Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle

We show that the Wannier obstruction and the fragile topology of the nearly flat bands in twisted bilayer graphene at magic angle are manifestations of the nontrivial topology of two-dimensional real wave functions characterized by the Euler class. To prove this, we examine the generic band topology of two dimensional real fermions in systems with space-time inversion $I_{ST}$ symmetry. The Euler class is an integer topological invariant classifying real two band systems. We show that a two-band system with a nonzero Euler class cannot have an $I_{ST}$-symmetric Wannier representation. Moreover, a two-band system with the Euler class $e_{2}$ has band crossing points whose total winding number is equal to $-2e_2$. Thus the conventional Nielsen-Ninomiya theorem fails in systems with a nonzero Euler class. We propose that the topological phase transition between two insulators carrying distinct Euler classes can be described in terms of the pair creation and annihilation of vortices accompanied by winding number changes across Dirac strings. When the number of bands is bigger than two, there is a $Z_{2}$ topological invariant classifying the band topology, that is, the second Stiefel Whitney class ($w_2$). Two bands with an even (odd) Euler class turn into a system with $w_2=0$ ($w_2=1$) when additional trivial bands are added. Although the nontrivial second Stiefel-Whitney class remains robust against adding trivial bands, it does not impose a Wannier obstruction when the number of bands is bigger than two. However, when the resulting multi-band system with the nontrivial second Stiefel-Whitney class is supplemented by additional chiral symmetry, a nontrivial second-order topology and the associated corner charges are guaranteed.Comment: 23 pages, 13 figure

Phonon angular momentum Hall effect

Spin Hall effect is the transverse flow of the electron spin in conductors under external electric field. Similarly, thermal gradient in magnetic insulators can drive a transverse flow of the spin angular momentum of magnons, which provides a thermal alternative for spin manipulation. Recently, the phonon angular momentum (PAM), which is the angular momentum of atoms as a result of their orbital motion around their equilibrium positions, has garnered attention as a quantity analogous to the magnon spin. However, can we manipulate PAM like magnon spin? Here, we show that temperature gradient generally induces a transverse flow of PAM, which we term the phonon angular momentum Hall effect (PAMHE). The PAMHE relies only on the presence of transverse and longitudinal acoustic phonons, and it is therefore ubiquitous in condensed matter systems. As a consequence of the PAMHE, PAM accumulates at the edges of a crystal. When the atoms in the crystal carry nonzero Born effective charge, the edge PAM induces edge magnetization, which may be observed through optical measurement. We believe that PAMHE provides a new principle for the manipulation of angular momenta in insulators and opens up an avenue for developing functional materials based on phonon engineering.Comment: 8+3 pages, 5 figures, additional discussion on 3D, some amendment

Topological Magnetoelastic Excitations in Non-Collinear Antiferromagnets

We study the topological property of the magnetoelastic excitation in non-collinear antiferromagnets. As a toy model, we consider the magnon-phonon coupling in a triangular antiferromagnet with a $120^\circ$ N\`eel order. We find that in the presence of out-of-plane external magnetic field, the magnon-polaron bands, which arise from hybridization of magnons and phonons, can carry Chern number, even though the individual magnon and phonon bands are topologically trivial. Large Berry curvature is induced from the anti-crossing regions between the magnon and phonon bands, which renormalizes the thermal Hall conductivity of phonon bands. To compute the Berry curvature and Chern number of magnon-polarons, we give a simple algorithm to diagonalize magnetoelastic Hamiltonian without diagonalizing the phonon Hamiltonian, by mapping the problem to the diagonalization of bosonic Bogoliubov-de-Gennes (BdG) Hamiltonian. This is necessary because the contribution to the Berry curvature from phonon cannot be properly captured if we compute the Berry curvature from magnetoelastic Hamiltonian whose phonon sector has been already diagonalized.Comment: 20 pages, 10 figure

Thermal Hall effect from two-dimensional Schwinger-boson gas with Rashba spin-orbit interaction: application to ferromagnets with in-plane Dzyaloshinskii-Moriya interaction

