This article discusses fluctuating order in a quantum disordered phase proximate to a quantum critical point, with particular emphasis on fluctuating stripe order. Optimal strategies are derived for extracting information concerning such local order from experiments, with emphasis on neutron scattering and scanning tunneling microscopy. These ideas are tested by application to two model systems---an exactly solvable one-dimensional (1D) electron gas with an impurity, and a weakly interacting 2D electron gas. Experiments on the cuprate high-temperature superconductors which can be analyzed using these strategies are extensively reviewed. The authors adduce evidence that stripe correlations are widespread in the cuprates. They compare and contrast the advantages of two limiting perspectives on the high-temperature superconductor: weak coupling, in which correlation effects are treated as a perturbation on an underlying metallic (although renormalized) Fermi-liquid state, and strong coupling, in which the magnetism is associated with well-defined localized spins, and stripes are viewed as a form of micro phase separation. The authors present quantitative indicators that the latter view better accounts for the observed stripe phenomena in the cuprates.

How to detect fluctuating stripes in the high-temperature superconductors

Recent studies on high-Tc superconductors have aroused new interest in tunnelling effects in unconventional superconductors. Unlike in conventional s-wave superconductors, the d-wave pairing state in these materials has an internal phase of the pair potential. The internal phase as a function of the wavevector of the Cooper pairs has a large influence on the electric properties of tunnelling junctions. Important effects of the internal phase on the Josephson current were first predicted theoretically. The idea has been established through several experiments using high-Tc Josephson junctions, which detect ?-phase shift between the a- and b-axis directions and fractional flux quanta. These results give convincing evidence for d-wave symmetry in high-Tc superconductors. In addition, the existence of new interference effects in the quasiparticle states near surfaces and boundaries has been suggested through theoretical predictions. Experimentally, a large number of tunnelling spectroscopy data showed zero-bias conductance peaks (ZBCPs), the origin of which cannot be explained in terms of the classical concept that a tunnelling conductance spectrum is a phase-insensitive probe of the electronic states. It is clarified theoretically that the observed ZBCPs reflect the formation of zero-energy states on the surface due to the ?-phase shift of internal phase in the d-wave pairing symmetry. The formulation developed for tunnelling spectroscopy suggests that tunnelling spectroscopy is essentially phase sensitive. In addition, the formation of the bound states has been shown to have a serious influence on the electrical properties of Josephson junctions. Several anomalous properties including strong enhancement of the Josephson current in the low-temperature region have been predicted theoretically. In this report, recent developments in tunnelling effects on surface bound states in unconventional superconductors are reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/63/10/202/pdf

Tunnelling effects on surface bound states in unconventional superconductors

Tunneling spectroscopy has played a central role in the experimental verification of the microscopic theory of superconductivity in classical superconductors. Initial attempts to apply the same approach to high-temperature superconductors were hampered by various problems related to the complexity of these materials. The use of scanning tunneling microscopy and spectroscopy (STM and STS) on these compounds allowed the main difficulties to be overcome. This success motivated a rapidly growing scientific community to apply this technique to high-temperature superconductors. This paper reviews the experimental highlights obtained over the last decade. The crucial efforts to gain control over the technique and to obtain reproducible results are first recalled. Then a discussion on how the STM and STS techniques have contributed to the study of some of the most unusual and remarkable properties of high-temperature superconductors is presented: the unusually large gap values and the absence of scaling with the critical temperature, the pseudogap and its relation to superconductivity, the unprecedented small size of the vortex cores and its influence on vortex matter, the unexpected electronic properties of the vortex cores, and the combination of atomic resolution and spectroscopy leading to the observation of periodic local density of states modulations in the superconducting and pseudogap states and in the vortex cores.

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Scanning tunneling spectroscopy of high-temperature superconductors

Scanning tunneling microscopy is used to image the additional quasi-particle states generated by quantized vortices in the high critical temperature superconductor Bi2Sr2CaCu2O8+δ. They exhibit a copper-oxygen bond–oriented “checkerboard” pattern, with four unit cell (4a0) periodicity and a ∼30 angstrom decay length. These electronic modulations may be related to the magnetic field–induced, 8a0periodic, spin density modulations with decay length of ∼70 angstroms recently discovered in La1.84Sr0.16CuO4. The proposed explanation is a spin density wave localized surrounding each vortex core. General theoretical principles predict that, in the cuprates, a localized spin modulation of wavelength λ should be associated with a corresponding electronic modulation of wavelength λ/2, in good agreement with our observations.

https://science.sciencemag.org/content/sci/295/5554/466.full.pdf

A Four Unit Cell Periodic Pattern of Quasi-Particle States Surrounding Vortex Cores in Bi2Sr2CaCu2O8+δ

The search for Majorana bound states (MBSs) has been fueled by the prospect of using their non-Abelian statistics for robust quantum computation. Two-dimensional superconducting topological materials have been predicted to host MBSs as zero-energy modes in vortex cores. By using scanning tunneling spectroscopy on the superconducting Dirac surface state of the iron-based superconductor FeTe0.55Se0.45, we observed a sharp zero-bias peak inside a vortex core that does not split when moving away from the vortex center. The evolution of the peak under varying magnetic field, temperature, and tunneling barrier is consistent with the tunneling to a nearly pure MBS, separated from nontopological bound states. This observation offers a potential platform for realizing and manipulating MBSs at a relatively high temperature.

https://science.sciencemag.org/content/sci/early/2018/08/15/science.aao1797.full.pdf

Evidence for Majorana bound states in an iron-based superconductor.

