The transition metal dichalcogenide 1T-TaS2 attract growing attention because of the formation of rich density-wave (DW) and superconducting transitions. However, the origin of the incommensurate DW state at the highest temperature (~ 550 K), which is "the parent state" of the rich physical phenomena, is still uncovered. Here, we present a natural explanation for the triple-q incommensurate DW in 1T-TaS2 based on the first-principles Hubbard model with on-site U. We apply the paramagnon interference mechanism that gives the nematic order in Fe-based superconductors. The derived order parameter has very unique characters: (i) the orbital-selective nature, and (ii) the unconventional sign-reversal in both momentum and energy spaces. The present study will be useful for understanding rich physics in 1T-TaS2, 1T-VSe2, and other transition metal dichalcogenides.
Low-dimensional electron systems, as realized naturally in graphene or created artificially at the interfaces of heterostructures, exhibit a variety of fascinating quantum phenomena with great prospects for future applications. Once electrons are confined to low dimensions, they also tend to spontaneously break the symmetry of the underlying nuclear lattice by forming so-called density waves; a state of matter that currently attracts enormous attention because of its relation to various unconventional electronic properties. In this study we reveal a remarkable and surprising feature of charge …
The magnetic and electronic properties of Ba$_4$Ru$_3$O$_{10}$ were investigated by the ab-initio and model calculations. It is shown that nonmagnetic ground state of the one-third Ru$^{4+}$ ions is not due to the correlation effects. It is rather caused by the charge disproportionation between crystallographically different Ru and the molecular orbital formation in the Ru's trimer.
Non-local order parameters in space-time are proposed to characterize the unconventional orbital-selective conducting state in fulleride superconductors, called the Jahn-Teller metal. In previous works, it has been argued that this state can be interpreted as a spontaneous orbital-selective Mott state, in which the electrons in two of the three $t_{1u}$ molecular orbitals are localized, while those in the third one are metallic. Here, based on the realistic band structure for fullerides, we provide a systematic study of nonlocal order parameters and characterize the Jahn-Teller metal, for whic…
Traditional routes to Charge-Density-Wave in transition metal dichalcogenides, relying on Fermi surface nesting or Jahn-Teller instabilities have recently been brought into question. While this calls for exploration of alternative views, paucity of theoretical guidance sustains lively controversy on the origin of, and interplay between CDW and superconductive orders in transition metal dichalcogenides. Here, we explore a preformed excitonic liquid route, heavily supplemented by modern correlated electronic structure calculations, to an excitonic-CDW order in 1T-TiSe$_{2}$. We show that orbital…
The pairing mechanism in A$_3$C$_{60}$ is investigated by studying the properties of a three-orbital Hubbard model with antiferromagnetic Hund coupling in the normal and superconducting phase. Local orbital fluctuations are shown to be substantially enhanced in the superconducting state, with a fluctuation energy scale that matches the low-energy peak in the spectral weight of the order parameter. Our results demonstrate that local orbital fluctuations provide the pairing glue in strongly correlated fulleride superconductors and support the spin/orbital freezing theory of unconventional superc…
We present a state-of-the-art density functional theory (DFT) study which models crucial features of the partially disordered orbital order stacking in the prototypical layered transition metal dichalcogenide 1T-TaS2 . Our results not only show that DFT models with realistic assumptions about the orbital order perpendicular to the layers yield band structures which agree remarkably well with experiments. They also demonstrate that DFT correctly predicts the formation of an excitation pseudo-gap which is commonly attributed to Mott-Hubbard type electron-electron correlations. These results high…
By constructing an effective model based on recently calculated \emph{ab }initio bare interaction parameters, we study the phase diagram of alkali doped fullerides as a function of temperature and internal pressure. We use a slave-rotor mean-field approach at the weak and intermediate coupling limits and a variational mean-field approach at the strong coupling limit, and find a good agreement with experimental phase diagram. We explain the unified description of the phase diagram including the proximity of s-wave superconducting state and the Mott-insulating state, and the existence of Jahn-Te…
