arXiv subjects

Masatoshi Sato

Publications and source records attributed to Masatoshi Sato.

At least 127 records · Page 7Linked to original sources

arXiv2012

Theory of tunneling spectroscopy for chiral topological superconductors

We study the charge conductance of an interface between a normal metal and a superconducting quantum anomalous Hall system, based on the recursive Green's function. The angle resolved conductance gamma(ky, eV) with the momentum ky parallel to the interface and the bias voltage V shows a rich structure depending on the Chern number N of the system. We find that when the bias voltage is tuned to the energy dispersion of the edge mode, eV = Eedge(ky), the angle resolved conductance gamma(ky,Eedge(ky)) shows a pronounced even-odd effect; the conductance vanishes for N = 0 or 2 while it takes a universal value 2e^2/h for N = 1. In particular, in N = 2 phase, we find that the conductance gamma(ky,Eedge(ky)) becomes zero due to interference of two degenerate Majorana edge modes, although the corresponding surface spectral weight remains non-zero.

cond-mat.supr-con↗

arXiv2012

Topological Field Theory for p-wave Superconductors

We propose a topological field theory for a spin-less two-dimensional chiral superconductor that contains fundamental Majorana fields. Due to a fermionic gauge symmetry, the Majorana modes survive as dynamical degrees of freedom only at magnetic vortex cores, and on edges. We argue that these modes have the topological properties pertinent to a p-wave superconductor including the non-abelian braiding statistics, and support this claim by calculating the ground state degeneracy on a torus. We also briefly discuss the connection to the Moore-Read Pfaffian quantum Hall state, and extensions to the spinful case and to three-dimensonal topological superconductors.

cond-mat.supr-con↗

arXiv2012

Tunneling Conductance and Surface States Transition in Superconducting Topological Insulators

We develop a theory of the tunneling spectroscopy for superconducting topological insulators (STIs), where the surface Andreev bound states (SABSs) appear as helical Majorana fermions. Based on the symmetry and topological nature of parent topological insulators, we find that the SABSs in the STIs have a profound structural transition in the energy dispersions. The transition results in a variety of Majorana fermions, by tuning the chemical potential and the effective mass of the energy band. We clarify that Majorana fermions in the vicinity of the transitions give rise to robust zero bias peaks in the tunneling conductance between normal metal/STI junctions.

cond-mat.supr-con↗

arXiv2011

A signature formula for hyperelliptic broken Lefschetz fibrations

A hyperelliptic broken Lefschetz fibration is a generalization of a hyperelliptic Lefschetz fibration. We construct and compute a local signature of hyperelliptic directed broken Lefschetz fibrations by generalizing Endo's local signature of hyperelliptic Lefschetz fibrations. It is described by his local signature and a rational-valued homomorphism on the subgroup of the hyperelliptic mapping class group which preserves a simple closed curve setwise.

math.GT↗

arXiv2011

Topological Superconductivity in CuxBi2Se3

A topological superconductor (TSC) is characterized by the topologically-protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator CuxBi2Se3, which superconducts below ~3 K, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting CuxBi2Se3 present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana Fermions and gives evidence for a topological superconductivity in CuxBi2Se3. In addition, we found an unusual pseudogap that develops below ~20 K and coexists with the topological superconducting state.

cond-mat.supr-con↗

arXiv2011

Four-manifolds admitting hyperelliptic broken Lefschetz fibrations

We introduce hyperelliptic simplified (more generally, directed) broken Lefschetz fibrations, which is a generalization of hyperelliptic Lefschetz fibrations. We construct involutions on the total spaces of such fibrations of genus $g\geq 3$ and extend these involutions to the four-manifolds obtained by blowing up the total spaces. The extended involutions induce double branched coverings over blown up sphere bundles over the sphere. We also show that the regular fiber of such a fibration of genus $g\geq 3$ represents a non-trivial rational homology class of the total space.

math.GT↗

arXiv2011

Symmetry and Topology in Superconductors - Odd-frequency pairing and edge states -

