Type II t-J model and shared antiferromagnetic spin coupling from Hund's rule in superconducting La3_3Ni2_2O7_7

Recently a 80 K superconductor was observed in La$_3$Ni$_2$O$_7$ under high pressure. Density function theory (DFT) calculations identify $d_{x^2-y^2}$ and $d_{z^2}$ as two active orbitals and a bilayer square lattice structure. The averange valence of Ni is $d^{8-x}$ with $x=0.5$ per site. Naively one may expect a description in terms of a two-orbital t-J model. However, there should be significant inter-orbital repulsion $U'$ and Hund's coupling $J_H$ larger than the bare value of $t$ and $J$. Especially the Hund's coupling can share the inter-layer super-exchange $J_\perp$ of $d_{z^2}$ to $d_{x^2-y^2}$, an effect beyond any perturbative and mean field treatment. In the limit that $d_{z^2}$ is Mott localized, we integrate it out and deal with a bialyer t-J model for $d_{x^2-y^2}$ only. We find strong inter-layer pairing due to the transmitted $J_\perp$ which can survive to $50\%$ hole doping relevant to the experiment. In real system we expect that $d_{z^2}$ orbital will also be slightly hole doped and can not be simply ignored. To deal with this situation, we take the $J_H\rightarrow +\infty$ limit and propose a type II t-J model with four singlon ($d^7$) states and three spin-triplet doublon ($d^8$) states. Through a parton mean field treatment of the constrained Hilbert space, we derive the bilayer one-orbital t-J model for an emergent `$d_{x^2-y^2}$' orbital with significant $J_\perp$, justifying our phenomenological treatment. The type II t-J model can also describe the regime where the $d_{z^2}$ orbital is also slightly hole doped through tuning an orbital energy splitting $\Delta$. From our calculation the pairing strength decreases with the hole doping $x$ and $x=0.5$ is likely larger than the optimal doping. We propose future experiments to electron dope the system to further enhance $T_c$.Comment: 5 pages, 2 figures, 1 tabl

S-wave pairing in a two-orbital t-J model on triangular lattice: possible application to Pb10−x_{10-x}Cux_x(PO4_4)6_6O

Recently room temperature superconductor was claimed in Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O (also known as LK-99) with $x\in (0.9,1.1)$. Density functional theory (DFT) calculations suggest that the conduction electrons are from the doped Cu atoms with valence close to $d^{9}$. Motivated by this picture, we build a two-orbital Hubbard model on a triangular lattice formed by the $d_{xz}$ and $d_{yz}$ orbitals with total hole density (summed over spin and orbital) $n=1-p$. When $p=0$, the system is in a Mott insulator within this model. When $p>0$, we derive a $t-J$ model and perform a self-consistent slave boson mean field calculation. Interestingly we find a s-wave pairing in contrast to the one-orbital t-J model which favors $d+id$ pairing. S wave pairing should be more robust to disorder and may lead to high Tc superconductor with sufficiently large values of $t$ and $J$. However, the DFT calculations predict a very small value of $t$ and then the $T_c$ is expected to be small. If LK99 is really a high Tc superconductor, ingredients beyond the current model are needed. We conjecture that the doped Cu atoms may distort the original lattice and form local clusters with smaller Cu -Cu distance and thus larger values of $t$ and $J$. Within these clusters, we may locally apply our t-J model calculation and expect high Tc s-wave superconductor. Then the superconducting islands couple together, which may eventually become a global superconductor, an insulator or even an anomalous metal depending on sample details.Comment: 6 pages, 2 figure

Strong pairing from small Fermi surface beyond weak coupling: Application to La3_3Ni2_2O7_7

The studies of high-temperature superconductors raise a fundamental question: Can a small Fermi surface phase, which violates the Luttinger theorem, exist and give rise to superconductivity? Our work provides a positive answer through a controlled theory based on a bilayer model with strong inter-layer spin-spin coupling ($J_\perp$) but no inter-layer hopping ($t_\perp$). Then small hole doping of the rung-singlet insulator with two electrons per rung naturally leads to small hole pockets with Fermi surface volume per flavor smaller than the free fermion result by $1/2$ of the Brillouin zone(BZ). We construct a new t-J model on a bilayer square lattice, so called ESD t-J model and employ a generalized slave boson theory, which captures this small Fermi surface phase at small hole doping $x$. This metallic state is an intrinsically strongly correlated Fermi liquid beyond weak coupling theory, violating the perturbative Luttinger theorem but consistent with the Oshikawa's non-perturbative proof. We further show that it transitions into an inter-layer paired $s'$-wave superconductor at lower temperature through Feshbach resonance with a virtual Cooper pair, with a surprising doping-induced crossover from Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BEC) at higher hole doping levels. This leads to a superconducting dome centered around $x=0.5$, with the normal state changing from the conventional Fermi liquid in the $x>0.5$ to the unusual small Fermi surface state in the $x<0.5$ side. Our theoretical findings including phase diagrams are also confirmed by density matrix renormalization group (DMRG) simulation in quasi one dimension. Applying our theoretical framework, we provide a plausible scenario for the recently found nickelate La$_3$Ni$_2$O$_7$ materials.Comment: 11+13 pages, 8+13 figur

