Non-fermi-liquid behavior in quasi-one-dimensional Li0.9Mo6O17

Reformation of La0.7Sr0.3MnO3 properties by using ZnO in La0.7Sr0.3MnO3-ZnO heterostructures grown on (001) oriented Si

Study of the available density of states (DOS) close-to-zero bias for conduction in strongly correlated electron systems, such as half-metallic La0.7Sr0.3MnO3 (LSMO) and its heterostructures, is important for fundamental and application reasons. As the DOS is proportional to the differential conductance (dI/dV), the dI/dV of a 120 Å LSMO film and its reformation in LSMO/ZnO heterostructures was investigated for different ZnO thicknesses. Unlike in conventional metals, the dI/dV of LSMO exhibits a power-law dependent zero-bias anomaly, i.e., dI/dV ∝ Vm (m ∼ 1) near zero bias in the ferromagnetic metallic state at 10 K. The growth of ZnO on LSMO reforms the linear dI/dVvs. V of LSMO near zero bias to non-linear. The exponent 'm' becomes ∼0.5 for a higher ZnO thickness, revealing increased electron-electron interactions and suppression of Kondo-like, double and superexchange interactions, which are responsible for the depression of the DOS of LSMO near zero bias. In a magnetically disordered state, i.e., around the Curie temperature, ZnO reforms the linear V-shaped dI/dV vs. V of LSMO to parabolic U-shaped dI/dVvs.V and controls the electron concentrations in the t2g-orbitals of Mn realized from the DOS simulations. Additionally, ZnO introduces a peak in the dI/dV vs. V due to Fowler-Nordheim tunnelling, and the peak voltage can be tuned by varying the ZnO thickness or temperature from 300 K to 360 K. Such functions of ZnO yield major perspectives for novel applications in thin-film-based devices.

Emergent symmetry in a low-dimensional superconductor on the edge of Mottness

Upon cooling, condensed-matter systems typically transition into states of lower symmetry. The converse-i.e., the emergence of higher symmetry at lower temperatures-is extremely rare. In this work, we show how an unusually isotropic magnetoresistance in the highly anisotropic, one-dimensional conductor Li0.9Mo6O17 and its temperature dependence can be interpreted as a renormalization group (RG) flow toward a so-called separatrix. This approach is equivalent to an emergent symmetry in the system. The existence of two distinct ground states, Mott insulator and superconductor, can then be traced back to two opposing RG trajectories. By establishing a direct link between quantum field theory and an experimentally measurable quantity, we uncover a path through which emergent symmetry might be identified in other candidate materials.

Precise Tuning of Band Structures and Electron Correlations by van der Waals Stacking of One-dimensional W6Te6 Wires

Stacking of two-dimensional (2D) van der Waals (vdW) atomic sheets has been established as a powerful approach to fabricating new materials with broad versatilities and emergent functionalities. Here we demonstrate a bottom-up approach to fabricating isolated single W₆Te₆ wires and their lateral assemblies, offering a unique platform for investigating the elegant role of vdW coupling in 1D systems with atomic precision. We find experimentally and theoretically a single W₆Te₆ wire is a 1D semiconductor with a band gap of ∼60 meV, and a semiconductor-to-metal transition takes place upon interwire vdW stacking. The metallic multiwires exhibit strong Tomonaga-Luttinger liquid characteristics with the correlation parameter g varying from g = 0.086 for biwire to g = 0.136 for six-wire assemblies, all much reduced from the Fermi liquid regime (g = 1). The present study demonstrates wire-by-wire vdW stacking is a versatile means for fabrication of 1D systems with tunable electronic properties.

Charge Density Modulation and the Luttinger Liquid State in MoSe2 Mirror Twin Boundaries

A mirror twin-domain boundary (MTB) in monolayer MoSe₂ represents a (quasi) one-dimensional metallic system. Its electronic properties, particularly the low-energy excitations in the so-called 4|4P-type MTB, have drawn considerable research attention. Reports of quantum well states, charge density waves, and the Tomonaga-Luttinger liquid (TLL) have all been made. Here, by controlling the lengths of the MTBs and employing different substrates, we reveal by low-temperature scanning tunneling microscopy/spectroscopy, Friedel oscillations and quantum confinement effects causing the charge density modulations along the defect. The results are inconsistent with charge density waves. Interestingly, for graphene-supported samples, TLL in the MTBs is suggested, whereas that grown on gold, an ordinary Fermi liquid, is indicated.

