SFB Q-M&S

This project part is purely administrative. Its central aim is to provide an ideal framework for creative collaborative research of highest standards.
FWF project number F 8601-N.

One of the most important problems in condensed matter physics is the understanding of strongly correlated electron systems. Strong correlations imply that standard solid-state tools such as order parameter and quasiparticles fail. As daunting as the task might seem, a closer look at empirical data hints that there might be simple regularities underlying seemingly complex behaviour of strongly correlated materials. In this emerging picture it is becoming increasingly evident that it is quantum criticality that lies at the heart of correlated physics determining its key properties and offering a universal description for it. Linear response is ideally suited for regular “Landau-style” systems but might not be as straightforward to apply in the case of strongly correlated ones.
Our aim is to explore quantum critical behaviour in the nonlinear domain to access information that has been inaccessible to previous linear-response based probes. We are going to measure nonlinear response of unconventional materials using intense THz pulses. Such pulses are short enough to probe nonlinearity avoiding heating and are also in the proper few-meV frequency range. We will first benchmark the method against a well understood materials and then turn our attention towards more complex systems. Probing nonlinear THz response of unconventional materials has become possible only recently and is expected to shed light on many long-standing puzzles of the field.
FWF project number F 8602-N.

In the Landau-Ginzburg-Wilson theory of phases and phase transitions, a state of matter is characterized by a local order parameter that is generically tied to the symmetry breaking properties of the phase: a complex number for superconductivity, a vector for magnetism. There are many phases of matter that escape this classification and that are at the forefront of research at the interface between the solid state, topology, and quantum information. They include symmetry protected topological phases such as topological insulators that are characterized by a topological invariant. Topologically ordered phases such as certain quantum spin liquids, exhibit geometry-dependent ground state degeneracy and hence cannot be described by a local order parameter. These phases can be detected only by using entanglement measures, and are uniquely defined by a sub-leading correction to the area law. Finally Kondo destruction phases remain challenging to characterize uniquely. Here, the only possible route is to use quantum information techniques based on the notion that Kondo destruction and heavy fermion phases exhibit different entanglement properties between the localized and itinerant degrees of freedom. In this project part, we will use state approximation free quantum Monte Carlo methods to address the following questions. (A) What are the unique signatures of the Kondo destruction transition from the perspective of entanglement? (B) Can we achieve a synergy between numerical calculations of thermodynamic properties of generalized Kitaev models and Kitaev materials such as RuCl3? (C) Can we provide experimentally realizable protocols to measure entanglement in correlated materials?
DFG project number 493886309, FWF project number LAP 8611-N.

Cuprates are among the most exciting correlated quantum materials (Q-M) in many aspects, exhibiting a number of fascinating quantum phenomena and quantum phase transitions. Nevertheless, in part due to their complexity, they are seldomly used for development of, or are studied by, solid states quantum systems (Q-S). Recently it was proposed that the strangeness of these materials and the superconducting pairing are closely related to i) a gradual localization of exactly one hole per CuO2 unit and ii) a delicate interplay between itinerant and localized charges. By applying a Q-S developed in this SFB on cuprates and by comparing the obtained results with those obtained from more “conventional” probes, e.g., dynamic magnetic susceptibility, we plan to study the interplay among the localized and itinerant charges in the context of possible Zhang-Rice/Kondo-like entanglement. We hope that the gained knowledge about entanglement in cuprates will shed a new light on the microscopic mechanism of the high-temperature superconductivity.
FWF project number F 8603-N.

Quantum critical points (QCP) in heavy fermion systems and superconductivity in cuprates are two of the most fascinating phenomena of solid state physics, but challenging for theory because of strong electronic correlations. Thanks to new methodologies, including cluster and Feynman diagrammatic extensions of dynamical mean field theory (DMFT), we are now able to study these phenomena without bias. Entanglement in electronic systems has, on the other hand, so far mainly been studied for impurity models, spin systems, and one-dimensional electronic systems where matrix product states provide a viable presentation. The aim of the project is to study entanglement in genuine models for strongly correlated electron systems and even actual materials calculations, with a focus on the entanglement across a QCP in heavy fermion systems and the formation of Zhang-Rice singlets and pseudogaps in cuprates. We will use DMFT and diagrammatic extensions thereof as well as exact diagonalization to calculate reduced density matrices and from these different measures of entanglement, including the quantum Fisher information and bipartite fluctuations that will be measured in the experimental projects. Entanglement will provide an entirely new perspective on quantum criticality and superconductivity. We hope for a better understanding of these two phenomena and of entanglement in strongly correlated electron systems in general.
FWF project number F 8604-N.

We are exploring how to integrate circuit quantum electrodynamics, a dominant experimental approach to quantum computing, with quantum materials. One goal is to build new and potentially useful devices, and another is to measure otherwise inaccessible material properties.
FWF project number F 8605-N.

The field of topological superconductivity is one of the most active fields of condensed matter physics due to the exotic properties of Majorana bound states (MBS) which might be used for topological quantum computation. However, a bit more than a decade after the first work reporting signatures of MBS in nanowires (NWs), there is no consensus in the scientific community whether they have been indeed observed. We aim to find robust signatures of topological superconductivity by moving beyond zero bias peak measurements and DC transport investigations. In addition, we are going to move to different materials than III-V semiconductors and investigate holes confined in Ge and unconventional superconductors.
FWF project number F 8606-N.

