Electronic Structure of Few-Layer Black Phosphorus from µ-ARPES.

Black phosphorus (BP) stands out among two-dimensional (2D) semiconductors because of its high mobility and thickness dependent direct band gap. However, the quasiparticle band structure of ultrathin BP has remained inaccessible to experiment thus far. Here we use a recently developed laser-based microfocus angle resolved photoemission (µ-ARPES) system to establish the electronic structure of 2-9 layer BP from experiment. Our measurements unveil ladders of anisotropic, quantized subbands at energies that deviate from the scaling observed in conventional semiconductor quantum wells. We quantify the anisotropy of the effective masses and determine universal tight-binding parameters, which provide an accurate description of the electronic structure for all thicknesses.

Band Filling and Cross Quantum Capacitance in Ion-Gated Semiconducting Transition Metal Dichalcogenide Monolayers.

Ionic liquid gated field-effect transistors (FETs) based on semiconducting transition metal dichalcogenides (TMDs) are used to study a rich variety of extremely interesting physical phenomena, but important aspects of how charge carriers are accumulated in these systems are not understood. We address these issues by means of a systematic experimental study of transport in monolayer MoSe2 and WSe2 as a function of magnetic field and gate voltage, exploring accumulated densities of carriers ranging from approximately 1014 cm-2 holes in the valence band to 4 × 1014 cm-2 electrons in the conduction band. We identify the conditions when the chemical potential enters different valleys in the monolayer band structure (the K and Q valley in the conduction band and the two spin-split K-valleys in the valence band) and find that an independent electron picture describes the occupation of states well. Unexpectedly, however, the experiments show very large changes in the device capacitance when multiple valleys are occupied that are not at all compatible with the commonly expected quantum capacitance contribution of these systems, CQ = e2/ (dµ/dn). A theoretical analysis of all terms responsible for the total capacitance shows that under general conditions a term is present besides the usual quantum capacitance, which becomes important for very small distances between the capacitor plates. This term, which we call cross quantum capacitance, originates from screening of the electric field generated by charges on one plate from charges sitting on the other plate. The effect is negligible in normal capacitors but large in ionic liquid FETs because of the atomic proximity between the ions in the gate and the accumulated charges on the TMD, and it accounts for all our experimental observations. Our findings therefore reveal an important contribution to the capacitance of physical systems that had been virtually entirely neglected until now.

Observation of Caroli-de Gennes-Matricon Vortex States in YBa_{2}Cu_{3}O_{7-δ}.

The copper oxides present the highest superconducting temperature and properties at odds with other compounds, suggestive of a fundamentally different superconductivity. In particular, the Abrikosov vortices fail to exhibit localized states expected and observed in all clean superconductors. We have explored the possibility that the elusive vortex-core signatures are actually present but weak. Combining local tunneling measurements with large-scale theoretical modeling, we positively identify the vortex states in YBa_{2}Cu_{3}O_{7-δ}. We explain their spectrum and the observed variations thereof from one vortex to the next by considering the effects of nearby vortices and disorder in the vortex lattice. We argue that the superconductivity of copper oxides is conventional, but the spectroscopic signature does not look so because the superconducting carriers are a minority.

Spectroscopic evidence for Fermi liquid-like energy and temperature dependence of the relaxation rate in the pseudogap phase of the cuprates.

Cuprate high-Tc superconductors exhibit enigmatic behavior in the nonsuperconducting state. For carrier concentrations near "optimal doping" (with respect to the highest Tcs) the transport and spectroscopic properties are unlike those of a Landau-Fermi liquid. On the Mott-insulating side of the optimal carrier concentration, which corresponds to underdoping, a pseudogap removes quasi-particle spectral weight from parts of the Fermi surface and causes a breakup of the Fermi surface into disconnected nodal and antinodal sectors. Here, we show that the near-nodal excitations of underdoped cuprates obey Fermi liquid behavior. The lifetime τ(ω, T) of a quasi-particle depends on its energy ω as well as on the temperature T. For a Fermi liquid, 1/τ(ω, T) is expected to collapse on a universal function proportional to (ℏω)(2) + (pπk(B)T)(2). Magneto-transport experiments, which probe the properties in the limit ω = 0, have provided indications for the presence of a T(2) dependence of the dc (ω = 0) resistivity of different cuprate materials. However, Fermi liquid behavior is very much about the energy dependence of the lifetime, and this can only be addressed by spectroscopic techniques. Our optical experiments confirm the aforementioned universal ω- and T dependence of 1/τ(ω, T), with p ∼ 1.5. Our data thus provide a piece of evidence in favor of a Fermi liquid-like scenario of the pseudogap phase of the cuprates.

