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Zhang TX, Coughlin AL, Lu CK, Heremans JJ, Zhang SX. Recent progress on topological semimetal IrO 2: electronic structures, synthesis, and transport properties. J Phys Condens Matter 2024; 36:273001. [PMID: 38597335 DOI: 10.1088/1361-648x/ad3603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/01/2023] [Accepted: 03/20/2024] [Indexed: 04/11/2024]
Abstract
5dtransition metal oxides, such as iridates, have attracted significant interest in condensed matter physics throughout the past decade owing to their fascinating physical properties that arise from intrinsically strong spin-orbit coupling (SOC) and its interplay with other interactions of comparable energy scales. Among the rich family of iridates, iridium dioxide (IrO2), a simple binary compound long known as a promising catalyst for water splitting, has recently been demonstrated to possess novel topological states and exotic transport properties. The strong SOC and the nonsymmorphic symmetry that IrO2possesses introduce symmetry-protected Dirac nodal lines (DNLs) within its band structure as well as a large spin Hall effect in the transport. Here, we review recent advances pertaining to the study of this unique SOC oxide, with an emphasis on the understanding of the topological electronic structures, syntheses of high crystalline quality nanostructures, and experimental measurements of its fundamental transport properties. In particular, the theoretical origin of the presence of the fourfold degenerate DNLs in band structure and its implications in the angle-resolved photoemission spectroscopy measurement and in the spin Hall effect are discussed. We further introduce a variety of synthesis techniques to achieve IrO2nanostructures, such as epitaxial thin films and single crystalline nanowires, with the goal of understanding the roles that each key parameter plays in the growth process. Finally, we review the electrical, spin, and thermal transport studies. The transport properties under variable temperatures and magnetic fields reveal themselves to be uniquely sensitive and modifiable by strain, dimensionality (bulk, thin film, nanowire), quantum confinement, film texture, and disorder. The sensitivity, stemming from the competing energy scales of SOC, disorder, and other interactions, enables the creation of a variety of intriguing quantum states of matter.
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Affiliation(s)
- T X Zhang
- Department of Physics, Indiana University, Bloomington, IN 47405, United States of America
| | - A L Coughlin
- Department of Physics, Indiana University, Bloomington, IN 47405, United States of America
| | - Chi-Ken Lu
- Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102, United States of America
| | - J J Heremans
- Department of Physics, Virginia Tech, Blacksburg, VA 24061, United States of America
| | - S X Zhang
- Department of Physics, Indiana University, Bloomington, IN 47405, United States of America
- Quantum Science and Engineering Center, Indiana University, Bloomington, IN 47405, United States of America
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Lu CK. Bayesian inference with finitely wide neural networks. Phys Rev E 2023; 108:014311. [PMID: 37583227 DOI: 10.1103/physreve.108.014311] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/07/2023] [Accepted: 07/10/2023] [Indexed: 08/17/2023]
Abstract
The analytic inference, e.g., predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in a Bayesian setting. The realistic widths, however, are finite and cause weak deviation from the Gaussianity under which partial marginalization of random variables in a model is straightforward. On the basis of multivariate Edgeworth expansion, we propose a non-Gaussian distribution in differential form to model a finite set of outputs from a random neural network, and derive the corresponding marginal and conditional properties. Thus, we are able to derive the non-Gaussian posterior distribution in Bayesian regression task. In addition, in the bottlenecked deep neural networks, a weight space representation of a deep Gaussian process, the non-Gaussianity is investigated through the marginal kernel and the accompanying small parameters.
