Quantum Materials in the Quantum Information Era

Entanglement is a fundamental quantum property that is related but distinct from correlations. How to quantify this in condensed matter through experiment has been puzzling. One of the issues has been that Bell-type inequalities are difficult to realize in practice due to quantum monogamy which can reduce the observation to below the classical-quantum witness threshold. Advances in quantum information theory are bringing to the fore other entanglement witnesses that are better suited to experiment. We have applied these in the form of one- and two-tangles, as well as quantum Fisher information to quantum critical and highly frustrated quantum magnets. The measurements use neutron scattering but other similar measurements are possible with other experimental probes of materials. As well as showing the results of experiments and comparison with theory I will discuss why quantum information provides a valuable viewpoint that can add to our understanding of quantum materials.

The quantum spin liquid is a highly entangled magnetic state characterized by the absence of static magnetism in its ground state. Instead, the spins fluctuate in a highly correlated way down to the lowest temperatures. Three-dimensional spin liquids are rare and have mostly been sought in materials where the magnetic ions form pyrochlore or hyperkagome lattices. Here we study the compound PbCuTe$_2$O$_6$ whose dominant interactions provide a rare example of the highly frustrated, hyper-hyperkagome lattice - a member of the three-dimensional defect windmill lattices. Using a combination of experiment and theory we show that this system exhibits features consistent with being a quantum spin liquid with no detectable static magnetism together with the presence of diffuse continua in the magnetic spectrum suggestive of fractional spinon excitations. The results are compared to classical and quantum simulations of the spectrum. More recently ferroelectric order was discovered in single crystal samples below $T_{FE}\approx1$~K, which is suppressed by small grain size in powder samples. This transition is accompanied by a lattice distortion and a modified magnetic response which however is still consistent with a quantum spin liquid ground state.

Localized or propagating Majorana boundary modes are the key feature of topological superconductors. They are rare in naturally-occurring compounds, but the tailored manipulation of quantum matter offers opportunities for their realization. Specifically, lattices of Yu-Shiba-Rusinov bound states – Shiba lattices – that arise when magnetic adatoms are placed on the surface of a conventional superconductor can be used to create topological bands within the superconducting gap of the substrate. I will discuss results using scanning tunnelling microscopy to create and probe adatom lattices with single atom precision. They reveal two signatures consistent with the realization of two types of mirror symmetry protected topological superconductors: The first has edge modes as well as higher-order corner states, and the second has symmetry-protected bulk nodal points. In principle, their topological character and boundary modes should be protected by the spatial symmetries of the adatom lattice. Our results highlight the potential of Shiba lattices as a platform to design the topology and sample geometry of 2D superconductors.

Time-reversal symmetry breaking most frequently has a pseudovector order parameter—magnetization—and therefore it is also accompanied by the breaking of spatial rotation symmetries. I will discuss how to create an isotropic amorphous material with a long-range-ordered breaking of time-reversal symmetry, which restores spatial symmetries, while breaking time-reversal. I will then discuss the topological properties of these materials and the protection of their surface states from localization.

Twisted bilayer graphene has proven itself as a highly tuneable, strongly interacting electron system harbouring physics bridging topology and correlated phenomena.Photocurrent measurements offer direct access to the quantum geometric properties of electrons through its dependence on wavefunction properties such as the berry curvature and quantum metric. We performed cryogenic near-field photocurrent measurements and reveal fragile electronic structure and their quantum geometric properties. Our work provides direct insights into the quantum geometry of interacting electrons in flat-band systems and uncovers hidden symmetries in twisted bilayer graphene heterostructures.

Quantum Hall states – the progenitors of the growing family of topological insulators – are also a source of exotic quantum states. These states can be abelian (e.g., integers & fractions) or non-abelian (e.g., particular fractions)., and thus may host electrons, fractionally charged quasiparticles, and neutral bosonic or Majorana (in general, para-fermionic) quasiparticles. Since the bulk is insulating (with the quasiparticles localized), counter-propagating gapless edge modes mirror the bulk’s topological order (due to ‘bulk-edge.’ correspondence). The most theoretically studied non-abelian state has a filling ????=5/2. The state supports charge-neutral quasiparticles accompanied by e/4 charges. This filling, however, permits different topological orders, which can be abelian or non-abelian. While numerical calculations favor the non-abelian Anti- Pfaffian (A-Pf) order, our recent thermal conductance measurements found the unexpected order, Particle- Hole Pfaffian (PH-Pf). Employing a novel interface method, where the bulk of the ????=5/2 filling was interfaced with a bulk of integer filling ????=2 or ????=3, an isolated interface channel of ????=1/2 emerged. Studying the latter via measuring heat flow, we re-verified the PH-Pf order of the ????=5/2 state (and its nonabelian nature). Identifying the correct topological order is crucial in testing numerical predictions. While such experiments are more complicated than the ubiquitous conductance measurements, their ‘power’ is already evident. Moreover, isolating the fractional channel can be most helpful in complex interference (braiding) experiments. Banerjee et al., Nature. 545, 7652, 75-79 (2017) Banerjee et al., Nature. 559, 7713, 205-210 (2018)

