arXiv subjects
Publications and source records attributed to Chenhan Liu.
Assuming the validity of the recently proposed \textit{``A compact complex threefold fibred by tori over the projective line, and the six-sphere''}, we construct an exotic complex structure on $\mathbb P^{3}$, distinct from the point-blowup structures of Huckleberry, Kebekus, and Peternell. Then we perform an Atiyah flop to produce a complex structure on the standard smooth manifold $S^{2}\times S^{4}$.
Decoupling heat and charge transport is a key challenge in thermoelectrics. Here, we identify a route to spatially separate phonon and carrier transport in quasi-one-dimensional materials through high-throughput screening of the Materials Project database. Representative Sn$_2$S$_3$ and SbTeI exhibit a strong-intrachain--weak-interchain bonding hierarchy that favors phonon propagation along the chains while suppressing transverse lattice heat transport. In contrast, transverse valence-band states provide effective interchain electronic coupling and relatively light hole transport. This mismatch between lattice and electronic transport dimensionalities produces an inverted thermal--electrical anisotropy. Across the screened candidates, interchain lattice thermal conductivity is strongly suppressed, whereas hole transport remains weakly anisotropic or even favors the interchain direction. For SbTeI, this decoupling yields a maximum $zT$ of approximately 2.1 near 900~K. These results establish dimensionality mismatch as a general strategy for decoupling phonon and carrier transport in thermoelectric materials.
For a finite family of representations of a reductive group, we define a Laurent polynomial on the group. The exponential sum associated this Laurent polynomial is called a hypergeometric exponential sum. We introduce an arithmetic hypergeometric $\mathcal D$-module to study the hypergeometric exponential sum. It is an overholonomic arithmetic $\mathcal D$-module with a Frobenius structure so that the trace of the Frobenius at a rational point is the exponential sum. Over the locus where the Laurent polynomial is nondegenerate, the arithmetic hypergeometric $\mathcal {D}$-module defines an $F$-isocrystal overconvergent along the degenerate locus. As an application, we get an estimation of the hypergeometric exponential sum.
MgAgSb, a promising thermoelectric material, undergoes reversible phase transitions that drastically alter its thermal transport behavior. Using first-principles calculations, we systematically investigate the lattice thermal conductivity ($\kappa_L$) of its three phases: $\alpha$, $\beta$, and $\gamma$, revealing a progressive increase following $\alpha < \beta < \gamma$. This trend originates from distinct scattering mechanisms. Four-phonon scattering substantially suppresses the particle-like conductivity ($\kappa_p$) in the $\beta$ and $\gamma$ phases, while electron-phonon scattering provides a minor additional reduction. In contrast, the wave-like conductivity ($\kappa_c$) from coherent phonon tunneling is highest in the complex $\alpha$ phase, contributing up to 44\% of $\kappa_L$. Notably, the temperature dependence of $\kappa_L$ differs fundamentally between phases: in $\beta$, the weak $\kappa_p$ variation arises from a decreasing Gr\"{u}neisen parameter with temperature; in $\alpha$, the strong rise in $\kappa_c$ with temperature counteracts the decay of $\kappa_p$. Our findings establish a comprehensive picture of thermal transport in MgAgSb, highlighting the phase-dependent interplay between particle-like and wave-like phonon contributions.
We establish that ultralow lattice thermal conductivity in halide perovskites and related octahedral framework materials arises from two distinct and complementary mechanisms: (i) halogen-halogen-enabled rotational soft modes that reshape the low-frequency spectrum and intensify phonon scattering, and (ii) static octahedral distortions that further enhance anharmonicity and reduce phonon lifetimes. Using first-principles calculations on CsPbBr3, we demonstrate that Br-Br interactions induce rotational soft modes that decongest the phonon spectrum and enhance three- and four-phonon scattering, strongly suppressing particle-like thermal conductivity (kappa_p). Independently, static octahedral distortions further reduce kappa_p by amplifying anharmonicity while leaving wave-like conductivity (kappa_c) intact. Based on these mechanistic insights, we introduce a geometric distortion factor rho and perform a high-throughput screening that first selects materials with halogen-coordinated octahedral building blocks-ensuring the presence of rotational soft modes-and then identifies those with pronounced distortion. This strategy uncovers TaGaI8 with an ultralow kappa_L = 0.11 W/mK at room temperature. This work establishes halogen-halogen-enabled rotational soft modes and octahedral distortions as transferable design principles for octahedra-containing halides, spanning both extended frameworks and molecular-cluster motifs, for discovering ultralow-kappa_L materials.
Mo-Si multilayer mirrors are central to extreme ultraviolet lithography, where nanoscale optical interference and heat accumulation together constrain reflectivity and operational stability. Here we develop an analytical electromagnetic-thermal coupling model that directly links transfer-matrix-based interference-controlled energy deposition with transient heat conduction in EUV-irradiated multilayers. The model reveals a fundamental trade-off whereby increasing the multilayer period number enhances reflectivity but simultaneously elevates temperature by impeding heat dissipation. Interference-driven volumetric absorption further gives rise to pronounced axial temperature gradients and a post-pulse downward migration of the heat-flux maximum, a delayed-heating effect inaccessible to conventional surface-flux-based models. Systematic analysis establishes scaling laws connecting interfacial thermal resistance, beam size, and incident energy density to thermal confinement and temperature rise. By incorporating interfacial compaction kinetics, the model enables a quantitative assessment of mirror lifetime. This work offers a theoretical tool for thermal-optical co-design of multilayer nanostructures including EUV mirrors under pulsed irradiation across a wide spectral range.
