Bias Peak Pro 6 Serial Number
Pablo Barjavel
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(a) Scaling IP (top row) and Input (bottom row) samples to equalize the read counts only in the background (enclosed by parentheses) preserves the statistical significance of the IP peak shown. (b) On the other hand, forcing the total number of reads to be equal between IP and Input would artificially redistribute the counts that accumulated within the IP peak to background regions, thus inflating the noise level in Input. Some true peaks can be lost in this process.
A comparison of Pol II and c-Myc peaks called by MACS, CCAT, Peak-Seq, and the ZINB model. A. Number of peaks called by each method and the percentage of c-Myc peaks overlapping with Pol II. B. The percentages of peaks called by other methods overlapping with ZINB peaks. C. The percentage of ZINB peaks that overlap with peaks detected by other methods.
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.
The search for Majorana Fermions1 in solid state systems, especially in s-wave superconductor (SC)-coupled semiconductor nanowires (NWs) with a strong spin-orbit interaction (SOI), is one of paramount research tasks in physics today2,3,4,5,6,7,8,9,10,11. By exposing an s-wave SC-coupled semiconductor NW with strong SOI to a sufficiently strong and appropriately oriented magnetic field and, thus, driving the system into topological superconductor (TS) phase, zero-energy quasi-particle states, i.e., Majorana Fermions (MFs), are expected to appear in pair at the two ends of the semiconductor NW. Recently, several groups have reported on their observations of the signatures of zero-energy MFs in charge transport measurements of hybrid SC-semiconductor NW devices12,13,14,15. In these experiments, InSb or InAs semiconductor NWs are used and contacted by an s-wave SC of NbTiN, Nb, or Al. At zero magnetic field, these superconductor contacted NWs show superconductivity at low temperatures due to the proximity effect. Under the application of an external magnetic field, these NWs can be turned to TS NWs and can host zero-energy MF modes at the ends of the NWs, provided that these NWs are of one-dimensional systems or of quasi-one-dimensional systems with an odd number of subbands occupied11. In the charge transport measurements, these MF states manifest themselves as a zero-bias conductance peak (ZBCP). The quasi-particles carrying these modes are shown theoretically to obey non-Abelian statistics and could be utilized for topological quantum computing. However, the non-Abelian statistics of Majorana quasi-particles in solid state has not been demonstrated experimentally. It has been suggested that an intriguing experimental demonstration of the non-Abelian statistics is to carry out a braiding experiment of two Majorana quasi-particles in a TS system. In such an experiment, the two MF modes from different MF pairs could be brought to interact via a non-topological object. It is, therefore, fundamentally important to study the novel physics of TS systems in the presence of such interaction.
Here, we report on the realization and measurements of a hybrid Nb-InSb NW-Nb quantum device, in which a normal InSb quantum dot (QD) is present between two superconductor Nb-contacted InSb NW segments. Under an sufficiently strong magnetic field applied perpendicularly to the substrate (and thus to the NW) and a suitable back-gate voltage, the two Nb-contacted InSb NW segments could turn to become two TS NWs and each could host a pair of Majorana fermion modes at its ends. Electrical measurements between the two Nb-contacted InSb NW segments in the trivial superconductor phase and in the TS phases are employed to detect possible appearance of the Majorana fermion modes and to study the effect of the interaction between the two Majorana modes located adjacent to the InSb QD. To block the contribution of the supercurrent, we tune the QD to the Coulomb blockade regime. When a sufficiently strong, perpendicular magnetic field is applied to the device, we observe a ZBCP in several consecutive Coulomb blockade diamonds of the QD with both odd and even quasi-particle occupation numbers. Our experiment conclusively rules out the possibility to assign the Kondo physics as a mechanism to the observed ZBCP.
Similar results as in figures 2 and 3 have also been observed in the charge transport measurements of a different NW based Nb-InSb QD-Nb hybrid device (see Supplementary Information). With the presence of several Coulomb blockade diamonds in the charge stability diagram measurements of the devices, we have showed for the first time that the ZBCP structure is independent of the even-odd parity of quasi-particle occupation numbers in the QD. This parity independence would not favor the assignment of the ZBCP structure to the Kondo physics. A possible scenario could be proposed by assignment of these ZBCPs to the MF physics. At a sufficiently strong applied magnetic field and a suitable gate voltage, it is possible to drive the two Nb-covered InSb NW segments in such a device to TS phase, leaving the intermediate QD to remain as a trivial object. Hence, two pairs of MF bound states, spatially separated by the QD, can be created in the TS-QD-TS hybrid system. However, in the presence of a finite coupling between the two TS NW segments, the two MF bound states located adjacent to the QD (i.e., the inner two MF bound states) can interact and hybridize into a pair of quasi-particle states with finite energies. The other pair of MF bound states (i.e., the outer two MF bound states) located at the two ends of the entire InSb NW remain at zero energy and thus the entire system, including the two Nb-contacted NW segments and the QD, would behave as a nontrivial TS NW (see the Supplementary Information in Ref. 13). In our experiment, it would be this outer pair of MF states that could make Cooper pair transport between the two Nb contacts possible, leading to an enhancement of the conductance at zero-bias voltage. Because the existence of MF bound states in the TS-QD-TS system is independent of the parity of the quasi-particle occupation number as well as the energy position of the quasi-particle states in the QD, the ZBCP can appear in more than ten consecutive Coulomb blockade diamonds, regardless of the parity of quasi-particle occupation numbers and the energy position of the quasi-particle states in the QD.
As we discussed previously, two coherently connected MFs will hybridize into a pair of quasi-particle states with finite energies (see also the Supporting Information in Ref. 13). This hybridization will lead to splitting of the ZBCP and can serve as an important signature of the Majorana physics. In our TS-QD-TS system, there would exist two pairs of zero-energy MFs when there were no coupling between the two TS NW segments. In reality, the two inner MFs can be coherently coupled through the QD, leading to the creation of a pair of quasi-particle states at finite energies, while the outer two MFs can remain intact and staying at zero energy. As a consequence, the transport measurements can show a triple conductance peak structure, with two side differential conductance peaks appearing at finite bias voltages tunable by tuning the quasi-particle states in the QD and with the middle peak still staying at the zero bias voltage irrespective of the energy positions of the quasi-particle states in the QD.
In summary, we have studied a Nb-InSb NW QD-Nb hybrid device made from an epitaxially grown InSb NW with strong SOI on a Si/SiO2 substrate by charge transport measurements. At zero magnetic field, the device shows a series of well defined Coulomb blockade diamonds and the Kondo effect. At a fixed but sufficiently strong magnetic field applied perpendicularly to the substrate and thus to the NW, a pronounced ZBCP structure is observed in the Coulomb blockade regions and is found to be present in more than ten consecutive Coulomb blockade diamonds, irrespective of the even-odd parity of the quasi-particle occupation number and of the energy position of the quasi-particle states in the QD. We have also observed that the ZBCP is in most cases accompanied by two side differential conductance peaks located at finite bias voltages, forming a triple conductance peak structure. The splitting of the two side peaks is found to be correlated to the background conductance of the device. These observations are consistent with the signatures of MF physics in the device: In a NW based TS-QD-TS system, the two inner MFs are coherently coupled via the QD and are hybridized into a pair of quasi-particles with finite energies, while the two outer MFs remain as zero-energy modes and the entire system behaves as a TS NW.
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