We will review remarkable recent progress in both experimental and theoretical research on flat bands materials. When a system exhibits flat bands despite having sizable hopping integrals/electron itineracy, the flat band is likely to be topological. In stoichiometric materials, one now has flat band catalogues of materials exhibiting such electronic states at the Fermi level. I will review the interacting and topological physics of such bands, first with simple one-body models and then adding interactions to obtain Kondo physics, magnets, charge density waves, and superconductors. In engineered moire materials, where the Fermi level can be gate-tuned, a new degree of precise controllability allows for the development of flat bands exhibiting Chern insulators, Superconductivity, and - most recently - Fractional Chern insulators. We will show that the physics of most of these bands holds a close resemblance to heavy Fermion physics

Floquet engineering has attracted significant interest given the recent developments in experimental techniques such as ultrafast spectroscopy and the potential to enhance the stability of phases of matter such as superconductivity. Here we explore how an external drive and intrinsic dissipation jointly affect superconductivity. Inspired by the fitness criterion for static superconductors, we recognize the distinct effects of external drives on superconductors based on their commutativity or anticommutativity with the superconducting order parameter within the Floquet-Keldish formalism. Our proposal goes beyond standard mechanisms, such as phonon squeezing and dynamical localization. It opens the door for further studies toward driven-dissipative engineering of exotic phases of complex matter in solid-state systems.

Systems with flat bands provide a rich platform for realizing correlation driven novel quantum phases with intriguing low energy properties, ranging from strange metallicity to emergent fractional excitations. When such flat bands are topologically non-trivial, they facilitate fascinating interplay between electronic topology and strong correlations. Here, we investigate flat bands in -electron-based systems on lattices that realize destructive kinematic interference. Within the Hubbard-model, we show that an effective Kondo description arises through orbital selective Mott correlations, with the flat band becoming pinned at the Fermi energy. Further, by utilizing space-group symmetry constrains on correlation effects, we demonstrate that symmetry-enforced spectral degeneracies survive in the highly correlated bands, which is exemplified by emergent Weyl-Kondo semimetal phases. We conclude with an overview of the interconnectedness of seemingly disparate systems, unified by correlation-driven emergent flat bands. == Work done with Lei Chen, Fang Xie, Haoyu Hu, Silke Paschen, Jennifer Cano and Qimiao Si L. Chen et al, arXiv:2212.08017. L. Chen et al., to be published (2023) H.Hu et al, Sci. Adv., in press (arXiv:2209.10396) ==

Crystalline materials hosting dispersionless flat bands are ideal platforms to study unconventional ground states arising from strong electron-electron interactions [1–3] . While a variety of engineered platforms, such as photonic lattices [4] , cold atom traps [5,6] , and moiré superlattices [7,8], have been employed to explore their behavior, there remains a paucity of solid-state materials which intrinsically host flat bands. Here, we report the realization of a novel flat band lattice model in a square-lattice van der Waals (vdW) metal. Electrical transport, angle-resolved photoemission spectroscopy (ARPES) measurements, and first-principles calculations reveal that the electronic structure is captured by an analog of the Lieb and Dice flat band lattice models [9,10]. While these prototypical models rely on special lattice structures to realize flat bands, here they arise from the combination of lattice geometry and atomic orbital composition. We comment on prospects of extending these insights to identify a wider family of flat band candidate materials, overlooked previously because they do not realize special lattice structures. Further, the materials remains stable even in ambient conditions down to the two-dimensional (2D) limit [11], raising it as a readily accessible platform to study flat band lattice models in 2D.

