Wave Function Engineering on Superconducting Substrates: Chiral Yu-Shiba-Rusinov Molecules.

Magnetic adatoms on superconductors give rise to Yu-Shiba-Rusinov (YSR) states that hold considerable interest for the design of topological superconductivity. Here, we show that YSR states are also an ideal platform to engineer structures with intricate wave function symmetries. We assemble structures of iron atoms on the quasi-two-dimensional superconductor 2-NbSe.

Yu-Shiba-Rusinov bands in a self-assembled kagome lattice of magnetic molecules.

Kagome lattices constitute versatile platforms for studying paradigmatic correlated phases. While molecular self-assembly of kagome structures on metallic substrates is promising, it is challenging to realize pristine kagome properties because of hybridization with the bulk degrees of freedom and modified electron-electron interactions. We suggest that a superconducting substrate offers an compelling platform for realizing a magnetic kagome lattice.

Robust Spectral π Pairing in the Random-Field Floquet Quantum Ising Model.

Motivated by an experiment on a superconducting quantum processor [X. Mi et al., Science 378, 785 (2022).

High-temperature Josephson diode.

Many superconducting systems with broken time-reversal and inversion symmetry show a superconducting diode effect, a non-reciprocal phenomenon analogous to semiconducting p-n-junction diodes. While the superconducting diode effect lays the foundation for realizing ultralow dissipative circuits, Josephson-phenomena-based diode effect (JDE) can enable the realization of protected qubits. The superconducting diode effect and JDE reported thus far are at low temperatures (~4 K), limiting their applications.

Non-Abelian Holonomy of Majorana Zero Modes Coupled to a Chaotic Quantum Dot.

If a quantum dot is coupled to a topological superconductor via tunneling contacts, each contact hosts a Majorana zero mode in the limit of zero transmission. Close to a resonance and at a finite contact transparency, the resonant level in the quantum dot couples the Majorana modes, but a ground-state degeneracy per fermion parity subspace remains if the number of Majorana modes coupled to the dot is five or larger. Upon varying shape-defining gate voltages while remaining close to resonance, a nontrivial evolution within the degenerate ground-state manifold is achieved.

Resistivity Tensor of Vortex-Lattice States in Josephson Junction Arrays.

Two-dimensional Josephson junction arrays frustrated by a perpendicular magnetic field are predicted to form a cascade of distinct vortex lattice states. Here, we show that the resistivity tensor provides both structural and dynamical information on the vortex-lattice states and intervening phase transitions, which allows for experimental identification of these symmetry-breaking ground states. We illustrate our general approach by a microscopic theory of the resistivity tensor for a range of magnetic fields exhibiting a rich set of vortex lattices as well as transitions to liquid-crystalline vortex states.

Hunting for Majoranas.

Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes.

Andreev Reflection in Scanning Tunneling Spectroscopy of Unconventional Superconductors.

We evaluate the differential conductance measured in an STM setting at arbitrary electron transmission between STM tip and a 2D superconductor with arbitrary gap structure. Our analytical scattering theory accounts for Andreev reflections, which become prominent at larger transmissions. We show that this provides complementary information about the superconducting gap structure beyond the tunneling density of states, strongly facilitating the ability to extract the gap symmetry and its relation to the underlying crystalline lattice.

Tuning a Two-Impurity Kondo System by a Moiré Superstructure.

Two-impurity Kondo models are paradigmatic for correlated spin-fermion systems. Working with Mn atoms on Au(111) covered by a monolayer of MoS_{2}, we tune the interadatom exchange via the adatom distance and the adatom-substrate exchange via the location relative to a moiré structure of the substrate. Differential-conductance measurements on isolated adatoms exhibit Kondo peaks with heights depending on the adatom location relative to the moiré structure.

Diode Effects in Current-Biased Josephson Junctions.

Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Here, we develop a theory for diodelike effects in the switching and retrapping currents of weakly damped Josephson junctions. We find that while the diodelike behavior of switching currents is rooted in asymmetric current-phase relations, nonreciprocal retrapping currents originate in asymmetric quasiparticle currents.

Diode effect in Josephson junctions with a single magnetic atom.

Current flow in electronic devices can be asymmetric with bias direction, a phenomenon underlying the utility of diodes and known as non-reciprocal charge transport. The promise of dissipationless electronics has recently stimulated the quest for superconducting diodes, and non-reciprocal superconducting devices have been realized in various non-centrosymmetric systems. Here we investigate the ultimate limits of miniaturization by creating atomic-scale Pb-Pb Josephson junctions in a scanning tunnelling microscope.

Anderson's Theorem for Correlated Insulating States in Twisted Bilayer Graphene.

The emergence of correlated insulating phases in magic-angle twisted bilayer graphene exhibits strong sample dependence. Here, we derive an Anderson theorem governing the robustness against disorder of the Kramers intervalley coherent (K-IVC) state, a prime candidate for describing the correlated insulators at even fillings of the moiré flat bands. We find that the K-IVC gap is robust against local perturbations, which are odd under PT, where P and T denote particle-hole conjugation and time reversal, respectively.

Promotion of superconductivity in magic-angle graphene multilayers.

Graphene moiré superlattices show an abundance of correlated insulating, topological, and superconducting phases. Whereas the origins of strong correlations and nontrivial topology can be directly linked to flat bands, the nature of superconductivity remains enigmatic. We demonstrate that magic-angle devices made of twisted tri-, quadri-, and pentalayer graphene placed on monolayer tungsten diselenide exhibit flavor polarization and superconductivity.