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Affiliation(s)
- Chi-Ken Lu
- Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey 07102, USA
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Lu CK, Shafto P. Conditional Deep Gaussian Processes: Multi-Fidelity Kernel Learning. Entropy (Basel) 2021; 23:e23111545. [PMID: 34828243 PMCID: PMC8625033 DOI: 10.3390/e23111545] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Revised: 11/10/2021] [Accepted: 11/18/2021] [Indexed: 11/25/2022]
Abstract
Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution propagation within the hierarchy. Recently, it was pointed out that the hierarchical structure of DGP well suited modeling the multi-fidelity regression, in which one is provided sparse observations with high precision and plenty of low fidelity observations. We propose the conditional DGP model in which the latent GPs are directly supported by the fixed lower fidelity data. Then the moment matching method is applied to approximate the marginal prior of conditional DGP with a GP. The obtained effective kernels are implicit functions of the lower-fidelity data, manifesting the expressivity contributed by distribution propagation within the hierarchy. The hyperparameters are learned via optimizing the approximate marginal likelihood. Experiments with synthetic and high dimensional data show comparable performance against other multi-fidelity regression methods, variational inference, and multi-output GP. We conclude that, with the low fidelity data and the hierarchical DGP structure, the effective kernel encodes the inductive bias for true function allowing the compositional freedom.
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Affiliation(s)
- Chi-Ken Lu
- Mathematics and Computer Science, Rutgers University, Newark, NJ 07102, USA;
- Correspondence:
| | - Patrick Shafto
- Mathematics and Computer Science, Rutgers University, Newark, NJ 07102, USA;
- School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA
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Lu CK, Shafto P. Conditional Deep Gaussian Processes: Empirical Bayes Hyperdata Learning. Entropy (Basel) 2021; 23:1387. [PMID: 34828085 PMCID: PMC8618322 DOI: 10.3390/e23111387] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Revised: 10/18/2021] [Accepted: 10/20/2021] [Indexed: 11/19/2022]
Abstract
It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the function model. Recently, it was suggested that, albeit training with marginal likelihood, the deterministic nature of a feature extractor might lead to overfitting, and replacement with a Bayesian network seemed to cure it. Here, we propose the conditional deep Gaussian process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. It follows our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference.
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Affiliation(s)
- Chi-Ken Lu
- Mathematics and Computer Science, Rutgers University, Newark, NJ 07102, USA;
| | - Patrick Shafto
- Mathematics and Computer Science, Rutgers University, Newark, NJ 07102, USA;
- School of Mathematics, Institute for Advanced Studies, Princeton, NJ 08540, USA
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Lu CK, Lee YC, Sun PL, Liang CL, Liliang PC. Life-Threatening Bleeding from the Pubic Branch of the Inferior Epigastric Artery after Pubic Ramus Fracture. HONG KONG J EMERG ME 2017. [DOI: 10.1177/102490791001700411] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Isolated pubic ramus fracture with concurrent life-threatening bleeding caused by injury to the inferior epigastric artery (IEA) or its branches has rarely been reported and can frequently be overlooked. This paper reports two cases of isolated pubic ramus fracture with concomitant injury to the pubic branch of the IEA, causing serious bleeding and hemodynamic instability. Pelvic angiography showed leakage of contrast from the pubic branch of the IEA. The complication in both cases was successfully treated with transcatheter arterial embolisation.
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Affiliation(s)
- CK Lu
- E-Da Hospital, Department of Orthopedics, I-Shou University, No. 1, Yi-Da Road, Jiau-Shu Tsuen, Yan-Chau Shiang, Kaohsiung County, 824, Taiwan
| | - YC Lee
- E-Da Hospital, Department of Radiology, I-Shou University, No. 1, Yi-Da Road, Jiau-Shu Tsuen, Yan-Chau Shiang, Kaohsiung County, 824, Taiwan
| | - PL Sun
- E-Da Hospital, Department of Radiology, I-Shou University, No. 1, Yi-Da Road, Jiau-Shu Tsuen, Yan-Chau Shiang, Kaohsiung County, 824, Taiwan
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Abstract
We predict a new class of 3D topological insulators (TIs) in which the spin-orbit coupling (SOC) can more effectively generate band gap. Band gap of conventional TI is mainly limited by two factors, the strength of SOC and, from electronic structure perspective, the band gap when SOC is absent. While the former is an atomic property, the latter can be minimized in a generic rock-salt lattice model in which a stable crossing of bands at the Fermi level along with band character inversion occurs in the absence of SOC. Thus large-gap TIs or TIs composed of lighter elements can be expected. In fact, we find by performing first-principles calculations that the model applies to a class of double perovskites A2BiXO6 (A = Ca, Sr, Ba; X = Br, I) and the band gap is predicted up to 0.55 eV. Besides, surface Dirac cones are robust against the presence of dangling bond at boundary.
