Mesoscale and Nanoscale Physics
Presence versus absence of charging energies in PbTe quantum dots
Yuhao Wang, Lining Yang, Wenyu Song et al. (+18 more)
Charging energy ($E_C$) is essential in
quantum dot (QD) devices. Previous studies on PbTe QDs have reported both the presence and absence of $E_C$. To resolve this ambiguity, we vary the QD size, i.e. the cross-sectional area of PbTe nanowires, and track the
evolution of $E_C$. For large crosssectional areas ($\sim$ 16000 nm$^2$), the PbTe QDs exhibit no measurable $E_C$, while quantized levels are well resolved. Decreasing this area successively to 5000, 1500, and 460 nm$^2$, $E_C$ becomes finite and increases to 80, 160, and 210 $\mu$eV, respectively. We further demonstrate the strong tunability of local gates, which can tune the PbTe device from the QD regime to the regime of ballistic transport. These results address concerns regarding the large dielectric constant of PbTe and provide key insights in engineering advanced PbTe
quantum devices.
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All authors Yuhao Wang, Lining Yang, Wenyu Song, Li Chen, Zehao Yu, Xinchen He, Zeyu Yan, Jiaye Xu, Ruidong Li, Weizhao Wang, Zonglin Li, Shuai Yang, Shan Zhang, Xiao Feng, Tiantian Wang, Yunyi Zang, Lin Li, Runan Shang, Qi-Kun Xue, Ke He, Hao Zhang
Soft Condensed Matter · Cross-listed from physics.flu-dyn
Stokes flows in a sessile hemispherical drop due to evaporation and surface tension gradient
Peter Lebedev-Stepanov
Viscous hydrodynamic flow in a small, slowly evaporating, sessile hemispherical droplet with a pinned contact line is considered. Analytical solutions are obtained for the Deegan outward flow, which is responsible for the coffee ring effect, as well as the Marangoni flow excited by a surface tension gradient. It is assumed that the surface tension gradient may be caused by anisotropic cooling of droplet surface or other factors, such as nonuniform illumination of an optically active surfactant. Two main types of boundary conditions, no-slip and full-slip, are considered in describing the flow-substrate interaction. It is shown that under the no-slip condition, there is a rigid relationship between the evaporation rate and the surface tension gradient, which imposes strict requirements on the temperature regime inside the droplet. This result offers a new
vision of the critical Marangoni number, which describes the threshold for the transition of an evaporating droplet from capillary flow to developed Marangoni convection. The results of this work may attract the
attention of experimenters to the study of the sensitivity of viscous flow in an evaporating droplet to the
liquid-substrate boundary conditions, especially if the system under consideration passes into the Marangoni regime, when the no-slip condition changes to a partial or full slip condition due to the increase in viscous shear stress near the substrate.
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Strongly Correlated Electrons
Quantum Anomalous Hall Effect in Rhombohedral Multilayer Graphene/hBN Moiré Superlattices
Jiannan Hua, Jing Ding, W. Zhu et al. (+1 more)
The recent discovery of robust
quantum anomalous
Hall (QAH) effect in rhombohedral multilayer
graphene (RMG) aligned with hexagonal boron nitride (hBN) has established a highly versatile platform for correlated topological matter. This review synthesizes the experimental and theoretical progress in understanding these interaction-driven topological phases. Experimentally, the landscape has rapidly expanded from initial Chern
insulators in trilayer systems to fully quantized QAH states in thicker systems. Theoretically, it is believed that moiré potential and electron-electron interaction cooperate and produce the QAH effect in such systems. Theoretical calculations also bring interesting questions, such as the formation of an interaction-driven topological phase known as an anomalous
Hall crystal (AHC). This review comprehensively covers the experimental hallmarks, the theoretical frameworks, including continuum models and many-body approaches, and the ensuing physical picture that reconciles the roles of interactions, displacement fields, and the moiré potentials. We conclude by outlining outstanding open questions and future directions, positioning RMG/hBN systems at the forefront of topological
quantum matter.