Superconductivity is a phenomenon where the macroscopic quantum coherence appears due to the pairing of electrons. This offers a fascinating arena to study the physics of broken gauge symmetry. However, the important symmetries in superconductors are not only the gauge invariance. Especially, the symmetry properties of the pairing, i.e., the parity and spin-singlet/spin-triplet, determine the physical properties of the superconducting state. Recently it has been recognized that there is the important third symmetry of the pair amplitude, i.e., even or odd parity with respect to the frequency. The conventional uniform superconducting states correspond to the even-frequency pairing, but the recent finding is that the odd-frequency pair amplitude arises in the spatially non-uniform situation quite ubiquitously. Especially, this is the case in the Andreev bound state (ABS) appearing at the surface/interface of the sample. The other important recent development is on the nontrivial topological aspects of superconductors. As the band insulators are classified by topological indices into (i) conventional insulator, (ii) quantum Hall insulator, and (iii) topological insulator, also are the gapped superconductors. The influence of the nontrivial topology of the bulk states appears as the edge or surface of the sample. In the superconductors, this leads to the formation of zero energy ABS (ZEABS). Therefore, the ABSs of the superconductors are the place where the symmetry and topology meet each other which offer the stage of rich physics. In this review, we discuss the physics of ABS from the viewpoint of the odd-frequency pairing, the topological bulk-edge correspondence, and the interplay of these two issues. It is described how the symmetry of the pairing and topological indices determines the absence/presence of the ZEABS, its energy dispersion, and properties as the Majorana fermions.

cond-mat.supr-con↗

arXiv2011

Edge states and topological phases in non-Hermitian systems

Topological stability of the edge states is investigated for non-Hermitian systems. We examine two classes of non-Hermitian Hamiltonians supporting real bulk eigenenergies in weak non-Hermiticity: SU(1,1) and SO(3,2) Hamiltonians. As an SU(1,1) Hamiltonian, the tight-binding model on the honeycomb lattice with imaginary on-site potentials is examined. Edge states with ReE=0 and their topological stability are discussed by the winding number and the index theorem, based on the pseudo-anti-Hermiticity of the system. As a higher symmetric generalization of SU(1,1) Hamiltonians, we also consider SO(3,2) models. We investigate non-Hermitian generalization of the Luttinger Hamiltonian on the square lattice, and that of the Kane-Mele model on the honeycomb lattice, respectively. Using the generalized Kramers theorem for the time-reversal operator Theta with Theta^2=+1 [M. Sato et al., arXiv:1106.1806], we introduce a time-reversal invariant Chern number from which topological stability of gapless edge modes is argued.

cond-mat.mes-hall↗

arXiv2011

Time-Reversal Symmetry in Non-Hermitian Systems

For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy when the system has a half-odd-integer spin and the time reversal operator obeys Θ^2=-1, but no such a degeneracy exists when Θ^2=+1. Here we point out that for non-hermitian systems, there exists a degeneracy similar to Kramers even when Θ^2=+1. It is found that the new degeneracy follows from the mathematical structure of split-quaternion, instead of quaternion from which the Kramers degeneracy follows in the usual hermitian cases. Furthermore, we also show that particle/hole symmetry gives rise to a pair of states with opposite energies on the basis of the split quaternion in a class of non-hermitian Hamiltonians. As concrete examples, we examine in detail NxN Hamiltonians with N=2 and 4 which are non-hermitian generalizations of spin 1/2 Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.

cond-mat.stat-mech↗

arXiv2011

Theory of edge states in a quantum anomalous Hall insulator/ spin-singlet s-wave superconductor hybrid system

