Mesoscale and Nanoscale Physics · Cross-listed from quant-ph
Fast On-Chip Thermometry with TiN Kinetic Inductance Resonators in 22 nm Process Technology
Johann Drayne, George Ridgard, Lorenzo Peri et al. (+9 more)
Understanding the temporal and spatial dependence of temperature is critical in high-performance cryogenic devices. Typical thermometry techniques struggle to simultaneously combine high bandwidth, sensitivity and on-chip integration, limiting their ability to measure fast intra-device thermal fluctuations. Here, we demonstrate a time-resolved thermometry platform based on TiN kinetic inductance resonators integrated in a 22 nm FDSOI chip. By tracking temperature-dependent shifts in the resonant frequency, we achieve sub-millikelvin temperature sensitivity down to temperatures of 100 mK. Time-resolved on-chip pulsed heating experiments as a function of distance reveal an onset delay, consistent with a quasi-ballistic heat propagation velocity of 3.9 ${\pm}$ 0.1 mm ${\mu}$s${}^{-1}$. We also show that elevated temperatures increase net thermal conductance, shortening thermal relaxation times across all spatial separations. This behaviour manifests in two distinct regimes: a substrate-limited regime at 100 mK, where cooling rates vary with heater distance, and a Kapitza boundary-limited regime at 400 mK, where thermal relaxation becomes more spatially uniform. These measurements demonstrate kinetic inductance thermometry's ability to rapidly probe non-
equilibrium temperature dynamics in cryogenic devices such as
quantum processors.
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All authors Johann Drayne, George Ridgard, Lorenzo Peri, Frederic Schlattner, Fabio Olivieri, Mathieu de Kruijf, Isaac Harris, Grayson Noah, James Kirkman, Alberto Gomez-Saiz, M. Fernando Gonzalez-Zalba, Thomas Swift
Mesoscale and Nanoscale Physics · Cross-listed from quant-ph
A Superconducting Phase Transition Single-Electron Transistor
Gorka Aizpurua-Iraola, Thomas H. Swift, Felix-Ekkehard von Horstig et al. (+6 more)
Quantum computers require fast and accurate methods for
qubit state detection. Phase-transition sensors exploit the abrupt change between two physical states of a material to achieve enhanced sensitivity and have enabled advanced detectors for
quantum technologies, such as superconducting nanowire single-
photon detectors. However, this sensing principle has not yet been applied to
semiconductor spin qubits. Here, we demonstrate a superconducting phase-transition
radio-frequency single-electron transistor (PTSET), a charge sensor for
semiconductor spin qubits whose response is enhanced by a superconducting-to-normal phase transition. The transition is engineered by linking the sensor current to a low-critical-current, high-kinetic-inductance inductor integrated into the
radio-frequency matching network. We demonstrate improvements in sensitivity of one and two orders of magnitude over conventional rfSETs in the large- and small-signal regimes, respectively. Our results establish phase-transition sensing as a route towards ultrasensitive, integrated charge sensors for
semiconductor quantum computing and point to broader applications, including cryogenic
photon detection for
radio astronomy.
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All authors Gorka Aizpurua-Iraola, Thomas H. Swift, Felix-Ekkehard von Horstig, Domenic Prete, James Kirkman, Grayson M. Noah, Fabio Olivieri, Alberto Gomez-Saiz, M. Fernando Gonzalez-Zalba
Mesoscale and Nanoscale Physics · Cross-listed from cond-mat.quant-gas
Crossing the Rotational Sound Barrier in a Quantum Solvent
Baptiste Coquinot, Giacomo Bighin, Mikhail Lemeshko et al. (+1 more)
Molecules embedded in superfluids provide an experimentally controllable platform for investigating impurity physics. Here, we investigate a driven molecule rotating in a superfluid environment, including helium and Bose–Einstein condensates, at rotation frequencies similar to the bath dynamics. Within the experimentally relevant platform of an optical centrifuge, we show that the rotor remains localized up to a characteristic harmonic frequency that can realistically exceed the excitation energies of the bath, enabling access to ultrafast rotating impurities. In the co-rotating frame, the bath excitations experience a rotational Doppler shift, generating angular-momentum-resolved resonances absent in
equilibrium angulon theory. We identify a dissipative rotational sound barrier at which the molecule resonantly emits bath excitations and undergoes strong angular momentum exchange with the surrounding medium. Overall, we establish the dynamical phase diagram of the driven rotor in a
quantum solvent and introduce a generic platform for investigating fast driven rotating impurities in
quantum many-body systems.
