Scanning-tunneling-microscopy study of distortion and instability of inclined flux-line-lattice structures in the anisotropic superconductor 2H-NbSe2

A spectroscopic-imaging scanning tunneling microscope in vector magnetic field

Cryogenic scanning tunneling microscopy and spectroscopy (STM/STS) performed in a high vector magnetic field provide unique possibilities for imaging surface magnetic structures and anisotropic superconductivity and exploring spin physics in quantum materials with atomic precision. Here, we describe the design, construction, and performance of a low-temperature, ultra-high-vacuum (UHV) spectroscopic-imaging STM equipped with a vector magnet capable of applying a field of up to 3 T in any direction with respect to the sample surface. The STM head is housed in a fully bakeable UHV compatible cryogenic insert and is operational over variable temperatures ranging from ∼300 down to 1.5 K. The insert can be easily upgraded using our home-designed ³He refrigerator. In addition to layered compounds, which can be cleaved at a temperature of either ∼300, ∼77, or ∼4.2 K to expose an atomically flat surface, thin films can also be studied by directly transferring using a UHV suitcase from our oxide thin-film laboratory. Samples can be treated further with a heater and a liquid helium/nitrogen cooling stage on a three-axis manipulator. The STM tips can be treated in vacuo by e-beam bombardment and ion sputtering. We demonstrate the successful operation of the STM with varying the magnetic field direction. Our facility provides a way to study materials in which magnetic anisotropy is a key factor in determining the electronic properties such as in topological semimetals and superconductors.

Relation of Superconducting Pairing Symmetry and Non-Magnetic Impurity Effects in Vortex States

Non-magnetic impurity scattering effects on the vortex core states are theoretically studied to clarify the contributions from the sign-change of the pairing function in anisotropic superconductors. The vortex states are calculated by the Eilenberger theory in superconductors with p x -wave pairing symmetry, as well as the corresponding anisotropic s-wave symmetry. From the spatial structure of the pair potential and the local electronic states around a vortex, we examine the differences between anisotropic superconductors with and without sign-change of the pairing function, and estimate how twofold symmetric vortex core images change with increasing the impurity scattering rate both in the Born and the unitary limits. We found that twofold symmetric vortex core image of zero-energy local density of states changes the orientation of the twofold symmetry with increasing the scattering rate when the sign change occurs in the pairing function. Without the sign change, the vortex core shape reduces to circular one with approaching dirty cases. These results of the impurity effects are valuable for identifying the pairing symmetry by observation of the vortex core image by the STM observation.

Stripe domains and first-order phase transition in the vortex matter of anisotropic high-temperature superconductors

We report the direct imaging of a novel modulated flux striped domain phase in a nearly twin-free YBCO crystal. These domains arise from instabilities in the vortex structure within a narrow region of tilted magnetic fields at small angles from the in-plane direction. By comparing the experimental and theoretically derived vortex phase diagrams we infer that the stripe domains emerge from a first-order phase transition of the vortex structure. The size of domains containing vortices of certain orientations is controlled by the balance between the vortex stray field energy and the positive energy of the domain boundaries. Our results confirm the existence of the kinked vortex chain phase in an anisotropic high temperature superconductor and reveal a sharp transition in the state of this phase resulting in regular vortex domains.

A scanning tunneling microscope for a dilution refrigerator

We present the main features of a home-built scanning tunneling microscope that has been attached to the mixing chamber of a dilution refrigerator. It allows scanning tunneling microscopy and spectroscopy measurements down to the base temperature of the cryostat, T approximately 30 mK, and in applied magnetic fields up to 13 T. The topography of both highly ordered pyrolytic graphite and the dichalcogenide superconductor NbSe(2) has been imaged with atomic resolution down to T approximately 50 mK as determined from a resistance thermometer adjacent to the sample. As a test for a successful operation in magnetic fields, the flux-line lattice of superconducting NbSe(2) in low magnetic fields has been studied. The lattice constant of the Abrikosov lattice shows the expected field dependence proportional to 1/square root of B and measurements in the scanning tunneling spectroscopy mode clearly show the superconductive density of states with Andreev bound states in the vortex core.

Attraction between pancake vortices in the crossing lattices of layered superconductors

The intervortex interaction is investigated in very anisotropic layered superconductors in tilted magnetic field. In such a case, the crossing lattice of Abrikosov vortices (AVs) and Josephson vortices (JVs) appears. The interaction between pancake vortices, forming the AVs and JVs, produces the deformation of the AV line. It is demonstrated that, as a result of this deformation, a long range attraction between AVs is induced. This phenomenon is responsible for the dense vortex chain formation. The vortex structure in the weak perpendicular magnetic field is the vortex chain phase, where only a small part of JVs is occupied by AVs.

Symmetry breaking in one-dimensional diffusion

The mean free passage time for one-dimensional diffusion on a line segment under the influence of a deterministic telegraph signal proves to be a nonmonotonic function of the signal rate ("stochastic resonance") if symmetry breaking takes place. The symmetry breaking may be expressed either in nonsymmetric boundary conditions (one end absorbing and the other reflecting) or in a nonsymmetric telegraph signal. The latter case is considered in detail. It turns out that the larger the asymmetry of a telegraph signal, the wider the range of parameters for which a stochastic resonance occurs.

Stochastic resonance in one-dimensional diffusion with one reflecting and one absorbing end point

An analysis of the nonmonotonic dependence of the mean-free-passage time on the frequency of a periodic signal [stochastic resonance (SR)] for diffusion on a segment with one absorbing and one reflecting end point shows that SR exists only for some restricted values of parameters. SR always exists if the periodic telegraph signal is replaced by a random one. The latter case is considered in detail.

Inclined-Field Structure, Morphology, and Pinning of the Vortex Lattice in Microtwinned YBa 2 Cu 3 O 7

A detailed small-angle neutron scattering study of the vortex lattice in a single crystal of YBa(2)Cu(3)O(7) was made for a field of 0.5 tesla inclined at angles between 0 and 80 degrees to the crystalline c axis. The vortex lattice is triangular for all angles, and for angles less than or equal to 70 degrees its orientation adjusts itself to maximize the pinning energy to densely and highly regularly spaced twin planes. These observations have important implications for the microscopic flux-pinning mechanism, and hence for the critical current achievable in YBa(2)Cu(3)O(7). For large angles (about 80 degrees) the vortex lattice consists of independent chains in the orientation predicted by anisotropic London theory.