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Affiliation(s)
- Shu-Ting Pi
- Department of Physics and Astronomy, University of California , Irvine, California 92697-4575, United States
| | - Hui Wang
- Department of Physics and Astronomy, University of California , Irvine, California 92697-4575, United States
| | - Jeongwoo Kim
- Department of Physics and Astronomy, University of California , Irvine, California 92697-4575, United States
| | - Ruqian Wu
- Department of Physics and Astronomy, University of California , Irvine, California 92697-4575, United States
| | - Yin-Kuo Wang
- Center of General Education, National Taiwan Normal University , Taipei 116, Taiwan
| | - Chi-Ken Lu
- Department of Physics, National Taiwan Normal University , Taipei 11677, Taiwan
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Lu CK. Friedel oscillation near a van Hove singularity in two-dimensional Dirac materials. J Phys Condens Matter 2016; 28:065001. [PMID: 26795372 DOI: 10.1088/0953-8984/28/6/065001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
We consider Friedel oscillation in the two-dimensional Dirac materials when the Fermi level is near the van Hove singularity. Twisted graphene bilayer and the surface state of topological crystalline insulator are the representative materials which show low-energy saddle points that are feasible to probe by gating. We approximate the Fermi surface near saddle point with a hyperbola and calculate the static Lindhard response function. Employing a theorem of Lighthill, the induced charge density [Formula: see text] due to an impurity is obtained and the algebraic decay of [Formula: see text] is determined by the singularity of the static response function. Although a hyperbolic Fermi surface is rather different from a circular one, the static Lindhard response function in the present case shows a singularity similar with the response function associated with circular Fermi surface, which leads to the [Formula: see text] at large distance R. The dependences of charge density on the Fermi energy are different. Consequently, it is possible to observe in twisted graphene bilayer the evolution that [Formula: see text] near Dirac point changes to [Formula: see text] above the saddle point. Measurements using scanning tunnelling microscopy around the impurity sites could verify the prediction.
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Affiliation(s)
- Chi-Ken Lu
- Physics Department, National Taiwan Normal University, Taipei 11677, Taiwan
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Abstract
We show that the electric charge of the Skyrmion in the vector order parameters that characterize the quantum anomalous spin Hall state and the layer antiferromagnet in a graphene bilayer is four and zero, respectively. The result is based on the demonstration that a vortex configuration in two broken symmetry states in bilayer graphene with the quadratic band crossing has the number of zero modes doubled relative to the single layer. The doubling can be understood as a result of Kramers's theorem implied by the "pseudo time reversal" symmetry of the vortex Hamiltonian. Disordering the quantum anomalous spin Hall state by Skyrmion condensation should produce a superconductor of an elementary charge 4e.
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Affiliation(s)
- Chi-Ken Lu
- Department of Physics, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
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Crider AM, Lu CK, Floss HG, Cassady JM, Clemens JA. Ergot alkaloids. Synthesis of nitrosourea derivatives of ergolines as potential anticancer agents. J Med Chem 1979; 22:32-5. [PMID: 423180 DOI: 10.1021/jm00187a008] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
Nitrosourea derivatives of ergolines have been synthesized for the purpose of obtaining agents with both prolactin-and tumor-inhibitory activity. Two derivatives of 8-amino-6-methylergoline (3), 8-[3-(2-chloroethyl)-3-nitrosoureido]-1-nitroso-6-methylergoline (5c) and 8-[3-2-chloroethyl)-3-nitrosoureido]-6-methylergoline (5a), have been prepared. In addition, nitroso (7) and chloroethylcarbamyl (8) derivatives of elymoclavine (6) are reported. Compounds 5a and 5c have activity against L1210 leukemia in mice but only moderate prolactin-inhibiting activity. The chloroethylcarbamyl derivative 8 of elymoclavine is a potent prolacting inhibitor.
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