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All authors Baptiste Coquinot, Giacomo Bighin, Mikhail Lemeshko, Ragheed Alhyder
Mesoscale and Nanoscale Physics · Cross-listed from cond-mat.mtrl-sci
Intrinsic anomalous Hall response in the bilayer kagome ferromagnet Co$_3$Sn
Yuqi Qin, Soumya Sankar, Xingkai Cheng et al. (+4 more)
Transition-metal kagome magnets provide a rich platform for investigating the interplay between layer stacking,
magnetic order, and band
topology. Here, we report the molecular beam epitaxy and experimental investigation of high-quality thin films of the kagome metal Co$_3$Sn, which has not been synthesized in bulk form yet. Structural and chemical analyses confirm a hexagonal
lattice structure ($P6_3/mmc$) composed of direct A-B stacked Co$_3$Sn kagome bilayers. Magnetometry reveals robust easy-plane ferromagnetism with a Curie temperature exceeding $300\,\text{K}$. Magneto-transport measurements demonstrate metallic behavior (carrier density $n\approx5.01\times10^{22}\,\text{cm}^{-3}$) alongside a temperature-independent anomalous Hall conductivity of $\sigma_{\rm AHE}\approx90\,\Omega^{-1}\cdot{\rm cm}^{-1}$, extending from $2\,\text{K}$ up to room temperature. Results from first-principles density functional theory calculations attribute this anomalous Hall response to intrinsic Berry
curvature hotspots near the Fermi level in the
spin-split band structure. Our results establish Co$_3$Sn as a room-temperature kagome ferromagnet and highlight the impact of the layer stacking sequence on the material properties of kagome metals from the CoSn family.
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All authors Yuqi Qin, Soumya Sankar, Xingkai Cheng, Yifan Jiang, Shiming Lei, Junwei Liu, Berthold Jäck
Mesoscale and Nanoscale Physics · Cross-listed from cond-mat.mtrl-sci
Atomic-scale composition of the ternary III-V semiconductor (Al,Ga)Sb visualized by cross-sectional scanning tunneling microscopy
Hitesh Kumar, Vladimir Kaganer, Zijin Lei et al. (+3 more)
Cross-sectional scanning tunneling microscopy at 5 K is used to investigate cation mixing in (Al,Ga)Sb layers grown by molecular beam epitaxy, via direct atom counting at the (1-10) and (110) cleavage planes. Electronic contrast between Al and Ga surface cations enables statistical analysis of the metal sublattice along the non-equivalent <110> directions within the zincblende (001) surface and along the [001] growth direction. The cation distribution is found to be random both along the growth direction and within the growth plane, with no evidence of long-range order or anisotropic growth kinetics; notably, the mean numbers of consecutive cations of the same type along the two in-plane directions are equal, possibly due to statistical averaging over randomly distributed subsurface cations. The results are compatible with either strain-mediated interactions during cation incorporation at the growth front or ideal, uncorrelated cation mixing. Overall, the examined (Al,Ga)Sb
alloy shows an exceptionally high degree of atomic-level homogeneity.
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All authors Hitesh Kumar, Vladimir Kaganer, Zijin Lei, Rüdiger Schott, Werner Wegscheider, Stefan Fölsch
Mesoscale and Nanoscale Physics
Rui-Chang Shen, Yihao Yang and Haoran Xue
High-frequency artificial phononic
crystals offer a low-loss platform compatible with on-chip integration, yet realizing Chern phononic phases at GHz frequencies remains challenging. Here, we propose a
magnon-induced phononic Chern
insulator in a honeycomb phononic
crystal hybridized with ferromagnetic islands at the hexagon centers. A circularly polarized Kittel mode couples to the surrounding
phonons with a phase winding, which breaks time-reversal
symmetry and opens a full Chern gap. In the large-detuning regime, this mechanism leads to an effective Haldane-type phononic model with
magnon-induced complex hopping. By tuning the
magnon-
phonon interaction, the full hybrid system accesses Chern phases with tunable Chern numbers |C|=1 and |C|=2. The predicted gaps can exceed realistic
phonon and
magnon linewidths, enabling their observation in GHz acoustic devices. Our work establishes chiral
magnon–
phonon hybridization as a route to magnetically reconfigurable topological phononics.
