Lifshitz transition enabling superconducting dome around the quantum critical point in TiSe$_2$
R. D. H. Hinlopen, Owen Moulding, Will Broad, Jonathan Buhot, Femke Bangma, Alix McCollam, Jake Ayres, Charles Sayers, Enrico Da Como, Felix Flicker, Jasper van… 展开作者
R. D. H. Hinlopen, Owen Moulding, Will Broad, Jonathan Buhot, Femke Bangma, Alix McCollam, Jake Ayres, Charles Sayers, Enrico Da Como, Felix Flicker, Jasper van Wezel, Sven Friedemann
Superconductivity often emerges as a dome around a quantum critical point (QCP) where long-range order is suppressed to zero temperature. So far, this has been mostly studied in magnetically ordered materials. By contrast, the interplay between charge order and superconductivity at a QCP is not fully understood. Here, we present resistance measurements proving that a dome of superconductivity surrounds the charge-density-wave (CDW) QCP in pristine samples of 1$T$-TiSe$_2$ tuned with hydrostatic pressure. Furthermore, we use quantum oscillation measurements to show that the superconductivity sets in at a Lifshitz transition in the electronic band structure. We use density functional theory to identify the Fermi pockets enabling superconductivity: large electron and hole pockets connected by the CDW wave vector $\vec{Q}$ which emerge upon partial suppression of the zero-pressure CDW gap. Hence, we conclude that superconductivity is of interband type enabled by the presence of hole and electron bands connected by the CDW $\vec{Q}$ vector. Earlier calculations show that interband interactions are repulsive, which suggests that unconventional s$_{\pm}$ superconductivity is realised in TiSe$_2$ - similar to the iron pnictides. These results highlight the importance of Lifshitz transitions in realising unconventional superconductivity and help understand its interaction with CDW order in numerous materials.
We use a first-principles based self-consistent momentum-resolved density fluctuation (MRDF) model to compute the combined effects of electron-electron and electron-phonon interactions to describe the superconducting dome in the correlated MoS2 thin flake and TiSe2. We find that without including the electron-electron interaction, the electron-phonon coupling and the superconducting transition temperature (Tc) are overestimated in both these materials. However, once the full angular and dynamical fluctuations of the spin and charge density induced quasiparticle self-energy effects are included…
At low temperature TiSe2 undergoes a charge density wave instability. Superconductivity is stabilized either by pressure or by Cu intercalation. We show that the pressure phase diagram of TiSe2 is well described by first-principles calculations. At pressures smaller than 4 GPa charge density wave ordering occurs, in agreement with experiments. At larger pressures the disappearing of the charge density wave is due to a stiffening of the short-range force-constants and not to the variation of nesting with pressure. Finally we show that the behavior of Tc as a function of pressure is entirely det…
Superconductivity (SC) in so-called "unconventional superconductors" is nearly always found in the vicinity of another ordered state, such as antiferromagnetism, charge density wave (CDW), or stripe order. This suggests a fundamental connection between SC and fluctuations in some other order parameter. To better understand this connection, we used high-pressure x-ray scattering to directly study the CDW order in the layered dichalcogenide TiSe2, which was previously shown to exhibit SC when the CDW is suppressed by pressure [1] or intercalation of Cu atoms [2]. We succeeded in suppressing the …
The strong coupling between lattice modes and charges which leads to the formation of charge density waves in materials such as the transition-metal dichalcogenides may also give rise to superconductivity in the same materials, mediated by the same exciton or phonon modes that dominate the charge ordered state. Such a superconducting phase has recently been observed for example in TiSe2, both upon intercalation with Copper and in the pristine material under pressure. Here we investigate the interplay of exciton formation and electron-phonon coupling within a simplified model description. We fi…