The valence band maxima of most group-VI transition metal dichalcogenide thin films remain at the $Γ$-point all the way from bulk to bilayer. In this paper we develop a continuum theory of the moirè minibands that are formed in the valence bands of $Γ$-valley homobilayers by a small relative twist. Our effective theory is benchmarked against large-scale ab initio electronic structure calculations that account for lattice relaxation. As a consequence of an emergent $D_6$ symmetry we find that low-energy $Γ$-valley moirè holes differ qualitatively from their K-valley counterparts addressed previ…
Quantum Phases in Twisted Homobilayer Transition Metal Dichalcogenides
School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）；Wuhan Institute of Quantum Technology（武汉量子技术研究院）；Department of Physics, University of Texas at Austin（德克萨斯大学奥斯汀分校物理系）
A sufficiently high magnetic field applied to a superconductor will act on both the charge and the spin of the individual electrons breaking up the Cooper pairs. If the spin effect dominates, the superconducting state can develop a texture before eventually entering the normal state with increasing magnetic field. This spatially varying superconducting state is a periodic array of magnetic walls separated by superconducting regions. Known as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, it was predicted in 1964. We report heat capacity measurements on the heavy fermion superconductor, CeC…
The vicinity of a Mott insulating phase has constantly been a fertile ground for finding exotic quantum states, most notably the high Tc cuprates and colossal magnetoresistance manganites. The layered transition metal dichalcogenide 1T-TaS2 represents another intriguing example, in which the Mott insulator phase is intimately entangled with a series of complex charge-density-wave (CDW) orders. More interestingly, it has been recently found that 1T-TaS2 undergoes a Mott-insulator-to-superconductor transition induced by high pressure, charge doping, or isovalent substitution. The nature of the M…
The complex Fermi surfaces of transition-metal dichalcogenides (TMDCs) challenge the standard Peierls-instability-driven charge-density-wave (CDW) formation. Recently, evidence has been accumulating of a prominent role of ionic thermal fluctuations, which frozen out below $T_{CDW}$ inducing a periodic lattice distortion (PLD). We focus on $2H$-NbSe$_2$, displaying a quasi-commensurate CDW below $T_{CDW}$ $\approx$33 K, and use time-resolved optical spectroscopy (TR-OS) to detect and disentangle the electronic and lattice degrees of freedom. We reveal a fingerprint of the ordered phase at h$ν$ …
We extend the study of the Fermi surface instability of the Pomeranchuk type into systems with orbital band structures, which are common features in transition metal oxides. Band hybridization significantly shifts the spectra weight of the Landau interactions from the conventional s-wave channel to unconventional non-s-wave channels, which results in anisotropic (nematic) Fermi surface distortions even with ordinary interactions in solids. The Ginzburg-Landau free energy is constructed by coupling the charge-nematic, spin-nematic and ferromagnetic order parameters together, which shows that ne…
It is known that the Field-Induced Spin-Density-Wave (FISDW) phases are experimentally observed in the quasi-one-dimensional (Q1D) organic conductors with chemical formula (TMTSF)$_2$X (X=PF$_6$, ClO$_4$, etc.) and some others in moderate magnetic fields. From a theoretical point of view, they appear as a result of "one-dimensionalization" of the Q1D electron spectra due to the orbital electron effect in a magnetic field. We predict that the novel FISDW phases with different physical meaning have to appear in inclined high magnetic fields in Q1D conductors as a result of combination of the spi…
We study a twisted Hubbard tube modeling the [CrAs] structure of quasi-one-dimensional superconductors A2Cr3As3 (A = K, Rb, Cs). The molecular-orbital bands emerging from the quasi-degenerate atomic orbitals are exactly solved. An effective Hamiltonian is derived for a region where three partially filled bands intersect the Fermi energy. The deduced local interactions among these active bands show a significant reduction compared to the original atomic interactions. The resulting three-channel Luttinger liquid shows various interaction-induced instabilities including two kinds of spin-triplet …
Orbital degrees of freedom of a Cooper pair play an important role in the unconventional superconductivity. To elucidate the orbital effect in the Kondo problem, we investigated a single magnetic impurity coupled to Cooper pairs with a $p_x +i p_y$ ($d_{x^2-y^2}+id_{xy}$) symmetry using the numerical renormalization group method. It is found that the ground state is always a spin doublet. The analytical solution for the strong coupling limit explicitly shows that the orbital dynamics of the Cooper pair generates the spin 1/2 of the ground state.
