Session V31: Superconductivity and Correlated States in 2D Materials III

Superconductivity of 2D materials with metal intercalation

In this report, the electronic structure and lattice dynamics of 2D materials with monolayer metal intercalated have been calculated via first-principles density functional theory and density functional perturbation theory. According to the electron-phonon interaction, it is predicted that these 2D materials can be transformed from semiconductors to superconductors by metal intercalation. More interestingly, the biaxial tensile strain can significantly enhance the superconducting temperature up to about 10 K in Na-intercalated MoS$_2$, and we also predicted above 20 K superconductivity in blue phosphorus bilayer. In addition, the phonon mean free path at room temperature is also greatly improved in Na-intercalated MoSe$_2$, which is advantageous for related applications.   

Strong coupling charge-density waves in doped transition metal dichalcogenides

We present a theoretical study on a phase transition from quantum spin Hall insulating phase to strong coupling charge density wave (CDW) in adatom-doped single layer transition metal dichalcogenides (TMDs) 1T$'-M$Te$_2$ ($M$ = Mo and W) using first-principles calculation methods. It is shown that when 1T$'$ phase TMDs are doped by alkali metals or hydrogen atom, their Fermi surface shows quasi-one-dimensional features and phonon dispersion at the corresponding nesting vectors becomes unstable, turning 1T$'$ structure to diamond-shape (DS) chain phase with a substantial energy gap. The resulting CDW phase is compatible with a ground state of ReS$_2$ and ReSe$_2$. To unveil the origin of CDW phase transition, we calculate the electronic non-interacting susceptibility and electron-phonon coupling strength as a function of doping concentration and then find out that origin of phase transition is the strong electron-phonon coupling of the doped TMDs.   

Negative Compressibility and External Electric Field Induce Charge Density Waves in Two-Dimensional Materials.

In the last few decades, experimental observations of negative compressibility in two-dimensional materials have been successfully realized in the form of a correction to the classical capacitance[1], electron transport in MoS$_2$[2] and angle-resolved photoemissions in WSe$_2$[3]. However, the possible applications of negative compressibility have not been explored fully. Here we demonstrate that in a low density, two-dimensional material, the presence of negative compressibility along with an applied electric field can induce charge density waves throughout the length of the material. This stands in contrast to the classical case where charge accumulates only on two opposite edges of the material. These results can be further exploited by changing the strength of the applied field and screening length of the material, which alters the amplitude and wavelength of the charge density waves respectively. REFERENCES: [1] Eisenstein, J. P., Pfeiffer, L. N., & West, K. W. Physical review letters, 68(5), 674. (1992) [2] Larentis, S., Tolsma, J. R., Fallahazad, B., Dillen, D. C., Kim, K., MacDonald, A. H., & Tutuc, E. Nano letters, 14(4), 2039-2045. (2014). [3] Riley, J. M., et al. Nature nanotechnology, 10(12), 1043-1047. (2015).   

Tuneable highly-correlated phases in two-dimensional superconductors

Research on two-dimensional (2D) crystals, triggered by the discovery of graphene, is now expanding towards more complex strongly-correlated materials like superconductors, Mott insulators, and antiferromagnets. The ability to access different many-body phases by electrostatic gating and to finely tune to critical transition regions of the phase diagram, offers an exciting platform for studying strongly-correlated materials. Recently we demonstrated the electrostatic tuning of atomically thin TiSe$_{\mathrm{2}}$ across charge density wave order and superconductivity [1]. Here I will also discuss the extension of such experiments to ultrathin layers of high-temperature cuprate superconductors that could help shed more light on the rich phase diagram and pairing mechanism. We studied the 2D phases and gate-tunability of exfoliated few-layers samples. We found that they exhibit a zero-resistance state, which is different from the Meissener superconductivity of the bulk, and is highly sensitive to external magnetic fields. [1] Controlling many-body states by the electric field effect in a two-dimensional material; \newline Li, L. J., O'Farrell, E. C. T., Loh, K. P., Eda, G., \"{O}zyilmaz, B., and Castro Neto, A. H., Nature 529, 185--189 (Jan 2016)   

Studies of Charge Density Waves in Reduced Dimensions by Surface X-Ray Scattering