Among iron chalcogenide superconductors, FeS can be viewed as a simple, highly compressed relative of FeSe without nematic phase and with weaker electronic correlations. Under pressure, however, the superconductivity of stoichiometric FeS disappears and reappears, forming two domes. We perform electronic structure and spin fluctuation theory calculations for tetragonal FeS in order to analyze the nature of the superconducting order parameter. In the random phase approximation we find a gap function with d-wave symmetry at ambient pressure, in agreement with several reports of a nodal supercond…
The competition between superconductivity and other ground states of solids is one of the challenging topics in condensed matter physics. Apart from high-temperature superconductors [1,2] this interplay also plays a central role in the layered transition-metal dichalcogenides, where superconductivity is stabilized by suppressing charge-density-wave order to zero temperature by intercalation [3] or applied pressure [4-7]. 1T-TiSe$_2$ forms a prime example, featuring superconducting domes on intercalation as well as under applied pressure. Here, we present high energy-resolution inelastic x-ray …
Superconductivity and charge density wave (CDW) appear in the phase diagram of a variety of materials including the high - $T$$_c$ cuprate family and many transition metal dichalcogenides (TMDs). Their interplay may give rise to exotic quantum phenomena. Here, we show that superconducting arrays can spontaneously form in TiSe$_2$ - a TMD with coexisting superconductivity and CDW - after lithium ion intercalation. We induce a superconducting dome in the phase diagram of Li$_x$TiSe$_2$ by using the ionic solid-state gating technique. Around optimal doping, we observe magnetoresistance oscillatio…
Superconductivity emerges in $1T$-TiSe$_2$ when its charge density wave (CDW) order is suppressed by Cu intercalation or pressure. Since the CDW state is thought to be an excitonic insulator, an interesting question is whether the superconductivity is also mediated by the excitonic fluctuations. We investigated this question as to the nature of doping induced superconductivity in Cu$_x$TiSe$_2$ by asking if it is consistent with the phonon-mediated pairing. We employed the {\it ab initio} density functional theory and density functional perturbation theory to compute the electron-phonon coupli…
In a recent publication [Chen et al., Phys. Rev. B 86, 165136 (2012)], we identified a line of Lifshitz transition points separating the Fermi liquid and pseudogap regions in the hole-doped two dimensional Hubbard model. Here we extend the study to further determine the superconducting transition temperature in the phase diagram. By means of large-scale dynamical cluster quantum Monte Carlo simulations, we are able to identify the evolution of the d-wave superconducting dome in the hole-dope side of the phase diagram, with next-nearest-neighbor hopping (t'), chemical potential and temperature …
The interplay between superconductivity and Eu$ ^{2+}$ magnetic moments in EuFe$_2$(As$_{1-x}$P$_x$)$_2$ is studied by electrical resistivity measurements under hydrostatic pressure on $x=0.13$ and $x=0.18$ single crystals. We can map hydrostatic pressure to chemical pressure $x$ and show, that superconductivity is confined to a very narrow range $0.18\leq x \leq 0.23$ in the phase diagram, beyond which ferromagnetic (FM) Eu ordering suppresses superconductivity. The change from antiferro- to FM Eu ordering at the latter concentration coincides with a Lifshitz transition and the complete depre…
The rise and fall of the superconducting transition temperature $T_c$ upon tuning carrier density or external parameters, such as pressure or magnetic field, is ubiquitously observed in a wide range of quantum materials. In order to investigate such domes of $T_c$, we go beyond the prototypical attractive Hubbard model, and consider a lattice model of electrons coupled via instantaneous, spatially extended, attractive interactions. By numerically solving the mean-field equations, as well as going beyond mean field theory using a functional renormalization group approach, we find that for a cha…