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Mesoscale and Nanoscale Physics
Spin preservation in screw-symmetric molecules
Jonas Bloch, Fedor Baranov and Maxim Breitkreiz
In electronic transport through long molecules,
spin is expected to be preserved only when the dwell time is much shorter than the characteristic
spin-mixing timescale $\hbar/\Delta$, where $\Delta$ is the magnitude of a
spin-dependent potential, such as
spin-orbit coupling. We show that, in molecules featuring discrete screw
symmetry,
spin preservation can be enhanced far beyond this timescale owing to strong
spin separation in quasi-momentum. This
spin fidelity in long molecules is consistent with chirality-induced
spin selectivity (CISS), suggesting
spin-dependent transport in long, chiral molecules with amplified
spin-splitting mechanisms. We provide analytical derivation of the enhanced
spin preservation and test it on tight-binding models, which confirm that the effect gradually weakens when the screw
symmetry is broken or changes from discrete to continuous. Furthermore, we perform transport simulations to show that a strong magnetoresistance trace of
symmetry-protected
spin fidelity emerges in a
spin-valve setup with two
magnetic leads, which we propose as an experimentally accessible signature.
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Mesoscale and Nanoscale Physics
Hall effect in viscous flows of two-dimensional electrons in samples with edges of arbitrary roughness
A.V. Gert and P.S. Alekseev
In ultra-clean conductors, fast inter-particle collisions can lead to the formation of a viscous electron fluid and realization of the hydrodynamic transport regime. Here we develop a theory of hydrodynamic magnetotransport of two-dimensional (2D) electrons in samples with low densities of defects and edges of arbitrary roughness. Within our model the roughness is described by a single parameter with the dimension of speed in the boundary conditions on sample edges. The electron-fluid flow profiles in long samples, as well as the corresponding longitudinal and Hall resistances, are calculated. The contribution to the Hall resistance associated with the relaxation processes exhibits a saturation in the limit of high
magnetic field and a minimum as a function of the
magnetic field for sufficiently rough edges. The minimum disappears as the edge roughness decreases or the sample width and bulk scattering by defects increase. These properties of the Hall resistance can serve as the signs to identify the hydrodynamic regime of electron transport in experiments and can be used to determine its parameters, in particular, the degree of edge roughness.
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Mesoscale and Nanoscale Physics · Cross-listed from quant-ph
Isotropic Nanoscale Quantum Sensor at Room-Temperature
Daniel T. Möller, Baha Sakar, Ekrem T. Güldeste et al. (+9 more)
Color-center based
quantum sensors provide nanoscale resolution under ambient conditions, yet their applicability remains limited. Because the quantization axes are locked to the host
lattice, conventional color centers suffer severe signal loss in off-axis
magnetic fields. To address this, we report an isotropic magnetometer enabled by the neutrally charged nitrogen-vacancy center (NV0) in diamond. Here,
spin-to-charge dynamics yield an NV0-dark
spin pair whose quantization axis dynamically aligns with the external field. Read out through NV charge-state-selective fluorescence, this system exhibits microsecond room-temperature coherence and nanotesla sensitivity for arbitrary field directions. We demonstrate
alignment-free mapping of steep field gradients and single paramagnetic micro-targets, alongside isotropic readout from randomly oriented nanodiamonds. Resolving longstanding orientation constraints, this platform unlocks unrestricted nanoscale magnetometry across life sciences and
quantum materials.
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All authors Daniel T. Möller, Baha Sakar, Ekrem T. Güldeste, Dhruv Wadhwani, Olt Gashi, Daniel A. García Vaca, Mokessh K. Ciwan, Simone P. Crozier, Christian Laube, Sirswa K. Shree Ram, Matteo Slaviero, Nabeel Aslam
Mesoscale and Nanoscale Physics
Exceptional point induced by hyperbolicity in an electrostatic spherical shell
Álvaro Buendía, Marcelo S. Barreiro and Nuno M.R. Peres
Exceptional points (EPs) are non–Hermitian degeneracies at which both
eigenvalues and eigenvectors coalesce, usually engineered through balanced gain and loss or non–reciprocity. In this work, we show that the radial electrostatic problem of an anisotropic core–shell nanoparticle realizes an EP without any of the alluded conditons. Written in the logarithmic radial coordinate, the problem is a Cauchy–Euler equation that maps onto a damped oscillator and, equivalently, onto a two-site Hatano–Nelson
Hamiltonian, so that the non-Hermiticity is emulated in space rather than in time and the sole control parameter is the degree of dielectric anisotropy, $\varepsilon_t/\varepsilon_r$. The shell is passive, reciprocal, and lossless, yet it hosts an EP and a non–Hermitian phase transition governed by hyperbolicity alone. Beyond a hyperbolicity threshold the electric field inside the shell turns from monotonic decay into spatial oscillation, producing hotspots at intermediate radii which can be exploited to tailor fluorescence, strong coupling, sensing, or cloaking. More broadly, this establishes
hyperbolic media as a platform to simulate non–Hermitian physics without gain, loss, or non–reciprocity.
