Topological superconductors carry globally protected gapless boundary excitations, which are robust under local perturbations, and thus exhibit both fundamental and applicational importance. An unconventional pairing ...Topological superconductors carry globally protected gapless boundary excitations, which are robust under local perturbations, and thus exhibit both fundamental and applicational importance. An unconventional pairing with p-wave symmetry, such as a nontrivial topology in the superconductor’s wavefunction, is required to generate a non-zero Berry phase. Until now, the Bi2 Te3/2 H–NbSe2 heterostructure has proven to be a practical way to realize a topological superconductor in real materials. This complex system, where odd numbers of spin-momentum locked Dirac cone surface states on the topological insulator Bi2 Te3 become superconducting, induced by the proximate effect from the underlying s-wave superconductor 2 H–NbSe2, realizes an effective two-dimensional(2 D) spinless px + i py topological superconductor. In this review article, we summarize the recent experimental progress of the successful synthesis of Bi2 Te3/2 H–NbSe2 heterostructures using molecular beam epitaxy, determining the thickness limit of the heterostructure, detecting the long thought Majorana quasiparticle inside a magnetic vortex core state by means of scanning tunneling microscopy and demonstration of the unique spatial and spin properties of a Majorana zero mode.展开更多
In this paper, we apply the K-theory to classify topological trivial fermionic phases which, nonetheless,host symmetry-protected non-trivial defects. An important implication of our work is that the existence of Major...In this paper, we apply the K-theory to classify topological trivial fermionic phases which, nonetheless,host symmetry-protected non-trivial defects. An important implication of our work is that the existence of Majorana zero mode in the vortex core is neither a necessary nor a sufficient condition for the superconductor in question being topologically non-trivial.展开更多
In a superconducting topological insulator, a superconducting vortex line can trap a one-dimensional topological band with localized Majorana zero modes at the ends. Here, we study the effect of hexagonal warping and ...In a superconducting topological insulator, a superconducting vortex line can trap a one-dimensional topological band with localized Majorana zero modes at the ends. Here, we study the effect of hexagonal warping and its corresponding symmetry-breaking effect on vortex phase transition. We perform both analytical calculations based on a semiclassical formula and numerical calculations based on full quantum mechanics using the Bogoliubov-de Gennes equation. We find that the hexagonal warping term extends the topological region of the vortex line as the chemical potential changes and leads to MZMs, even in the absence of topological surface states.展开更多
We study the transport of chiral Majorana edge modes(CMEMs) in a hybrid quantum anomalous Hall insulator-topological superconductor(QAHI-TSC) system in which the TSC region contains a Josephson junction and a cavity. ...We study the transport of chiral Majorana edge modes(CMEMs) in a hybrid quantum anomalous Hall insulator-topological superconductor(QAHI-TSC) system in which the TSC region contains a Josephson junction and a cavity. The Josephson junction undergoes a topological transition when the magnetic flux through the cavity passes through half-integer multiples of magnetic flux quantum. For the trivial phase, the CMEMs transmit along the QAHI-TSC interface as without magnetic flux. However, for the nontrivial phase, a zero-energy Majorana state appears in the cavity, leading to that a CMEM can resonantly tunnel through the Majorana state to a different CMEM. These findings may provide a feasible scheme to control the transport of CMEMs by using the magnetic flux and the transport pattern can be customized by setting the size of the TSC.展开更多
We study the effects of the next-nearest-neighbor hopping and nearest-neighbor interactions on topological phases in a one-dimensional generalized Kitaev model. In the noninteracting case, we define a topological numb...We study the effects of the next-nearest-neighbor hopping and nearest-neighbor interactions on topological phases in a one-dimensional generalized Kitaev model. In the noninteracting case, we define a topological number and calculate exactly the phase diagram of the system. With addition of the next-nearest-neighbor hopping, the change of phase boundary between the topological and trivial regions can be described by an effective shift of the chemical potential. In the interacting case, we obtain the entanglement spectrum, the degeneracies of which correspond to the topological edge modes, by using the infinite time-evolving block decimation method. The results show that the interactions change the phase boundary as adding an effective chemical potential which can be explained by the change of the average number of particles.展开更多