We study the $p$-adic analogue of the $\ell$-adic hypergeometric sheaves for reductive groups, called the hypergeometric $\mathscr{D}^{\dagger}(\infty)$-modules. They are overholonomic objects in the derived category of arithmetic $\mathscr{D}$-modules with Frobenius structures. Over the non-degenerate locus, the hypergeometric $\mathscr{D}^{\dagger}(\infty)$-modules define $F$-isocrystals overconvergent along the complement of the non-degenerate locus. As an application, we use the theory of $L$-functions of overholonomic arithmetic $\mathscr{D}$-modules to study hypergeometric exponential sums on reductive groups.
We propose a novel design principle for achieving ultralow thermal conductivity in crystalline materials via a "heavy-light and soft-stiff" structural motif. By combining heavy and light atomic species with soft and stiff bonding networks, both particle-like ($\kappa_p$) and wave-like ($\kappa_c$) phonon transport channels are concurrently suppressed. First-principles calculations show that this architecture induces a hierarchical phonon spectrum: soft-bonded heavy atoms generate dense low-frequency modes that enhance scattering and reduce $\kappa_p$, while stiff-bonded light atoms produce sparse high-frequency optical branches that disrupt coherence and lower $\kappa_c$. High-throughput screening identifies Tl$_4$SiS$_4$ ($\kappa_p$ = 0.10, $\kappa_c$ = 0.06 W/mK) and Tl$_4$GeS$_4$ ($\kappa_p$ = 0.09, $\kappa_c$ = 0.06 W/mK) as representative candidates with strongly suppressed transport in both channels. A minimal 1D triatomic chain model further demonstrates the generality of this mechanism, offering a new paradigm for phonon engineering beyond the conventional $\kappa_p$-$\kappa_c$ trade-off.
First-principles calculations demonstrate an exceptional decoupling of charge and thermal transport along the \textit{a}-axis in CuBiSCl$_2$. The material achieves superior electron mobility (138 cm$^2$/V$\cdot$s at 300 K) through delocalized Bi-6\textit{p}/S-3\textit{p} networks while maintaining ultralow lattice thermal conductivity (0.40 W/mK at 300 K) via Cu-dominated anharmonic phonon scattering - both optimized along the same crystallographic direction. This simultaneous optimization originates from the anisotropic bonding hierarchy where [BiSCl$_2$]$_n$ ribbons enable efficient charge transport along \textit{a}-axis, while the soft vibrational modes associated with Cu atoms strongly scatter heat-carrying phonons. The resulting high power factor (1.71 mW/mK$^2$ at 700 K) and peak \textit{ZT} of 1.57 establish CuBiSCl$_2$ as a model system that realizes the long-sought "phonon glass-electron crystal" paradigm through crystallographically engineered transport channels.
Antiferroelectrics have received blooming interests because of a wide range of potential applications in energy storage, solid-state cooling, thermal switch, transducer, actuation, and memory devices. Many of those applications are the most prospective in thin film form. The antiferroelectric ordering in thin films is highly sensitive to a rich set of factors, such as lattice strain, film thickness, surface and interface effects as well as film stoichiometry. To unlock the full potential of these materials and design high-quality thin films for functional devices, a comprehensive and systematic understanding of their behavior is essential. In conjunction with the necessary fundamental background of antiferroelectrics, we review recent progress on various antiferroelectric oxide thin films, the key parameters that trigger their phase transition and the device applications that rely on the robust responses to electric, thermal, and optical stimuli. Current challenges and future perspectives highlight new and emerging research directions in this field. It is hoped that this review can boost the development of antiferroelectric thin-film materials and device design, stimulating more researchers to explore the unknowns together.
Polar skyrmions are topologically stable, swirling polarization textures with particle-like characteristics, which hold promise for next-generation, nanoscale logic and memory. While understanding of how to create ordered polar skyrmion lattice structures and how such structure respond to applied electric fields, temperature, and film thickness remains elusive. Here, using phase-field simulations, the evolution of polar topology and the emergence of a phase transition to a hexagonal close-packed skyrmion lattice is explored through the construction of a temperature-electric field phase diagram for ultrathin ferroelectric PbTiO3 films. The hexagonal-lattice skyrmion crystal can be stabilized under application of an external, out-of-plane electric field which carefully adjusts the delicate interplay of elastic, electrostatic, and gradient energies. In addition, the lattice constants of the polar skyrmion crystals are found to increase with film thickness, consistent with expectation from Kittel law. Our studies pave the way for the development of novel ordered condensed matter phases assembled from topological polar textures and related emergent properties in nanoscale ferroelectrics.