The electronic-structural modulations of Ir$_{1-x}$Pt$_x$Te$_2$ (0 $\leqq x\leqq$ 0.12) have been examined by resonant elastic x-ray scattering (REXS) and resonant inelastic x-ray scattering (RIXS) techniques at both the Ir and Te edges. Charge-density-wave-like superstructure with wave vectors of $\mathbf{Q}$=(1/5 0 $-$1/5), (1/8 0 $-$1/8), and (1/6 0 $-$1/6) are observed on the same sample of IrTe$_2$ at the lowest temperature, the patterns of which are controlled by the cooling speeds. In contrast, superstructures around $\mathbf{Q}$=(1/5 0 $-$1/5) are observed for doped samples (0.02 $\leq…
The maximum critical temperature for superconductivity in pressurized hydrides appears at the top of superconducting domes in Tc versus pressure curves at a particular pressure, which is not predicted by standard superconductivity theories. The a high-order anisotropic van Hove singularity near the Fermi level observed in band structure calculations of pressurized sulfur hydride, typical of a supermetal, has been associated with the array of metallic hydrogen wires modules forming a nanoscale heterostructure at atomic limit called superstripes phase. Here we propose that pressurized sulfur hyd…
While it is known that a resonant amplification of Tc in two-gap superconductors can be driven by using the Fano-Feshbach resonance tuning the chemical potential near a Lifshitz transition, little is known on tuning the Tc resonance by cooperative interplay of the Rashba spin-orbit coupling (RSOC) joint with phonon mediated (e-ph) pairing at selected k-space spots. Here we present first-principles quantum calculation of superconductivity in an artificial heterostructure of metallic quantum wells with 3 nm period where quantum size effects give two-gap superconductivity with RSOC controlled by …
We report the characterization of the misfit compound (Pb1-xSnxSe2)1.16(TiSe2)2, in which a [100] rocksalt bilayer of Pb1-xSnxSe, which is a topological crystalline insulator in bulk form, alternates with a double layer of the normally non-superconducting layered transition metal dichalcogenide TiSe2. The x dependence of Tc displays a weak dome-like shape with a maximum Tc of 4.5 K at x = 0.2; there is only a subtle change in Tc corresponding to the expected trivial to topological transition in the Pb1-xSnxSe bi-layer. We present a more detailed characterization of the superconductor at x = 0.…
How the macroscopic quantum coherence can resist to the decoherence attacks of high temperature is a major challenge for the science of the 21st century. Superstripes 2017 conference held in Ischia on June 2017 has been focused on the new physics of high $T_c$ superconductors made of complex quantum matter. Today the standard model of high $T_c$ superconductivity which grabs the physics of complex quantum matter is the multi-band Hubbard model where the dome of $T_c$ occurs by driving the chemical potential in the proximity of a topological Lifshitz transition. The multi-gap superconductivity …
In the iron-based superconductors, understanding the relation between superconductivity and electronic structure upon doping is crucial for exploring the pairing mechanism. Recently it was found that in iron selenide (FeSe), enhanced superconductivity (Tc over 40K) can be achieved via electron doping, with the Fermi surface only comprising M-centered electron pockets. Here by utilizing surface potassium dosing, scanning tunneling microscopy/spectroscopy (STM/STS) and angle-resolved photoemission spectroscopy (ARPES), we studied the electronic structure and superconductivity of (Li0.8Fe0.2OH)Fe…
Combining electronic Raman scattering experiments with cellular dynamical mean field theory, we present evidence of the pseudogap in the superconducting state of various hole-doped cuprates. In Bi2Sr2CaCu2O8+d we track the superconducting pseudogap hallmark, a peak-dip feature, as a function of temperature T and doping p, well beyond the optimal one. We show that, at all temperatures under the superconducting dome, the pseudogap disappears at the doping pc, between 0.222 and 0.226, where also the normal-state pseudogap collapses at a Lifshitz transition. This demonstrates that the superconduct…