Quantum Confined Tomonaga-Luttinger Liquid in Mo6Se6 Nanowires Converted from an Epitaxial MoSe2 Monolayer

Confining interacting particles in one-dimension (1D) changes the electronic behavior of the system fundamentally, which has been studied extensively in the past. Examples of 1D metallic systems include carbon nanotubes, quasi-1D organic conductors, metal chains, and domain boundary defects in monolayer thick transition-metal dichalcogenides such as MoSe₂. Here single and bundles of Mo₆Se₆ nanowires were fabricated through annealing a MoSe₂ monolayer grown by molecular-beam epitaxy on graphene. Conversion from two-dimensional (2D) MoSe₂ film to 1D Mo₆Se₆ nanowire is reversible. Mo₆Se₆ nanowires form preferentially at the Se-terminated zigzag edges of MoSe₂ and stitch to it via two distinct atomic configurations. The Mo₆Se₆ wire is metallic and its length is tunable, which represents one of few 1D systems that exhibit properties pertinent to quantum confined Tomonaga-Luttinger liquid, as evidenced by scanning tunneling microscopic and spectroscopic studies.

Emergence of a real-space symmetry axis in the magnetoresistance of the one-dimensional conductor Li0.9Mo6O17

We report on an emerging symmetry axis in the magnetoresistance of bulk single crystals of quasi-one-dimensional Li_0.9Mo₆O₁₇ below T _min = 25 K, the temperature at which the electrical resistivity experiences a minimum. Detailed angle-dependent magnetoresistance sweeps reveal that this symmetry axis is induced by the development of a negative magnetoresistance, which is suppressed only for magnetic fields oriented along the poles of the MoO₆ octahedra that form the conducting chains. We show that this unusual negative magnetoresistance is consistent with the melting of dark excitons, composed of previously omitted orbitals within the t _2g manifold that order below T _min. The unveiled symmetry axis in directional magnetic fields not only provides evidence for the crystallization of these dark excitons but also sheds new light on the long-standing mystery of the metal-insulator transition in Li_0.9Mo₆O₁₇.

Tunneling into a Finite Luttinger Liquid Coupled to Noisy Capacitive Leads

Tunneling spectroscopy of one-dimensional interacting wires can be profoundly sensitive to the boundary conditions of the wire. Here, we analyze the tunneling spectroscopy of a wire coupled to capacitive metallic leads. Strikingly, with increasing many-body interactions in the wire, the impact of the boundary noise becomes more prominent. This interplay allows for a smooth crossover from standard 1D tunneling signatures into a regime where the tunneling is dominated by the fluctuations at the leads. This regime is characterized by an elevated zero-bias tunneling alongside a universal power-law decay at high energies. Furthermore, local tunneling measurements in this regime show a unique spatial dependence that marks the formation of plasmonic standing waves in the wire. Our result offers a tunable method by which to control the boundary effects and measure the interaction strength (Luttinger parameter) within the wire.

Progress in Cr- and Mn-based superconductors: a key issues review

The presence of magnetic ions was first believed to be detrimental to superconductivity. However, unconventional superconductivity has been widely induced by doping or applying external pressure in magnetic systems such as heavy fermion, cuprate and iron-based superconductors in which magnetic fluctuations are suggested to serve as the pairing glue for Cooper pairs. The discovery of superconductivity in the magnetic compounds CrAs and MnP under high pressures has further expanded this family of superconductors and provided new platforms for investigating the interplay between magnetism and superconductivity. CrAs and MnP represent the first superconductors among the transition metal Cr- and Mn-based compounds in which the electronic states near the Fermi level are dominated by Cr/Mn 3d electrons. Shortly after their discovery, new types of Cr-based quasi-one-dimensional superconductors A₂Cr₃As₃ and ACr₃As₃ (A [Formula: see text] K, Rb, Cs or Na) were discovered at ambient pressure. The close proximity of superconductivity to magnetic instability in these systems suggests that spin fluctuations may play crucial roles in mediating the Cooper pairing. In this article we review the basic physical properties of these novel superconductors and the progress achieved in recent studies.

One dimensional transport in silicon nanowire junction-less field effect transistors

Junction-less nanowire transistors are being investigated to solve short channel effects in future CMOS technology. Here we demonstrate 8 nm diameter silicon nanowire junction-less transistors with metallic doping densities which demonstrate clear 1D electronic transport characteristics. The 1D regime allows excellent gate modulation with near ideal subthreshold slopes, on- to off-current ratios above 10⁸ and high on-currents at room temperature. Universal conductance scaling as a function of voltage and temperature similar to previous reports of Luttinger liquids and Coulomb gap behaviour at low temperatures suggests that many body effects including electron-electron interactions are important in describing the electronic transport. This suggests that modelling of such nanowire devices will require 1D models which include many body interactions to accurately simulate the electronic transport to optimise the technology but also suggest that 1D effects could be used to enhance future transistor performance.

