Session S22: Strong Electronic Correlations in Topological Materials: Theory and Experiment

Resolving the electronic structure of Kagome metal ScV6Sn6

The unique shared-corner triangular crystal structure of Kagome lattice yields a band structure with Dirac point, flat band, and van Hove singularities, leading to strong correlations and non-trivial topological states. ScV₆Sn₆ is a new synthesized Kagome metal with a charge density wave transition at 92 K. Here, we carried out the Density Functional Theory (DFT) modeling of the electronic structure and measured the quantum oscillations in electrical resistance and magnetic torque in ScV₆Sn₆. Comparing the angular mapping of the resolved orbits with the DFT calculations provides a comprehensive study of the electronic structure and Fermi surface.   

Quantum oscillations of Kagome Metal ScV6Sn6 in intense magnetic field

Quantum oscillations in strong magnetic fields give us direct insight into the bandstructure of solids via the quantization of electron motion. The Kagome lattice structure allows for topologically protected surface states that can be realized via the frequency of observed quantum oscillations. A crucial question remains about the fate of the small orbits when the magnetic field is strong enough to push the electronic state to the quantum limit. By utilizing proximity detector oscillators (PDOs) in a 65 T  pulsed field, we resolved strong quantum oscillations corresponding to Fermi surface orbits in ScV₆Sn₆. The study will be compared with the Landau level indexing mapping with the quantum oscillation results in the DC fields.   

Differentiating Dirac from non-Dirac bands in Kagome metal ScV6Sn6

The Kagome lattice is an ideal platform to present topological properties within the strong electron correlation regime due to its special geometric structure. The Kagome metal family AV₃Sb₅ (A=K, Cs, Rb) has been discovered recently to host the entanglement of charge density wave (CDW), superconductivity, and topological electronic structure. Here, we measured another Kagome metal ScV₆Sn₆, which also exhibits CDW ordering without superconductivity in the ground state. We conducted the resistance and magnetic torque measurements at base temperature to search the quantum oscillations in order to map the Fermi surface. The Landau Level indexing resolved the trivial and nontrivial Berry phases from different bands. We will compare the observations with the electronic structure modeling to shed light on the “Diracness” of the related bands.

    

Topological flat bands in a kagome lattice multiorbital system

Flat bands and dispersive Dirac bands are known to coexist in the electronic bands in a two-dimensional kagome lattice. Including the relativistic spin-orbit coupling, such systems often exhibit nontrivial band topology, allowing for gapless edge modes between flat bands at several locations in the band structure, and dispersive bands or at the Dirac band crossing. Here, we theoretically investigate the electronic property of a multiorbital system on a kagome lattice. We found that the multiorbital kagome model with the atomic spin-orbit coupling naturally supports topological bands characterized by nonzero Chern numbers C, including a flat band with |C| =1. We further investigate the effect of Coulomb repulsive interactions. When such a flat band is 1/3 filled, the non-local repulsive interactions induce a fractional Chern insulating state. Thus, the multiorbital system on a kagome lattice is a versatile platform to explore the interplay between nontrivial band topology and electronic interaction. We also discuss the possible realization of our findings in real kagome materials.

    

Tunable Mott Dirac and kagome bands engineered on 1T-TaS2

Strongly interacting electrons in hexagonal and kagome lattices exhibit rich phase diagrams of exotic quantum states, including superconductivity and correlated topological orders intermixed with magnetic orders. However, material realizations of these electronic states have been scarce in nature or by design. Here, we theoretically propose an approach to realize artificial hexagonal and kagome lattices by metal adsorption on a 2D Mott insulator 1T-TaS₂. Alkali, alkaline-earth, and group-13 metal atoms are deposited stably in (√3×√3)R30° and 2×2 TaS₂ superstructures of honeycomb- and kagome-lattice symmetries exhibiting Dirac and kagome bands, respectively. The strong electron correlation of 1T-TaS₂ drives the honeycomb and kagome systems into correlated topological phases described by Kane-Mele-Hubbard and kagome-Hubbard models with nontrivial Z₂ invariant and helical edge modes, respectively. We further show that the 2/3- or 3/4-band filling of these Mott Dirac and flat bands can be achieved with a proper concentration of Mg adsorbates. Our proposal may be readily implemented in experiments, offering an attractive condensed-matter platform to exploit the interplay of topological order and superconductivity under the strong electron correlation.   

