In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of $^{4}$He belongs to the same three dimensional $mathrm{O}(2)$ universality class as the onset of ferromagnetism in a
lattice of classical spins with $XY$ symmetry. Below the transition, the superfluid density $rho_s$ and superfluid velocity $v_s$ increase as power laws of temperature described by a universal critical exponent constrained to be equal by scale invariance. As the dimensionality is reduced towards one dimension (1D), it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single $30~$nm long nanopores with radii ranging down from 20~nm to 3~nm. As the pore size is reduced towards the 1D limit, we observe: {it i)} a suppression of the pressure dependence of the superfluid velocity; {it ii)} a temperature dependence of $v_{s}$ that surprisingly can be well-fitted by a powerlaw with a single exponent over a broad range of temperatures; and {it iii)} decreasing critical velocities as a function of radius for channel sizes below $R simeq 20$~nm, in stark contrast with what is observed in micron sized channels. We interpret these deviations from bulk behaviour as signaling the crossover to a quasi-1D state whereby the size of a critical topological defect is cut off by the channel radius.
Geometrical Berry phase is recognized as having profound implications for the properties of electronic systems. Over the last decade, Berry phase has been essential to our understanding of new materials, including graphene and topological insulators.
The Berry phase can be accessed via its contribution to the phase mismatch in quantum oscillation experiments, where electrons accumulate a phase as they traverse closed cyclotron orbits in momentum space. The high-temperature cuprate superconductors are a class of materials where the Berry phase is thus far unknown despite the large body of existing quantum oscillations data. In this report we present a systematic Berry phase analysis of Shubnikov - de Haas measurements on the hole-doped cuprates YBa$_2$Cu$_3$O$_{y}$, YBa$_2$Cu$_4$O$_8$, HgBa$_2$CuO$_{4 + delta}$, and the electron-doped cuprate Nd$_{2-x}$Ce$_x$CuO$_4$. For the hole-doped materials, a trivial Berry phase of 0 mod $2pi$ is systematically observed whereas the electron-doped Nd$_{2-x}$Ce$_x$CuO$_4$ exhibits a significant non-zero Berry phase. These observations set constraints on the nature of the high-field normal state of the cuprates and points towards contrasting behaviour between hole-doped and electron-doped materials. We discuss this difference in light of recent developments related to charge density-wave and broken time-reversal symmetry states.
The electronic transport properties of an SNS junction formed by an InN nanowire (N) and Al contacts (S) with a superconducting transition temperature T_c ~ 0.92 K were investigated. As a function of dc bias, superconducting quasiparticle transport r
esonance peaks at E=2Delta were observed, in agreement with BCS theory with 2Delta(T=0) equiv Delta_0=275mueV. Several additional transport resonances scaling linearly in energy were observed at high-bias above 2Delta, up to Esimeq 15Delta_0, consistent with McMillan-Rowell oscillations. The persistence of McMillan-Rowell oscillations at high-bias and under applied magnetic field were investigated.