Multiband One-Dimensional Electronic Structure and Spectroscopic Signature of Tomonaga-Luttinger Liquid Behavior in K_{2}Cr_{3}As_{3}

We present angle-resolved photoemission spectroscopy measurements of the quasi-one-dimensional superconductor K_{2}Cr_{3}As_{3}. We find that the Fermi surface contains two Fermi surface sheets, with linearly dispersing bands not displaying any significant band renormalizations. The one-dimensional band dispersions display a suppression of spectral intensity approaching the Fermi level according to a linear power law, over an energy range of ∼200  meV. This is interpreted as a signature of Tomonoga-Luttinger liquid physics, which provides a new perspective on the possibly unconventional superconductivity in this family of compounds.

Coexistence of Two Electronic Nano-Phases on a CH3NH3PbI3-xClx Surface Observed in STM Measurements

Scanning tunneling microscopy is utilized to investigate the local density of states of a CH₃NH₃PbI_3-xCl_x perovskite in cross-sectional geometry. Two electronic phases, 10-20 nm in size, with different electronic properties inside the CH₃NH₃PbI_3-xCl_x perovskite layer are observed by the dI/dV mapping and point spectra. A power law dependence of the dI/dV point spectra is revealed. In addition, the distinct electronic phases are found to have preferential orientations close to the normal direction of the film surface. Density functional theory calculations indicate that the observed electronic phases are associated with local deviation of I/Cl ratio, rather than different orientations of the electric dipole moments in the ferroelectric phases. By comparing the calculated results with experimental data we conclude that phase A (lower contrast in dI/dV mapping at -2.0 V bias) contains a lower I/Cl ratio than that in phase B (higher contrast in dI/dV).

Direct observation of charge state in the quasi-one-dimensional conductor Li0.9Mo6O17

The quasi-one-dimensional conductor Li_0.9Mo₆O₁₇ has been of great interest because of its unusual properties. It has a conducting phase with properties different from a simple Fermi liquid, a poorly understood “insulating” phase as indicated by a metal-“insulator” crossover (a mystery for over 30 years), and a superconducting phase which may involve spin triplet Cooper pairs as a three-dimensional (p-wave) non-conventional superconductor. Recent evidence suggests a density wave (DW) gapping regarding the metal-“insulator” crossover. However, the nature of the DW, such as whether it is due to the change in the charge state or spin state, and its relationship to the dimensional crossover and to the spin triplet superconductivity, remains elusive. Here by performing ⁷Li-/⁹⁵Mo-nuclear magnetic resonance (NMR) spectroscopy, we directly observed the charge state which shows no signature of change in the electric field gradient (nuclear quadrupolar frequency) or in the distribution of it, thus providing direct experimental evidences demonstrating that the long mysterious metal-“insulator” crossover is not due to the charge density wave (CDW) that was thought, and the nature of the DW gapping is not CDW. This discovery opens a parallel path to the study of the electron spin state and its possible connections to other unusual properties.

Investigation of the magnetic dipole field at the atomic scale in quasi-one-dimensional paramagnetic conductor Li0.9Mo6O17

We report magnetic dipole field investigation at the atomic scale in a single crystal of quasi-one-dimensional (Q1D) paramagnetic conductor Li0.9Mo6O17, using a paramagnetic electron model and (7)Li-NMR spectroscopy measurements with an externally applied magnetic field B 0  =  9 T. We find that the magnetic dipole field component ([Formula: see text]) parallel to B 0 at the Li site from the Mo electrons has no lattice axial symmetry; it is small around the middle between the lattice a and c axes in the ac-plane with the minimum at the field orientation angle [Formula: see text], while the [Formula: see text] maximum is at [Formula: see text] when B 0 is applied perpendicular to b ([Formula: see text]), where [Formula: see text] represents the direction of [Formula: see text]. Further estimation indicates that [Formula: see text] has a maximum value of 0.35 G at B 0  =  9 T. By minimizing the potential magnetic contributions to the NMR spectra satellites with the NMR spectroscopy measurements at the direction where the value of the magnetic dipole field component [Formula: see text] is  ∼0, the behavior of the electron charge statics is exhibited. This work demonstrates that the magnetic dipole field of the Mo electrons is the dominant source of the local magnetic fields at the Li site, and suggests that the unknown metal-'insulator' crossover at low temperatures is not a charge effect. The work also reveals valuable local electric and magnetic field information for further NMR investigation as recently suggested (2012 Phys. Rev. B 85 235128) regarding the unusual properties of the material.