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All authors Jiannan Hua, Jing Ding, W. Zhu, Shui-gang Xu
Mesoscale and Nanoscale Physics
Magnetoplasmons in $N$-layer structures
Jinu Park, Taehun Kim, E. H. Hwang et al. (+1 more)
We provide a systematic framework to investigate the magnetoplasmons of multilayer two-dimensional electron systems by using the Kac–Murdock–Szegő (KMS) Toeplitz
matrix to consider interlayer Coulomb interactions. In the absence of interlayer tunneling, we show that the single-layer magnetoplasmon branch splits into $N$ collective modes – one in-phase mode and $N-1$ out-of-phase modes – and derive their asymptotic behaviors in the long-wavelength limit, as well as in the limit of large layer separation and strong
magnetic fields. When interlayer tunneling is present, we clarify the magnetoplasmon dispersion, both qualitatively and quantitatively, by identifying the magnetoplasmon mode associated with each interband transition, as well as tunneling magnetoplasmons arising from interband transitions with the same Landau level index. Our study presents the hybridization between the modes governed by underlying
symmetries, along with an enhanced tunneling magnetoplasmon gap exceeding the associated interband gap. The KMS-based analytic formalism thus provides a comprehensive physical understanding of magnetoplasmons in multilayer structures.
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All authors Jinu Park, Taehun Kim, E. H. Hwang, Hongki Min
Strongly Correlated Electrons · Cross-listed from quant-ph
Floquet implementation of a 3d fermionic toric code with full logical code space
Yoshito Watanabe, Bianca Bannenberg and Simon Trebst
Floquet
quantum error-correcting codes provide an operationally economical route to fault tolerance by dynamically generating stabilizer structures using only two-body Pauli measurements. But while it is well established that stabilizer codes in higher spatial dimensions gain additional levels of intrinsic robustness, higher-dimensional Floquet codes have hitherto been explored only in limited scope. Here we introduce a 3d generalization of a Floquet code whose instantaneous stabilizer group realizes a 3d fermionic toric code, while crucially preserving all three logical
qubits throughout the entire measurement sequence. One central ingredient is the identification of a 3d
lattice geometry that generalizes the features of the Kekulé
lattice underlying the 2d Hastings-Haah code - specifically, a structure where deleting any one edge color yields a two-color subgraph that decomposes into short, closed loops rather than homologically nontrivial chains. This loop property avoids the collapse of logical information that plagues naive sequential two-color measurement schedules on many 3d
lattices. Although, for our
lattice geometry, a simple 3-round cycle that sequentially measures the three types of parity checks does not expose the full error syndrome set, we show that one can append a measurement sequence to extract the missing syndromes without disturbing the logical subspace. Beyond code design, 3d tricoordinated
lattice geometries define a family of 3d monitored Kitaev models, in which random measurements of the non-commuting parity checks give rise to dynamically created entangled phases with nontrivial
topology. In discussing the general structure of their underlying phase diagrams and, in particular, the existence of certain
quantum critical points, we again make a connection to the general preservation of logical information in time-ordered Floquet protocols.
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Strongly Correlated Electrons · Cross-listed from hep-th
Boundary mutual information in double holography
Yuxuan Liu, Yi Ling and Zhuo-Yu Xian
We consider a composite system where AdS$_3$
gravity is coupled to a flat heat bath and investigate the mutual information between two subregions on the intersection of the AdS$_3$ and bath, referred to as the boundary mutual information (BMI). The corresponding
entanglement entropy is captured via
quantum extremal surfaces (QES), which holographically be computed by a surface optimization
algorithm based on “Surface Evolver”. We focus on both connected and disconnected configurations of the
quantum entanglement wedge (Q-EW) in the AdS$_3$ bulk and analyze the finite corrections to the BMI. Our numerical results reveal a phase transition of the BMI as the separation between two subregions increases. Furthermore, we find that the BMI can naturally be decomposed into two distinct components: a
geometric term arising from the areas of the
quantum extremal surfaces, and a correction term resulting from bulk
quantum fields within the Q-EW. Interestingly, the
geometric contribution always exceeds the total BMI, indicating a negative correction from the bulk matter fields. This negativity can be understood as the result of subtracting a greater contribution from
quantum fields in the connected Q-EW than in the disconnected one. We also reproduce the negative contribution of bulk
quantum fields to BMI within a random tensor network (RTN) toy model of double holography. Modeling the bulk as a highly mixed state entangled with a large bath leads to a volume-law bulk
entropy. In the large bond-dimension limit, the
geometric part of the BMI remains non-negative, while the bulk
entropy contribution becomes non-positive when the Q-EWs merge.
