast to many common quasiperiodic structures that are defined on the atomic scale, the quasiperiodicity in our system is defined on moir\'e length scales of several nanometers. This novel "moir\'e quasiperiodic crystal" allows us to tune the chemical potential and thus the electronic system between a periodic-like regime at low energies and a strongly quasiperiodic regime at higher energies, the latter hosting a large density of weakly dispersing states. Interestingly, in the quasiperiodic regime we observe superconductivity near a flavor-symmetry-breaking phase transition, the latter indicative of the important role electronic interactions play in that regime. The prevalence of interacting phenomena in future systems with in situ tunability is not only useful for the study of quasiperiodic systems, but it may also provide insights into electronic ordering in related periodic moir\'e crystals. We anticipate that extending this new platform to engineer quasiperiodic crystals by varying the number of layers and twist angles, and by using different two-dimensional components, will lead to a new family of quantum materials to investigate the properties of strongly interacting quasiperiodic crystals.

Novel many-body and topological electronic phases can be created in assemblies of interacting spins coupled to a superconductor, such as one-dimensional topological superconductors with Majorana zero modes (MZMs) at their ends. Understanding and controlling interactions between spins and the emergent band structure of the in-gap Yu-Shiba-Rusinov (YSR) states they induce in a superconductor are fundamental for engineering such phases. Here, by precisely positioning magnetic adatoms with a scanning tunneling microscope (STM), we demonstrate both the tunability of exchange interaction between spins and precise control of the hybridization of YSR states they induce on the surface of a bismuth (Bi) thin film that is made superconducting with the proximity effect. In this platform, depending on the separation of spins, the interplay between Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, spin-orbit coupling, and surface magnetic anisotropy stabilizes different types of spin alignments. Using high-resolution STM spectroscopy at millikelvin temperatures, we probe these spin alignments through monitoring the spin-induced YSR states and their energy splitting. Such measurements also reveal a quantum phase transition between the ground states with different electron number parity for a pair of spins in a superconductor tuned by their separation. Experiments on larger assemblies show that spin-spin interactions can be mediated in a superconductor over long distances. Our results show that controlling hybridization of the YSR states in this platform provides the possibility of engineering the band structure of such states for creating topological phases., Comment: 26 pages, 4 figures, and Supplementary Information (42 pages, 27 figures, 2 tables)

Magic-angle twisted bilayer graphene (MATBG) has recently emerged as a highly tunable two-dimensional (2D) material platform exhibiting a wide range of phases, such as metal, insulator, and superconductor states. Local electrostatic control over these phases may enable the creation of versatile quantum devices that were previously not achievable in other single material platforms. Here, we exploit the electrical tunability of MATBG to engineer Josephson junctions and tunneling transistors all within one material, defined solely by electrostatic gates. Our multi-gated device geometry offers complete control over the Josephson junction, with the ability to independently tune the weak link, barriers, and tunneling electrodes. We show that these purely 2D MATBG Josephson junctions exhibit nonlocal electrodynamics in a magnetic field, in agreement with the Pearl theory for ultrathin superconductors. Utilizing the intrinsic bandgaps of MATBG, we also demonstrate monolithic edge tunneling spectroscopy within the same MATBG devices and measure the energy spectrum of MATBG in the superconducting phase. Furthermore, by inducing a double barrier geometry, the devices can be operated as a single-electron transistor, exhibiting Coulomb blockade. These MATBG tunneling devices, with versatile functionality encompassed within a single material, may find applications in graphene-based tunable superconducting qubits, on-chip superconducting circuits, and electromagnetic sensing in next-generation quantum nanoelectronics.

We examine the spectroscopic signatures of tunneling through a Kitaev quantum spin liquid (QSL) barrier in a number of experimentally relevant geometries. We combine contributions from elastic and inelastic tunneling processes and find that spin-flip scattering at the itinerant spinon modes gives rise to a gaped contribution to the tunneling conductance spectrum. We address the spectral modifications that arise in a magnetic field necessary to drive the candidate material $\alpha$-RuCl$_3$ into a QSL phase, and we propose a lateral 1D tunnel junction as a viable setup in this regime. The characteristic spin gap is an unambiguous signature of the fractionalized QSL excitations, distinguishing it from magnons or phonons. The results of our analysis are generically applicable to a wide variety of topological QSL systems.

Symmetry and topology play key roles in the identification of phases of matter and their properties. Both concepts are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties. Domain walls between distinct broken symmetry QHFM phases are predicted to host gapless one-dimensional (1D) modes that emerge due to a topological change of the underlying electronic wavefunctions at such interfaces. Although a variety of QHFMs have been identified in different materials, probing interacting electronic modes at these domain walls has not yet been accomplished. Here we use a scanning tunneling microscope (STM) to directly visualize the spontaneous formation of boundary modes, within a sign-changing topological gap, at domain walls between different valley-polarized quantum Hall phases on the surface of bismuth. By changing the valley occupation and the corresponding number of modes at the domain wall, we can realize different regimes where the valley-polarized channels are either metallic or develop a spectroscopic gap. This behavior is a consequence of Coulomb interactions constrained by the symmetry-breaking valley flavor, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting Luttinger liquids.