We study the edge states for a quantum anomalous Hall system (QAHS) coupled with a spin-singlet s-wave superconductor through the proximity effect, and clarify the topological nature of them. When we consider a superconducting pair potential induced in the QAHS, there appear topological phases with nonzero Chern numbers, $i.e.$, ${\cal N}=1$ and ${\cal N}=2$, where Andreev bound states appear as chiral Majorana edge modes. We calculate the energy spectrum of the edge modes and the resulting local density of states. It is found that the degenerate chiral Majorana edge modes for ${\cal N}=2$ are lifted off by applying Zeeman magnetic field along the parallel to the interface or the shift of the chemical potential by doping. The degeneracy of the chiral Majorana edge modes and its lifting are explained by two different winding numbers defined at the time-reversal invariant point of the edge momentum.

cond-mat.supr-con↗

arXiv2011

Study of Ni-doping Effect of Specific Heat and Transport Properties for LaFe1-yNiyAsO0.89F0.11

Specific heats and transport quantities of the LaFe1-yNiyAsO0.89F0.11 system have been measured, and the results are discussed together with those reported previously by our group mainly for LaFe1-yCoyAsO0.89F0.11 and LaFeAsO0.89-xF0.11+x systems. The y dependence of the electronic specific heat coefficient gamma can basically be understood by using the rigid-band picture, where Ni ions provide 2 electrons to the host conduction bands and behave as nonmagnetic impurities. The superconducting transition temperature Tc of LaFe1-yNiyAsO0.89F0.11 becomes zero, as the carrier density p (=2y+0.11) doped to LaFeAsO reaches its critical value p_c_ ~0.2. This p_c_ value of ~0.2 is commonly observed for LaFe1-yCoyAsO0.89F0.11 and LaFeAsO0.89-xF0.11+x systems, in which the relations p = x+0.11 and p = y+0.11 hold, respectively. As we pointed out previously, the critical value corresponds to the disappearance of the hole-Fermi surface. These results indicate that the carrier number solely determines the Tc value. We have not observed appreciable effects of pair breaking, which originates from the nonmagnetic impurity scattering of conduction electrons and strongly suppresses T_c_ values of systems with sign-reversing of the order parameter over the Fermi surface(s). On the basis of the results, the so-called s_+-_ symmetry of the order parameter with the sign-reversing is excluded.

cond-mat.supr-con↗

arXiv2011

Topology of Andreev Bound States with Flat Dispersion

A theory of dispersionless Andreev bound states on surfaces of time-reversal invariant unconventional superconductors is presented. The generalized criterion for the dispersionless Andreev bound state is derived from the bulk-edge correspondence, and the chiral spin structure of the dispersionless Andreev bound states is argued from which the Andreev bound state is stabilized. Then we summarize the criterion in a form of index theorems. The index theorems are proved in a general framework to certify the bulk-edge correspondence. As concrete examples, we discuss (i) dxy-wave superconductor (ii) px-wave superconductor, and (iii) noncentrosymmetric superconductors. In the last example, we find a peculiar time-reversal invariant Majorana fermion. The time-reversal invariant Majorana fermion shows an unusual response to the Zeeman magnetic field, which can be used to identify it experimentally.

cond-mat.supr-con↗

arXiv2010

Magnetic Ordering in V-Layers of the Superconducting System of Sr2VFeAsO3

Results of transport, magnetic, thermal, and 75As-NMR measurements are presented for superconducting Sr2VFeAsO3 with an alternating stack of FeAs and perovskite-like block layers. Although apparent anomalies in magnetic and thermal properties have been observed at ~150 K, no anomaly in transport behaviors has been observed at around the same temperature. These results indicate that V ions in the Sr2VO3-block layers have localized magnetic moments and that V-electrons do not contribute to the Fermi surface. The electronic characteristics of Sr2VFeAsO3 are considered to be common to those of other superconducting systems with Fe-pnictogen layers.

cond-mat.supr-con↗

arXiv2010

Surface density of states and topological edge states in non-centrosymmetric superconductors

We study Andreev bound state (ABS) and surface density of state (SDOS) of non-centrosymmetric superconductor where spin-singlet $d$-wave pairing mixes with spin-triplet $p$ (or $f)$-wave one by spin-orbit coupling. For $d_{xy} + p$-wave pairing, ABS appears as a zero energy state. The present ABS is a Majorana edge mode preserving the time reversal symmetry. We calculate topological invariant number and discuss the relevance to a single Majorana edge mode. In the presence of the Majorana edge mode, the SDOS depends strongly on the direction of the Zeeman field.