Direct Probing of a Large Spin-Orbit Coupling in the FeSe Superconducting Monolayer on STO.

Spin-orbit coupling (SOC) is a fundamental physical interaction, which describes how the electrons' spin couples to their orbital motion. It is the source of a vast variety of fascinating phenomena in nanostructures. Although in most theoretical descriptions of high-temperature superconductivity SOC has been neglected, including this interaction can, in principle, revise the microscopic picture. Here by preforming energy-, momentum-, and spin-resolved spectroscopy experiments we demonstrate that while probing the dynamic charge response of the FeSe monolayer on strontium titanate, a prototype two-dimensional high-temperature superconductor using electrons, the scattering cross-section is spin dependent. We unravel the origin of the observed phenomenon and show that SOC in this two-dimensional superconductor is strong. We anticipate that such a strong SOC can have several consequences on the electronic structures and may compete with other pairing scenarios and be crucial for the mechanism of superconductivity.

Reconciling scaling of the optical conductivity of cuprate superconductors with Planckian resistivity and specific heat.

Materials tuned to a quantum critical point display universal scaling properties as a function of temperature T and frequency ω. A long-standing puzzle regarding cuprate superconductors has been the observed power-law dependence of optical conductivity with an exponent smaller than one, in contrast to T-linear dependence of the resistivity and ω-linear dependence of the optical scattering rate. Here, we present and analyze resistivity and optical conductivity of La2-xSrxCuO4 with x = 0.24. We demonstrate ℏω/kBT scaling of the optical data over a wide range of frequency and temperature, T-linear resistivity, and optical effective mass proportional to [Formula: see text] corroborating previous specific heat experiments. We show that a T, ω-linear scaling Ansatz for the inelastic scattering rate leads to a unified theoretical description of the experimental data, including the power-law of the optical conductivity. This theoretical framework provides new opportunities for describing the unique properties of quantum critical matter.

Revisiting the vortex-core tunnelling spectroscopy in YBa2Cu3O7-δ.

The observation by scanning tunnelling spectroscopy of Abrikosov vortex cores in the high-temperature superconductor YBa2Cu3O7-δ (Y123) has revealed a robust pair of electron-hole symmetric states at finite subgap energy. Their interpretation remains an open question because theory predicts a different signature in the vortex cores, characterized by a strong zero-bias conductance peak. Here, we present scanning tunnelling spectroscopy data on very homogeneous Y123 at 0.4 K revealing that the subgap features do not belong to vortices: they are actually observed everywhere along the surface with high spatial and energy reproducibility, even in the absence of magnetic field. Detailed analysis and modelling show that these states remain unpaired in the superconducting phase and belong to an incoherent channel, which contributes to the tunnelling signal in parallel with the superconducting density of states.

Preeminent role of the van Hove singularity in the strong-coupling analysis of scanning tunneling spectroscopy for two-dimensional cuprate superconductors.

In two dimensions the noninteracting density of states displays a van Hove singularity (VHS) which introduces an intrinsic electron-hole asymmetry, absent in three dimensions. We show that due to this VHS the strong-coupling analysis of tunneling spectra in high-Tc superconductors must be reconsidered. Based on a microscopic model which reproduces the experimental data with excellent accuracy, we elucidate the peculiar role played by the VHS in shaping the tunneling spectra, and show that more conventional analysis of strong-coupling effects can lead to severe errors.