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Mesoscale and Nanoscale Physics
Gapped out-of-phase plasmon modes in alternating-twist multilayer graphene
Taehun Kim and Hongki Min
We theoretically investigate the plasmon modes of alternating-twist multilayer
graphene. In multilayer systems, interlayer coupling gives rise to distinctive plasmon modes, but calculations in moiré systems remain challenging due to their complex tunneling structures. Using the Kac-Murdock-Szegő Toeplitz formalism, we derive that the in-phase mode exhibits the conventional $\sqrt{q}$ behavior, while the out-of-phase modes acquire plasmon gaps determined by specific interband transitions between Dirac cones with different velocities in the long-wavelength limit. We demonstrate that these out-of-phase modes remain undamped in the weak Coulomb-interaction limit when the twist angle exceeds a critical value ($\theta \gtrsim 2.75^\circ$ for the alternating-twist trilayer case), regardless of the carrier density as long as the low-energy effective Dirac
Hamiltonian remains valid. Furthermore, we consider the effect of a perpendicular electric field, and demonstrate how plasmon modes can be tuned by a gate voltage.
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Materials Science
Room-Temperature Terahertz Photoconductivity Polarity Switching in High Entropy Nickelates with Implications for Photonic Synapses
Sanjeev Kumar, Brijesh Singh Mehra, Gaurav Dubey et al. (+5 more)
High
entropy oxides (HEO) hold the potential to revolutionize the conventional material paradigms by leveraging high order of chemical disorder that induces highly desirable exotic phases for advanced applications. Here, we devise a methodology to enhance the efficiency of an artificial photonic synapse using a high
entropy rare earth nickelate. Combined with epitaxial strain, we show that high
entropy can further manipulate the phase of these locally disordered materials. Using time-averaged and time resolved Terahertz (THz) spectroscopy as dynamic probe, for the first time we show a rare combination of i)
crystal axis dependent
insulator to metal THz electronic phase transition and ii) coexistence of negative and positive THz photoconductivity at room temperature. Detailed analysis within theoretical models, including density functional theory (DFT)-based band structure calculations, suggest origin of these properties as disproportionate ordering of oxygen vacancies. Based on these findings, a conceptual THz-based artificial photonic synapse is proposed. This work underlines the pivotal role of HEO in advancing diverse THz functionalities, representing a critical step toward futuristic applications like THz-based high-speed computing and communication with an emphasis in THz frequency domain.
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All authors Sanjeev Kumar, Brijesh Singh Mehra, Gaurav Dubey, Prakhar Vashishtha, Neeraj Bhatt, Jayaprakash Sahoo, Ravi Shankar Singh, Dhanvir Singh Rana
Superconductivity
Introduction to High-Temperature Superconductivity for Solid State Chemists
Zenji Hiroi
Superconductivity is one of the most amazing properties that metallic conductors exhibit. Electrical resistance is completely eliminated below the critical temperature (Tc), which is the most important parameter in superconductivity. Since the discovery of copper
oxide superconductors 39 years ago, many solid state chemists have made significant contributions to the field by discovering new compounds and producing high-quality samples for physical measurements. However, superconductivity research remains challenging for most solid state chemists because it requires knowledge of complicated solid state physics. This manuscript aims to provide a simple, intuitive introduction to superconductivity using only fundamental physics concepts that solid state chemists are familiar with. The author investigates a wide range of materials and classifies them according to the superconductivity mechanisms that may drive them. Specifically focusing on a series of copper
oxide superconductors with the highest Tc at ambient conditions, the remarkable material dependence of Tc and the underlying, unconventional superconductivity mechanism that leads to the high Tc are thoroughly examined. Although our understanding of cuprate superconductivity is still fragmented, the author believes that once the branches and leaves are removed, the story will be fairly simple, similar to the
phonon-based superconductivity mechanism revealed by the BCS theory. Furthermore, potential strategies for raising the Tc of cuprates and other
superconductors are discussed. The author hopes that this article will pique interest in
superconductors in young solid state chemists and encourage them to pursue the discovery of still unknown and unexplored room-temperature
superconductors in the future.