We analyze the two-orbital (with $d_{x^2-y^2}$ and $d_{3z^2-r^2}$ orbitals) analogue of the $t$-$J$-$U$ model as applied to the description of the copper-oxide monolayer deposited on the Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ substrate (CuO$_2$/BSCCO). We show, that an $extended$ $s$-$wave$ superconducting dome appears in the heavily hole overdoped regime of the model, with dominant contribution to the pairing coming from the $d_{3z^2-r^2}$ orbitals. Also, the lower critical doping for the appearance of the SC state concurs with the Lifshitz Transition after which the hole-like Fermi pockets are create…
In high-temperature cuprate superconductors, the anti-ferromagnetic spin fluctuations are thought to have a very important role in naturally producing an attractive interaction between the electrons in the $d$-wave channel. The connection between superconductivity and spin fluctuations is expected to be especially consequential at the overdoped end point of the superconducting dome. In some materials, that point seems to coincide with a Lifshitz transition, where the Fermi surface changes from the hole-like centered at ($π, π$) to the electron-like, centered at the $Γ$ point causing a loss of …
FeSe is a unique high-$T_c$ iron-based superconductor in which nematicity, superconductivity, and magnetism are entangled with each other in the $P$-$T$ phase diagram. We performed $^{77}$Se-nuclear magnetic resonance measurements under pressures of up to 3.9 GPa on 12% S-substituted FeSe, in which the complex overlap between the nematicity and magnetism are resolved. A pressure-induced Lifshitz transition was observed at 1.0 GPa as an anomaly of the density of states and as double superconducting (SC) domes accompanied by different types of antiferromagnetic (AF) fluctuations. The low-$T_{\rm…
The nematic electronic state and its associated nematic critical fluctuations have emerged as potential candidates for superconducting pairing in various unconventional superconductors. However, in most materials their coexistence with other magnetically-ordered phases poses significant challenges in establishing their importance. Here, by combining chemical and hydrostatic physical pressure in FeSe$_{0.89}$S$_{0.11}$, we provide a unique access to a clean nematic quantum phase transition in the absence of a long-range magnetic order. We find that in the proximity of the nematic phase transiti…
Emergence of Double-Dome Superconductivity in the Pressurized Dirac Semimetal BaMg2Bi2
State Key Laboratory of Quantum Functional Materials, School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院量子功能材料国家重点实验室）；ShanghaiTech Laboratory for Topological Physics, ShanghaiTech University（上海科技大学拓扑物理实验室）；Anhui Provincial Key Laboratory of Magnetic Functional Materials and Devices, Institutes of Physical Science and Information Technology, Anhui University（安徽大学物质科学与信息技术研究院安徽省磁性功能材料与器件重点实验室）；Shanghai Key Laboratory of High-resolution Electron Microscopy, ShanghaiTech University（上海科技大学高分辨电子显微镜上海市重点实验室）
Recently room temperature superconductivity with Tc=15 degrees Celsius has been discovered in a pressurized complex ternary hydride, CSHx, which is a carbon doped H3S alloy. The nanoscale structure of H3S is a particular realization of the 1993 patent claim of superlattice of quantum wires for room temperature superconductors where the maximum Tc occurs at the top of a superconducting dome. Here we focus on the electronic structure of materials showing nanoscale heterostructures at atomic limit made of a superlattice of quantum wires like hole doped cuprate perovskites, organics, A15 intermeta…
In general, magnetism and superconductivity are antagonistic to each other. However, there are several families of superconductors, in which superconductivity may coexist with magnetism, and only a few examples are known, when superconductivity itself induces spontaneous magnetism. The most known compounds are Sr$_2$RuO$_4$ and some noncentrosymmetric superconductors. Here, we report the finding of a narrow dome of a novel $s+is'$ superconducting (SC) phase with broken time-reversal symmetry (BTRS) inside the broad $s$-wave SC region of the centrosymmetric multiband superconductor Ba$_{\rm 1-x…