Using two piezoelectric transducers, one measures the stress tensor response from the strain field generated by the second transducer. The ratio between the stress response and strain velocity determines the dissipati...Using two piezoelectric transducers, one measures the stress tensor response from the strain field generated by the second transducer. The ratio between the stress response and strain velocity determines the dissipative response. In the first part, we show that the dissipative stress response can be used for studying excitations in a topological superconductor. We investigate a topological superconductor for the case when an Abrikosov vortex lattice is formed. In this case, the Majorana fermions are dispersive, a fact that is used to compute the dissipative stress response. In the second part, we analyse the dissipative superfluid flow through solid 4He discoused recently. We identify low energy, an excitation which plays the role of the Majorana mode which is free to move in a direction perpendicular to the two dimensional plane spaces of the dislocations.展开更多
Majorana fermions in two-dimensional systems satisfy non-Abelian statistics. They are possible to exist in topological superconductors as quasi particles, which is of great significance for topological quantum computi...Majorana fermions in two-dimensional systems satisfy non-Abelian statistics. They are possible to exist in topological superconductors as quasi particles, which is of great significance for topological quantum computing. In this paper, we study a new promising system of superconducting topological surface state topological insulator thin films. We also study the phase diagrams of the model by plotting the Majorana edge states and the density of states in different regions of the phase diagram. Due to the mirror symmetry of the topological surface states, the Hamiltonian can be block diagonalized into two spin-triplet <i>p</i>-wave superconductors, which are also confirmed by the phase diagrams. The chiral Majorana edge modes may provide a new route for realizing topological quantum computation.展开更多
作为凝聚态物理中一类新奇准粒子态,Majorana零能模(Majorana zero mode)由于可用来实现拓扑量子计算而成为当前的研究热点.理论预言,Majorana零能模可作为特殊的束缚态出现在一些拓扑超导体的磁通涡旋中.但实际超导体磁通中还可能存在...作为凝聚态物理中一类新奇准粒子态,Majorana零能模(Majorana zero mode)由于可用来实现拓扑量子计算而成为当前的研究热点.理论预言,Majorana零能模可作为特殊的束缚态出现在一些拓扑超导体的磁通涡旋中.但实际超导体磁通中还可能存在其他低能束缚态或杂质态,这给Majorana零能模的辨别和具体应用带来了困难.目前实验上寻找合适的拓扑超导体系、分辨出清晰的Majorana零能模仍然是十分迫切的.本文主要介绍最近利用高能量分辨的扫描隧道显微镜,对电子掺杂铁硒类超导体(Li,Fe)OHFeSe和单层FeSe/SrTiO3磁通态进行的研究.实验上在前者的自由磁通中观测到清晰的零能模,并进一步测量到Majorana零能模的重要特征—量子化电导.而在后者磁通中只发现常规Caroli-de Gennes-Matricon(CdGM)束缚态,反映出s波对称性的特征.这系列实验既为Majorana零能模物性的进一步研究提供了合适平台,也为澄清铁基超导体中拓扑超导电性的来源提供了线索.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674226,11790313,11521404,11634009,U1632102,11504230,11674222,11574202,11674226,11574201,U1632272,U1732273,U1732159,11655002,1674220,and 11447601)the National Key Research and Development Program of China(Grant Nos.2016YFA0300403,2016YFA0301003,2016YFA0300500,and 2016YFA0300501)+2 种基金the Fund from the Technology Commission of Shanghai Municipality(Grant Nos.15JC402300 and 16DZ2260200)the Key Research Program of the Chinese Academy of Sciences(Grant No.XDPB08-2)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB28000000)
文摘Topological superconductors carry globally protected gapless boundary excitations, which are robust under local perturbations, and thus exhibit both fundamental and applicational importance. An unconventional pairing with p-wave symmetry, such as a nontrivial topology in the superconductor’s wavefunction, is required to generate a non-zero Berry phase. Until now, the Bi2 Te3/2 H–NbSe2 heterostructure has proven to be a practical way to realize a topological superconductor in real materials. This complex system, where odd numbers of spin-momentum locked Dirac cone surface states on the topological insulator Bi2 Te3 become superconducting, induced by the proximate effect from the underlying s-wave superconductor 2 H–NbSe2, realizes an effective two-dimensional(2 D) spinless px + i py topological superconductor. In this review article, we summarize the recent experimental progress of the successful synthesis of Bi2 Te3/2 H–NbSe2 heterostructures using molecular beam epitaxy, determining the thickness limit of the heterostructure, detecting the long thought Majorana quasiparticle inside a magnetic vortex core state by means of scanning tunneling microscopy and demonstration of the unique spatial and spin properties of a Majorana zero mode.
基金supported by the Theory Program at the Lawrence Berkeley National Laboratory, which is funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05CH11231
文摘In this paper, we apply the K-theory to classify topological trivial fermionic phases which, nonetheless,host symmetry-protected non-trivial defects. An important implication of our work is that the existence of Majorana zero mode in the vortex core is neither a necessary nor a sufficient condition for the superconductor in question being topologically non-trivial.
基金supported by the Air Force Office of Scientific Research(AFOSR)(Grant No.FA9550-14-1-0168)supported by the National Natural Science Foundation of China(Grant No.11674278)+1 种基金the National Basic Research Program of China(Grant No.2014CB921203)the CAS Center for Excellence in Topological Quantum Computation,and the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB28000000)
文摘In a superconducting topological insulator, a superconducting vortex line can trap a one-dimensional topological band with localized Majorana zero modes at the ends. Here, we study the effect of hexagonal warping and its corresponding symmetry-breaking effect on vortex phase transition. We perform both analytical calculations based on a semiclassical formula and numerical calculations based on full quantum mechanics using the Bogoliubov-de Gennes equation. We find that the hexagonal warping term extends the topological region of the vortex line as the chemical potential changes and leads to MZMs, even in the absence of topological surface states.