Bayesian Disturbance Injection: Robust Imitation Learning of Flexible Policies for Robot Manipulation

Humans demonstrate a variety of interesting behavioral characteristics when performing tasks, such as selecting between seemingly equivalent optimal actions, performing recovery actions when deviating from the optimal trajectory, or moderating actions in response to sensed risks. However, imitation learning, which attempts to teach robots to perform these same tasks from observations of human demonstrations, often fails to capture such behavior. Specifically, commonly used learning algorithms embody inherent contradictions between the learning assumptions (e.g., single optimal action) and actual human behavior (e.g., multiple optimal actions), thereby limiting robot generalizability, applicability, and demonstration feasibility. To address this, this paper proposes designing imitation learning algorithms with a focus on utilizing human behavioral characteristics, thereby embodying principles for capturing and exploiting actual demonstrator behavioral characteristics. This paper presents the first imitation learning framework, Bayesian Disturbance Injection (BDI), that typifies human behavioral characteristics by incorporating model flexibility, robustification, and risk sensitivity. Bayesian inference is used to learn flexible non-parametric multi-action policies, while simultaneously robustifying policies by injecting risk-sensitive disturbances to induce human recovery action and ensuring demonstration feasibility. Our method is evaluated through risk-sensitive simulations and real-robot experiments (e.g., table-sweep task, shaft-reach task and shaft-insertion task) using the UR5e 6-DOF robotic arm, to demonstrate the improved characterisation of behavior. Results show significant improvement in task performance, through improved flexibility, robustness as well as demonstration feasibility.Comment: 69 pages, 9 figures, accepted by Elsevier Neural Networks - Journa

Bayesian Disturbance Injection: Robust Imitation Learning of Flexible Policies

Scenarios requiring humans to choose from multiple seemingly optimal actions are commonplace, however standard imitation learning often fails to capture this behavior. Instead, an over-reliance on replicating expert actions induces inflexible and unstable policies, leading to poor generalizability in an application. To address the problem, this paper presents the first imitation learning framework that incorporates Bayesian variational inference for learning flexible non-parametric multi-action policies, while simultaneously robustifying the policies against sources of error, by introducing and optimizing disturbances to create a richer demonstration dataset. This combinatorial approach forces the policy to adapt to challenging situations, enabling stable multi-action policies to be learned efficiently. The effectiveness of our proposed method is evaluated through simulations and real-robot experiments for a table-sweep task using the UR3 6-DOF robotic arm. Results show that, through improved flexibility and robustness, the learning performance and control safety are better than comparison methods.Comment: 7 pages, Accepted by the 2021 International Conference on Robotics and Automation (ICRA 2021

Electric field control of nonvolatile four-state magnetization at room temperature

We find the realization of large converse magnetoelectric (ME) effects at room temperature in a multiferroic hexaferrite Ba$_{0.52}$Sr$_{2.48}$Co$_{2}$Fe$_{24}$O$_{41}$ single crystal, in which rapid change of electric polarization in low magnetic fields (about 5 mT) is coined to a large ME susceptibility of 3200 ps/m. The modulation of magnetization then reaches up to 0.62 $\mu$$_{B}$/f.u. in an electric field of 1.14 MV/m. We find further that four ME states induced by different ME poling exhibit unique, nonvolatile magnetization versus electric field curves, which can be approximately described by an effective free energy with a distinct set of ME coefficients

Band-selective gap opening by a C4-symmetric order in a proximity-coupled heterostructure Sr2VO3FeAs

Complex electronic phases in strongly correlated electron systems are manifested by broken symmetries in the low-energy electronic states. Some mysterious phases, however, exhibit intriguing energy gap opening without an apparent signature of symmetry breaking (e.g., high-TC cuprates and heavy fermion superconductors). Here, we report an unconventional gap opening in a heterostructured, iron-based superconductor Sr2VO3FeAs across a phase transition at T0 ∼150 K. Using angle-resolved photoemission spectroscopy, we identify that a fully isotropic gap opens selectively on one of the Fermi surfaces with finite warping along the interlayer direction. This band selectivity is incompatible with conventional gap opening mechanisms associated with symmetry breaking. These findings, together with the unusual field-dependent magnetoresistance, suggest that the Kondo-type proximity coupling of itinerant Fe electrons to localized V spin plays a role in stabilizing the exotic phase, which may serve as a distinct precursor state for unconventional superconductivity