Physical Review B最新文献

{"title":"Subradiant entanglement in plasmonic nanocavities","authors":"Kalun Bedingfield, Ben Yuen, Angela Demetriadou","doi":"10.1103/physrevb.111.075420","DOIUrl":"https://doi.org/10.1103/physrevb.111.075420","url":null,"abstract":"Plasmonic nanocavities are known for their extreme field enhancement and subwavelength light confinement in gaps of just a few nanometers. Pairing this with the ability to host quantum emitters, they form highly promising platforms to control or engineer quantum states at room temperature. Here, we use the lossy nature of plasmonic nanocavities to form subradiant entangled states between two or more quantum emitters, that persist for ∼</a:mo>100</a:mn></a:mrow></a:math> times longer than the plasmonic excitation. We develop a theoretical description that directly links quantum variables to experimentally measurable quantities, such as the extinction cross section, and unlike previous studies includes plasmonic excitations necessary to resonantly form subradiant states. This work paves the way towards engineering quantum entangled states in ambient conditions with plasmonic nanocavities. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"2 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143443190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quasiparticle wave function and its equation of motion","authors":"F. Aryasetiawan, K. Karlsson","doi":"10.1103/physrevb.111.075139","DOIUrl":"https://doi.org/10.1103/physrevb.111.075139","url":null,"abstract":"The quasiparticle wave function of a many-electron system is traditionally defined as the eigenfunction of the quasiparticle eigenvalue equation involving the self-energy. In this article a different concept of a quasiparticle wave function is derived from the general definition of the Green's function without reference to self-energy. The proposed quasiparticle wave function can decay in time, and in contrast to the traditional one it contains not only the main quasiparticle mode but also other modes due to coupling to collective excitations in the system. In the recently developed dynamical exchange-correlation potential formalism, this definition of a quasiparticle wave function leads to an equation of motion with an effective field, which appears to have a simple form expected to be amenable to realistic approximations. A simple model for the effective potential is proposed which is suitable for materials whose valence electrons are dominated by itinerant s</a:mi>−</a:mtext>p</a:mi></a:mrow></a:math> electrons such as simple metals. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"14 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143443187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Current noise in quantum dot thermoelectric engines","authors":"Simon Wozny, Martin Leijnse","doi":"10.1103/physrevb.111.075422","DOIUrl":"https://doi.org/10.1103/physrevb.111.075422","url":null,"abstract":"We theoretically investigate a thermoelectric heat engine based on a single-level quantum dot, calculating average quantities such as current, heat current, output power, and efficiency, as well as fluctuations (noise). Our theory is based on a diagrammatic expansion of the memory kernel together with counting statistics, and we investigate the effects of strong interactions and next-to-leading order tunneling. Accounting for next-to-leading order tunneling is crucial for a correct description when operating at high power and high efficiency, and in particular affect the qualitative behavior of the Fano factor and efficiency. We compare our results with the so-called thermodynamic uncertainty relations, which provide a lower bound on the fluctuations for a given efficiency. In principle, the conventional thermodynamic uncertainty relations can be violated by the non-Markovian quantum effects originating from next-to-leading order tunneling, providing a type of quantum advantage. However, for the specific heat engine realization we consider here, we find that next-to-leading order tunneling does not lead to such violations, but in fact always pushes the results further away from the bound set by the thermodynamic uncertainty relations. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"85 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143443189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Low-temperature magnetic behavior on the triangular lattice in hexagonal Ba3Tb(BO3)3","authors":"Nicola D. Kelly, M. Duc Le, Denis Sheptyakov, Camilla Tacconis, Cheng Liu, Gavin B. G. Stenning, Peter J. Baker, Siân E. Dutton","doi":"10.1103/physrevb.111.054427","DOIUrl":"https://doi.org/10.1103/physrevb.111.054427","url":null,"abstract":"The hexagonal polymorph of Ba</a:mi>3</a:mn></a:msub>Tb</a:mi>(</a:mo>BO</a:mi>3</a:mn></a:msub>)</a:mo></a:mrow>3</a:mn></a:msub></a:mrow></a:math> contains <b:math xmlns:b=\"http://www.w3.org/1998/Math/MathML\"><b:msup><b:mrow><b:mi>Tb</b:mi></b:mrow><b:mrow><b:mn>3</b:mn><b:mo>+</b:mo></b:mrow></b:msup></b:math> ions on a quasi-2D triangular lattice, resulting in geometric magnetic frustration. Powder samples of <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\"><c:mrow><c:msub><c:mi>Ba</c:mi><c:mn>3</c:mn></c:msub><c:mi>Tb</c:mi><c:msub><c:mrow><c:mo>(</c:mo><c:msub><c:mi>BO</c:mi><c:mn>3</c:mn></c:msub><c:mo>)</c:mo></c:mrow><c:mn>3</c:mn></c:msub></c:mrow></c:math> have been investigated using specific heat, powder neutron diffraction (PND), inelastic neutron scattering (INS), and muon-spin relaxation spectroscopy (<d:math xmlns:d=\"http://www.w3.org/1998/Math/MathML\"><d:mrow><d:mi>μ</d:mi><d:mi>SR</d:mi></d:mrow></d:math>). No long-range magnetic ordering is observed down to the lowest measured temperatures of 75 mK in PND and specific heat data and 1.5 K in the <e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\"><e:mrow><e:mi>μ</e:mi><e:mi>SR</e:mi></e:mrow></e:math> data. Modeling the INS spectrum using a point charge model suggests that the ground state is a singlet with a low-lying doublet on each of the two crystallographically independent <f:math xmlns:f=\"http://www.w3.org/1998/Math/MathML\"><f:msup><f:mrow><f:mi>Tb</f:mi></f:mrow><f:mrow><f:mn>3</f:mn><f:mo>+</f:mo></f:mrow></f:msup></f:math> sites and that both the Tb ions display weak <g:math xmlns:g=\"http://www.w3.org/1998/Math/MathML\"><g:mrow><g:mi mathvariant=\"italic\">XY</g:mi></g:mrow></g:math> single-ion anisotropy. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"11 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143443188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Microscopic approach to the problem of enhancement and suppression of superconductivity on twinning planes","authors":"Anton Talkachov, Sahal Kaushik, Egor Babaev","doi":"10.1103/physrevb.111.054513","DOIUrl":"https://doi.org/10.1103/physrevb.111.054513","url":null,"abstract":"Using a microscopic approach, we revisit the problem of superconducting critical temperature change in the presence of twin boundaries. We show that both critical temperature enhancement and suppression can come purely from single-electron geometric effects. These include aspects of scattering of electrons on these crystalline defects even when the coupling constant is unchanged. We consider two-dimensional rectangular and three-dimensional body-centered-cubic lattices with on-site s</a:mi></a:math>-wave superconducting pairing, nearest- and next-nearest-neighbor hoppings. In the considered two-dimensional lattice with twin boundaries, the superconducting critical temperature associated with twinning planes is suppressed for moderate band filling and enhanced for an almost empty or filled band. The superconducting phase diagram is more diverse for the three-dimensional lattice, which is caused by the interplay of van Hove singularity, changing coordination number, and modification of distances to nearest and next-nearest neighbors. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"63 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143417353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Persistent Haldane phase in carbon tetris chains","authors":"Anas Abdelwahab, Christoph Karrasch, Roman Rausch","doi":"10.1103/physrevb.111.075129","DOIUrl":"https://doi.org/10.1103/physrevb.111.075129","url":null,"abstract":"We introduce the concept of “tetris chains,” which are linear arrays of four-site molecules that differ by their intermolecular hopping geometry. We investigate the fermionic symmetry-protected topological Haldane phase in these systems using Hubbard-type models. The topological phase diagrams can be understood via different competing limits and mechanisms: strong coupling U</a:mi>≫</a:mo>t</a:mi></a:mrow></a:math>, weak coupling <b:math xmlns:b=\"http://www.w3.org/1998/Math/MathML\"><b:mrow><b:mi>U</b:mi><b:mo>≪</b:mo><b:mi>t</b:mi></b:mrow></b:math>, and the weak intermolecular hopping limit <c:math