arXiv subjects

Masahiko Machida

Publications and source records attributed to Masahiko Machida.

At least 37 records · Page 2Linked to original sources

arXiv2014

Two-dimensional macroscopic quantum tunneling in multi-gap superconductor Josephson junctions

Low-temperature characters of superconducting devices yield definite probes for different superconducting phenomena. We study the macroscopic quantum tunneling (MQT) in a Josephson junction, composed of a single-gap superconductor and a two-gap superconductor. Since this junction has two kinds to the superconducting phase differences, calculating the MQT escape rate requires the analysis of quantum tunneling in a multi-dimensional configuration space. Our approach is the semi-classical approximation along a 1D curve in a 2D potential- energy landscape, connecting two adjacent potential (local) minimums through a saddle point. We find that this system has two plausible tunneling paths; an in-phase path and an out-of-phase path. The former is characterized by the Josephson-plasma frequency, whereas the latter is by the frequency of the characteristic collective mode in a two-band superconductor, Josephson- Leggett mode. Depending on external bias current and inter-band Josephson-coupling energy, one of them mainly contributes to the MQT. Our numerical calculations show that the difference between the in-phase path and the out-of-phase path is manifest, with respect to the bias- current-dependence of the MQT escape rate. This result suggests that our MQT setting be an indicator of the Josephson-Leggett mode.

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arXiv2014

Non-magnetic impurity effects in a three-dimensional topological superconductor: From p- to s-wave behaviors

Unconventional features in superconductivity are revealed by responses to impurity scattering. We study non-magnetic impurity effects in a three-dimensional topological superconductor, focusing on an effective model (massive Dirac Hamiltonian with s-wave on-site pairing) of Copper-doped bismuth-selenium compounds. Using a self-consistent T-matrix approach for impurity scattering, we examine in-gap states in density of states. We find that the results are well characterized by a single material variable, which measures relativistic effects in the Dirac Hamiltonian. In non-relativistic regime, an odd-parity superconducting state is fragile against non-magnetic impurities. We show that this behavior is caused by a p-wave character involved in the topological superconducting state. In contrast, we show that in relativistic regime the superconductivity is robust against non-magnetic impurities, owing to an s-wave character. To summarize, the system has two aspects, p- and s-wave features, depending on the weight of relativistic effects.

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arXiv2014

Impurity effects in a two-dimensional topological superconductor: A link of Tc-robustness with a topological number

Impurity effects are probes for revealing an unconventional property in superconductivity. We study effects of non-magnetic impurities, in a 2D topological superconductor with s-wave pairing, the Rashba spin-orbit coupling, and the Zeeman term. Using a self-consistent T-matrix approach, we calculate a phenomenological formula for the Thouless-Kohmoto-Nightingale-Nijs (TKNN) invariant in interacting systems, as well as density of states, with different magnetic fields. This quantity weakly depends on the magnetic field, when a spectral gap opens, whereas this changes drastically, when in-gap states occurs. Furthermore, in the latter case, we find that the Anderson's theorem (robustness of s-wave superconductivity against non-magnetic impurities) breaks down. We discuss the origin, from the viewpoints of both unconventional superconductivity and the TKNN invariant.

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arXiv2014

Theory of macroscopic quantum tunneling with Josephson-Leggett collective excitations in multi-band superconducting Josephson junctions

Collective excitations reveal fundamental properties and potential applications of superconducting states. We theoretically study macroscopic quantum tunneling (MQT) in a Josephson junction composed of multi-band superconductors, focusing on a phase mode induced by inter-band fluctuations: the Josephson-Leggett (JL) collective excitation mode. Using the imaginary-time path-integral method, we derive a formula for the MQT escape rate for low-temperature switching events. We clarify that the JL mode has two major effects on the MQT: (i) the zero-point fluctuations enhance the escape rate, and (ii) the quantum dissipation induced by the couplings to the gauge-invariant phase difference suppresses the quantum tunneling. We show that the enhancement exceeds the suppression for a wide range of junction parameters. This enhancement originates from the single-mode interaction between the tunneling variable and the inter-band fluctuations.

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arXiv2014

Spin-polarized Majorana Bound States inside a Vortex Core in Topological Superconductors

We reveal that Majorana bound states inside the vortex core in an odd-parity topological superconductivity classified as "pseudo-scalar" type in the gap function are distinctly spin-polarized by solving the massive Dirac Bogoliubov-de Gennes (BdG) equation considering the spin-orbit coupling. This result is universal for "Dirac superconductivity" whose rotational degree of freedom is characterized by the total angular momentum J = S + L and in marked contrast to the spin-degeneracy of the core bound states as the consequence of the conventional BdG equation. The spin-polarized vortex core can be easily detected by spin-sensitive probes such as the neutron scattering and other measurements well above the first critical magnetic field H_{c1}.