Quantum correlations are a fundamental property of quantum many-body states, yet a very elusive one for experiments, especially so in the case of bulk quantum materials. Here we show that the knowledge of the momentum-dependent dynamical susceptibility, measured via inelastic neutron scattering, enables the systematic reconstruction of quantum correlation functions, which express the degree of quantum coherence in the fluctuations of two spins at arbitrary mutual distance. Making use of neutron scattering data on the compound KCuF3 -- a system of weakly coupled Heisenberg chains -- and of numerically exact quantum Monte Carlo simulations, we show that quantum correlations possess a radically different spatial structure with respect to conventional correlations. Indeed they exhibit a new emergent length of quantum-mechanical origin -- the quantum coherence length -- which is finite at any finite temperature, including when the system develops long-range magnetic order upon cooling. Moreover we show theoretically that, at low temperature, quasi-one-dimensional compounds exhibit stronger short-range quantum correlations than systems with more strongly coupled chains, unveiling an effective form of monogamy of quantum correlations in Heisenberg spin systems. This is work in preparation together with A. Scheie, E. Dagotto, D. A. Tennant, and T. Roscilde.

Local inversion-symmetry breaking in a crystal combined with strong Rashba interaction can lead to a field-induced transition from an even to an odd-parity superconducting state, when the orbital limit is large due to correlations [1]. The first realisation of this phenomenology is likely found in the locally non-centrosymmetric CeRh$_2$As$_2$ in which two superconducting states (SC1 and SC2) occur in a magnetic field along the crystallographic c axis [2,3]. The superconducting state with $T_\mathrm{c} = 0.3$ K develops out of a possible quadrupole-density-wave order (QDW) setting in at $T_\mathrm{0} = 0.5$ K [4]. Furthermore, signatures of antiferromagnetism (AF) are observed below $T_\mathrm{c}$ by NQR [5]. The low ordering temperatures and non-Fermi-liquid behavior suggest the proximity to a quantum critical point but the role of QDW and AF orders for superconductivity remains unclear. In this talk I will give a comprehensive overview of experimental results on this unique material including the discovery [2], the strong anisotropy of the phase diagram in different field directions [2,3,4,6], as well as the response to hydrostatic pressure. These results support the even to odd-parity transition scenario for the superconducting states and suggest a weak competitive coupling between the QDW and SC order parameters [6]. I will also discuss the relevance of quantum criticality and the roles of tuned interactions based on results from recent high-pressure experiments. [1] T. Yoshida et al., Phys. Rev. B 86, 134514 (2012). [2] S. Khim & J. Landaeta et al., Science 373, 1012–1016 (2021). [3] J. Landaeta et al., Phys. Rev. X 12, 031001 (2022). [4] D. Hafner et al., Phys. Rev. X 12, 011023 (2022). [5] K. Kibune et al., Phys. Rev. Lett. 128, 057002 (2022). [6] K. Semeniuk et al., arXiv:2301.09151 (2023).

The characteristic excitation of a metal is its plasmon, which is a quantized sound wave in its valence electron density. In 1965, David Pines predicted that a distinct type of plasmon, which he named a "demon," could exist in multiband metals that contain more than one species of charge carrier. Unlike conventional plasmons, demons are acoustic excitations, meaning they are ``massless," i.e., their energy tends toward zero as the momentum q->0. So demons may play a central role in the low-energy physics of multiband metals. However, demons are neutral excitations that do not couple to light, so they have never been observed experimentally, at least in a 3D material. In this talk I will present the discovery of a demon in the multiband metal Sr$_2$RuO$_4$. Formed of electrons in the $\beta$ and $\gamma$ bands, the demon is gapless with critical momentum $q_c$ = 0.08 reciprocal lattice units and room temperature velocity v = 1.065(120)$\times 10^5$ m/s. Our observation confirms a 67-year old prediction and may have implications for multicompinent Fermi systems ranging from vdW materials to cold atomic gases to neutron starts. *A. A. Husain, et al., arxiv:2007.06670 (to appear in Nature)

The Kitaev model, characterized by bond-dependent Ising spin interactions among spin-orbit entangled dipole moments in Mott insulators, offers a new approach to quantum spin liquids. Such bond-dependent interactions are not limited to Kramers doublets. In the 5d^2 Mott insulators with strong spin -orbit coupling, the non-Kramers doublet hosts quadrupole and octupole moments while lacking a dipole moment. After a quick review of multipolar physics in double perovskites, I will present a microscopic theory of the multipolar interactions that exhibit bond-dependent quadrupole-quadrupole interactions. Remarkably, these interactions on the honeycomb lattice take the form of the extended Kitaev model including the bond-dependent off-diagonal and Heisenberg interactions. I will discuss a way to realize the exactly solvable Kitaev limit in honeycomb Mott insulators.