Nematic susceptibility in the kagome superconductor CsV3Sb5

The recently discovered kagome superconductors AV₃Sb₅ (A = K, Rb, Cs)  exhibit unusual charge-density-wave (CDW) order with time reversal and rotational symmetry breaking, which may be related to chiral loop current order. In order to clarify the origin of the nontrivial CDW order, it is essential to clarify the relationship between time-reversal symmetry breaking and nematicity. Here, we report on the nematic susceptibility of CsV₃Sb₅. We performed elastoresistance measurements in two different configurations (four-probe and Montgomery methods), from which we obtained the same results for elastoresistance coefficients with A_1g (symmetric) and E_2g (nematic) symmetries. Both elastoresistance coefficients exhibit a steep jump at T_CDW, reflecting the occurrence of a first-order phase transition at T_CDW. The E_2g elastoresistance coefficient corresponding to the nematic susceptibility is temperature-independent below T_CDW, indicating that the nematic state in CsV₃Sb₅ is not even-parity ferroic order (q ≠ 0). In contrast, the elastoresistance coefficient with symmetric A_1g symmetry shows a broad peak structure around 30 K, which may be related to an anomaly reported in other experiments such as non-reciprocal transport measurements.

    

Charge density wave interaction in a Kagome-honeycomb antiferromagnet

Recent experiments report a charge density wave (CDW) in the antiferromagnet FeGe, but the nature of charge ordering, and the associated structural distortion remains elusive. Here, we unravel the structural and electronic properties of FeGe through in-depth first-principles calculations. Our proposed 2×2×1 CDW, which is driven by the nesting of the hexagonal features of the Fermi surface, accurately captures atomic topographies observed via scanning tunneling microscopy as well as the enhancement of the kagome-Fe magnetic moment upon transition into the CDW phase. In contrast to earlier studies, we show that the coupling of CDW and magnetism results in the motions of Ge atoms and FeGe exhibits a generalized Kekul'e distortion in the Ge honeycomb atomic layers. Our results set the stage for further exploration of the topological nature of the ground state of magnetic kagome-honeycomb lattices and their implications for novel transport, magnetic, and optical responses.   

Electron correlations and charge density wave in the topological kagome metal FeGe

Recently, a charge density wave was discovered in the magnetic binary kagome metal FeGe [1].

In analogy to its predecessor, the non-magnetic AV3Sb5 (A=K, Cs, Rb), the in-plane ordering

occurs at the M point. In contrast, however, the system manifestly shows effects of

substantial correlations.  Here [2], we identify the topological bands crossing the Fermi energy in

FeGe and characterize the correlation-induced renormalization of these bands. We derive a

charge order from an effective model comprising topological kagome `flat' bands in the presence

of a magnetic order. We demonstrate edge states and excess out-of-plane magnetic moments

associated with the charge order; both are fingerprints of non-trivial band topology and

consistent with experimental observations [1,3]. Our results point to FeGe as an ideal platform to

realize and elucidate correlated topological physics.

Supported by the DOE BES Award # DE-SC0018197, LANL LDRD, UC Lab. Fees Research

Program, Quantum Science Center, a U.S. DOE Office of Science National QIS Research

Center, & CINT, a DOE BES user facility.

[1] X. Teng et al. Nature 609, 490 (2022) 

[2] C. Setty et al., Electron correlations and charge density wave in the topological kagome metal

FeGe. arXiv:2203.01930.

[3] J. X. Yin et al., PRL 129, 166401 (2022)   

Topological charge density waves in MoTe2/WSe2 moiré superlattices

Transition metal dichalcogenide (TMD) semiconductor moiré system has been demonstrated as a versatile platform for studying exotic physics such as Hubbard physics and Kane-Mele physics. AB-stacked MoTe2/WSe2 moiré system has enabled both optical and transport studies and shown vivid phase diagram such as topological phase transition at filling 1. Here we report a new Chern state at fractional filling with well quantized Hall resistance and vanishing longitudinal resistance in AB-stacked MoTe2/WSe2. It is consistent with a topological charge density wave (CDW) state with spontaneously broken translational symmetry and a non-zero Chern number. Transport measurements further show that this topological CDW state is closely related to Kondo breakdown. More theoretical studies of the origin of this topological CDW state and the interplay between it and Kondo physics are needed.

    

Topological moiré minibands and correlated Chern insulator from periodically confined massive Dirac fermions

Strong electronic correlation in topological flat minibands renders moiré superlattices fascinating for accessing novel quantum states.  Here we demonstrate a generic mechanism to realize topological flat minibands by confining massive Dirac fermions in a periodic moiré potential, which can be potentially realized in a heterobilayer of transition metal dichalcogenides. We show that the topological phase can be protected by the symmetry of moiré potential and survive to arbitrarily large Dirac band gap. We take the MoTe₂/WSe₂ heterobilayer as an example and find that the topological phase can be driven by a vertical electric field. By projecting the Coulomb interaction onto the topological fat minibands, we identify a correlated Chern insulator at half filling and a quantum valley-spin Hall insulator at full filling. Our work clarifies the importance of Dirac structure for the topological minibands and unveils a general strategy to design topological moiré materials.

