arXiv subjects

Raffael L. Klees

Publications and source records attributed to Raffael L. Klees.

16 recordsLinked to original sources

arXiv2026

Torsional Hall Viscosity of Massive Chern Insulators: Magnetic Field and Momentum Deformations

This work focuses on the non-dissipative, parity-odd spin transport of $(2+1)$-dimensional relativistic electrons, generated by torsion, and the torsional Hall viscosity $ζ_{\rm H}$. We first determine $ζ_{\rm H}$ for massive Dirac fermions in the presence of a constant electromagnetic field. We predict that the magnetic field induces a contribution to $ζ_{\rm H}$ competing with the one originating from the Dirac mass. Moreover, we quantify the impact on $ζ_{\rm H}$ originating from the band structure deformation quadratic in momentum terms that was proposed by Bernevig-Hughes-Zhang (BHZ). We find that the BHZ deformation substantially enhances $ζ_{\rm H}$ in magnitude as measured in a domain wall configuration, when compared to the free Dirac fermion result. Nevertheless, the torsional Hall viscosity still discriminates between topologically trivial and non-trivial regimes. Our results, hence, pave the way for a deeper understanding of hydrodynamic spin transport and its possible verification in experiments.

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arXiv2026

Lindblad theory of linear response susceptibility and dispersive readout in minimal Kitaev junctions

The field of hybrid superconductor-semiconductor quantum dots is advancing toward the development of functional devices that leverage the advantages of both types of materials. However, the inherent complexity of these devices demands a comprehensive theoretical framework for a complete understanding of their responses to external probes, readout and the dissipation arising from environmental coupling. We present a Lindblad-based linear response formalism that captures the multi-level nature of these devices, their probe-readout flexibility, and the non-unitary effects of finite-frequency response, including the so-called Sisyphus and Hermes dynamical susceptibilities. These arise from fluctuations in the rates and jump operators, and are hence absent in standard Kubo linear response treatments. We exemplify the framework using quantum dot-based Kitaev chain setups which are promising candidates for topologically protected Majorana-based parity qubits. Our results shed light onto the validity of the standard curvature-based approximation for fermionic parity and qubit readout, show that Hermes terms compensate decoherence in dispersive readout and implement important corrections beyond thermalized states.

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arXiv2026

Limits of Thermal Conductance Quantization in Chiral Topological Josephson Junctions

We investigate thermal and non-local electrical transport in four-terminal Josephson junctions formed by a normal region coupled to two transverse chiral superconducting leads, supporting phases characterized by Chern numbers ${\cal C}=0,\,1$\,and\,2. We identify the conditions under which a single chiral Majorana mode (${\cal C}=1$) produces a robust half-quantized thermal conductance, while non-local electrical conductance remains strongly suppressed by particle-hole symmetry. Thermal conductance quantization occurs near a superconducting phase difference $π$, but only in the low-doping regime of the central region and in the intermediate- to long-junction limits. At finite Zeeman fields, the thermal response broadly follows the topology of the isolated superconducting leads for the $C=1$ phase while, in the ${\cal C}=2$ phase, the thermal conductance generally deviates from quantization, depending on the momentum-space location of the Majorana modes. Our results establish clear criteria for probing chiral Majorana modes in Josephson junctions and highlight the essential role of momentum-space structure, finite-size geometry, and sample parameters in thermal transport.

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arXiv2025

Readout of multi-level quantum geometry from electronic transport

The quantum geometric tensor (QGT) of a quantum system in a given parameter space captures both the geometry of the state manifold and the topology of the system. While the local QGT elements have been successfully measured in various platforms, the challenge of detecting them in electronic transport systems - such as tunnel or molecular junctions - has yet to be resolved. To fill this gap, we propose a measurement protocol based on weak and resonant parameter modulations, and theoretically demonstrate how the local QGT in such systems can be directly probed from changes of the tunnel conductance. This approach enables the measurement of both geometrical and topological features of quantum states in a broad class of transport-based quantum systems.

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arXiv2025

Transport signatures of inverted Andreev bands in topological Josephson junctions

We study the thermoelectrical transport transverse to conventional and topological Josephson junctions with a central quantum dot (QD). For that purpose, we derive an effective resonant tunneling model where the QD is renormalized with an induced superconducting gap. By applying the Keldysh Green's function technique, we compute the local density of states as well as the transmission functions. In the latter case, we observe that the Andreev bound states forming on the QD are inverted if the junction has $p$-wave symmetry, meaning that electron and hole orbitals switch roles. We calculate the thermoelectric transport coefficients both analytically and numerically and show how the induced gaps and the band inversion are reflected in the electrical and heat conductance as well as the Seebeck coefficient, the latter experiencing a sign change in the topological case.