Local spectral properties of Luttinger liquids: scaling versus nonuniversal energy scales

Motivated by recent scanning tunneling and photoemission spectroscopy measurements on self-organized gold chains on a germanium surface, we reinvestigate the local single-particle spectral properties of Luttinger liquids. In the first part we use the bosonization approach to exactly compute the local spectral function of a simplified field theoretical low-energy model and take a closer look at scaling properties as a function of the ratio of energy and temperature. Translational-invariant Luttinger liquids as well as those with an open boundary (cut chain geometry) are considered. We explicitly show that the scaling functions of both set-ups have the same analytical form. The scaling behavior suggests a variety of consistency checks which can be performed on measured data to experimentally verify Luttinger liquid behavior. In the second part we approximately compute the local spectral function of a microscopic lattice model-the extended Hubbard model-close to an open boundary using the functional renormalization group. We show that it follows the field theoretical prediction in the low-energy regime as a function of energy and temperature, and point out the importance of nonuniversal energy scales inherent to any microscopic model. The spatial dependence of this spectral function is characterized by oscillatory behavior and an envelope function which follows a power law in accordance with the field theoretical continuum model. Interestingly, for the lattice model we find a phase shift which is proportional to the two-particle interaction and not accounted for in the standard bosonization approach to Luttinger liquids with an open boundary. We briefly comment on the effects of several one-dimensional branches cutting the Fermi energy and Rashba spin-orbit interaction.

Luttinger liquid behaviour of Li0.9Mo6O17 studied by scanning tunnelling microscopy

Scanning tunnelling spectroscopy (STS) was used to study the Luttinger liquid behaviour of the purple bronze Li(0.9)Mo(6)O(17) in the temperature range 5 K < T < 300 K. In the entire temperature range the suppression of the density of states at the Fermi energy can be fitted very well by a model describing the tunnelling into a Luttinger liquid at ambient temperature. The power-law exponent extracted from these fits reveals a significant increase above 200 K. It changes from α = 0.6 at low temperature to α = 1.0 at room temperature.

Local density of states of the one-dimensional spinless fermion model

We investigate the local density of states of the one-dimensional half-filled spinless fermion model with nearest-neighbour hopping t > 0 and interaction V in its Luttinger liquid phase -2t < V ≤ 2t. The bulk density of states and the local density of states in open chains are calculated over the full band width ∼4t with an energy resolution ≤0.08t using the dynamical density-matrix renormalization group (DDMRG) method. We also perform DDMRG simulations with a resolution of 0.01t around the Fermi energy to reveal the power-law behaviour D(ϵ) ∼ |ϵ - ϵ(F)|(α) predicted by the Luttinger liquid theory for bulk and boundary density of states. The exponents α are determined using a finite-size scaling analysis of DDMRG data for lattices with up to 3200 sites. The results agree with the exact exponents given by the Luttinger liquid theory combined with the Bethe Ansatz solution. The crossover from boundary to bulk density of states is analysed. We have found that boundary effects can be seen in the local density of states at all energies, even far away from the chain edges.

Photoemission spectroscopy and the unusually robust one-dimensional physics of lithium purple bronze

Temperature-dependent photoemission spectroscopy in Li(0.9)Mo(6)O(17) contributes to evidence for one-dimensional (1D) physics that is unusually robust. Three generic characteristics of the Luttinger liquid are observed: power law behavior of the k-integrated spectral function down to temperatures just above the superconducting transition, k-resolved lineshapes that show holon and spinon features, and quantum critical (QC) scaling in the lineshapes. Departures of the lineshapes and the scaling from expectations in the Tomonaga-Luttinger model can be partially described by a phenomenological momentum broadening that is presented and discussed. The possibility that some form of 1D physics obtains even down to the superconducting transition temperature is assessed.

Giant Nernst effect and bipolarity in the quasi-one-dimensional metal Li0.9Mo6O17

The Nernst coefficient for the quasi-one-dimensional metal, Li{0.9}Mo{6}O{17}, is found to be among the largest known for metals (ν≃500  μV/KT at T∼20  K), and is enhanced in a broad range of temperature by orders of magnitude over the value expected from Boltzmann theory for carrier diffusion. A comparatively small Seebeck coefficient implies that Li{0.9}Mo{6}O{17} is bipolar with large, partial Seebeck coefficients of opposite sign. A very large thermomagnetic figure of merit, ZT∼0.5, is found at high field in the range T≈35-50  K.