We consider domain walls in nematic quantum Hall ferromagnets predicted to form in multivalley semiconductors, recently probed by scanning tunnelling microscopy experiments on Bi(111) surfaces. We show that the domain wall properties depend sensitively on the filling factor $\nu$ of the underlying (integer) quantum Hall states. For $\nu=1$ and in the absence of impurity scattering we argue that the wall hosts a single-channel Luttinger liquid whose gaplessness is a consequence of valley and charge conservation. For $\nu=2$, it supports a two-channel Luttinger liquid, which for sufficiently strong interactions enters a symmetry-preserving thermal metal phase with a charge gap coexisting with gapless neutral intervalley modes. The domain wall physics in this state is identical to that of a bosonic topological insulator protected by $U(1)\times U(1)$ symmetry, and we provide a formal mapping between these problems. We discuss other unusual properties and experimental signatures of these `anomalous' one-dimensional systems., Comment: 11 pages, 3 figures, published version

Novel broken symmetry states can spontaneously form due to Coulomb interactions in electronic systems with multiple internal degrees of freedom. Multi-valley materials offer an especially rich setting for the emergence of such states, which have potential electronic and optical applications. To date, identification of these broken symmetry phases has mostly relied on the examination of macroscopic transport or optical properties. Here we demonstrate a powerful direct approach by visualizing the wave functions of bismuth surface states with a scanning tunneling microscope. Strong spin-orbit coupling on the surface of bismuth leads to six degenerate teardrop-shaped hole pockets. Our spectroscopic measurements reveal that this degeneracy is fully lifted at high magnetic field as a result of exchange interactions, and we are able to determine the nature of valley ordering by imaging the broken symmetry Landau level (LL) wave functions. The remarkable spatial features of singly degenerate LL wave functions near isolated defects contain unique signatures of interference between spin-textured valleys, which identify the electronic ground state as a quantum Hall ferroelectric. Our observations confirm the recent prediction that interactions in strongly anisotropic valley systems favor the occupation of a single valley, giving rise to emergent ferroelectricity in the surface state of bismuth., Comment: Accepted to Nature Physics, available through Advance Online Publication

Layered material structures play a key role in enhancing electron-electron interactions to create correlated metallic phases that can transform into unconventional superconducting states. The quasi-two-dimensional electronic properties of such compounds are often inferred indirectly through examination of their bulk properties. Here we use scanning tunneling microscopy and spectroscopy to directly probe in cross section the quasi-two-dimensional correlated electronic states of the heavy fermion superconductor CeCoIn5. Our measurements reveal the strong confined nature of heavy quasi-particles, anisotropy of tunneling characteristics, and layer-by-layer modulated behavior of the precursor pseudogap gap phase in this compound. Examining the interlayer coupled superconducting state at low temperatures, we find that the orientation of line defects relative to the d-wave order parameter determines whether in-gap states form due to scattering. Spectroscopic imaging of the anisotropic magnetic vortex cores directly characterizes the short interlayer superconducting coherence length and shows an electronic phase separation near the upper critical in-plane magnetic field, consistent with a Pauli-limited first-order phase transition into a pseudogap phase.

Ordered assemblies of magnetic atoms on the surface of conventional superconductors can be used to engineer topological superconducting phases and realize Majorana fermion quasiparticles (MQPs) in a condensed matter setting. Recent experiments have shown that chains of Fe atoms on Pb generically have the required electronic characteristics to form a 1D topological superconductor and have revealed spatially resolved signatures of localized MQPs at the ends of such chains. Here we report higher resolution measurements of the same atomic chain system performed using a dilution refrigerator scanning tunneling microscope (STM). With significantly better energy resolution than previous studies, we show that the zero bias peak (ZBP) in Fe chains has no detectable splitting from hybridization with other states. The measurements also reveal that the ZBP exhibits a distinctive 'double eye' spatial pattern on nanometer length scales. Theoretically we show that this is a general consequence of STM measurements of MQPs with substantial spectral weight in the superconducting substrate, a conclusion further supported by measurements of Pb overlayers deposited on top of the Fe chains. Finally, we report experiments performed with superconducting tips in search of the particle-hole symmetric MQP signature expected in such measurements., Comment: Accepted to Nature Physics; available through Advance online publication

Nematic quantum fluids with wavefunctions that break the underlying crystalline symmetry can form in interacting electronic systems. We examine the quantum Hall states that arise in high magnetic fields from anisotropic hole pockets on the Bi(111) surface. Spectroscopy performed with a scanning tunneling microscope shows that a combination of local strain and many-body Coulomb interactions lift the six-fold Landau level (LL) degeneracy to form three valley-polarized quantum Hall states. We image the resulting anisotropic LL wavefunctions and show that they have a different orientation for each broken-symmetry state. The wavefunctions correspond precisely to those expected from pairs of hole valleys and provide a direct spatial signature of a nematic electronic phase.

The Josephson effect provides a direct method to probe the strength of the pairing interaction in superconductors. By measuring the phase fluctuating Josephson current between a superconducting tip of a scanning tunneling microscope (STM) and a BCS superconductor with isolated magnetic adatoms on its surface, we demonstrate that the spatial variation of the pairing order parameter can be characterized on the atomic scale. This system provides an example where the local pairing potential suppression is not directly reflected in the spectra measured via quasipartcile tunneling. Spectroscopy with such superconducting tips also show signatures of previously unexplored Andreev processes through individual impurity-bound Shiba states. The atomic resolution achieved here establishes scanning Josephson spectroscopy as a promising technique for the study of novel superconducting phases.

High quality hexagon plate-like Na3Bi crystals with large (001) plane surfaces were grown from a molten Na flux. The freshly cleaved crystals were analyzed by low temperature scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES), allowing for the characterization of the three-dimensional (3D) Dirac semimetal (TDS) behavior and the observation of the topological surface states. Landau levels (LL) were observed, and the energy-momentum relations exhibited a linear dispersion relationship, characteristic of the 3D TDS nature of Na3Bi. In transport measurements on Na3Bi crystals the linear magnetoresistance and Shubnikov-de Haas (SdH) quantum oscillations are observed for the first time., Comment: To be published in a special issue of APL Materials