New signatures of the spin gap in quantum point contacts.

One dimensional semiconductor systems with strong spin-orbit interaction are both of fundamental interest and have potential applications to topological quantum computing. Applying a magnetic field can open a spin gap, a pre-requisite for Majorana zero modes. The spin gap is predicted to manifest as a field dependent dip on the first 1D conductance plateau. However, disorder and interaction effects make identifying spin gap signatures challenging. Here we study experimentally and numerically the 1D channel in a series of low disorder p-type GaAs quantum point contacts, where spin-orbit and hole-hole interactions are strong. We demonstrate an alternative signature for probing spin gaps, which is insensitive to disorder, based on the linear and non-linear response to the orientation of the applied magnetic field, and extract a spin-orbit gap ΔE ≈ 500 µeV. This approach could enable one-dimensional hole systems to be developed as a scalable and reproducible platform for topological quantum applications.

Global Phase Diagram of a Spin-Orbital Kondo Impurity Model and the Suppression of Fermi-Liquid Scale.

Many correlated metallic materials are described by Landau Fermi-liquid theory at low energies, but for Hund metals the Fermi-liquid coherence scale T_{FL} is found to be surprisingly small. In this Letter, we study the simplest impurity model relevant for Hund metals, the three-channel spin-orbital Kondo model, using the numerical renormalization group (NRG) method and compute its global phase diagram. In this framework, T_{FL} becomes arbitrarily small close to two new quantum critical points that we identify by tuning the spin or spin-orbital Kondo couplings into the ferromagnetic regimes. We find quantum phase transitions to a singular Fermi-liquid or a novel non-Fermi-liquid phase. The new non-Fermi-liquid phase shows frustrated behavior involving alternating overscreenings in spin and orbital sectors, with universal power laws in the spin (ω^{-1/5}), orbital (ω^{1/5}) and spin-orbital (ω^{1}) dynamical susceptibilities. These power laws, and the NRG eigenlevel spectra, can be fully understood using conformal field theory arguments, which also clarify the nature of the non-Fermi-liquid phase.

Nonequilibrium Steady-State Transport in Quantum Impurity Models: A Thermofield and Quantum Quench Approach Using Matrix Product States.

The numerical renormalization group (NRG) is tailored to describe interacting impurity models in equilibrium, but it faces limitations for steady-state nonequilibrium, arising, e.g., due to an applied bias voltage. We show that these limitations can be overcome by describing the thermal leads using a thermofield approach, integrating out high energy modes using NRG, and then treating the nonequilibrium dynamics at low energies using a quench protocol, implemented using the time-dependent density matrix renormalization group. This yields quantitatively reliable results for the current (with errors ≲3%) down to the exponentially small energy scales characteristic of impurity models. We present results of benchmark quality for the temperature and magnetic field dependence of the zero-bias conductance peak for the single-impurity Anderson model.

Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal.

We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.

Transmission phase in the Kondo regime revealed in a two-path interferometer.

We report on the direct observation of the transmission phase shift through a Kondo correlated quantum dot by employing a new type of two-path interferometer. We observed a clear π/2-phase shift, which persists up to the Kondo temperature TK. Above this temperature, the phase shifts by more than π/2 at each Coulomb peak, approaching the behavior observed for the standard Coulomb blockade regime. These observations are in remarkable agreement with two-level numerical renormalization group calculations. The unique combination of experimental and theoretical results presented here fully elucidates the phase evolution in the Kondo regime.

Proposed Rabi-Kondo correlated state in a laser-driven semiconductor quantum dot.

Spin exchange between a single-electron charged quantum dot and itinerant electrons leads to an emergence of Kondo correlations. When the quantum dot is driven resonantly by weak laser light, the resulting emission spectrum allows for a direct probe of these correlations. In the opposite limit of vanishing exchange interaction and strong laser drive, the quantum dot exhibits coherent oscillations between the single-spin and optically excited states. Here, we show that the interplay between strong exchange and nonperturbative laser coupling leads to the formation of a new nonequilibrium quantum-correlated state, characterized by the emergence of a laser-induced secondary spin screening cloud, and examine the implications for the emission spectrum.