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arXiv2024

Majorana-mediated thermoelectric transport in multiterminal junctions

The unambiguous identification of Majorana zero modes (MZMs) is one of the most outstanding problems of condensed matter physics. Thermal transport provides a detection tool that is sensitive to these chargeless quasiparticles. We study thermoelectric transport between metallic leads transverse to a Josephson junction. The central double quantum dot hosts conventional or topological Andreev states that depend on the phase difference $ϕ$. We show that the presence of MZMs can be identified by a significant amplification of both the electrical and thermal conductance at $ϕ\approx π$ as well as the Seebeck coefficient at $ϕ\approx 0$. In addition, we show that the Wiedemann-Franz law is strongly violated in the presence of MZMs around $ϕ\approx π$ when compared to the conventional case. We further investigate the robustness of our results against Cooper pair splitting processes.

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arXiv2024

Boosting the STM's spatial and energy resolution with double-functionalized probe tips

Scattering of superconducting pairs by magnetic impurities on a superconducting surface leads to pairs of sharp in-gap resonances, known as Yu-Shiba-Rusinov (YSR) bound states. Similarly to the interference of itinerant electrons scattered by defects in normal metals, these resonances reveal a periodic texture around the magnetic impurity. However, the wavelength of these resonances is often too short to be resolved even by methods capable of atomic resolution, like scanning tunneling microscopy (STM). Here, we combine a CO molecule with a superconducting cluster pre-attached to an STM tip to maximize both spatial and energy resolution. The superior properties of such a double-functionalized probe are demonstrated by imaging the spatial distribution of YSR states around magnetic Fe atoms on a Nb(110) surface. Our approach reveals rich interference patterns of the hybridized YSR state, previously inaccessible with conventional STM probes. This advancement extends the capabilities of STM techniques, providing insights into superconducting phenomena at the atomic scale.

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arXiv2023

Ground state topology of a four-terminal superconducting double quantum dot

In recent years, various classes of systems were proposed to realize topological states of matter. One of them are multiterminal Josephson junctions where topological Andreev bound states are constructed in the synthetic space of superconducting phases. Crucially, the topology in these systems results in a quantized transconductance between two of its terminals comparable to the quantum Hall effect. In this work, we study a double quantum dot with four superconducting terminals and show that it has an experimentally accessible topological regime in which the non-trivial topology can be measured. We also include Coulomb repulsion between electrons which is usually present in experiments and show how the topological region can be maximized in parameter space.

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arXiv2023

Fractional transconductance via non-adiabatic topological Cooper pair pumping

Many robust physical phenomena in quantum physics are based on topological invariants arising due to intriguing geometrical properties of quantum states. Prime examples are the integer and fractional quantum Hall effects that demonstrate quantized Hall conductances, associated with topology both in the single particle and the strongly correlated many-body limit. Interestingly, the topology of the integer effect can be realized in superconducting multiterminal systems, but a proposal for the more complex fractional counterpart is lacking. In this work, we theoretically demonstrate how to achieve fractional quantized transconductance in an engineered chain of Josephson junctions. Crucially, similar to the stabilization of the conductance plateaus in Hall systems by disorder, we obtain stable transconductance plateaus as a result of non-adiabatic Landau-Zener transitions. We furthermore show that the fractional plateaus are robust to disorder and study the optimal operation regime to observe these effects. Our proposal paves the way for quantum simulation of exotic many-body out-of-equilibrium states in Josephson junction systems.

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arXiv2022

Hall viscosity and hydrodynamic inverse Nernst effect in graphene

Motivated by Hall viscosity measurements in graphene sheets, we study hydrodynamic transport of electrons in a channel of finite width in external electric and magnetic fields. We consider electric charge densities varying from close to the Dirac point up to the Fermi liquid regime. We find two competing contributions to the hydrodynamic Hall and inverse Nernst signals that originate from the Hall viscous and Lorentz forces. This competition leads to a non-linear dependence of the full signals on the magnetic field and even a cancellation at different critical field values for both signals. In particular, the hydrodynamic inverse Nernst signal in the Fermi liquid regime is dominated by the Hall viscous contribution. We further show that a finite channel width leads to a suppression of the Lorenz ratio, while the magnetic field enhances this ratio. All of these effects are predicted in parameter regimes accessible in experiments.

