Research

Materials at Van Hove singularity (VHS): Kagome metals and moiré systems

Van Hove singularity (VHS) is known to support various unconventional phenomena. Such a singularity can occur at the dispersion-energy saddle points, which drives the density of states logarithmically divergent. At the VHS, the interaction-driven correlated phases are strongly enhanced and intertwine with each other. An important question is whether the VHS can be found near the Fermi level in the practical materials. Another relevant question following is what correlated phases are the leading instabilities at the VHS.

Recently, a new series of kagome metals AV3Sb5 with A = K, Rb, and Cs were uncovered [Phys. Rev. Mater. 3, 094407 (2019)]. Crucially, the normal Fermi surface occurs at the VHS of V-based kagome network. The experiments observed unconventional charge density waves (CDWs) below 80-100 K [Nat. Mater. 20, 1353 (2021)], where nontrivial time-reversal symmetry breaking was hinted by giant anomalous Hall effect, Kerr effect, muon-spin relaxation, etc. Further translation and rotation symmetry breakings were also identified at lower temperatures [Nature 599, 216 (2021)]. More exotic phenomena were observed from the superconductivity at ~ 1 K [Phys. Rev. Lett. 125, 247002 (2020)]. These complicated interaction effects have attracted enormous attention in the condensed matter physics community in the past few years.

Another platform for the accessible VHS at Fermi level is the family of moiré systems. Based on the 2D materials such as graphene and transition metal dichalcogenides (TMDs), these materials utilize the mismatch between adjacent layers to create low-energy flat bands on large moiré superlattice. Due to the band flatness and the large moiré unit cells, the filling can be easily tuned across the whole flat band by gating. This allows the achievement of VHS at the Fermi level, which presents a new setup for the study of correlated phases at the VHS. Experimentally, a host of ill-understood insulating and superconducting phases were observed [Nature 556, 43 (2018)]. The according research was one of the mainstreams of modern condensed matter research in the past few years.

My research has pioneered the theories of many correlated phases in the quantum materials at the VHS. In my doctoral research (2019), I made the first discovery of imaginary CDW, also known as the charge loop current (CLC) order, at the Van Hove singularity through a parquet renormalization group (RG) analysis [1]. Our analysis showed that this novel charge order is the leading instability at the VHS, as long as the fermion flavor number is greater than 2 (that is, there are additional degrees of freedom other than the spin-1/2 ones, such as the orbitals). Originally, we were aiming at explaining the correlated phases in the graphene moiré systems. This aim further motivated us to study the correlated phases at the high-order VHS in the moiré systems [2]. However, after two years (2021), our work found its greatest impact in the CDWs of kagome metals AV3Sb5 with possible time-reversal symmetry breaking. We thus conducted a series of analysis on AV3Sb5. Through the phenomenological theories, we identified the precise forms and possible nontrivial topology of the real CDWs with tri-hexagonal (TrH) charge bond order, the imaginary CDWs with CLCs, and their combinations [3,4]. We further studied the low-temperature superconductivity and proposed the possible theories that could be consistent with the experiments [5].

Related publications

1. Chiral twist on the high-Tc phase diagram in moiré heterostructures

Yu-Ping Lin and Rahul M. Nandkishore

Phys. Rev. B 100, 085136 (2019) [Editors' Suggestion]

2. Parquet renormalization group analysis of weak-coupling instabilities with multiple high-order Van Hove points inside the Brillouin zone

Yu-Ping Lin and Rahul M. Nandkishore

Phys. Rev. B 102, 245122 (2020) [Editors' Suggestion]

3. Complex charge density waves at Van Hove singularity on hexagonal lattices: Haldane-model phase diagram and potential realization in the kagome metals AV3Sb5 (A = K, Rb, Cs)

Yu-Ping Lin and Rahul M. Nandkishore

Phys. Rev. B 104, 045122 (2021) [Editors' Suggestion]

4. Higher-order topological insulators from 3Q charge bond orders on hexagonal lattices: A hint to kagome metals

Yu-Ping Lin

arXiv:2106.09717

5. Multidome superconductivity in charge density wave kagome metals

Yu-Ping Lin and Rahul M. Nandkishore

Phys. Rev. B 106, L060507 (2022)

Flat-band materials: Kagome and pyrochlore metals

The study of flat bands has become a major focus of condensed matter research in the past decade. Due to the massive density of states, the flat bands can support strongly enhanced correlated phases. Recent studies have uncovered various ways of realizing the flat bands in practical materials. Among various flat-band systems, there is a family in which the flat bands are inherent to frustrated hoppings on the lattice [Phys. Rev. B 78, 125104 (2008)]. The search among frustrated materials has identified many candidates over the past few years. In particular, recent experiments observe (approximately) flat bands in the quasi-two-dimensional (2D) kagome metals FeSn and CoSn and their relevance to FeGe. For FeSn and FeGe, the flat-band ferromagnetism are observed below ~ 400 K [Nat. Mater. 19, 163 (2020) and Nature 609, 490 (2022)], consistent with the expectation from Stoner criterion. Interestingly, additional charge density waves are recently discovered below ~ 100 K [Nature 609, 490 (2022)], which potentially support time-reversal symmetry breaking. A natural question is whether the other unconventional correlated phases can also develop in the kagome flat bands.