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Mesoscale and Nanoscale Physics · Cross-listed from cond-mat.mtrl-sci
The Effect of Geometry on Thermodynamic Response
Bojana Bokic, Sébastien R. Mouchet, Biljana Stankov et al. (+9 more)
At the nano- and microscale, various patterns influence and shape thermal and optical response, making them essential for the survival of various biological species. In addition, controlling thermal radiation is vital for a broad range of applications, such as thermal management, spectroscopy, optoelectronics, and energy conversion technologies. For this reason, there is strong pressure to elucidate the physics of thermal radiation at the nanoscale. In this article, we provide evidence that complex nanoscale geometries affect thermal management, leading to an unusual thermal response in heat-capacity measurements as a function of temperature. Beyond identifying the structural constraints associated with this unusual thermodynamic response, the current study introduces the possibility of shaping the apparent heat-capacity response through geometry without necessarily altering the system's chemistry.
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All authors Bojana Bokic, Sébastien R. Mouchet, Biljana Stankov, Sanja Ostojic, Nicolas Roy, Darko Vasiljevic, Yin Chang, Marija Radmilovic-Radjenovic, Branislav Radjenovic, Thierry Verbiest, Mohamed Hatifi, Branko Kolaric
Mesoscale and Nanoscale Physics
Switchable giant room-temperature nonlinear Hall effect in Bilayer Graphene
Margherita Melegari, Ignacio Gutiérrez-Lezama, Justin C. W. Song et al. (+1 more)
Utilizing
quantum second-order nonlinear transport for practical junction-free devices require materials with large and tunable nonlinearites at room temperature – a current materials platform challenge. Here, we report the nonlinear Hall effect (NLHE) in double-ionic gated bilayer
graphene devices that enable unusually strong inversion breaking. We observe NLHE that are readily switchable (on, off, and sign reversed) with second order nonlinear susceptibilities $\chi^{(2)}_{yxx}$ that reaches giant room-temperature values of $3\,10^{-3}\,\mu\mathrm{m}\,\mathrm{S/V}$, comparable to values commonly observed at low temperature in WTe$_2$ or in
graphene-based moiré superlattices, and three-to-four orders of magnitude larger than values reported in material systems recently employed in search of a room-temperature NLHE. Our devices produce corresponding THz voltage responsivities $\simeq 4\,10^{4}\,\mathrm{V/W}$, comparable to commercially available Schottky diodes. These are orders of magnitude better than for previously reported room-temperature NLHE devices rendering double-ionic gated bilayer
graphene a choice platform for junction-free nonlinear technology.
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All authors Margherita Melegari, Ignacio Gutiérrez-Lezama, Justin C. W. Song, Alberto F. Morpurgo
Mesoscale and Nanoscale Physics
Observation of dodecagonal replica bands in 30$^{\circ}$-twisted bilayer WSe$_2$
Christian Valentiner-Branth Fokdal, Chakradhar Sahoo, Thomas S. Nielsen et al. (+6 more)
Twisted bilayers of two-dimensional (2D) transition metal dichalcogenides are promising systems for achieving tunable quasicrystalline orders with emergent properties. The underpinning electronic structure and scattering processes in 2D quasicrystals with multiorbital dodecagonal replica bands have so far not been determined. Here, we utilize angle-resolved photoemission spectroscopy (ARPES) with micrometer spatial resolution to directly observe replica bands in 30$^{\circ}$-twisted bilayer WSe$_2$. The
symmetry and intensity distribution of the observed replicas are explained by interlayer Umklapp scattering from bottom to top WSe$_2$ layers. Our spectral function measurements are consistent with the presence of a van Hove singularity adjacent to the $\mathrm{K}$-valleys, which underlines the possibility of inducing electronic reconstructions in bilayers with a large interlayer twist angle.