Quantum spins and hybridization in artificially-constructed chains of magnetic adatoms on a superconductor.

Magnetic adatom chains on surfaces constitute fascinating quantum spin systems. Superconducting substrates suppress interactions with bulk electronic excitations but couple the adatom spins to a chain of subgap Yu-Shiba-Rusinov (YSR) quasiparticles. Using a scanning tunneling microscope, we investigate such correlated spin-fermion systems by constructing Fe chains adatom by adatom on superconducting NbSe.

Quantum Magnetism and Topological Superconductivity in Yu-Shiba-Rusinov Chains.

Chains of magnetic adatoms on superconductors have been discussed as promising systems for realizing Majorana end states. Here, we show that dilute Yu-Shiba-Rusinov (YSR) chains are also a versatile platform for quantum magnetism and correlated electron dynamics, with widely adjustable spin values and couplings. Focusing on subgap excitations, we derive an extended t-J model for dilute quantum YSR chains and use it to study the phase diagram as well as tunneling spectra.

Moiré Tuning of Spin Excitations: Individual Fe Atoms on MoS_{2}/Au(111).

Magnetic adatoms on properly designed surfaces constitute exquisite systems for addressing, controlling, and manipulating single quantum spins. Here, we show that monolayers of MoS_{2} on a Au(111) surface provide a versatile platform for controllably tuning the coupling between adatom spins and substrate electrons. Even for equivalent adsorption sites with respect to the atomic MoS_{2} lattice, we observe that Fe adatoms exhibit behaviors ranging from pure spin excitations, characteristic of negligible exchange and dominant single-ion anisotropy, to a fully developed Kondo resonance, indicating strong exchange and negligible single-ion anisotropy.

Hilbert Space Geometry of Random Matrix Eigenstates.

The geometry of multiparameter families of quantum states is important in numerous contexts, including adiabatic or nonadiabatic quantum dynamics, quantum quenches, and the characterization of quantum critical points. Here, we discuss the Hilbert space geometry of eigenstates of parameter-dependent random matrix ensembles, deriving the full probability distribution of the quantum geometric tensor for the Gaussian unitary ensemble. Our analytical results give the exact joint distribution function of the Fubini-Study metric and the Berry curvature.

Interfering Tunneling Paths through Magnetic Molecules on Superconductors: Asymmetries of Kondo and Yu-Shiba-Rusinov Resonances.

Magnetic adsorbates on superconductors induce a Kondo resonance outside and Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap. When probed by scanning tunneling spectroscopy, the associated differential-conductance spectra frequently exhibit characteristic bias-voltage asymmetries. Here, we observe correlated variations of Kondo and YSR asymmetries across an Fe-porphyrin molecule adsorbed on Pb(111).

Quantum Hall Response to Time-Dependent Strain Gradients in Graphene.

Mechanical deformations of graphene induce a term in the Dirac Hamiltonian that is reminiscent of an electromagnetic vector potential. Strain gradients along particular lattice directions induce local pseudomagnetic fields and substantial energy gaps as indeed observed experimentally. Expanding this analogy, we propose to complement the pseudomagnetic field by a pseudoelectric field, generated by a time-dependent oscillating stress applied to a graphene ribbon.

Yu-Shiba-Rusinov States in the Charge-Density Modulated Superconductor NbSe.

NbSe is a remarkable superconductor in which charge-density order coexists with pairing correlations at low temperatures. Here, we study the interplay of magnetic adatoms and their Yu-Shiba-Rusinov (YSR) bound states with the charge density order. Exploiting the incommensurate nature of the charge-density wave (CDW), our measurements provide a thorough picture of how the CDW affects both the energies and the wave functions of the YSR states.

Universal Scaling Theory of the Boundary Geometric Tensor in Disordered Metals.

We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and reveals the crossover between the orthogonal and unitary critical states in weak random magnetic fields. The flow of the QGT near the critical points determines the critical exponents.

Tuning the Coupling of an Individual Magnetic Impurity to a Superconductor: Quantum Phase Transition and Transport.

The exchange scattering at magnetic adsorbates on superconductors gives rise to Yu-Shiba-Rusinov (YSR) bound states. Depending on the strength of the exchange coupling, the magnetic moment perturbs the Cooper pair condensate only weakly, resulting in a free-spin ground state, or binds a quasiparticle in its vicinity, leading to a (partially) screened spin state. Here, we use the flexibility of Fe-porphin (FeP) molecules adsorbed on a Pb(111) surface to reversibly and continuously tune between these distinct ground states.

Wave-Function Hybridization in Yu-Shiba-Rusinov Dimers.

Magnetic adsorbates on superconductors induce local bound states within the superconducting gap. These Yu-Shiba-Rusinov (YSR) states decay slowly away from the impurity compared to atomic orbitals, even in 3D bulk crystals. Here, we use scanning tunneling spectroscopy to investigate their hybridization between two nearby magnetic Mn adatoms on a superconducting Pb(001) surface.

Landauer-Büttiker Approach to Strongly Coupled Quantum Thermodynamics: Inside-Outside Duality of Entropy Evolution.

We develop a Landauer-Büttiker theory of entropy evolution in time-dependent, strongly coupled electron systems. The formalism naturally avoids the problem of the system-bath distinction by defining the entropy current in the attached leads. This current can then be used to infer changes of the entropy of the system which we refer to as the inside-outside duality.