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Soft Condensed Matter
Anomalous electrowetting of physicochemically heterogeneous surfaces
Rumal Singh, Donjo George, Prashant Hitaishi et al. (+2 more)
In the present work, a physiochemically heterogeneous surface has been fabricated to investigate the electrowetting behaviour of the surface. The polystyrene (PS) micro-humps with varied size are developed on the polydimethylsiloxane (PDMS) surface, which show an anomalous electrowetting behaviour. The surfaces are observed to be more electro-wettable than it is predicted by the classical Lippmann-Young equation. The observations are well understood considering the chemical heterogeneity of the surface, exhibiting a surface energy mismatch between the PS micro-humps and the PDMS layer. Further, the anomaly is comprehended by following the ridge formation around the triple-phase contact line and the varied surface roughness. A surface parameter is introduced in the Lippmann-Young equation that follows the experimental data with varied values of the parameter representing the physicochemically heterogeneous surfaces. A positive value of the surface parameter indicates strong pinning while a negative value represents depinning of the droplet. This parameter explains the faster electrowetting than predicted by the Lippmann-Young equation.
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All authors Rumal Singh, Donjo George, Prashant Hitaishi, Samarendra P Singh, Sajal K Ghosh
Disordered Systems and Neural Networks · Cross-listed from math.PR
Michel Talagrand and the Rigorous Theory of Mean Field Spin Glasses
Sourav Chatterjee
Michel Talagrand played a decisive role in the transformation of mean-field
spin glass theory into a rigorous mathematical subject. This chapter offers a narrative account of that development. We begin with the physical origins of the Sherrington-Kirkpatrick (SK) model and the emergence of the TAP and Almeida-Thouless stability frameworks, culminating in Parisi's replica
symmetry breaking (RSB) ansatz and its hierarchical order parameter. We then review early rigorous milestones, including high-temperature results and stability identities, and describe the consolidation of interpolation and cavity methods through the work of Guerra and of Aizenman-Sims-Starr. The central event in this narrative is Talagrand's 2006 proof of the Parisi formula for the SK model and for a broad class of mixed $p$-
spin models, and his subsequent analysis of Parisi measures. We also discuss Talagrand's later program constructing pure states under extended Ghirlanda-Guerra identities and an atom at the maximal overlap, together with the structural results that followed, notably Panchenko's ultrametricity
theorem and extensions of the Parisi formula. Throughout, we indicate how related contributions by many authors fit into the same long-running program across probability, analysis, and mathematical physics.
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Mesoscale and Nanoscale Physics
Topology and edge modes surviving criticality in non-Hermitian Floquet systems
Longwen Zhou
The discovery of critical points that can host quantized nonlocal order parameters and degenerate edge modes relocate the study of
symmetry-protected topological phases (SPTs) to gapless regions. In this letter, we reveal gapless SPTs (gSPTs) in systems tuned out-of-
equilibrium by periodic drivings and non-Hermitian couplings. Focusing on one-dimensional models with sublattice
symmetry, we introduce winding numbers by applying the Cauchy's argument principle to generalized Brillouin zone (GBZ), yielding unified topological characterizations and bulk-edge correspondence in both gapped phases and at gapless critical points. The theory is demonstrated in a broad class of Floquet bipartite
lattices, unveiling unique topological criticality of non-Hermitian Floquet origin. Our findings identify gSPTs in driven open systems and uncover robust topological edge modes at phase transitions beyond
equilibrium.
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Materials Science
Strain-enhanced edge ferromagnetism and bipolar magnetic semiconducting behavior in Janus graphene nanoribbons
Ran Liu, Hongxing Liu, Junfeng Ren et al. (+1 more)
Using first-principles density functional theory and determinant
quantum Monte Carlo methods, we show that Janus
graphene nanoribbons with topological defect arrays ($m=2$) exhibit robust intrinsic ferromagnetism across widths $W=2-6$, with bandgaps exceeding 200 $meV$ and stable
ferromagnetic ground states. Notably, uniaxial tensile strain significantly enhances their
ferromagnetic properties: at 25% strain, the Curie temperature increases to $222K$, a fivefold improvement over unstrained systems and the highest reported for
graphene-based nanoribbons. Strain also induces a reversible transition to a bipolar
magnetic semiconductor, with
spin-flipped valence and conduction band edges beyond 10% strain. This dual functionality, strain-enhanced ferromagnetism and strain-induced
spin flip, stems from strain-modulated $p_{z}$ orbital hybridization and strong direct exchange interaction. Among these, $W=5$ Janus
graphene nanoribbons emerge as potential candidates for room-temperature spintronic devices and strain-programmable
quantum transport systems.