The high-temperature superconducting state in cuprates appears if charge carriers are doped into a Mott insulating parent compound. An unresolved puzzle is the unconventional nature of the normal state above the superconducting dome, and its connection to the superconducting instability. At weak hole-doping, a "pseudo-gap" metal state with signatures of time-reversal symmetry breaking is observed, which near optimal doping changes into a "strange metal" with non-Fermi liquid properties. Qualitatively similar phase diagrams are found in multi-orbital systems, such as pnictides, where the unconv…
We report the synthesis and characterization of a rare-earth dichalcogenide EuTe$_2$. An antiferromagnetic transition was found at T$_M$ = 11 K. The antiferromagnetic order can be tuned by an applied magnetic field to access a first-order spin flop transition and a spin flip transition. These transitions are associated with a giant negative magnetoresistance with a value of nearly 100\%. Heat capacity measurements reveal strong electronic correlations and a reduced magnetic entropy. Furthermore, density functional theory calculations demonstrate that the electrons near the Fermi surface mainly…
Charge fluctuations in the quasi-one-dimensional material Li0.9Mo6O17 are analyzed based on a multi orbital extended Hubbard model. A charge ordering transition induced by Coulomb repulsion is found with a charge ordering pattern different from a conventional charge density wave driven by Fermi surface nesting. The metallic state displays a characteristic charge collective mode which softens signalling the proximity to the transition. We argue that the strong scattering between electrons generated by these charge order fluctuations can lead to the unconventional metallic state observed above t…
A new type of Kondo effect peculiar to unconventional superconductors is studied theoretically by using the Wilson's numerical renormalization group method. In this case, an angular momentum of a Cooper pair plays an important role in the Kondo effect. It produces multichannel exchange couplings with a local spin. Here we focus on a $p_x +i p_y$-wave state which is a full gap system. The calculated impurity susceptibility shows that the local spin is almost quenched by the Kondo effect in the strong coupling region ($T_{\rm K}/Δ\to \infty$), while the ground state is always a spin doublet over…
Based on a microscopic theoretical study, we show that novel superconductivity is induced by carrier doping in layered perovskite Ir oxides where a strong spin-orbit coupling causes an effective total angular momentum J_{eff}=1/2 Mott insulator. Using a variational Monte Carlo method, we find an unconventional superconducting state in the ground state phase diagram of a t_{2g} three-orbital Hubbard model on the square lattice. This superconducting state is characterized by a d_{x^2-y^2}-wave "pseudospin singlet" formed by the J_{eff}=1/2 Kramers doublet, which thus contains inter-orbital as we…
Quasiparticle interference (QPI) in spectroscopic imaging scanning tunneling microscopy provides a powerful method to detect orbital band structures and orbital ordering patterns in transition metal oxides. We use the $T$-matrix formalism to calculate the QPI spectra for the unconventional metamagnetic system of Sr$_3$Ru$_2$O$_7$ with a $t_{2g}$-orbital band structure. A detailed tight-binding model is constructed accounting for features such as spin-orbit coupling, bilayer splitting, and the staggered rotation of the RuO octahedra. The band parameters are chosen by fitting the calculated Ferm…
Twisted bilayer transition metal dichalcogenides have emerged as important model systems for the investigation of correlated electron physics because their interaction strength, carrier concentration, band structure, and inversion symmetry breaking are controllable by device fabrication, twist angle, and most importantly, gate voltage, which can be varied in situ. The low energy physics of some of these materials has been shown to be described by a "moiré Hubbard model" generalized from the usual Hubbard model by the addition of strong, tunable spin orbit coupling and inversion symmetry breaki…
Feynman's "no-node" theorem states that the conventional many-body ground-state wavefunctions of bosons in the coordinate representation is positive-definite. This implies that time-reversal symmetry cannot be spontaneously broken. In this article, we review our progress in studying a class of new states of unconventional Bose-Einstein condensations beyond this paradigm. These states can either be the long-lived metal-stable states of ultra-cold bosons in high orbital bands in optical lattices as a result of the "orbital-Hund's rule" interaction, or the ground states of spinful bosons with spi…
The recently discovered cuprate superconductor Ba$_2$CuO$_{3+δ}$ exhibits a high $T_c\simeq73$K at $δ\simeq0.2$. The polycrystal grown under high pressure has a structure similar to La$_2$CuO$_4$, but with dramatically different lattice parameters due to the CuO$_6$ octahedron compression. The crystal field in the compressed Ba$_2$CuO$_4$ leads to an inverted Cu $3d$ $e_g$ complex with the $d_{x^2-y^2}$ orbital sitting below the $d_{3z^2-r^2}$ and an electronic structure highly unusual compared to the conventional cuprates. We construct a two-orbital Hubbard model for the Cu $d^9$ state at hol…