Multipolar quantum materials possess local moments carrying higher-rank quadrupolar or octupolar moments. These higher-rank multipolar moments arise due to strong spin-orbit coupling and local symmetry of the crystal-electric-field environment. In magnetic insulators, the interaction between multipolar local moments on frustrated lattices may promote novel quantum spin liquids. In this talk, we discuss a novel quantum spin ice state, a three-dimensional quantum spin liquid with emergent gauge field, that may have been realized in Ce2Zr2O7 and Ce2Sn2O7, where Ce3+ ions carry dipolar-octupolar moments. We present a theoretical analysis of possible quantum spin ice states in this system and compare the theoretical results of dynamical spin structure factors with recent neutron scattering experiments on Ce2Zr2O7 and Ce2Sn2O7. we show that the dynamical spin structure factor computed for the π-flux octupolar quantum spin ice regime is most compatible with the neutron scattering results on Ce2Zr2O7 and Ce2Sn2O7. We also suggest an ultrasound experiment that can detect the emergent photon excitations in this system.

We report on the direct observation of fractional statistics and fractional charge in the fractional quantum Hall effect (FQHE) using electronic Fabry-Perot interferometry. Central to our ability to measure fractional statistics has been the development of novel AlGaAs/GaAs heterostructures and mesoscopic devices. Direct evidence of fractionalization at filling factors $\nu=1/3$ and $\nu=2/5$ will be presented. The interplay of heterostructure design, device fabrication, and expression of anyonic statistics will be emphasized.

Quantum information can be coded by the topologically protected edges of fractional quantum Hall (FQH) states. Investigation on FQH edges in the hope of searching and utilizing non-Abelian statistics has been a focused challenge for years. Manipulating the edges, e.g. to bring edges close to each other or to separate edges spatially, is a common and essential step for such studies. The FQH edge structures in a confined region are typically presupposed to be the same as that in the open region in analysis of experimental results, but whether they remain unchanged with extra confinement is obscure. In this work, we present a series of unexpected plateaus in a confined single-layer two-dimensional electron gas (2DEG), which are quantized at anomalous fractions such as 9/4, 17/11, 16/13 and the reported 3/2. We explain all the plateaus by assuming surprisingly larger filling factors in the confined region. Our findings enrich the understanding of edge states in the confined region and in the applications of gate manipulation, which is crucial for the experiments with quantum point contact and interferometer.

Moiré heterostructures of transition metal dichalcogenides (TMDs) have recently proven to be versatile systems to explore strongly correlated electronic phases in two dimensions. While electronic topological phases have been confirmed experimentally, exotic magnetic orders have not been reported so far. In this work, we investigate TMD moiré bilayers at $n=3/4$ filling of the moiré flat band, where they develop a kagome charge order. We derive an effective spin model for the resulting localized spins and find that its further neighbor spin interactions can be much less suppressed than the corresponding electron hopping strength. Using density matrix renormalization group simulations, we study its phase diagram and, for realistic model parameters relevant for WSe$_2$/WS$_2$, we show that this material can realize the exotic chiral spin liquid phase and the highly debated kagome spin liquid. Our work thus demonstrates that the frustration and strong interactions present in TMD heterobilayers provide an exciting platform to study spin liquid physics, including anyonic excitations. We also comment on possible detection mechanims to identify the phases.

Even in the absence of external illumination a resonator supports modes populated with virtual particles: cavity vacuum fields. By placing a complimentary split ring resonator (CSRR) around a GaAs Hall bar we immerse it in cavity vacuum fields. The cavity opens a scattering channel for electrons in both the bulk and edge states, introducing a long-range perturbation to the system. This results in a breakdown of the topological protection of edge modes in the integer quantum hall regime where instead of a quantized hall resistance and the associated zero longitudinal resistance we observe a loss of quantization of the Hall plateaus and a finite longitudinal resistance. This non-resonant effect decays exponentially in magnetic field, with a decay rate associated to the system’s Rabi frequency. Resonant features most prominently manifest in the longitudinal traces, with the cavity either enhancing or drastically suppressing scattering when (depending on the polarization of the resonant cavity mode). A suppression of resistance suggests the striking realization of polariton transport, a novel phenomenon within the field cavity engineered quantum materials.