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All authors Christian Valentiner-Branth Fokdal, Chakradhar Sahoo, Thomas S. Nielsen, Alfred J. H. Jones, Zhihao Jiang, Kenji Watanabe, Takashi Taniguchi, Marcin Mucha-Kruczyński, Søren Ulstrup
Mesoscale and Nanoscale Physics · Cross-listed from cond-mat.mtrl-sci
Self-selective growth of GaAs1-xBix on GaAs zinc blende/wurtzite nanowire heterostructures
Rohit Yadav, Sebastian Lehmann, Vidar Flodgren et al. (+5 more)
Site-selective nanostructure growth and material incorporation at the atomic scale offer a promising pathway for engineering
quantum materials and nanodevices. Here, GaAs nanowires (NWs) with an axial
heterostructure of alternating zinc blende (Zb) and wurtzite (Wz)
crystal phases are employed as templates for site-selective Ga and Bi overgrowth. Using X-ray photoemission electron microscopy (XPEEM) with nanoscale spatial resolution, we map elemental distribution and local chemical bonding to reveal the incorporation behavior of Bi atoms in {110} Zb and {11-20} Wz facets. Bi incorporation proceeds through an anion-exchange process, where Bi atoms replace As, forming local Ga-Bi bonds and producing a thin GaAs1-xBix shell. We observe
crystal-phase-dependent Bi incorporation, with higher Bi concentration in the Zb segments than in the neighboring Wz segments within the same NW. Furthermore, the Zb segment with higher Bi content exhibits reduced susceptibility to oxidation compared with the Wz segment, resulting in increased Ga-oxide in the Wz surfaces. This study highlights GaAs NW Zb/Wz
heterostructures as a template for controlled growth of GaBi and GaAs1-xBix nanostructures with tailored functionalities for
quantum applications
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All authors Rohit Yadav, Sebastian Lehmann, Vidar Flodgren, Evangelos Golias, Alexei Zakharov, Kimberly A. Dick, Anders Mikkelsen, Rainer Timm
Mesoscale and Nanoscale Physics · Cross-listed from cond-mat.supr-con
Stabilization of Interband Phase Solitons in Two-Band Noncentrosymmetric Superconducting Rings
Yuriy Yerin, Boris Malomed, Stefan-Ludwig Drechsler et al. (+1 more)
Two-band
superconductors maintain a relative interband phase which can carry winding
soliton excitations in a superconducting ring, supported by independent winding numbers in the two bands. In rings of
superconductors obeying the inversion
symmetry the interband phase
solitons are metastable states, separated from the uniform ground state by the energy of screening currents. In this work we find that, breaking the inversion
symmetry strongly enough, one can make the
soliton a true ground state. In that case, a magneto-electric coupling, absent in centrosymmetric materials, contributes critically above a certain threshold, a relevant, free-energy term, odd with respect to the winding number, which biases the energy balance in favor of a particular winding sign. Once the bias outweighs the energy cost that originally made the
soliton metastable, a phase
soliton with a finite winding number becomes the ground state, with chirality set by the applied field. In current–flux measurements performed in
equilibrium states, the effect is demonstrated by field-odd
soliton branches, that replace the metastable ones existing in mesoscopic rings, built by two-component
superconductors, realizing a magneto-electric analog of the Little–Parks fluxoid-branch physics in the interband relative-phase sector.
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All authors Yuriy Yerin, Boris Malomed, Stefan-Ludwig Drechsler, F. Sebastian Bergeret
Mesoscale and Nanoscale Physics · Cross-listed from physics.optics
Circular Dichroism Spectroscopy of Single Objects: Problems, Artifacts, and Corrections
Stefan Goppelt, Lisa M. Günther and Jürgen Köhler
Molecular aggregates are at the basis of a broad range of functional systems, including photosynthetic light-harvesting complexes, organic photovoltaics, optoelectronic devices, and molecular sensors. Their structural organization, however, is often difficult to resolve because intrinsic heterogeneity. In this context, circular dichroism (CD) spectroscopy is particularly powerful because of its sensitivity to the three-dimensional organization of molecular building blocks. Extending CD measurements from ensembles to individual objects therefore offers a unique approach to probing supramolecular architecture in heterogeneous, non-crystallizable systems. However, without spatial and orientational averaging, measurements are highly sensitive to imbalances between left- and right-circularly polarized excitation, deviations from ideal circular polarization, and polarization imperfections coupled to linear dichroism, which creates spurious CD signals. Here, we present a systematic theoretical and experimental framework for understanding, quantifying, and controlling artifacts in single-object CD spectroscopy. We develop a mathematical description of the principal artifact mechanisms, identify their origins in practical implementations, including Pockels-
cell-based polarization modulation, and establish strategies for their minimization. We validate this framework using an experimental implementation capable of acquiring CD spectra from individual molecular aggregates over 690-785 nm. Our results demonstrate that reliable single-object CD measurements are achievable when polarization-related artifacts are rigorously characterized and controlled. This Tutorial Review provides a unified theoretical framework and practical guide for single-object CD spectroscopy and its application to single-particle chirality, supramolecular photonics, and biophotonics.