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arXiv2014

Quasiclassical Treatment and Odd-parity/Triplet Correspondence in Topological Superconductors

We construct a quasiclassical framework for topological superconductors with the strong spin-orbit coupling such as CuxBi2Se3. In the manner of the quasiclassical treatment, decomposing the slowly varying component from the total quasi-particle wave function, the original massive Dirac Bogoliubov-de Gennes (BdG) Hamiltonian derived from the tight-binding model represented by 8 x 8 matrix is reduced to 4 x 4 one. The resultant equations are equivalent to Andreev-type equations of singlet or triplet superconductors, in which the apparent spin-orbit coupling vanishes. Using this formalism, we find a fact that the odd-parity superconductivity in topological superconductors turns to the spin-triplet one. % without the spin-orbit coupling through the quasiclassical treatment. Moreover, in terms of the quasiclassical treatment, we show that the topologically-protected zero-energy states in topological superconductors has the correspondence to the Andreev bound states established in a long history of studies for the unconventional superconductors. This clearly indicates that low-energy non-trivial superconducting properties in the topological superconductors can be analyzed by the established theoretical descriptions on the spin-triplet superconductors.

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arXiv2014

Field-angle Resolved Flux-flow Resistivity as a Phase-sensitive Probe of Unconventional Cooper Pairing

We theoretically investigate the applied magnetic field-angle dependence of the flux-flow resistivity $ρ_{\rm f}(α_{\rm M})$ for an uniaxially anisotropic Fermi surface. $ρ_{\rm f}$ is related to the quasiparticle scattering rate $\varGamma$ inside a vortex core, which reflects the sign change in the superconducting pair potential. We find that $ρ_{\rm f}(α_{\rm M})$ is sensitive to the sign-change in the pair potential and has its maximum when the magnetic field is parallel to the gap-node direction. We propose the measurement of the field-angle dependent oscillation of $ρ_{\rm f}(α_{\rm M})$ as a phase-sensitive field-angle resolved experiment.

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arXiv2014

Quantum phases in $p$-orbital degenerated attractive 1D fermionic optical lattices

We examine quantum phases emerged by double degeneracy of $p$-orbital bands in attractive atomic Fermi gases loaded on a 1D optical lattice. Our numerical simulations by the density-matrix renormalization group predict the emergence of a state with a charge excitation gap, the Haldane insulator phase. A mapping onto an effective spin-$1$ model reveals its physical origin. Moreover, we show that population imbalance leads to richer diversity of the quantum phases, including a phase-separated polarized state. Finally, we study the effects of harmonic trap potential in this 1D chain.

cond-mat.quant-gas↗

arXiv2013

Massless collective excitations in frustrated multi-band superconductors

We study collective excitations in three- and four-band superconductors with inter-band frustration, which causes neither 0 nor $π$ inter-band phases in the superconducting state. Using a low-energy spin-Hamiltonian originating from a multi-band tight-binding model, we find that a massless Leggett mode occurs in a wide parameter region of this four-band system. This massless mode is related to the fact that the mean-field energy does not depend on a continuous superconducting phase. In other words, we find a link of the massless mode with a degeneracy between a time-reversal-symmetry-breaking state (neither 0 nor $π$ phases) and a time-reversal-symmetric state (either 0 or $π$ phases). Therefore, the mass of this collective mode characterizes well the time-reversal symmetry in frustrated multi-band superconductors.

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arXiv2013

Phonons and Spin Excitations in Fe-Based Superconductor Ca10Pt4As8(Fe1-xPtxAs)10 (x ~ 0.2)

By means of neutron inelastic scattering, magnetic excitations and phonons were measured for a single crystal of slightly overdoped superconductor Ca10Pt4As8(Fe1-xPtxAs)10 (x ~ 0.2) with the transition temperature Tc of ~33 K. Below Tc, magnetic excitation spectra \{chi}"(Q, ω) measured at Q = QM [magnetic Γ points] are gapped, and in the relatively higher ω region, the \{chi}"(QM, ω)-increase was observed with decreasing T, where the maximum of the increase was found at ~18 meV at 3 K (<< Tc). These characteristics are favorable to orbital-fluctuation-mediated superconductivity with the so-called S++symmetry of the order parameter. The energy dependence of δQ-temperature(T) curve of the magnetic excitations seems to have anomalous behavior in rather wide T region above Tc, δQ being the width of the Q scan profile. In the phonon measurements, we observed softening of the in-plane TA mode, which corresponds to the elastic constant C66. This softening seems to start at rather high temperature T, as T is lowered. Additionally, anomalous increase in spectral weights of the TO-phonons at around QM in the region 35 < ω < 40 meV was found even above Tc, as T is lowered from ambient T . Because the spectral weights in this ω region mainly correspond to the in-plane motions of Fe atoms and because orbital fluctuations are expected to be strong at around QM, the result may present clues to investigate a possible coupling between the fluctuations of the orbitals and lattice system.