Universality of the Kondo effect in quantum dots with ferromagnetic leads.

We investigate quantum dots in clean single-wall carbon nanotubes with ferromagnetic PdNi-leads in the Kondo regime. Most of the Kondo resonances exhibit a splitting, which depends on the tunnel coupling to the leads and an external magnetic field B, but only weakly on the gate voltage. Using numerical renormalization group calculations, we demonstrate that all salient features of the data can be understood using a simple model for the magnetic properties of the leads. The magnetoconductance at zero bias and low temperature depends in a universal way on gµ(B)(B-B(c))/k(B)T(K), where T(K) is the Kondo temperature and B(c) the external field compensating the splitting.

Quantum quench of Kondo correlations in optical absorption.

The interaction between a single confined spin and the spins of an electron reservoir leads to one of the most remarkable phenomena of many-body physics--the Kondo effect. Electronic transport measurements on single artificial atoms, or quantum dots, have made it possible to study the effect in great detail. Here we report optical measurements on a single semiconductor quantum dot tunnel-coupled to a degenerate electron gas which show that absorption of a single photon leads to an abrupt change in the system Hamiltonian and a quantum quench of Kondo correlations. By inferring the characteristic power-law exponents from the experimental absorption line shapes, we find a unique signature of the quench in the form of an Anderson orthogonality catastrophe, induced by a vanishing overlap between the initial and final many-body wavefunctions. We show that the power-law exponent that determines the degree of orthogonality can be tuned using an external magnetic field, which unequivocally demonstrates that the observed absorption line shape originates from Kondo correlations. Our experiments demonstrate that optical measurements on single artificial atoms offer new perspectives on many-body phenomena previously studied using transport spectroscopy only.

Many-body dynamics of exciton creation in a quantum dot by optical absorption: a quantum quench towards Kondo correlations.

We study a quantum quench for a semiconductor quantum dot coupled to a fermionic reservoir, induced by the sudden creation of an exciton via optical absorption. The subsequent emergence of correlations between spin degrees of freedom of dot and reservoir, culminating in the Kondo effect, can be read off from the absorption line shape and understood in terms of the three fixed points of the single-impurity Anderson model. At low temperatures the line shape is dominated by a power-law singularity, with an exponent that depends on gate voltage and, in a universal, asymmetric fashion, on magnetic field, indicative of a tunable Anderson orthogonality catastrophe.

Kondo decoherence: finding the right spin model for iron impurities in gold and silver.

We exploit the decoherence of electrons due to magnetic impurities, studied via weak localization, to resolve a long-standing question concerning the classic Kondo systems of Fe impurities in the noble metals gold and silver: which Kondo-type model yields a realistic description of the relevant multiple bands, spin, and orbital degrees of freedom? Previous studies suggest a fully screened spin S Kondo model, but the value of S remained ambiguous. We perform density functional theory calculations that suggest S=3/2. We also compare previous and new measurements of both the resistivity and decoherence rate in quasi-one-dimensional wires to numerical renormalization group predictions for S=1/2, 1, and 3/2, finding excellent agreement for S=3/2.

Numerical renormalization group calculation of near-gap peaks in spectral functions of the Anderson model with superconducting leads.

We use the numerical renormalization group method (NRG) to investigate a single-impurity Anderson model with a coupling of the impurity to a superconducting host. Analysis of the energy flow shows that, contrary to previous belief, NRG iterations can be performed up to a large number of sites, corresponding to energy differences far below the superconducting gap Δ. This allows us to calculate the impurity spectral function A(ω) very accurately for frequencies |ω|∼Δ, and to resolve, in a certain parameter regime, sharp peaks in A(ω) close to the gap edge.