To explore the other possible phases, we compute the mean-field phase diagram of repulsive electrons in kagome flat band. Our unbiased Hartree-Fock analysis remarkably reveals cascades of unconventional magnetic orders, including a series of spin-charge stripes and an evolution from 120-degree to tetrahedral spin orders. A fractionalization analysis identifies potential spin liquids beyond the mean-field level. Comparisons to experiments help inform the search for unconventional orders in kagome metals.

Related publications

1. Complex magnetic and spatial symmetry breaking from correlations in kagome flat bands

Yu-Ping Lin, Chunxiao Liu, and Joel E. Moore

Phys. Rev. B 110, L041121 (2024)

Sublattice polarization: Understanding and systematic search on common lattices

Sublattice polarization (SLP) is an important pathway for unconventional interaction-driven phases in the kagome metals AV3Sb5 and FeGe. While the presence of SLP has been taken as a fact in the large volume of theoretical literature, its origin and general applicability to common lattices remain elusive. My work establishes the first systematic study of SLP states (SLPSs) from a destructive-interference scenario. The SLPSs are identified broadly on the one-, two-, and three-dimensional common lattices, and are proven robust against further-neighbor hoppings. The profound effects on interaction-driven phases are studied by Hartree-Fock analysis. This work goes beyond the recent mainstream of kagome metals and guides the search for unconventional interaction-driven phases in a wider range of quantum materials.

Related publications

1. Sublattice polarization from destructive interference on common lattices

Yu-Ping Lin

arXiv:2406.02671

Odd-parity altermagnetism through sublattice currents

Altermagnetism (ALM) was recently proposed as the third type of collinear magnetism. Due to the combination of compensated magnetization, like antiferromagnetism (AFM), and nonrelativistic spin splitting in the bands, similar to ferromagnetism (FM), it has been proposed as a fertile ground for unconventional phenomena and innovative spintronics applications. Previous symmetry classification assumed time-reversal symmetry in nonmagnetic crystal structures, thereby concluding all ALMs as even-parity. Here I establish the first discovery of odd-parity ALMs under sublattice currents, which breaks nonmagnetic time-reversal symmetry and supports nonrelativistic odd-parity spin splitting under sublattice imbalance. Starting from the Haldane-Hubbard model, I systematically construct a series of 2D and 3D bipartite-lattice models that host the odd-parity ALMs.

Related publications

1. Odd-parity altermagnetism through sublattice currents: From Haldane-Hubbard model to general bipartite lattices

Yu-Ping Lin

arXiv:2503.09602

Ultrafast optical control of kagome metals: Dynamics in pump-probe setup

The kagome metals AV3Sb5 are known to host complex interaction effects, leading to various unconventional charge orders and superconductivity. This complex nature further enriches the possibilities of novel phenomena in the nonequilibrium dynamics. One way of exploring the nonequilibrium dynamics is the ultrafast optical control, where ultrashort pump pulses are applied to the material and alter its properties. Many pump-probe techniques have been applied to the kagome metals AV3Sb5, including the usage of coherent phonon spectroscopy, time-resolved optical polarization-rotation measurement, time- and angle-resolved photoemission spectroscopy (trARPES), time-resolved X-ray diffraction measurements (trXRD), and laser-coupled scanning tunneling microscopy (STM). Remarkably, the laser-coupled STM experiment has shown successful control of the charge-density-wave (CDW) strengths at different momenta. This result suggests the great potential of ultrafast optical control in the pursuit of novel dynamical phenomena in the kagome metals AV3Sb5. Despite the reports of these many pump-probe experiments, theoretical study has remained absent.

Our recent work established the first theoretical study of pump-probe dynamics in the kagome metals AV3Sb5. Employing the time-dependent Hartree-Fock theory, our analysis identified distinct terahertz dynamics of the charge orders under linearly and circularly polarized pumps. These pumps not only modify the symmetry of the CDW, but also trigger emergent orders such as charge nematicity (CN) and topological loop currents. Our analysis sheds light on the ultrafast optical control of quantum materials with complex interaction effects. We take this work as our first step into the ultrafast optical control of novel quantum materials with complex interaction effects.

Related publications

1. Ultrafast optical control of charge orders in kagome metals

Yu-Ping Lin, Vidya Madhavan, and Joel E. Moore

arXiv:2411.10447

Band geometry: Position-momentum-duality interpretation of quantum metric

The modern study of semimetals has uncovered various unconventional band structures with fascinating phenomena. These systems accommodate band crossings in the Brillouin zone, which may take the form of nodal points, nodal lines, or nodal surfaces. The band crossings generically host nontrivial topological and/or geometric structures in the band eigenstates. The band topology of semimetals has been studied extensively in the past few decades. Meanwhile, the band geometry has not received as much attention, leaving a wide realm of fascinating topics to be explored.