Recently, uncovering the sources of thermal Hall effect in insulators has become an important issue. In the case of ferromagnetic insulators, it is well known that Dzyaloshinskii-Moriya (DM) interaction can induce magnon thermal Hall effect. Specifically, the DM vector parallel to the magnetization direction induces complex magnon hopping amplitudes, so that magnons act as if they feel Lorentz force. However, the DM vector which is orthogonal to the magnetization direction has hitherto been neglected as a possible source of magnon thermal Hall effect. This is because they play no role in the linear spin wave theory, an often invoked approximation when computing the magnon thermal Hall effect. Here, we challenge this expectation by presenting the self-consistent Schwinger-boson mean field study of two-dimensional magnets with ferromagnetic Heisenberg interaction and in-plane DM interaction. We find that the relevant Schwinger-boson mean field Hamiltonian takes the form of two-dimensional electron gas with Rashba spin-orbit interaction, which is known to show anomalous Hall effect, spin Hall effect, and Rashba-Edelstein effect, whose thermal counterparts also appear in our system. Importantly, the thermal Hall effect can be induced when out-of-plane magnetic field is applied, and persists even when the magnetic field is large, so that the spins are significantly polarized, and the linear spin wave theory is expected to be a reasonable approximation. Since the linear spin wave theory predicts vanishing thermal Hall effect, our result implies that linear spin wave is not a sufficient approximation, and that magnon-magnon interaction must be taken into account to predict the correct thermal Hall conductivity.Comment: 5+2 pages, 4 figure

Fresnel-type Solid Immersion Lens for efficient light collection from quantum defects in diamond

Quantum defects in diamonds have been studied as a promising resource for quantum science. The subtractive fabrication process for improving photon collection efficiency often require excessive milling time that can adversely affect the fabrication accuracy. We designed and fabricated a Fresnel-type solid immersion lens using the focused ion beam. For a 5.8 um-deep Nitrogen-vacancy (NV-) center, the milling time was highly reduced (1/3 compared to a hemispherical structure), while retaining high photon collection efficiency (> 2.24 compared to a flat surface). In numerical simulation, this benefit of the proposed structure is expected for a wide range of milling depths.Comment: 16 pages, 9 figure

SPOTS: Stable Placement of Objects with Reasoning in Semi-Autonomous Teleoperation Systems

Pick-and-place is one of the fundamental tasks in robotics research. However, the attention has been mostly focused on the ``pick'' task, leaving the ``place'' task relatively unexplored. In this paper, we address the problem of placing objects in the context of a teleoperation framework. Particularly, we focus on two aspects of the place task: stability robustness and contextual reasonableness of object placements. Our proposed method combines simulation-driven physical stability verification via real-to-sim and the semantic reasoning capability of large language models. In other words, given place context information (e.g., user preferences, object to place, and current scene information), our proposed method outputs a probability distribution over the possible placement candidates, considering the robustness and reasonableness of the place task. Our proposed method is extensively evaluated in two simulation and one real world environments and we show that our method can greatly increase the physical plausibility of the placement as well as contextual soundness while considering user preferences.Comment: 7 page

SOCRATES: Text-based Human Search and Approach using a Robot Dog

In this paper, we propose a SOCratic model for Robots Approaching humans based on TExt System (SOCRATES) focusing on the human search and approach based on free-form textual description; the robot first searches for the target user, then the robot proceeds to approach in a human-friendly manner. In particular, textual descriptions are composed of appearance (e.g., wearing white shirts with black hair) and location clues (e.g., is a student who works with robots). We initially present a Human Search Socratic Model that connects large pre-trained models in the language domain to solve the downstream task, which is searching for the target person based on textual descriptions. Then, we propose a hybrid learning-based framework for generating target-cordial robotic motion to approach a person, consisting of a learning-from-demonstration module and a knowledge distillation module. We validate the proposed searching module via simulation using a virtual mobile robot as well as through real-world experiments involving participants and the Boston Dynamics Spot robot. Furthermore, we analyze the properties of the proposed approaching framework with human participants based on the Robotic Social Attributes Scale (RoSAS)Comment: Project page: https://socratesrobotdog.github.io