Gross violation of the Wiedemann-Franz law in a quasi-one-dimensional conductor

When charge carriers are spatially confined to one dimension, conventional Fermi-liquid theory breaks down. In such Tomonaga-Luttinger liquids, quasiparticles are replaced by distinct collective excitations of spin and charge that propagate independently with different velocities. Although evidence for spin-charge separation exists, no bulk low-energy probe has yet been able to distinguish successfully between Tomonaga-Luttinger and Fermi-liquid physics. Here we show experimentally that the ratio of the thermal and electrical Hall conductivities in the metallic phase of quasi-one-dimensional Li(0.9)Mo(6)O(17) diverges with decreasing temperature, reaching a value five orders of magnitude larger than that found in conventional metals. Both the temperature dependence and magnitude of this ratio are consistent with Tomonaga-Luttinger liquid theory. Such a dramatic manifestation of spin-charge separation in a bulk three-dimensional solid offers a unique opportunity to explore how the fermionic quasiparticle picture recovers, and over what time scale, when coupling to a second or third dimension is restored.

Quantum critical scaling in the single-particle spectrum of a novel anisotropic metal

We report an angle resolved photoemission spectroscopy study of quantum critical scaling in the single-particle spectral function of a novel anisotropic metal Li_{0.9}Mo_{6}O_{17}. We find a temperature (T) scaling exponent value and also low-T angle resolved photoemission spectroscopy line shapes that are very challenging for current one-dimensional theory frameworks. These results add a new spectroscopic component to a growing collection of puzzling low-T transport behaviors of this material.

Playing pinball with atoms

We demonstrate the feasibility of controlling an atomic scale mechanical device by an external electrical signal. On a germanium substrate, a switching motion of pairs of atoms is induced by electrons that are directly injected into the atoms with a scanning tunneling microscope tip. By precisely controlling the tip current and distance we make two atom pairs behave like the flippers of an atomic-sized pinball machine. This atomic scale mechanical device exhibits six different configurations.

Recent ARPES experiments on quasi-1D bulk materials and artificial structures

The spectroscopy of quasi-one-dimensional (1D) systems has been a subject of strong interest since the first experimental observations of unusual line shapes in the early 1990s. Angle-resolved photoemission (ARPES) measurements performed with increasing accuracy have greatly broadened our knowledge of the properties of bulk 1D materials and, more recently, of artificial 1D structures. They have yielded a direct view of 1D bands, of open Fermi surfaces, and of characteristic instabilities. They have also provided unique microscopic evidence for the non-conventional, non-Fermi-liquid, behavior predicted by theory, and for strong and singular interactions. Here we briefly review some of the remarkable experimental results obtained in the last decade.

New model system for a one-dimensional electron liquid: self-organized atomic gold chains on Ge(001)

Unique electronic properties of self-organized Au atom chains on Ge(001) in novel c(8 x 2) long-range order are revealed by scanning tunneling microscopy. Along the nanowires an exceptionally narrow conduction path exists which is virtually decoupled from the substrate. It is laterally confined to the ultimate limit of single atom dimension, and is strictly separated from its neighbors, as not previously reported. The resulting tunneling conductivity shows a dramatic inhomogeneity of 2 orders of magnitude. The atom chains thus represent an outstandingly close approach to a one-dimensional electron liquid.

Dimensional crossover in the purple bronze Li0.9Mo6O17

Thermal expansion of Li0.9Mo6O17 is a-axis dominated which reduces the separation of the conducting chains at low temperature enhancing the interchain coupling. This destabilizes the Luttinger-liquid fixed point leading to an electronic charge- (or spin-) density wave dominated by Coulomb repulsion, as predicted by theories for Luttinger liquids.

New Luttinger-liquid physics from photoemission on Li0.9M06O17

Temperature dependent high resolution photoemission spectra of quasi-one-dimensional Li(0.9)Mo(6)O(17)evince a strong renormalization of its Luttinger-liquid density-of-states anomalous exponent. We trace this new effect to interacting charge neutral critical modes that emerge naturally from the two-band nature of the material. Li(0.9)Mo(6)O(17) is shown thereby to be a paradigm material that is capable of revealing new Luttinger physics.