We show that the position-momentum duality offers a transparent interpretation of the band geometry at the topological band crossings. Under this duality, the band geometry with Berry connection is dual to the free-electron motion under gauge field. This identifies the trace of quantum metric as the dual energy in momentum space. The band crossings with Berry defects thus induce the dual energy quantization in the trace of quantum metric. More recently, we introduce a novel concept of geometric semimetals. While these semimetals are topologically trivial, they receive protection from symmetries and carry nontrivial band geometry with possible quantization. Our model and its band geometry can be directly realized and tested in synthetic-matter experiments, such as superconducting quantum circuits.

Related publications

1. Band geometry from position-momentum duality at topological band crossings

Yu-Ping Lin and Wei-Han Hsiao

Phys. Rev. B 105, 075127 (2022)

2. Dual Haldane sphere and quantized band geometry in chiral multifold fermions

Yu-Ping Lin and Wei-Han Hsiao

Phys. Rev. B 103, L081103 (2021) [Letter]

3. Geometric semimetals and their simulation in synthetic matter

Yu-Ping Lin and Giandomenico Palumbo

Phys. Rev. B 109, L201107 (2024) [Letter]

Band topology: Symmetry protection, edge and corner states, etc

The modern research of topological insulators has laid out many classifications under different setups of symmetries. Marching from the well-known tenfold-way classification [Rev. Mod. Phys. 88, 035005 (2016)] with onsite symmetries, recent studies have gone further with the inclusion of crystalline symmetries.

In a recent work, we introduce the reduced Chern number, defined in subregions of the Brillouin zone (BZ), and construct a family of Chern dartboard insulators (CDIs) with quantized reduced Chern numbers in the sub-BZ (sBZ) but with trivial bulk topology. CDIs are protected by mirror symmetries and exhibit distinct pseudospin textures, including (anti)skyrmions, inside the sBZ. These CDIs host exotic gapless edge states, such as Möbius fermions and midgap corner states, and can be realized in photonic crystals. Our work opens up new possibilities for exploring sBZ topology and nontrivial surface responses in topological systems.

Related publications

1. Chern dartboard insulator: sub-Brillouin zone topology and skyrmion multipoles

Yun-Chung Chen, Yu-Ping Lin, and Ying-Jer Kao

Commun Phys 7, 32 (2024)

Nonsaturating large magnetoresistance in semimetals

The intensive recent investigations of topological semimetals have revealed a large number of semimetal compounds that exhibit very large nonsaturating magnetoresistance. Multiple mechanisms for this magnetoresistance phenomenon have been theoretically proposed, but experimentally it is unclear how to identify which mechanism is responsible in a particular sample or how to make a clean connection between experimental observations and theoretical models. Our results show that the magnetic susceptibility and the tangent of the Hall angle successfully capture the fundamental differences in seemingly similar nonsaturating large magnetoresistance, where charge compensation, energy dispersion, and the roles of disorder are markedly distinct, and provide empirical templates to characterize the origins of the extraordinary magnetotransport properties in the newly discovered topological semimetals and beyond. 

Related publications

1. Nonsaturating large magnetoresistance in semimetals

Ian A. Leahy, Yu-Ping Lin, Peter E. Siegfried, Andrew C. Treglia, Justin C. W. Song, Rahul M. Nandkishore, and Minhyea Lee

Proc. Natl. Acad. Sci. 115, 10570 (2018)

Griffiths singularities in the random quantum Ising antiferromagnet

Rare events can have major effects on quantum matter.  Extremely unlikely events cause certain physical properties to diverge to infinity near the quantum phase transition of the disordered Ising antiferromagnet in a transverse field, but destroy criticality of the clean system completely when the longitudinal component of the field is present.  Using a tree tensor network renormalization group method combined with a novel matrix product operator presentation, we detect signatures of rare events and determine the zero-temperature phase diagram of the disordered antiferromagnetic Ising chainin the presence of both longitudinal and transverse magnetic fields. The new numerical technique used in this paper is generalizable to more complicated many-body systems and higher dimensions.

Related publications

1. Griffiths singularities in the random quantum Ising antiferromagnet: A tree tensor network renormalization group study

Yu-Ping Lin, Ying-Jer Kao, Pochung Chen, and Yu-Cheng Lin

Phys. Rev. B 96, 064427 (2017) [Editors' Suggestion]

Latest presentation

Tree Tensor Network Strong Disorder Renormalization Group on a Disordered Antiferromagnetic Ising Chain

Fourth Workshop on Tensor Network States: Algorithms and Applications, December 2016 [Website] [Slides]

Hsinchu, Taiwan