基金supported by the National Key Research and Development Program of China(Grant No.2017YFA0303301)the National Basic Research Program of China(Grant No.2015CB921102)+1 种基金the National Natural Science Fundation of China(Grants Nos.11574007,and 11534001)and the Key Research Program of the Chinese Academy of Sciences(Grant No.XDPB08-4)
文摘We study the transport of chiral Majorana edge modes(CMEMs) in a hybrid quantum anomalous Hall insulator-topological superconductor(QAHI-TSC) system in which the TSC region contains a Josephson junction and a cavity. The Josephson junction undergoes a topological transition when the magnetic flux through the cavity passes through half-integer multiples of magnetic flux quantum. For the trivial phase, the CMEMs transmit along the QAHI-TSC interface as without magnetic flux. However, for the nontrivial phase, a zero-energy Majorana state appears in the cavity, leading to that a CMEM can resonantly tunnel through the Majorana state to a different CMEM. These findings may provide a feasible scheme to control the transport of CMEMs by using the magnetic flux and the transport pattern can be customized by setting the size of the TSC.
基金Project supported by the National Basic Research Program of China(Grant No.2012CB921704)
文摘We study the effects of the next-nearest-neighbor hopping and nearest-neighbor interactions on topological phases in a one-dimensional generalized Kitaev model. In the noninteracting case, we define a topological number and calculate exactly the phase diagram of the system. With addition of the next-nearest-neighbor hopping, the change of phase boundary between the topological and trivial regions can be described by an effective shift of the chemical potential. In the interacting case, we obtain the entanglement spectrum, the degeneracies of which correspond to the topological edge modes, by using the infinite time-evolving block decimation method. The results show that the interactions change the phase boundary as adding an effective chemical potential which can be explained by the change of the average number of particles.
文摘Using two piezoelectric transducers, one measures the stress tensor response from the strain field generated by the second transducer. The ratio between the stress response and strain velocity determines the dissipative response. In the first part, we show that the dissipative stress response can be used for studying excitations in a topological superconductor. We investigate a topological superconductor for the case when an Abrikosov vortex lattice is formed. In this case, the Majorana fermions are dispersive, a fact that is used to compute the dissipative stress response. In the second part, we analyse the dissipative superfluid flow through solid 4He discoused recently. We identify low energy, an excitation which plays the role of the Majorana mode which is free to move in a direction perpendicular to the two dimensional plane spaces of the dislocations.
文摘Majorana fermions in two-dimensional systems satisfy non-Abelian statistics. They are possible to exist in topological superconductors as quasi particles, which is of great significance for topological quantum computing. In this paper, we study a new promising system of superconducting topological surface state topological insulator thin films. We also study the phase diagrams of the model by plotting the Majorana edge states and the density of states in different regions of the phase diagram. Due to the mirror symmetry of the topological surface states, the Hamiltonian can be block diagonalized into two spin-triplet <i>p</i>-wave superconductors, which are also confirmed by the phase diagrams. The chiral Majorana edge modes may provide a new route for realizing topological quantum computation.
基金supported in part by the National Natural Science Foundation of China (Nos. 61771234, 12004251)National Key Projects for Research and Development of China (No. 2017YFB0503302)+3 种基金the Natural Science Foundation of Shanghai (No. 20ZR1436100)the Science and Technology Commission of Shanghai Municipalitythe startup funding from ShanghaiTech UniversityBeijing National Laboratory for Condensed Matter Physics
文摘作为凝聚态物理中一类新奇准粒子态,Majorana零能模(Majorana zero mode)由于可用来实现拓扑量子计算而成为当前的研究热点.理论预言,Majorana零能模可作为特殊的束缚态出现在一些拓扑超导体的磁通涡旋中.但实际超导体磁通中还可能存在其他低能束缚态或杂质态,这给Majorana零能模的辨别和具体应用带来了困难.目前实验上寻找合适的拓扑超导体系、分辨出清晰的Majorana零能模仍然是十分迫切的.本文主要介绍最近利用高能量分辨的扫描隧道显微镜,对电子掺杂铁硒类超导体(Li,Fe)OHFeSe和单层FeSe/SrTiO3磁通态进行的研究.实验上在前者的自由磁通中观测到清晰的零能模,并进一步测量到Majorana零能模的重要特征—量子化电导.而在后者磁通中只发现常规Caroli-de Gennes-Matricon(CdGM)束缚态,反映出s波对称性的特征.这系列实验既为Majorana零能模物性的进一步研究提供了合适平台,也为澄清铁基超导体中拓扑超导电性的来源提供了线索.