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arXiv2021

Controlling charge and spin transport in an Ising-superconductor Josephson junction

An in-plane magnetic field applied to an Ising superconductor converts spin-singlet Cooper pairs to spin-triplet ones. In this work, we study a Josephson junction formed by two Ising superconductors that are proximitized by ferromagnetic layers. This leads to highly tunable spin-triplet pairing correlations which allow to modulate the charge and spin supercurrents through the in-plane magnetic exchange fields. For a junction with a nonmagnetic barrier, the charge current is switchable by changing the relative alignment of the in-plane exchange fields, and a $π$-state can be realized. Furthermore, the charge and spin current-phase relations display a $ϕ_0$-junction behavior for a strongly spin-polarized ferromagnetic barrier.

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arXiv2021

Ground-state quantum geometry in superconductor-quantum dot chains

Multiterminal Josephson junctions constitute engineered topological systems in arbitrary synthetic dimensions defined by the superconducting phases. Microwave spectroscopy enables the measurement of the quantum geometric tensor, a fundamental quantity describing both the quantum geometry and the topology of the emergent Andreev bound states in a unified manner. In this work we propose an experimentally feasible multiterminal setup of $N$ quantum dots connected to $N+1$ superconducting leads to study nontrivial topology in terms of the many-body Chern number of the ground state. Moreover, we generalize the microwave spectroscopy scheme to the multiband case and show that the elements of the quantum geometric tensor of the noninteracting ground state can be experimentally accessed from the measurable oscillator strengths at low temperature.

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arXiv2020

Spin-dependent tunneling between individual superconducting bound states

Magnetic impurities on superconductors induce discrete bound levels inside the superconducting gap, known as Yu-Shiba-Rusinov (YSR) states. YSR levels are fully spin-polarized such that the tunneling between YSR states depends on their relative spin orientation. Here, we use scanning tunneling spectroscopy to resolve the spin dynamics in the tunneling process between two YSR states by experimentally extracting the angle between the spins. To this end, we exploit the ratio of thermally activated and direct spectral features in the measurement to directly extract the relative spin orientation between the two YSR states. We find freely rotating spins down to 7mK, indicating a purely paramagnetic nature of the impurities. Such a non-collinear spin alignment is essential not only for producing Majorana bound states but also as an outlook manipulating and moving the Majorana state onto the tip.

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arXiv2020

Microwave Spectroscopy Reveals the Quantum Geometric Tensor of Topological Josephson Matter

Quantization effects due to topological invariants such as Chern numbers have become very relevant in many systems, yet key quantities such as the quantum geometric tensor providing local information about quantum states remain experimentally difficult to access. Recently, it has been shown that multiterminal Josephson junctions constitute an ideal platform to synthesize topological systems in a controlled manner. We theoretically study properties of Andreev states in topological Josephson matter and demonstrate that the quantum geometric tensor of Andreev states can be extracted by synthetically polarized microwaves. The oscillator strength of the absorption rates provides direct evidence of topological quantum properties of the Andreev states.

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arXiv2020

Interplay Between Yu-Shiba-Rusinov States and Multiple Andreev Reflections

Motivated by recent scanning tunneling microscopy experiments on single magnetic impurities on superconducting surfaces, we present here a comprehensive theoretical study of the interplay between Yu-Shiba-Rusinov bound states and (multiple) Andreev reflections. Our theory is based on a combination of an Anderson model with broken spin degeneracy and nonequilibrium Green's function techniques that allows us to describe the electronic transport through a magnetic impurity coupled to superconducting leads for arbitrary junction transparency. Using this combination we are able to elucidate the different tunneling processes that give a significant contribution to the subgap transport. In particular, we predict the occurrence of a large variety of Andreev reflections mediated by Yu-Shiba-Rusinov bound states that clearly differ from the standard Andreev processes in non-magnetic systems. Moreover, we provide concrete guidelines on how to experimentally identify the subgap features originating from these tunneling events. Overall, our work provides new insight into the role of the spin degree of freedom in Andreev transport physics.

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arXiv2017

Nonequilibrium Andreev bound states population in short superconducting junctions coupled to a resonator

Inspired by recent experiments, we study a short superconducting junction of length $L\ll ξ$ (coherence length) inserted in a dc-SQUID containing an ancillary Josephson tunnel junction. We evaluate the nonequilibrium occupation of the Andreev bound states (ABS) for the case of a conventional junction and a topological junction, with the latter case of ABS corresponding to a Majorana mode. We take into account small phase fluctuations of the Josephson tunnel junction, acting as a damped LC resonator, and analyze the role of the distribution of the quasiparticles of the continuum assuming that these quasiparticles are in thermal distribution with an effective temperature different from the environmental temperature. We also discuss the effect of strong photon irradiation in the junction leading to a nonequilibrium occupation of the ABS. We systematically compare the occupations of the bound states and the supercurrents carried by these states for conventional and topological junctions.

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