Mesoscopic to universal crossover of the transmission phase of multilevel quantum dots.

Transmission phase alpha measurements of many-electron quantum dots (small mean level spacing delta) revealed universal phase lapses by pi between consecutive resonances. In contrast, for dots with only a few electrons (large delta), the appearance or not of a phase lapse depends on the dot parameters. We show that a model of a multilevel quantum dot with local Coulomb interactions and arbitrary level-lead couplings reproduces the generic features of the observed behavior. The universal behavior of alpha for small delta follows from Fano-type antiresonances of the renormalized single-particle levels.

Frequency-dependent transport through a quantum dot in the Kondo regime.

We study the ac conductance and equilibrium current fluctuations of a Coulomb-blockaded quantum dot in the Kondo regime. To this end we have developed an extension of the numerical renormalization group suitable for the nonperturbative calculation of finite-frequency transport properties. We demonstrate that ac transport gives access to the many-body resonance in the equilibrium spectral density. It provides a new route for measuring this key signature of Kondo physics, which so far has defied direct experimental observation.

Atomic quantum dots coupled to a reservoir of a superfluid Bose-Einstein condensate.

We study the dynamics of an atomic quantum dot, i.e., a single atom in a tight optical trap which is coupled to a superfluid reservoir via laser transitions. Quantum interference between the collisional interactions and the laser induced coupling results in a tunable dot-bath coupling, allowing an essentially complete decoupling from the environment. Quantum dots embedded in a 1D Luttinger liquid of cold bosonic atoms realize a spin-boson model with Ohmic coupling, which exhibits a dissipative phase transition and allows us to directly measure atomic Luttinger parameters.

Variational ansatz for the superfluid Mott-insulator transition in optical lattices.

We develop a variational wave function for the ground state of a one-dimensional bosonic lattice gas. The variational theory is initially developed for the quantum rotor model and later on extended to the Bose- Hubbard model. This theory is compared with quasi-exact numerical results obtained by Density Matrix Renormalization Group (DMRG) studies and with results from other analytical approximations. Our approach accurately gives local properties for strong and weak interactions, and it also describes the crossover from the superfluid phase to the Mott-insulator phase.

Kondo effect in the presence of itinerant-electron ferromagnetism studied with the numerical renormalization group method.

The Kondo effect in quantum dots (QDs)-artificial magnetic impurities-attached to ferromagnetic leads is studied with the numerical renormalization group method. It is shown that the QD level is spin split due to the presence of ferromagnetic electrodes, leading to a suppression of the Kondo effect. We find that the Kondo effect can be restored by compensating this splitting with a magnetic field. Although the resulting Kondo resonance then has an unusual spin asymmetry with a reduced Kondo temperature, the ground state is still a locally screened state, describable by Fermi liquid theory and a generalized Friedel sum rule, and transport at zero temperature is spin independent.

Magnetic anisotropy variations and nonequilibrium tunneling in a cobalt nanoparticle.

We present detailed measurements of the discrete electron-tunneling level spectrum within nanometer-scale cobalt particles as a function of magnetic field and gate voltage, in this way probing individual quantum many-body eigenstates inside ferromagnetic samples. Variations among the observed levels indicate that different quantum states within one particle are subject to different magnetic anisotropy energies. Gate-voltage studies demonstrate that the low-energy tunneling spectrum is affected dramatically by the presence of nonequilibrium spin excitations.

Transmission phase shift of a quantum dot with kondo correlations

We study the effects of Kondo correlations on the transmission phase shift of a quantum dot in an Aharonov-Bohm ring. We predict in detail how the development of a Kondo resonance should affect the dependence of the phase shift on transport voltage, gate voltage, and temperature. This system should allow the first direct observation of the well-known scattering phase shift of pi/2 expected (but not directly measurable in bulk systems) at zero temperature for an electron scattering off a spin- 1 / 2 impurity that is screened into a singlet.