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All authors Ran Liu, Hongxing Liu, Junfeng Ren, Tianxing Ma
Mesoscale and Nanoscale Physics
Three-body Fermi-liquid corrections for Andreev transport through quantum dots
Akira Oguri, Masashi Hashimoto and Yoshimichi Teratani
We study crossed Andreev reflection occurring in
quantum dots connected to one superconducting lead and two normal leads at low temperatures $T$. Specifically, we derive an exact formula for the conductance up to order $T^2$ in the large superconducting gap limit, which is expressed in terms of the transmission probabilities of Cooper pairs and interacting Bogoliubov quasiparticles. Our formulation is based on the latest version of
Fermi-
liquid theory for the Anderson
impurity model, which has clarified the quasiparticle energy shifts of order $\omega^2$ and $T^2$ – namely, corrections of the same order as those arising from the finite lifetime of quasiparticles – can be expressed exactly in terms of three-body correlations of
impurity electrons. We also demonstrate how the three-body contributions evolve and affect the Cooper-pair tunneling as the Andreev level moves away from the
Fermi level, using the numerical renormalization group approach. The results show that the Cooper-pair contribution to the $T^2$ terms of the local and nonlocal conductances becomes comparable to the Bogoliubov-quasiparticle contribution in the parameter region, in which superconducting proximity effects dominate over the Kondo effect.
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Materials Science
Mechanism-driven CO2 Capture and Activation on Two-dimensional Transition-metal Diborides
Jakkapat Seeyangnok, Rungkiat Nganglumpoon, Joongjai Panpranot et al. (+1 more)
The urgent need to mitigate rising atmospheric CO2 levels motivates the search for stable, efficient, and tunable adsorbent materials. In this study, we employ first-principles density functional theory to investigate the adsorption of CO2 molecules on two-dimensional hexagonal transition-metal diboride monolayers, M2B2 (M = Sc, Y, Ti, Zr, Nb). The adsorption energies, structural distortions, and bonding characteristics are systematically analyzed to understand how the metal center governs CO2 activation. The calculated adsorption energies range from -1.84 to -2.16 eV (or -1.98 to -4.42 eV), with Ti2B2 and Sc2B2 exhibiting the strongest CO2 binding, while Y2B2, Zr2B2, and Nb2B2 show moderately strong chemisorption. Adsorption induces significant molecular activation, evidenced by elongated C-O bonds (1.27-1.29 Angstrom) and bent O-C-O angles (129-132 degrees), compared to the linear gas-phase configuration (1.17 Angstrom, 180 degrees). Charge analysis further reveals substantial electron transfer from the monolayer to CO2, consistent with strong chemisorption and structural deformation. Correspondingly, the shift toward less negative IpCOHP(Ef) values indicates a pronounced weakening of the internal C-O bonds, reflecting increased population of antibonding pi* orbitals. Ab initio molecular dynamics simulations show that the activated CO2 species is thermally sensitive: while most M2B2 surfaces retain stable adsorption at 300 K, Ti2B2 drives spontaneous CO2 dissociation into CO and O, revealing a temperature-assisted activation pathway. These findings highlight how the choice of transition metal tunes electronic interactions, adsorption energetics, and activation pathways on M2B2 surfaces. Overall, this work identifies two-dimensional transition-metal diborides as promising candidates for next-generation CO2 capture and activation technologies.
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All authors Jakkapat Seeyangnok, Rungkiat Nganglumpoon, Joongjai Panpranot, Udomsilp Pinsook
Mesoscale and Nanoscale Physics
Photogalvanic Effects in Surface States of Topological Insulators under Perpendicular Magnetic Fields
Haoyu Li, Kainan Chang, Wang-Kong Tse et al. (+1 more)
We present a theoretical study of the nonlinear magneto-optical shift conductivity in the surface states of the prototypical topological
insulator Bi$_2$Se$_3$ under a perpendicular quantizing
magnetic field. By describing the electronic states as Landau levels and using a perturbative approach, we derive the microscopic expression for the shift conductivity $\sigma^{(2);\alpha\beta\gamma}(-\omega,\omega)$, where $\alpha,\beta,\gamma=\pm$ stand for the circular polarization of light and $\omega$ is the light frequency; the spectra are further decomposed into contributions from the interband and intraband optical transitions, for which the selection rules are identified. Considering that the system possesses $C_3$ point group of
symmetry, the nonzero components of the conductivity tensor are $\sigma^{(2);-++}=[\sigma^{(2);+--}]^\ast$. Therefore, a pure circularly polarized light generates zero shift current. In the clean limit, the conductivities are nonzero only for discrete
photon energies because of the discrete Landau levels and energy conservation, and they become Lorentzian lineshapes with the inclusion of damping, which relaxes the condition of energy conservation. The dependence of the spectra on the damping parameters, the
magnetic fields, and the chemical potentials is investigated in detail. Our results reveal that the shift current is highly tunable by the chemical potential and the
magnetic field. These results underscore the potential of topological
insulators for tunable, strong nonlinear magneto-optical applications.