cond-mat.supr-con↗

arXiv2010

75As-NMR Studies of LaFeAsO1-xFx for Various x Values

Results of 75As NMR and NQR measurements are reported for superconducting samples of LaFeAsO1-xFx with various x values. The x dependent widths of the superconducting transition and those of the NQR spectra indicate that the optimally doped LaFeAsO1-xFx sample with the superconducting transition temperature Tc ~28 K has the smallest width or smallest inhomogeneity of the superconducting order parameter Δ. In the analyses of the temperature (T) dependence of the NMR longitudinal relaxation rate 1/T1, we have tried to use a simple relation 1/T1 ~ T^n to see how fast 1/T1 decreases when the superconducting order parameter grows. The relation holds rather well in the T region of ~0.3Tc < T =< Tc, and n varies from 2.5-6 with varying x, having the maximum value 5-6 at the optimal x. These results indicate that the x dependence of n originates from the spatial distribution of Δ, and that the T^{5-6} behavior is considered to be intrinsic to this system.

cond-mat.supr-con↗

arXiv2010

Non-Abelian Topological Orders and Majorana Fermions in Spin-Singlet Superconductors

The non-Abelian topological order for superconductors is characterized by the existence of zero-energy Majorana fermions in edges of systems and in a vortex of a macroscopic condensate, which obey the non-Abelian statistics. This paper is devoted to an extensive study on the non-Abelian topological phase of spin-singlet superconductors with the Rashba spin-orbit interaction proposed in our previous letter [M. Sato, Y. Takahashi, and S. Fujimoto, Phys. Rev. Lett. 103, 020401 (2009)]. We mainly consider the s-wave pairing state and the d+id pairing state. In the case of d+id-wave pairing, Majorana fermions appear in almost all parameter regions of the mixed state under an applied magnetic field, provided that the Fermi level crosses k-points in the vicinity of the Gamma point or the M point in the Brillouin zone, while in the case of s-wave pairing, a strong magnetic field, the Zeeman energy of which is larger than the superconducting gap is required to realize the topological phase. We clarify that Majorana fermions in Rashba spin-singlet superconductors are much more stable than those realized in spin-triplet p+ip superconductors in certain parameter regions. We also investigate the topological number which ensures the topological stability of the phase in detail. Furthermore, as a byproduct, we found that topological order is also realized in conventional spin (or charge) density wave states with the Rashba spin-orbit interaction, for which massless Dirac fermions appear in the edge of the systems and charge fractionalization occurs.

cond-mat.supr-con↗

arXiv2010

Majorana Fermions in Nodal Superconductors: Gapless Topological Phase

We demonstrate that Majorana fermions exist in edges of systems and in a vortex core even for superconductors with nodal excitations such as the d-wave pairing state under a particular but realistic condition in the case with an anti-symmetric spin-orbit interaction and a nonzero magnetic field below the upper critical field. We clarify that the Majorana fermion state is topologically protected in spite of the presence of bulk gapless nodal excitations, because of the existence of a nontrivial topological number. Our finding drastically enlarges target systems where we can explore the Majorana fermion state.

cond-mat.supr-con↗

arXiv2010

Anomalous Andreev bound state in non-centrosymmetric superconductors

We study edge states of non-centrosymmetric superconductors where spin-singlet d-wave pairing mixes with spin-triplet p (or f)-wave one by spin-orbit coupling. For dxy-wave pairing, the obtained Andreev bound state has an anomalous dispersion as compared to conventional helical edge modes. A unique topologically protected time-reversal invariant Majorana fermion appears at the edge. The charge conductance in the non-centrosymmetric superconductor junctions reflects the anomalous structures of the dispersions, particularly the time-reversal invariant Majorana fermion is manifested as a zero bias conductance peak.

cond-mat.supr-con↗