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Observation of the Low Temperature Pseudogap in the Vortex Cores of Bi2Sr2CaCu2O8+δ

This paper reports very detailed low-temperature vacuum tunneling spectroscopy investigations of ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ (BSCCO) single crystals. For clean vacuum junctions formed between a cleaved BSCCO single crystal and the normal-metal tip of a scanning tunneling microscope, we obtain stable c-axis vacuum tunneling conditions that allow very reproducible low-temperature electron tunneling spectroscopy. A vacuum junction is identified by tunneling spectra which neither depend on tip/sample spacing nor change as a function of time and position on the sample in the Meissner state. In contrast to the frequently reported linear or parabolic increase with increasing bias voltage, the background conductance of such spectra is largely constant with a slight decrease up to \ifmmode\pm\else\textpm\fi{}300 meV bias. The normal-state conductance inferred from this background has a local maximum at negative sample bias, indicating a pileup below the Fermi level in the (ab)-plane normal-state density of states of BSCCO. Vacuum junctions at 4.8 K show a well developed superconducting gap with large peaks at the gap edges and a finite density of quasiparticle excitations filling the gap. These characteristics are not consistent with an isotropic BCS-like gap parameter. Outside the superconducting gap, the differential conductance curves are very asymmetric, with a striking dip which appears at negative sample bias only. This dip contributes a substantial amount of states to satisfy the conservation of states we find between normal and superconducting BSCCO.

Vacuum tunneling spectroscopy and asymmetric density of states of Bi 2 Sr 2 CaCu 2 O 8 + δ

We have developed a linear translation device using piezoelectric‐induced slip‐stick motion. Reproducible single steps of about 30 A, as well as continuous stepping with an overall translation speed of 0.25 mm/s, are routinely realized. The notable feature of this device is that this performance is achieved in the vertical orientation with the translator moving against gravity. This remarkable result is made possible using cycloidal functions instead of sawtooth signals to activate the motion. We have realized a very simple translator which can be used in any orientation with a displacement onset voltage of 15 V. The instrument was successfully tested in the temperature range from 1.6 to 300 K. Since no mechanical connections are required, this design is well suited for many applications, including scanning tunneling microscopy.

/pdf/a-vertical-piezoelectric-inertial-slider-3niybi5nyw.pdf

A vertical piezoelectric inertial slider

We present a scanning tunneling microscope (STM) designed to operate between 275 mK and room temperature, in magnetic fields up to 14 T and in ultrahigh vacuum (UHV). The system features a compact STM connected to an UHV compatible 3He refrigerator fitting into a bottom loading cryostat with a superconducting magnet. In this configuration, the cryostat is sitting on top of the UHV chamber, resulting in a very short distance between the STM access and the experimental position. It further enables proper thermal anchoring of the entire STM setup, allowing millikelvin temperatures to be reached in true UHV conditions. We achieve a hold time of about 40 h at 275 mK and a turnaround time of 10 h between room and base temperature. We demonstrate atomic resolution and present tunneling spectra obtained at 275 mK on the high-Tc superconductors Bi2Sr2CaCu2O8+δ and YBa2Cu3O7−δ.

/pdf/a-3he-refrigerated-scanning-tunneling-microscope-in-high-3kroeyk6gs.pdf

A 3He refrigerated scanning tunneling microscope in high magnetic fields and ultrahigh vacuum

We present a new scanning tunneling microscope (STM) developed specifically for use at low temperatures within a standard helium cryostat. This compact STM (diameter 25 mm and length 61 mm) has been designed to be compatible with a superconducting magnet. It incorporates a novel approach system which operates in any orientation including the vertical one, without any mechanical connections to the STM. It is able to translate a sample by 30 A steps in any orientation. The coarse and the fine approach are driven by a single piezoelectric tube via inertial slip‐stick motion of the sample holder. During the coarse approach, the translator can be moved over 15 mm at 0.25 mm/s against gravity. We have operated this STM down to 1.6 K and we have obtained images with atomic resolution on highly oriented pyrolitic graphite (HOPG) and NbSe2 from 300 K down to 90 K. This partially thermal compensated instrument is able to monitor temperature dependent surface changes on atomic scale in real time.

Ch. Renner

Papers

Observation of the Low Temperature Pseudogap in the Vortex Cores of Bi2Sr2CaCu2O8+δ

Vacuum tunneling spectroscopy and asymmetric density of states of Bi 2 Sr 2 CaCu 2 O 8 + δ

A vertical piezoelectric inertial slider

A 3He refrigerated scanning tunneling microscope in high magnetic fields and ultrahigh vacuum

A versatile low‐temperature scanning tunneling microscope