We expand the concept of frustration in Mott insulators and quantum spin liquids to metals with flat bands. We show that when inter-orbital hopping $t_2$ dominates over intra-orbital hopping $t_1$ in a multiband system with strong spin-orbit coupling $\lambda$, electronic states with a narrow bandwidth $\Delta\sim (t_2)^2/\lambda$ are formed compared to a bandwidth of order $t_1$ for intra-orbital hopping dominated models. We demonstrate the evolution of the electronic structure, Berry phase distributions for time-reversal and inversion breaking cases, and their imprint on the optical absorption in a tight-binding model of d-orbital hopping on a honeycomb lattice. Going beyond quantum Hall effects and twisted bilayer graphene, we provide an alternative mechanism and a richer materials' platform for achieving flat bands poised at the brink of instabilities toward novel correlated and fractionalized metallic phases and fractional Chern insulators.

Strange metal behavior is ubiquitous in many classes of strongly correlated electron systems [1], and has recently also been observed in new flat band platforms, calling for a unified understanding. I will first discuss the key characteristics of the heavy fermion metal YbRh2Si2, including dynamical scaling of the optical conductivity [2], superconductivity at ultralow temperatures [3], and strongly suppressed shot noise [4]. Interestingly, strange metallicity has also been evidenced in the inelastic neutron scattering data of the noncentrosymmetric heavy fermion semimetal CeRu4Sn6 [5], and a dome of Weyl-Kondo semimetal appears to nucleate out of it at very low temperatures [6]. [1] S. Paschen and Q. Si, Nat. Rev. Phys. 3, 9 (2021); S. Paschen and Q. Si, Europhys. News 52/4, 30 (2021). [2] L. Prochaska et al., Science 367, 285 (2020). [3] D. H. Nguyen et al., Nat. Commun. 12, 4341 (2021). [4] L. Chen et al., arXiv:2206.00673 (2022); Y. Wang et al., arXiv:2211.11735 (2022). [5] W. T. Fuhrman et al., Sci. Adv. 7/21, eabf9134 (2021). [6] D. Kirschbaum et al., unpublished (2023); poster presentation at this workshop.

Topological magnon insulators (TMI) are ordered magnets supporting chiral edge magnon excitations. These edge states are envisioned to serve as topologically protected information channels in next-generation low- loss magnonic devices. The standard description of TMI is based on linear spin-wave theory (LSWT), which approximates magnons as free non-interacting particles. However, magnon excitations of TMI are genuinely interacting even at zero temperature, calling into question descriptions based on LSWT alone. Here we perform a detailed non-linear spin-wave analysis to investigate the stability of chiral edge magnons. We identify three general breakdown mechanisms: (1) The edge magnon couples to itself, generating a finite lifetime that can be large enough to lead to a spectral annihilation of the chiral state; (2) The edge magnon hybridizes with the extended bulk magnons and, as a consequence, delocalizes away from the edge; (3) Due to a bulk-magnon mediated edge-to-edge coupling, the chiral magnons at opposite edges may hybridize. We argue that, in general, these breakdown mechanisms may invalidate predictions based on LSWT and violate the notion of topological protection. We discuss strategies how the breakdwon of chiral edge magnons can be avoided, e.g. via the application of large magnetic fields. Our results point to a previously overlooked challenge for the realization of chiral edge states in TMI and in other bosonic topological systems without particle number conservation.

I will present our recent finding of a new non-equilibrium state that emerges in systems of fermions that are driven periodically in time (Floquet systems) while coupled to a heat reservoir. In equilibrium these fermions would occupy states according to the Fermi-Dirac distribution, which has a single step-like discontinuity defining the location of the Fermi surface. We will show, however, that when the Fermions are periodically driven in time, the Fermi Dirac occupation is replaced by a stair-case-like function which has several step-like discontinuities, leading to a "Floquet Fermi Liquid” state that contains several Fermi surfaces enclosed inside each other resembling a matryoshka doll. We will discuss several properties of this state in particular those related to current rectification and also to the phenomenon of microwave-induced-resistance oscillations (MIRO). We will show that this state allows to clarify an old controversy in the field of opto-electronics allowing us to demonstrate that current rectification is possible even when the photon energy lies within the optical gap of an ideal metal. And we will discuss several characteristic signatures to help detect the presence of multiple fermi surfaces in experiments.

