arXiv subjects

Jie Fan

Publications and source records attributed to Jie Fan.

62 records · Page 4Linked to original sources

arXiv2015

Logics of Essence and Accident

In the literature, essence is formalized in two different ways, either de dicto, or de re. Following \cite{Marcos:2005}, we adopt its de dicto formalization: a formula is essential, if once it is true, it is necessarily true; otherwise, it is accidental. In this article, we study the model theory and axiomatization of the logic of essence and accident, i.e. the logic with essence operator (or accident operator) as the only primitive modality. We show that the logic of essence and accident is less expressive than modal logic on non-reflexive models, but the two logics are equally expressive on reflexive models. We prove that some frame properties are undefinable in the logic of essence and accident, while some are. We propose the suitable bisimulation for this logic, based on which we characterize the expressive power of this logic within modal logic and within first-order logic. We axiomatize this logic over various frame classes, among which the symmetric case is missing, and our method is more suitable than those in the literature. We also find a method to compute certain axioms used to axiomatize this logic over special frames in the literature. As a side effect, we answer some open questions raised in \cite{Marcos:2005}.

cs.LO↗

arXiv2015

Logics of Strong Noncontingency

Inspired by Hintikka's treatment of question embedding verbs in [8] and the variations of noncontingency operator, we propose a logic with strong noncontingency operator $\blacktriangle$ as the only primitive modality. A proposition is strongly noncontingent, if no matter whether it is true or false, it does it necessarily; otherwise, it is weakly contingent. This logic is not a normal modal logic, since $\blacktriangle(ϕ\toψ)\to(\blacktriangleϕ\to\blacktriangleψ)$ is invalid. We compare the relative expressivity of this logic and other logics, such as standard modal logic, noncontingency logic, and logic of essence and accident, and investigate its frame definability. Apart from these results, we also propose a suitable notion of bisimulation for the logic of strong noncontingency, based on which we characterize this logic within modal logic and within first-order logic. We also axiomatize the logic of strong noncontingency over various frame classes. Our work is also related to the treatment of agreement operator in [10].

cs.LO↗

arXiv2013

Knowing Whether

Knowing whether a proposition is true means knowing that it is true or knowing that it is false. In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that. This logic is not a normal modal logic, because we do not have Kw (phi -> psi) -> (Kw phi -> Kw psi). Knowing whether logic cannot define many common frame properties, and its expressive power less than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing knowing whether logics non-trivial. We axiomatize knowing whether logic over various frame classes. We also present an extension of knowing whether logic with public announcement operators and we give corresponding reduction axioms for that. We compare our work in detail to two recent similar proposals.

cs.AI↗

arXiv2013

Anomalous Cooper pair interference on Bi2Te3 surface

It is believed that the edges of a chiral p-wave superconductor host Majorana modes, relating to a mysterious type of fermions predicted seven decades ago. Much attention has been paid to search for p-wave superconductivity in solid-state systems, including recently those with strong spin-orbit coupling (SOC). However, smoking-gun experiments are still awaited. In this work, we have performed phase-sensitive measurements on particularly designed superconducting quantum interference devices constructing on the surface of topological insulators Bi2Te3, in such a way that a substantial portion of the interference loop is built on the proximity-effect-induced superconducting surface. Two types of Cooper interference patterns have been recognized at low temperatures. One is s-wave like and is contributed by a zero-phase loop inhabited in the bulk of Bi2Te3. The other, being identified to relate to the surface states, is anomalous for that there is a phase shift between the positive and negative bias current directions. The results support that the Cooper pairs on the surface of Bi2Te3 have a 2πBerry phase which makes the superconductivity p_x+ip_y-wave-like. Mesoscopic hybrid rings as constructed in this experiment are presumably arbitrary-phase loops good for studying topological quantum phenomena.

cond-mat.mes-hall↗

arXiv2012

Proximity-effect-induced superconductivity in topological insulator-related material Bi2Se3

We have studied the electron transport properties of topological insulator-related material Bi2Se3 near the superconducting Pb-Bi2Se3 interface, and found that a superconducting state is induced over an extended volume in Bi2Se3. This state can carry a Josephson supercurrent, and demonstrates a gap-like structure in the conductance spectra as probed by a normal-metal electrode. The establishment of the gap is not by confining the electrons into a narrow space close to the superconductor-normal metal interface, as previously observed in other systems, but presumably via electron-electron attractive interaction in Bi2Se3.

cond-mat.supr-con↗

arXiv2012

Proximity effect at superconducting Sn-Bi2Se3 interface

We have investigated the conductance spectra of Sn-Bi2Se3 interface junctions down to 250 mK and in different magnetic fields. A number of conductance anomalies were observed below the superconducting transition temperature of Sn, including a small gap different from that of Sn, and a zero-bias conductance peak growing up at lower temperatures. We discussed the possible origins of the smaller gap and the zero-bias conductance peak. These phenomena support that a proximity-effect-induced chiral superconducting phase is formed at the interface between the superconducting Sn and the strong spin-orbit coupling material Bi2Se3.

cond-mat.supr-con↗

arXiv2011

Strong Superconducting Proximity Effect in Pb-Bi2Te3 Hybrid Structures

Majarona fermions (MFs) were predicted more than seven decades ago but are yet to be identified [1]. Recently, much attention has been paid to search for MFs in condensed matter systems [2-10]. One of the seaching schemes is to create MF at the interface between an s-wave superconductor (SC) and a 3D topological insulator (TI) [11-13]. Experimentally, progresses have been achieved in the observations of a proximity-effect-induced supercurrent [14-16], a perfect Andreev reflection [17] and a conductance peak at the Fermi level [18]. However, further characterizations are still needed to clarify the nature of the SC-TI interface. In this Letter, we report on a strong proximity effect in Pb-Bi2Te3 hybrid structures, based on which Josephson junctions and superconducting quantum interference devices (SQUIDs) can be constructed. Josephson devices of this type would provide a test-bed for exploring novel phenomena such as MFs in the future.

cond-mat.mes-hall↗

arXiv2011

Aharonov-Casher effect in Bi$_{\rm 2}$Se$_{\rm 3}$ square-ring interferometers

Electrical control of spin dynamics in Bi$_{\rm 2}$Se$_{\rm 3}$ was investigated in ring-type interferometers. Aharonov-Bohm and Altshuler-Aronov-Spivak resistance oscillations against magnetic field, and Aharorov-Casher resistance oscillations against gate voltage were observed in the presence of a Berry phase of $π$. A very large tunability of spin precession angle by gate voltage has been obtained, indicating that Bi$_{\rm 2}$Se$_{\rm 3}$-related materials with strong spin-orbit coupling are promising candidates for constructing novel spintronic devices.

cond-mat.mes-hall↗