We performed $^{77}$Se-NMR measurements on FeSe$_{1-x}$S$_x$, ($x$ = 0.12) up to 3.0 GPa at an applied magnetic field of 6.02 T, and found that the superconducting (SC) phase exhibits a remarkable double-dome structure in the pressure($P$)-temperature($T$) phase diagram which is hidden at 0 T. From the relaxation rate $1/T_1$ divided by $T$, $1/T_1T$, a Lifshitz transition may occur at 1.0 GPa, and the dominant nesting vector could change due to topological changes in Fermi surfaces. In other words, two types of antiferromagnetic (AFM) fluctuations would exist in the $P-T$ phase diagram. We co…
A first-order-like resistivity hysteresis is induced by a subtle structural transition under hydrostatic pressure in the topological nodal-line superconductor PbTaSe$_2$. This structure transition is quickly suppressed to zero at pressure $\sim$0.25 GPa. As a result, superconductivity shows a marked suppression, accompanied with fundamental changes in the magnetoresistance and Hall resistivity, suggesting a Lifshitz transition around $\sim$0.25 GPa. The first principles calculations show that the spin-orbit interactions partially gap out the Dirac nodal line around $K$ point in the Brillouin z…
The two-dimensional electron gas at the interface between LaAlO$_3$ and SrTiO$_3$ (LAO/STO) exhibits gate tunable superconductivity with a characteristic dome-like shape of the critical temperature ($T_c$) in the phase diagram. As shown recently [Phys. Rev. B 102, 085420 (2020)], such an effect can be explained as a consequence of the extended $s-$wave symmetry of the gap within an intersite real space pairing scenario, leading to a good agreement between the experiment and theory. In this work, we turn to a detailed analysis of the influence of spin-orbit coupling on the LAO/STO phase diagram…
The phase diagram of a correlated material is the result of a complex interplay between several degrees of freedom, providing a map of the material's behavior. One can understand (and ultimately control) the material's ground state by associating features and regions of the phase diagram, with specific physical events or underlying quantum mechanical properties. The phase diagram of the newly discovered iron arsenic high temperature superconductors is particularly rich and interesting. In the AE(Fe1-xTx)2As2 class (AE being Ca, Sr, Ba, T being transition metals), the simultaneous structural/ma…
Quasi-two-dimensional kagome metals AV3Sb5 (A = K, Rb, and Cs) have attracted much recent interest due to exotic quantum phenomena such as unconventional superconductivity, topological charge order and giant anomalous Hall effect. Here we report pressure-induced reemergent superconductivity in CsV3Sb5 by electrical transport measurements under high pressures up to 47.9 GPa. We show that the superconducting critical temperature Tc is first enhanced by pressure and reaches its first maximum ~ 8.9 K at 0.8 GPa, then the Tc is suppressed by pressure and cannot be detected above 7.5 GPa, forming a …
Upper critical magnetic field and multiband superconductivity in artificial high-Tc superlattices of nano quantum wells
Institute of Crystallography, National Research Council, CNR（意大利国家研究委员会晶体学研究所）；Rome International Center for Materials Science Superstripes RICMASS（罗马超带材料科学国际中心）；Department of Industrial, Electronic and Mechanical Engineering, Roma Tre University（罗马第三大学工业、电子与机械工程系）；Istituto Nazionale di Fisica Nucleare INFN, Sezione Roma Tre（意大利国家核物理研究所罗马三分部）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）；National High Magnetic Field Laboratory, (NHMFL) Los Alamos National Laboratory (LANL)（洛斯阿拉莫斯国家实验室国家高磁场实验室）；National High Magnetic Field Laboratory (NHMFL), Florida State University (FSU)（佛罗里达州立大学国家高磁场实验室）；Istituto di Ingegneria e Fisica dei Materiali, Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino（都灵理工学院应用科学与技术学院材料与物理工程研究所）；School of Science and Technology, Physics Division, University of Camerino（卡梅里诺大学理学院物理系）；Istituto Nazionale di Fisica Nucleare, Sezione di Perugia（意大利国家核物理研究所佩鲁加分部）；School of Pharmacy, Physics Unit, University of Camerino（卡梅里诺大学药学院物理组）；Institute for Microelectronics and Microsystems, National Reesearch Council CNR（意大利国家研究委员会微电子与微系统研究所）
