Semiconductor InSb nanowires are expected to provide an excellent material platform for the study of Majorana fermions in solid state systems. Here, we report on the realization of a Nb-InSb nanowire-Nb hybrid quantum device and the observation of a zero-bias conductance peak structure in the device. An InSb nanowire quantum dot is formed in the device between the two Nb contacts. Due to the proximity effect, the InSb nanowire segments covered by the superconductor Nb contacts turn to superconductors with a superconducting energy gap Δ(InSb) ∼ 0.25 meV. A tunable critical supercurrent is observed in the device in high back gate voltage regions in which the Fermi level in the InSb nanowire is located above the tunneling barriers of the quantum dot and the device is open to conduction. When a perpendicular magnetic field is applied to the devices, the critical supercurrent is seen to decrease as the magnetic field increases. However, at sufficiently low back gate voltages, the device shows the quasi-particle Coulomb blockade characteristics and the supercurrent is strongly suppressed even at zero magnetic field. This transport characteristic changes when a perpendicular magnetic field stronger than a critical value, at which the Zeeman energy in the InSb nanowire is E(z) ∼ Δ(InSb), is applied to the device. In this case, the transport measurements show a conductance peak at the zero bias voltage and the entire InSb nanowire in the device behaves as in a topological superconductor phase. We also show that this zero-bias conductance peak structure can persist over a large range of applied magnetic fields and could be interpreted as a transport signature of Majorana fermions in the InSb nanowire.

Studying the topological invariance and Berry phase in non-Hermitian systems, we give the basic properties of the complex Berry phase and generalize the global Berry phases Q to identify the topological invariance to non-Hermitian models. We find that Q can identify a topological invariance in two kinds of non-Hermitian models, two-level non-Hermitian Hamiltonian and bipartite dissipative model. For the bipartite dissipative model, the abrupt change of the Berry phase in the parameter space reveals quantum phase transition and relates to the exceptional points.These results give the basic relationships between the Berry phase, quantum and topological phase transitions.

Over the past decade, many efforts have been devoted to designing and fabricating substrates for surface-enhanced Raman spectroscopy (SERS) with abundant hot spots to improve the sensitivity of detection. However, there have been many difficulties involved in causing molecules to enter hot spots actively or effectively. Here, we report a general SERS method for actively capturing target molecules in small gaps (hot spots) by constructing a nanocapillary pumping model. The ubiquity of hot spots and the inevitability of molecules entering them lights up all the hot spots and makes them effective. This general method can realize the highly sensitive detection of different types of molecules, including organic pollutants, drugs, poisons, toxins, pesticide residues, dyes, antibiotics, amino acids, antitumor drugs, explosives, and plasticizers. Additionally, in the dynamic detection process, an efficient and stable signal can be maintained for 1–2 min, which increases the practicality and operability of this method. Moreover, a dynamic detection process like this corresponds to the processes of material transformation in some organisms, so the method can be used to monitor transformation processes such as the death of a single cell caused by photothermal stimulation. Our method provides a novel pathway for generating hot spots that actively attract target molecules, and it can achieve general ultratrace detection of diverse substances and be applied to the study of cell behaviors in biological systems.

We explore the signatures of Majorana fermions in a nanowire based topological superconductor-quantum dot-topological superconductor hybrid device by charge transport measurements. At zero magnetic field, well-defined Coulomb diamonds and the Kondo effect are observed. Under the application of a finite, sufficiently strong magnetic field, a zero-bias conductance peak structure is observed. It is found that the zero-bias conductance peak is present in many consecutive Coulomb diamonds, irrespective of the even-odd parity of the quasi-particle occupation number in the quantum dot. In addition, we find that the zero-bias conductance peak is in most cases accompanied by two differential conductance peaks, forming a triple-peak structure, and the separation between the two side peaks in bias voltage shows oscillations closely correlated to the background Coulomb conductance oscillations of the device. The observed zero-bias conductance peak and the associated triple-peak structure are in line with Majorana fermion physics in such a hybrid topological system.

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We study the driven dynamics across the critical points of the Yang-Lee edge singularities (YLESes) in a finite-size quantum Ising chain with an imaginary symmetry-breaking field. In contrast to the conventional classical or quantum phase transitions, these phase transitions are induced by tuning the strength of the dissipation in a non-Hermitian system and can occur even at finite size. For conventional phase transitions, universal behaviors in driven dynamics across critical points are usually described by the Kibble-Zurek mechanism, which states that the scaling in dynamics is dictated by the critical exponents associated with one critical point and topological defects will emerge after the quench. While the mechanism leading to topological defects breaks down in the YLES, we find that for small lattice size, the driven dynamics can still be described by the Kibble-Zurek scaling with the exponents determined by the (0 + 1)-dimensional YLES. For medium finite size, however, the driven dynamics can be described by the Kibble-Zurek scaling with two sets of critical exponents determined by both the (0 + 1)-dimensional and the (1 + 1)-dimensional YLESes.PACS numbers: 03.67. Mn, 64.60.De, 64.60.Ht, 64.70.Tg The Kibble-Zurek mechanism [1, 2] describes universal scaling behavior in the driven critical dynamics in a variety of systems, ranging from classical to quantum phase transitions [3, 4]. It separates the whole driven process into three stages: two adiabatic stages and one impulse stage. In the adiabatic region, the relaxation rate is larger than the transition rate and the system evolves along the instantaneous equilibrium state; while in the impulse stage, the relaxation rate is smaller than the transition rate because of the critical slowing down, and thus the system falls out of equilibrium essentially. Furthermore, the Kibble-Zurek scaling (KZS) [1, 2] shows that only the equilibrium critical exponents are needed to characterise the dynamic scaling behavior. All these exponents belong to one set, which is determined by the renormalization group flow near the critical point [3][4][5]. According to the KZS, the external driving will induce an effective correlation length, which divides the system into different domains. The domain walls will form topological defects, whose number can be scaled by the driving rate [3, 4]. Additionally, for a finite-size system, the system size also becomes an scaling variable [6][7][8]. The KZS has been verified numerically and experimentally in both classical and quantum phase transitions [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].On the other hand, Yang and Lee [27,28] paved the way to understand phase transitions by analysing the zeros of the partition function in the complex plane of a symmetry-breaking field. It was shown that singular behaviors exist not only at the critical point with a vanishing symmetry-breaking field but also near the edge of the Lee-Yang zeros, where the applied symmetrybreaking field is purely imaginary [29]. The la...

Association between dietary intake of vegetables and fruits and risk of hip fracture has been reported for many years. However, the findings remain inconclusive. We conducted a meta-analysis to evaluate the relationship between intake of vegetables and fruits, and risk of hip fracture. Literature search for relevant studies was performed on PubMed and Embase databases. Five observational studies were included in the meta-analysis. Summary hazard ratio (HR) with corresponding 95% confidence interval (CI) was calculated from pooled data using the random-effects model irrespective of heterogeneity. Sensitivity and subgroup analysis were performed to explore possible reasons for heterogeneity. The summary HR for hip fracture in relation to high intake vs. low intake of only vegetables, only fruits, and combined intake of fruits and vegetables, was 0.75 (95% CI, 0.61–0.92), 0.87 (95% CI, 0.74–1.04), and 0.79 (95% CI, 0.61–1.03), respectively. Subgroup analyses based on study design, geographical location, number of cases, and gender showed similar results. Increased intake of vegetables, but not fruits, was found to be associated with a lower risk of hip fracture. Large prospective clinical trials with robust methodology are required to confirm our findings.

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