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All authors Haoyu Li, Kainan Chang, Wang-Kong Tse, Jin Luo Cheng
Mesoscale and Nanoscale Physics
Effects of magnonic Kerr nonlinearity on magnon-polaritons with a soft-mode
Takahiro Chiba
We theoretically study the effects of magnonic Kerr nonlinearity on
magnon-polaritons (MPs) with a soft-mode in easy-axis ferromagnets coupled to a microwave cavity. Using an effective
circuit model capable of describing MPs up to the nonperturbative strong-coupling regime, we show that chaotic and frequency-comb-like behaviors of MPs emerge at the original modes crossing point. Furthermore, we demonstrate that the Kerr nonlinearity induces a finite excitation gap in the soft-mode, particularly in the strong-coupling regime.
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Soft Condensed Matter
Starch granules are instructive scaffolds for synergistic reinforcement and dissipation in hydrogel composites
Shirlaine Juliano, Jasmine Samaniego, Ian M Lillie et al. (+3 more)
A fundamental challenge in soft material design is the competition between
rigidity and dynamicity, as stiffening mechanisms typically suppress energy dissipation. Here, we demonstrate that starch granules serve as instructive scaffolds that overcome this constraint, enabling the synergistic amplification of both elastic reinforcement and dynamic dissipation in hydrogels. We show that engineering the charge and structure of the filler-
matrix interface enhances this synergistic response, which we propose arises from a dual-action physical mechanism: filler-induced
polymer bundling of the
polymer matrix provides structural reinforcement, while transient filler-
matrix hydrogen bonding facilitates dissipation. Moreover, we reveal that binary blends of disparate filler species unexpectedly suppress these emergent properties, which we argue arises from enhanced entropic mixing. Our results provide a physical framework to overcome current design limitations in soft composites and sculpt their viscoelastic response from synergistic enhancement to strategic suppression for applications ranging from high-performance soft robotics to biomimetic tissue engineering.
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All authors Shirlaine Juliano, Jasmine Samaniego, Ian M Lillie, Geraldine Ramirez, Peter M Iovine, Rae M Robertson-Anderson
Superconductivity
Warren E. Pickett
Roughly twenty reports (as of 2025) of time-reversal-
symmetry breaking (TRSB) states in low critical temperature (T$_c$) superconducting (SC), otherwise conventional
Fermi liquid, metals have emerged primarily from
muon spin relaxation ($\mu$SR) data. The detected fields, inferred from the current interpretation of depolarization data, are similar in magnitude and not far above the lower limit of detection, corresponding to magnetizations of no more than 10$^{-3}$ $\mu_B$/atom. These materials comprise a new class of fragile
magnetic superconductors modeled as triplet pairing. The measured SC state properties, excepting only the fields detected below T$_c$, are representative of low T$_c$ singlet BCS SCs, not showing unusual coherence lengths or critical fields. While it is recognized that the
muon does affect the sample by displacing nearby atoms and impacting
magnetic interaction parameters, the measurement process, changing the system from sample $\rightarrow$ sample+$\mu^+$ thereby breaking TRS, may deserve further scrutiny. This overview provides a survey of the environment of the
muon, from the normal state to the superfluid state, where the induced supercurrent and Yu-Shiba-Rusinov gap states provide coupling of the
muon moment to the superfluid. The unusual topological
superconductor LaNiGa$_2$, currently modeled as non-
unitary triplet, is used as a case study. Supposing that the prevailing $\mu$SR inference of a small spontaneous field within the bulk of theSC obtains, the current picture of (possibly non-
unitary) triplet pairing is discussed and an attractive alternative for LaNiGa$_2$ is noted.
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