The search is on for a verifiable Kitaev spin liquid because they intrinsically host Majorana fermions, which are of central interest for topological quantum computing. The main challenge is that we cannot study spin liquids with traditional experimental techniques because they i) do not break the standard symmetries around which most of our techniques have been developed and ii) their excitations are charge neutral. We aim to identify robust experimental signatures of topological spin liquids, such as high-field scale invariance and singularities in the free energy that may be topological phase transitions. These signatures were recently observed in the leading candidate RuCl3. The central goal of this proposal is to confirm that they result directly from a spin liquid state and relate them to the broader context of spin liquids. We will investigate the universality of scale-invariance and the presence of topological phase transitions among various spin liquid candidates using resonant torsion magnetometry. Our method is exclusively sensitive to anisotropy and is highly-compatible with fragile 2D samples – the prime setting for most spin liquids. Our approach will be upgraded to study the dynamic response of spin liquid excitations.
FWF project number F 8607-N.

Quantum criticality beyond the order parameter framework and strongly correlated topological phases are topics of great fundamental interest. Clear-cut examples are found in Kondo systems, in the form of Kondo destruction quantum critical points (KD QCPs) and Weyl-Kondo semimetals. Both phenomena, however, escape a full characterization with standard tools in the field. We hypothesize that assessing their entanglement properties is the way forward. In P9, we thus aim to develop “entanglement meters” for quantum critical and topological Kondo systems, both to advance the fundamental understanding of these systems and to explore their potential for quantum devices. To conceive, experimentally realize, and test these “meters” we will use YbRh2Si2. It features a well-studied and readily accessible KD QCP, at which recent theoretical work predicts the Kondo entanglement to become long ranged. Because high-quality molecular beam epitaxy grown thin films are now available, a series of (Kondo) entanglement measurements, elusive in bulk systems, may now be realized.
FWF project number F 8608-N.

Hybrid devices of superconductor-ferromagnet (SC-FM) hybrid systems may support Cooper pairs with unconventional symmetry giving rise to long-ranged, spin polarized supercurrents (SPSC) through the ferromagnet. On the other hand, these systems may host Andreev bound states (ABS) or Majorana bound states (MBS). SPSC and MBS may be used in quantum information technology for dissipationless information transfer by virtue of their entangled and coherent nature. However, the conditions to reliably create and detect MBS with these hybrid devices are still not settled, because details of the interface may play a crucial role and because the identification of MBS and distinguishing them from ABS solely by transport experiments is still a challenge. We hypothesize that knowing the spectral properties of low-energy excitations and their correlations and entanglement in highly-correlated Q-Ms like Kondo systems close to a quantum critical point or high-Tc SCs, is mandatory to leverage their potential for applications in Q-S. The central goal of project part P10 is to develop a route for detecting electronic correlations by combining scanning tunneling spectroscopy with electronic transport measurements. This project part complements the palette of detection techniques for these exotic electronic states, investigated throughout the whole SFB, by a local probe. It seeks to establish a correlation between the spatial dependence of the local density of states and current-voltage characteristics of devices made of unconventional material combinations. In particular we want to develop a scheme for distinguishing between MBS and ABS, identifying systems which may host long-ranged SPSCs, detect unconventional sc order parameter symmetries, contribute to the development of a Cooper pair splitter and the spatio-spectroscopic signatures of Kondo correlations.
DFG project number 493158779, FWF project number LAP 8610-N.

Recent breakthroughs in the field of Q-M resulted in numerous material realizations of new phases of matter, such as topological insulators, topological superconductors and gapless topological systems. At the same time, the ambitious goal of realizing quantum computing triggers a rapid growth of the Q-S community, where new materials could become instrumental in implementing new devices or improving existing ones. This leads to the ambitious goal of establishing synergy between the Q-M and Q-S communities. We aim to establish Q-S as a toolbox to investigate Q-M beyond the standard linear-response type probes and establish novel applications of Q-M in Q-S. To this end, going from Q-S to Q-M, we will aim to extend probes and methods used for quantum devices to quantum materials. Going in the reverse direction from Q-M to Q-S we will study the effects of novel quantum materials used as elements in quantum circuits and hybrid superconductor-semiconductor devices. We are going to consider unconventional superconductors as elements of a microwave resonator. The circuit provides a way to measure the superfluid density, and can be easily extended to an intrinsically nonequilibrium setting that could reveal the incoherent scattering rates and give access to other material properties. We will build theory for such probes for p-wave like proximity induced superconductors and other unconventional materials. In addition, we will consider nonlinear response of magnetic materials. In a second direction, we will study novel quantum materials as circuit elements in electrical circuits or as building blocks of quantum devices. Nonequilibrium response of superconductors in microwave circuits was considered theoretically predominantly for s-wave superconductors or one-dimensional topological materials. We are going to extend the existing results to more generic materials. Likewise, the planned research on the nonlinear response of magnetic materials and the utilization of Q-M as circuit elements are going the advance the current status of the theory that is at the early stages.
FWF project number F 8609-N.