xmlns:c=\"http://www.w3.org/1998/Math/MathML\"><c:mrow><c:msup><c:mi>t</c:mi><c:mo>′</c:mo></c:msup><c:mo>≪</c:mo><c:mi>t</c:mi></c:mrow></c:math>. Our particular focus is on two tetris chains that are of experimental relevance. First, we show that a “Y-chain” of coarse-grained nanographene molecules (triangulenes) is robustly in the Haldane phase in the whole <d:math xmlns:d=\"http://www.w3.org/1998/Math/MathML\"><d:mrow><d:msup><d:mi>t</d:mi><d:mo>′</d:mo></d:msup><d:mtext>−</d:mtext><d:mi>U</d:mi></d:mrow></d:math> plane due to the cooperative nature of the three limits. Secondly, we study a near-homogeneous “<e:math xmlns:e=\"http://www.w3.org/1998/Math/MathML\"><e:msup><e:mrow><e:mi mathvariant=\"normal\">Y</e:mi></e:mrow><e:mo>′</e:mo></e:msup></e:math>-chain” that is closely related to the electronic model for poly(p-phenylene vinylene). In the latter case, the above mechanisms compete, but the Haldane phase manifests robustly and is stable when long-ranged Pariser-Parr-Popple interactions are added. The site-edged Hubbard ladder can also be viewed as a tetris chain, which gives a very general perspective on the emergence of its fermionic Haldane phase. Our numerical results are obtained by large-scale, SU(2)-symmetric tensor network calculations. We employ the density-matrix-renormalization group as well as the variational uniform matrix-product state (VUMPS) algorithms for finite and infinite systems, respectively. The numerics are supplemented by analytical calculations of the band-structure winding number. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"189 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143417392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"2-form U(1) spin liquids: A classical model and quantum aspects","authors":"Kristian Tyn Kai Chung, Michel J. P. Gingras","doi":"10.1103/physrevb.111.064417","DOIUrl":"https://doi.org/10.1103/physrevb.111.064417","url":null,"abstract":"We introduce a geometrically frustrated classical Ising model, dubbed the “spin-vorticity model,” whose ground-state manifold is a classical spin liquid: a 2-form Coulomb phase. We study the thermodynamics of this model both analytically and numerically, exposing the presence of algebraically decaying correlations and an extensive ground-state entropy, and give a comprehensive account of its ground-state properties and excitations. Each classical ground state may be decomposed into collections of closed two-dimensional membranes, supporting fractionalized string excitations attached to the edges of open membranes. At finite temperature, the model can then be described as a gas of closed strings in a background of fluctuating membranes. The emergent gauge structure of this spin liquid is naturally placed in the language of 2-form electrodynamics, which describes one-dimensional charged strings coupled to a rank-2 antisymmetric gauge field. After establishing the classical spin-vorticity model, we consider perturbing it with quantum exchange interactions, deriving an effective “membrane exchange” model of the quantum dynamics, analogous to ring exchange in quantum spin ice. We demonstrate the existence of a Rokhsar-Kivelson point where the quantum ground state is an equal-weight superposition of all classical ground-state configurations, i.e., a quantum spin liquid. The quantum aspects of this spin liquid are exposed by mapping the membrane exchange model to a strongly coupled frustrated 2-form U(1) lattice gauge theory. We further demonstrate how to quantize the string excitations by coupling a 1-form string field to the 2-form U(1) gauge field, thus mapping a quantum spin model to a 2-form U(1) gauge-Higgs model. We discuss the stability of the gapless deconfined phase of this gauge theory and the possibility of realizing a class of quantum phases of matter: 2-form U(1) quantum spin liquids. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"42 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143417393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks","authors":"Luke Causer, Mari Carmen Bañuls, Juan P. Garrahan","doi":"10.1103/physrevb.111.l060303","DOIUrl":"https://doi.org/10.1103/physrevb.111.l060303","url":null,"abstract":"We study the nonequilibrium dynamics of the dissipative quantum East model via numerical tensor networks. We use matrix product states to represent evolution under quantum-jump unravellings for sizes beyond those accessible to exact diagonalization. This allows us to demonstrate that dynamical heterogeneity accompanies slow relaxation, in analogy with what is seen in classical glassy systems. Furthermore, using variational matrix product operators we (i) compute the spectral gap of the Lindbladian and show that glassiness is enhanced in the presence of weak quantum fluctuations compared to the pure classical case, and (ii) obtain the dynamical large deviations by calculating the leading eigenvector of the tilted Lindbladian and find clear evidence for a first-order active-inactive dynamical phase transition. We also show how to directly sample the rare quantum trajectories associated to the large deviations. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"79 6 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143417395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pseudo-Majorana functional renormalization for frustrated XXZ spin- 12 models with field or magnetization along the spin- Z direction at finite temperature","authors":"Frederic Bippus, Benedikt Schneider, Björn Sbierski","doi":"10.1103/physrevb.111.054420","DOIUrl":"https://doi.org/10.1103/physrevb.111.054420","url":null,"abstract":"The numerical study of high-dimensional frustrated quantum magnets remains a challenging problem. Here we present an extension of the pseudo-Majorana functional renormalization group to spin-1/2 XXZ-type Hamiltonians with field or magnetization along spin-Z</a:mi></a:math> direction at finite temperature. We consider a U(1) symmetry-adapted fermionic spin representation and derive the diagrammatic framework and its renormalization group flow equations. We discuss benchmark results and application to two antiferromagnetic triangular lattice materials recently studied in experiments with applied magnetic fields: First, we numerically reproduce the magnetization data measured for <b:math xmlns:b=\"http://www.w3.org/1998/Math/MathML\"><b:mrow><b:msub><b:mi>CeMgAl</b:mi><b:mn>11</b:mn></b:msub><b:msub><b:mi mathvariant=\"normal\">O</b:mi><b:mn>19</b:mn></b:msub></b:mrow></b:math> confirming model parameters previously estimated from inelastic neutron spectrum in high fields. Second, we showcase the accuracy of our method by studying the thermal phase transition into the spin solid up-up-down phase of <d:math xmlns:d=\"http://www.w3.org/1998/Math/MathML\"><d:mrow><d:msub><d:mi>Na</d:mi><d:mn>2</d:mn></d:msub><d:mi>BaCo</d:mi><d:msub><d:mrow><d:mo>(</d:mo><d:msub><d:mi>PO</d:mi><d:mn>4</d:mn></d:msub><d:mo>)</d:mo></d:mrow><d:mn>2</d:mn></d:msub></d:mrow></d:math> in good agreement with experiment. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"29 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143417394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spin-split Andreev bound states and diode effect in an Ising superconductor Josephson junction","authors":"Sourabh Patil, Gaomin Tang, Wolfgang Belzig","doi":"10.1103/physrevb.111.l060502","DOIUrl":"https://doi.org/10.1103/physrevb.111.l060502","url":null,"abstract":"The transition-metal dichalcogenides featuring Ising spin-orbit coupling in so-called Ising superconductors offer a unique system to study the interplay of singlet and triplet superconductivity. The presence of high critical fields, spectral properties such as the mirage gap, and field-tunable charge and spin currents in Ising superconductor Josephson junctions are some of the important features. In this Letter, we study an Ising superconductor Josephson junction with a transparent interface and show that Andreev bound states are spin split due to a relative misorientation of in-plane fields in the superconducting contacts. Correspondingly, supercurrent-phase relations display a strongly nonsinusoidal behavior. Introducing additional spin-polarized channels with low transmission results in a nonreciprocal current-phase relation with a diode effect that can be tuned by the in-plane exchange fields. The diode efficiency reaches high values of the order of 40% and is not sensitive to disorder in the junction. Such structures can be realized in van der Waals heterostructures of two-dimensional superconductors and magnets. <jats:supplementary-material> <jats:copyright-statement>Published by the American Physical Society</jats:copyright-statement> <jats:copyright-year>2025</jats:copyright-year> </jats:permissions> </jats:supplementary-material>","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":"2 1","pages":""},"PeriodicalIF":3.7,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143401767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}