    

Interaction-induced Quantum Anomalous and Spin Hall Mott Insulators: beyond Z_2 topology

We introduce interactions into two general models for quantum spin Hall physics. Although the traditional picture is that such physics appears at half-filling, we show that in the presence of strong interactions, the quarter-filled state instead exhibits the quantum spin Hall effect with spin Chern number $C_s=1$. A topological Mott insulator is the underlying cause that lies outside the standard $mathbb Z_2$ topological classification. An intermediate interacting regime emerges that exhibits a quantum anomalous Hall effect when the lower band is `flat'. This state transitions to the quantum spin Hall effect once the interactions are sufficiently large. We show that this intermediate regime is consistent with the simultaneous observation in transition metal dichalcogenide moir{'e} materials of a quantum anomalous Hall phase at quarter filling and a quantum spin Hall effect at half-filling. The valley coherence seen in such moir{'e} systems also matches expectations from a simple bi-layer extension of our results.   

Probing interaction effects at a topological crystalline step edge by Scanning tunneling Microscopy and Scanning tunneling Spectroscopy

Topological Crystalline Insulators (TCIs) are the class of materials in which the topological nature of electronic structure arises from crystal symmetries. With the realization of a TCI phase in Pb_1-xSn_xSe it was perceived that the step edges in TCIs can be viewed as predecessors of higher-order topology, as they embody one-dimensional (1D) edge channels embedded in an effective three-dimensional electronic vacuum emanating from the TCI. Here we use scanning tunneling microscopy and spectroscopy to investigate the behavior of these 1D step-edge channels under the influence of doping. By doping distinct 3d adatoms in Pb_1-xSn_xSe we observed that once the energy position of the 1D step-edge mode is brought close to the fermi level, a new correlation gap starts to open. Our experimental findings are rationalized in terms of enhanced interaction effects since the electron density of states is collapsed to a 1D channel. This enables us to realize a unique system to study how topology and many-body electronic effects intertwine.   

Phase interference for probing topological fractional charge in a TI-based Josephson junction array

Fractional charges can be induced by magnetic fluxes at the interface between a topological insulator (TI) and a type-II superconductor due to axion electrodynamics [1]. In a Josephson junction array with a hole in the middle, these electronic states can have phase interference in an applied magnetic field with 4×2π period, in addition to the 2π interference of the Cooper pairs.

In our previously published work [2], we test an experimental configuration for probing the fractional charge and report the observation of phase interference effect in superconducting arrays with a hole in the middle in both Au- and BiSbTeSe₂-based devices. Our numerical simulations based on the resistive shunted capacitive junction model are in good agreement with the experimental results. However, no clear sign of an axion charge-related interference effect was observed.

In the past year, we fabricated Josephson junction array devices on thin films of the topological insulator (Bi_1-xSb_x)₂Te₃, where these films were deposited by molecular beam epitaxy. These arrays again show clear oscillations that match the simulations very well, but in addition show oscillations with a period that hints towards the e/4 charges. More samples are being fabricated to investigate the exact nature in greater detail.

[1] F.S. Nogueira et al., Phys. Rev. Lett. 121, 227001 (2018).

[2] J.M. Brevoord, D.H. Wielens, et al., Nanotechnology 32, 435001 (2021).

    

Field-anisotropic geometrical Hall effect via f-d exchange fields in doped pyrochlore molybdates

Topological spin textures have been proven to play an important role in the quantum electromagnetic properties. For instance, as a conduction electron is coupled with non-coplanar localized spins, its wave function is endowed with the Berry phase proportional to the solid angles subtended by the neighboring spins, i.e., the scalar spin chirality. The emergent magnetic field (Berry curvature) acts on the conduction electrons, giving rise to unconventional geometrical Hall effect [1]. However, few studies have been done on the geometrical Hall effect in the weak coupling case where no long-range magnetic order exist at zero field.

We synthesized the single crystals of hole-doped pyrochlore (Tb_1-xCa_x)₂Mo₂O₇ using a floating zone furnace with a laser light source [2] and observed that the Hall resistivity of the barely-metallic sample x = 0.14 exhibits an explicit anisotropy between H//[100] and H//[111]. This behavior can be reasonably explained by the spin chirality of the Tb spins forming 2-in 2-out and 3-in 1-out configurations under respective magnetic fields (H) in real space.

[1] Y. Taguchi et al., Science 291, 5513 (2001).

[2] Y. Kaneko et al., J. Cryst. Growth 533 125435 (2020).   

Strong interactions in twisted bilayer graphene at the magic angle

Twisted bilayer graphene (TBG) has been an active area of research due to its promise as a novel material with remarkable tunable properties. We perform a fully self-consistent Hartree-Fock calculation on the lattice accounting for the Coulomb interaction among all the sites(more than 10,000) of the moiré unit cell at the magic angle. We derive the fully self-consistently reconstructed bands at the Hartree-Fock level as a function of the filling factor. Considering rotations around AA sites, which permit constructing exponentially localized Wannier orbitals without topological obstructions, we derive an effective lattice model for the mini-bands of TBG accounting for spin and valley quantum numbers. We numerically address their possible many-body insulating phases at various filling factors.