We investigate the impact of impurity scattering on superconductivity in an anisotropic multi-orbital model with spin-orbit coupling which describes the electron fluid at two-dimensional oxide interfaces. As the pairing mechanism is under debate, both conventional and unconventional superconducting states are analyzed. We consider magnetic and nonmagnetic spin-dependent intra- and interorbital scattering and discuss possible microscopic realizations leading to these processes. It is found that, for magnetic disorder, the unconventional superconductor is protected against interband scattering a…
Motivated by a growing interest in multi-orbital superconductors with spin-orbit interactions, we perform the group-theoretical classification of various unconventional superconductivity emerging in symmorphic $\rm O$, $\rm D_4$, and $\rm D_6$ space groups. The generalized Cooper pairs, which we here call "multipole" superconductivity, possess spin-orbital coupled (multipole) degrees of freedom, instead of the conventional spin singlet/triplet in single-orbital systems. From the classification, we obtain the following key consequences, which have been overlooked in the long history of research…
The newly discovered topological crystalline insulators (TCIs) harbor a complex band structure involving multiple Dirac cones. These materials are potentially highly tunable by external electric field, temperature or strain and could find future applications in field-effect transistors, photodetectors, and nano-mechanical systems. Theoretically, it has been predicted that different Dirac cones, offset in energy and momentum-space, might harbor vastly different orbital character, a unique property which if experimentally realized, would present an ideal platform for accomplishing new spintronic…
By enabling control of valley degrees of freedom in transition-metal dichalcogenides, valley-selective circular dichroism has become a key concept in valleytronics. In this manuscript, we show that valley excitons -- bound electron-hole pairs formed at either the K or K' valleys upon absorption of circularly-polarized light -- are chiral quasiparticles characterized by a finite orbital angular momentum (OAM). We further formulate an ab-initio many-body theory of valley-selective circular dichroism and valley excitons based on the Bethe-Salpeter equation. Beside governing the interaction with c…
The interplay between electronic orders and superconductivity is central to the physics of unconventional superconductors, and is particularly pronounced in the iron-based superconductors. Motivated by recent experiments on FeSe, we study the superconducting pairing in its nematic phase in a multiorbital model with frustrated spin-exchange interactions. The electron correlations in the presence of the nematic order give rise to an enhanced orbital selectivity in the superconducting pairing amplitudes. This orbital-selective pairing produces a large gap anisotropy on the Fermi surface. Our resu…
Understanding the crystal field splitting and orbital polarization in non-centrosymmetric systems such as ferroelectric materials is fundamentally important. In this study, taking BaTiO$_3$ (BTO) as a representative material we investigate titanium crystal field splitting and orbital polarization in non-centrosymmetric TiO$_6$ octahedra with resonant X-ray linear dichroism at Ti $L_{2,3}$-edge. The high-quality BaTiO$_3$ thin films were deposited on DyScO$_3$ (110) single crystal substrates in a layer-by-layer way by pulsed laser deposition. The reflection high-energy electron diffraction (RHE…
Electronic flat band systems are a fertile platform to host correlation-induced quantum phenomena such as unconventional superconductivity, magnetism and topological orders. While flat band has been established in geometrically frustrated structures, such as the kagome lattice, flat band-induced correlation effects especially in those multi-orbital bulk systems are rarely seen. Here we report negative magnetoresistance and signature of ferromagnetic fluctuations in a prototypical kagome metal CoSn, which features a flat band in proximity to the Fermi level. We find that the magnetoresistance i…
Competing incommensurability, electronic correlations, and superconductivity in a hybrid transition metal dichalcogenide
Weizmann Institute of Science（魏茨曼科学研究所）；University of Hamburg（汉堡大学）；Bar Ilan University（巴伊兰大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；Technion - Israel Institute of Technology（以色列理工学院）；Goethe Universität Frankfurt（法兰克福歌德大学）
Intertwining quantum order and nontrivial topology is at the frontier of condensed matter physics. A charge density wave (CDW) like order with orbital currents has been proposed as a powerful resource for achieving the quantum anomalous Hall effect in topological materials and for the hidden phase in cuprate high-temperature superconductors. However, the experimental realization of such an order is challenging. Here we use high-resolution scanning tunnelling microscopy (STM) to discover an unconventional charge order in a kagome material KV3Sb5, with both a topological band structure and a sup…