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Mesoscale and Nanoscale Physics · Cross-listed from cond-mat.other
Non-Hermitian Skin Effect from Radiative Coupling in a Reciprocal Chiral Medium
Kin Hung Fung, Changhao Meng, Yixin Xiao et al. (+1 more)
We show that long-range radiative coupling in a passive chiral medium produces an unusual non-Hermitian skin effect in a chain of dipoles. The skin-mode profile consists of a long-range light-line branch-cut contribution, a non-exponential factor $1/[n(\ln n)^2]$ with $n$ being the site number. Finite-chain calculations show that part of the open-boundary spectrum contracts toward the Bloch spectrum, whereas the number of boundary-localized modes remains extensive. The retarded radiative coupling makes both the real-space profile and the finite-size spectral signatures of boundary localization depart from standard finite-range and pure exponential coupling theory.
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All authors Kin Hung Fung, Changhao Meng, Yixin Xiao, C. T. Chan
Mesoscale and Nanoscale Physics
Topologically protected perfect crossed Andreev reflection in flux-engineered quantum wire junctions
Abhiram Soori
Generating non-locally entangled electron pairs via Cooper-pair splitting is vital for solid-state
quantum information processing. However, isolating the underlying crossed Andreev reflection (CAR) is challenging due to competing transport processes like electron tunneling (ET) and local Andreev reflection (AR). Here, we propose a flux-tunable four-terminal normal metal-
superconductor junction that achieves deterministic, 100% efficient CAR. We demonstrate that at exactly half a
magnetic flux
quantum ($\phi=\pi$), exact destructive Aharonov-Bohm and Peierls interferences structurally forbid ET and AR respectively. By tuning the central junction hopping, electron reflection is also suppressed to zero. Using the Cauchy argument principle, we prove that this suppression manifests as a quantized topological winding number, guaranteeing a topologically protected unit CAR probability. We establish that this regime is characterized by a strictly positive cross-correlation shot noise, providing an unambiguous experimental signature of Cooper-pair splitting. Furthermore, this perfect CAR is nearly broadband within the superconducting gap and remarkably robust against structural disorder, offering a highly resilient architecture for deterministic nonlocal
entanglement generation.
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Mesoscale and Nanoscale Physics
Optical spectroscopy of composite fermion edge states in the fractional quantum Hall effect
Maria Sebastian, Ashutosh Singh and Alexey Belyanin
We show that edge states in fractional
quantum Hall effect samples can be selectively probed and excited with sub-terahertz optical spectroscopy. Using the composite
fermion (CF) mean-field framework, which maps the strongly correlated fractional
quantum Hall problem onto an effective integer
quantum Hall problem, we calculate the absorbance spectrum for the Jain sequence of filling fractions including both bulk and edge states. The CF edge-state absorption peaks appear in the millimeter-wave to sub-terahertz range, e.g., 60-500 GHz at B = 10 T in GaAs, i.e. they are blueshifted with respect to the bulk CF cyclotron frequency but are well below the integer
quantum Hall cyclotron frequency scale at the same
magnetic fields. The number of resolved peaks in each series of the absorption spectrum counts the filled Lambda-levels and fingerprints the fraction. Inversion
symmetry breaking near the edge activates optical transitions forbidden in the bulk and enables second-order nonlinear processes in electric-dipole approximation. The absolute frequency scale of the spectrum is set by the CF effective mass, which is generated entirely by electron-electron interactions, so the absorption spectrum provides a direct optical probe of this interaction-induced mass.
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