TBD

The interplay between interactions and topology in quantum materials is of extensive current interest. For metallic systems, whether and how electron correlations lead to topological states is an open and pressing problem. The notion of Weyl-Kondo semimetal, introduced theoretically [1] and experimentally [2] concurrently, set the stage for progress. We have developed a general framework that elucidates how symmetry constraints on correlation-induced emergent excitations can give rise to gapless topological states [3]. Along this direction, we have i) established a design principle to determine new Weyl-Kondo semimetal phases and identify new correlated materials for their realization [4]; and ii) advanced the framework even when the Fermi-liquid description breaks down, and put forward a non-Fermi liquid topological semimetal phase [3] and a new topological semimetal quantum critical point  [5]. Here, the multi-channel Kondo effect or critical fluctuations of the local moments lead to both features of non-Fermi liquid and characteristics of nontrivial electronic topology [3,5]. Our work opens a new route to studying gapless topological phases in a broad range of strongly correlated materials. [1] H.-H. Lai et al., “Weyl-Kondo Semimetal in Heavy Fermion Systems'', PNAS 115, 93 (2018). [2] S. Dzsaber et al., “Kondo Insulator to Semimetal Transformation Tuned by Spin-Orbit Coupling'', Phys. Rev. Lett. 118, 246601 (2017). [3] Haoyu Hu et al., “Topological semimetals without quasiparticles”, arXiv:2110.06182. [4] L. Chen et al., “Topological semimetal driven by strong correlations and crystalline symmetry”, Nat. Phys. 18, 1341 (2022). [5] L. Chen, Haoyu Hu, et al., unpublished.

Chirality is a very active field of research in organic chemistry, closely linked to the concept of symmetry. Topology, a well-established concept in mathematics, has nowadays become essential to describe condensed matter [1,2]. At its core are chiral electron states on the bulk, surfaces and edges of the condensed matter systems, in which spin and momentum of the electrons are locked parallel or anti-parallel to each other. Magnetic and non-magnetic Weyl semimetals, for example, exhibit chiral bulk states that have enabled the realization of predictions from high energy and astrophysics involving the chiral quantum number, such as the chiral anomaly, the mixed axial-gravitational anomaly and axions [3-5]. Chiral topological crystals exhibit excellent chiral surface states [6,7] and different orbital angular momentum for the enantiomers, which can be advantageous in catalysis. The potential for connecting chirality as a quantum number to other chiral phenomena across different areas of science, including the asymmetry of matter and antimatter and the homochirality of life, brings topological materials to the fore [8]. References: [1] M. G. Vergniory, B. J. Wieder, L. Elcoro, S. S. P. Parkin, C. Felser, B. A. Bernevig, N. Regnault, Science 2022, 376, 6595. [2] P. Narang, C. A. C. Gracia and C. Felser, Nat. Mater. 2021, 20, 293. [3] J. Gooth et al., Nature 2017, 547, 324. [4] J. Gooth et al., Nature 2019, 575, 315. [5] D. M. Nenno, et al., Nat Rev Phys 2022, 2, 682. [6] B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava and B. A. Bernevig, Science 2016, 353, aaf5037. [7] N. B. M Schröter, et al., Science 2020, 369, 179. [8] C. Felser, J. Gooth, preprint arXiv:2205.05809

Non-abelian anyons are highly desired for topological quantum computation purposes, with Majorana fermions being a promising possibility. Realizing Majorana zero modes in matter is a challenge, with proposals in fractional quantum hall states, chiral superconductors and spin liquids, but no clear successes. Heavy fermion materials have long been known to host Majoranas at two-channel Kondo impurities, however, these impurities are difficult to manipulate and moreover occur in metals, where Majoranas at different impurities communicate and lose their topological nature. I will show how topological defects in a lattice of these two-channel Kondo impurities also host Majoranas, which can be engineered to avoid the above difficulties, providing the novel possibility of non-trivial, stable and manipulable Majorana zero modes in a two-channel Kondo insulator.

This talk will highlight new opportunities for exploring superconductor-semiconductor hybrid systems, enabled by the revolutionary measurement capabilities of engineered superconducting circuits. Resonant circuits can probe the fragile superconductor-semiconductor interface [1], revealing behavior that is invisible to conventional probes. A single Josephson junction can be added to realize a semiconductor-based amplifier operating near quantum limits [2]. Scaling up to junction arrays, the stage is set for studying the electrodynamics and radiometry of the anomalous metal. [1] D. Phan, J. Senior, A. Ghazaryan, M. Hatefipour, W.M. Strickland, J. Shabani, M. Serbyn, and A. P. Higginbotham. Detecting Induced p±ip Pairing at the Al-InAs Interface with a Quantum Microwave Circuit. Phys. Rev. Lett. 128, 107701 (2022). [2] D. Phan, P. Falthansl-Scheinecker, U. Mishra, W.M. Strickland, D. Langone, J. Shabani, A.P. Higginbotham.Semiconductor quantum-limited amplifier. arXiv:2206.05746 (2022).