TiSe$_{\mathrm{2}}$, a prototypical CDW system with a 1T structure in the bulk, undergoes a simple (2x2x2) CDW transition at around 205 K in connection with the softening of a phonon mode at the zone boundary. This transition is marked by substantial changes in the transport properties. Although this material has been studied extensively, the underlying physical mechanism for the structural distortion is still under debate. Ultrathin films, including a single molecular layer, of TiSe$_{\mathrm{2}}$ provide an excellent test ground for systematic tuning of the electronic interactions through dimensional control; the results will be relevant to a basic understanding of the mechanism of the CDW transition ranging from 2D to 3D. We have successfully grown, in situ, high quality single- and multi-layer films of TiSe$_{\mathrm{2}}$ on a bilayer-graphene-terminated SiC surface via MBE. Surface x-ray diffraction shows that single-layer TiSe$_{\mathrm{2}}$ exhibits a (2x2) CDW transition with a transition temperature of $T_{C}=$234 K, which is substantially higher than the bulk $T_{C}=$205 K. The CDW peak intensity follows closely a BCS mean-field behavior.   

Doping dependence of an excitonic-driven CDW phase in 1T-TiSe2

The origin of the robust charge density wave (CDW) phase in this system has been a perennial source of new ideas, concepts, and controversy. A foremost and recurring question has been whether the CDW instability is primarily driven by electron-electron or electron-phonon interactions. Whereas it is clear that both ultimately play an important role in its overall electronic, lattice, and transport properties, the very low carrier density and particular CDW wavevector of this system has led to the suggestion that electron-electron interactions can be the dominant factor driving the CDW instability through a transition to an excitonic insulator state. By gathering the latest quantitative information about the bandstructure parameters from ARPES and performing a self-consistent Hartree-Fock calculation as a function of doping and temperature, we demonstrate that electron-electron interactions alone can explain very well the variation of Tc with electron doping seen in recent experiments up to densities where the superconducting dome emerges. In addition, the renormalized bandstructure predicted by our model provides a consistent interpretation for the development of partial gaps and the changes in the nature of charge carriers that are known, experimentally, to take place near Tc.   

Dimensional effects on the charge density waves in ultrathin films of TiSe$_{\mathrm{2}}$

Charge density wave (CDW) formation in solids is a critical phenomenon involving the collective reorganization of the electrons and atoms in the system into a wave structure, and it is expected to be sensitive to the geometric constraint of the system at the nanoscale. Here, we study the CDW transition in TiSe$_{\mathrm{2}}$, a quasi-two-dimensional layered material, to determine the effects of quantum confinement and changing dimensions in films ranging from a single layer to multilayers. Of key interest is the characteristic length scale for the transformation from a two-dimensional case to the three-dimensional limit. Angle-resolved photoemission spectroscopy (ARPES) measurements of films with thicknesses up to six layers reveal substantial variations in the energy structure of discrete quantum well states; however, the temperature-dependent band gap renormalization converges at just three layers. The results indicate a layer-dependent mixture of two transition temperatures and a very-short-range CDW interaction within a three-dimensional framework.   

Collective modes in Cu$_x$TiSe$_2$ measured with meV-resolution EELS

The charge density wave (CDW) in 1$T$-TiSe$_2$ has been widely thought to be the result of an excitonic insulator transition. We recently observed a soft electronic mode in TiSe$_2$ using a new, momentum-resolved electron energy loss spectroscopy (M-EELS) technique, demonstrating a condensation of electron-hole pairs in this material. As TiSe$_2$ is doped with Cu to produce Cu$_x$TiSe$_2$, a superconducting dome emerges above $x \sim$ 0.04. In this talk, I describe how the electronic collective mode evolves with Cu doping. We find that the temperature dependence of the electronic mode reverses as Cu is introduced and that the mode is much broader at low temperature as compared to the undoped material. Additionally, the electronic mode no longer has a positive dispersion at 300 K as described by the Lindhard function, but has a slightly negative dispersion for small momentum transfers. We will discuss the implications of these results for the excitonic insulator transition in TiSe$_2$.   

Ultrafast Dynamics of Correlated Electronic States in Layered Cu$_x$TiSe$_2$

We investigate the transient optical response of electronic states in Cu$_x$TiSe$_2$ as a function of temperature and Cu doping from x=0 (semimetal and commensurate charge density wave phases) to x=0.08 (metallic and superconducting phases). We find that the cooperative driving mechanisms for the CDW, the excitonic insulator mechanism and the soft L$_1$$^-$ phonon mode, decouple at x=0.04, where fluctuations of a quantum critical point were observed in the folded Se-4p band. We also demonstrate a loss of coherence in the A$_{1g}$ phonon signal with increased Cu intercalation of the parent lattice, indicating a loss of long-range lattice order. These findings provide compelling evidence that TiSe$_2$ undergoes a quantum phase transition upon Cu intercalation from a state of commensurate charge order without superconductivity to a state with a different symmetry in which new charge order coexists with the superconducting phase.   

Observation of a Charge Density Wave Incommensuration Near the Superconducting Dome in Cu$_{\mathrm{x}}$TiSe$_{\mathrm{2}}$

X-ray diffraction was employed to study the evolution of the charge density wave (CDW) in Cu$_{\mathrm{x}}$TiSe$_{\mathrm{2}}$ as a function of copper intercalation in order to clarify the relationship between the CDW and superconductivity. The results show a CDW incommensuration arising at an intercalation value coincident with the onset of superconductivity at around x$=$0.055(5). Additionally, it was found that the charge density wave persists to higher intercalant concentrations than previously assumed, demonstrating that the CDW does not terminate inside the superconducting dome. A charge density wave peak was observed in samples up to x$=$0.091(6), the highest copper concentration examined in this study. The phase diagram established in this work suggests that charge density wave incommensuration may play a role in the formation of the superconducting state.   

Exciton condensation in 1$T$-TiSe$_2$ observed with meV-resolved electron energy-loss spectroscopy

The lowest excited state of an insulator is an electron-hole bound state, i.e., an exciton. In the 1960 it was predicted that, if the exciton binding energy of a material were larger than its band gap, excitons would have negative energy and spontaneously proliferate, creating a macroscopic condensate of electron-hole pairs called an ``excitonic insulator." Despite 50 years of searching, explicit evidence for condensation of excitons in a sold has never been achieved. Here, we apply a new, meV resolution, momentum resolved electron energy loss spectroscopy (M--EELS) technique to the transition metal dichalcogenide 1T‐-TiSe$_2$. We find that, near $T_C$ = 190 K, this material exhibits a soft electronic collective mode that disperses to zero energy, indicating condensation of electron-hole pairs with finite center-of-mass momentum. This excitation hardens at low temperature into an amplitude mode of an condensate coupled to the crystal lattice. Our study represents the first explicit evidence for the condensation of excitons in any material.   

Plasmonic Superconductivity in Layered Materials

Due to a lack of screening in two dimensions the Coulomb interaction is generally enhanced and consequently plays a major role to understand many-body effects within layered materials. In the field of superconductivity it is usually introduced as an approximate, static, and adjustable parameter $\mu^*$ which describes only effectively the Coulomb repulsion which is therefore responsible for reduced transition temperatures. Here, we overcome this inadequate handling and present an \emph{ab initio} based material-realistic Coulomb description for doped single layers of MoS$_2$ which captures simultaneously material-intrinsic, substrate, and dynamical screening processes. Using this model we can reliably describe the resulting plasmonic excitations including both, their coupling to the electrons and their dependence on the environmental screening and doping level. Utilizing Eliashberg theory we show that the low-energy plasmonic modes originating from the dynamically screened Coulomb \emph{repulsion} can actually lead to an effective Coulomb \emph{attraction} and thus to an enhanced transition temperature (T$_c$). Furthermore, we find an optimal ratio between the substrate screening and the electron doping which maximizes T$_c$ of the induced plasmonic superconducting state.   

Superconductivity and chiral superconducting transport in WS2 nanotube

We will report the first observation of superconductivity in individual nanotube of tungsten disulfide realized by electrochemical doping. We will also report the exotic nonreciprocity in superconducting transport originating from tube chirality, in which the forward and backward supercurrent flows are inequivalent due to inversion symmetry breaking. The nonreciprocal signal is significantly enhanced at low temperature reflecting the coherence of superconducting state, and simultaneously displays the periodic quantum oscillations associated with the Little-Parks effect. The present results indicate that the nonreciprocity should be a new approach toward the superconductors with chiral or noncentrosymmetric structures.