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arXiv2013

Inhomogeneity Effects in Topological Superconductors

We have constructed a quasiclassical framework on superconductors with strong spin-orbit couplings, applicable to CuxBi2Se3[Y. Nagai, H. Nakamura, and M. Machida: arXiv:1305.3025]. The notable point is that in this framework the Bogoliubov-de Gennes Hamiltonians with suggested odd-parity pairing states turn to quasiclassical ones with usual spin-triplet Cooper pairs. Using this quasiclassical theory, we can investigate inhomogeneity effects such as the phenomena with vortices and surfaces in this superconductors and shed light on the pairing state of topological superconductors. In this paper, we apply the quasiclassical framework to the surface bound states with the Dirac-cone energy dispersion originated from the topological invariant in the parent compound Bi2Se3 in order to investigate the robustness of these bound states under the superconducting order parameter. The odd-parity gap functions can not open on the Dirac-cone-dispersion band in the Cu-doped Bi$_{2}$Se$_{3}$ superconductor. We show that the massless Dirac quasiparticles originated from the normal-state topological invariant and the Majorana quasiparticles coexist with each other on the surface in the odd-parity topological superconductivity. Inhomogeneity effects can be easily investigated with the use of our quasiclassical framework in topological superconductors.

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arXiv2013

Effect of anisotropic Fermi surface on the flux-flow resistivity under rotating magnetic field

We numerically investigate the effect of in-plane anisotropic Fermi surface (FS) on the flux-flow resistivity $ρ_{\rm f}$ under rotating magnetic field on the basis of the quasiclassical Green's function method. We demonstrate that one can detect the phase in pairing potential of Cooper pair through the field-angular dependence of $ρ_{\rm f}$ even if the FS has in-plane anisotropy. In addition, we point out one can detect the gap-node directions irrespective of the FS anisotropy by measuring $ρ_{\rm f}$ under rotating field.

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arXiv2013

Field-angle dependence of the quasiparticle scattering inside a vortex core in unconventional superconductors

We theoretically investigate the quasiparticle scattering rate $\varGamma$ inside a vortex core in the existence of non-magnetic impurities distributed randomly in a superconductor. We show that the dependence of $\varGamma$ on the magnetic field direction is sensitive to the sign of the pair potential. The behavior of $\varGamma$ is quite different between an s-wave and a d-wave pair potential, where these are assumed to have the same amplitude anisotropy, but a sign change only for the d-wave one. It is suggested that measurements of the microwave surface impedance with changing applied-field directions would be used for the phase-sensitive identification of pairing symmetry.

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arXiv2013

Effect of uniaxially anisotropic Fermi surface on the quasiparticle scattering inside a vortex core in unconventional superconductors

We theoretically study the dependence of the quasiparticle (QP) scattering rate $\varGamma$ on the uniaxial anisotropy of a Fermi surface with changing the magnetic field angle $α_{\rm M}$. We consider the QP scattering due to the non-magnetic impurities inside a single vortex core. The field-angle dependence of the quasiparticle scattering rate $\varGamma(α_{\rm M})$ is sensitive to the sign-change of the pair potential. We show that with increasing the two dimensionality of the system, $\varGamma(α_{\rm M})$ reflects more clearly whether there is the sign-change in the pair potential.

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arXiv2013

Phase-Sensitive Flux-Flow resistivity in Unconventional Superconductors

We theoretically investigate the magnetic-field-angle dependence of the flux-flow resistivity $ρ_{\rm f}$ in unconventional superconductors. Two contributions to $ρ_{\rm f}$ are considered: one is the quasiparticle (QP) relaxation time $τ(\bm{k}_{\rm F})$ and the other is $ω_0(\bm{k}_{\rm F})$, which is a counterpart to the interlevel spacing of the QP bound states in the quasiclassical approach. Here, $\bm{k}_{\rm F}$ denotes the position on a Fermi surface. Numerical calculations are conducted for a line-node s-wave and a d-wave pair potential with the same anisotropy of their amplitudes, but with a sign change only for a d-wave one. We show that the field-angle dependence of $ρ_{\rm f}$ differs prominently between s-wave and d-wave pairs, reflecting the phase of the pair potentials. We also discuss the case where $τ$ is constant and compare it with the more general case where $τ$ depends on $\bm{k}_{\rm F}$.

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arXiv2012

Nontrivial Haldane phase of an atomic two-component Fermi gas trapped in a 1d optical lattice

We propose how to create a non-trivial Haldane phase in atomic two-component Fermi-gas loaded on one-dimensional (1-D) optical lattice with trap potential. The Haldane phase is naturally formed on $p$-band Mott core in a wide range of the strong on-site repulsive interaction. The present proposal is composed of two steps, one of which is theoretical derivation of an effective 1-D S=1 interacting-chain model from the original tight-binding Hamiltonian handling the two $p$-orbitals, and the other of which is numerical demonstration employing the density-matrix renormalization-group for the formation of the Haldane phase on $p$-band Mott core and its associated features in the original tight-binding model with the harmonic trap potential.

cond-mat.quant-gas↗

arXiv2012

Rotational Isotropy Breaking as Proof for Spin-polarized Cooper Pairs in the Topological Superconductor CuxBi2Se3

In a promising candidate of topological superconductors, CuxBi2Se3, we propose a way to exclusively determine the pairing symmetry. The proposal suggests that the angle dependence of the thermal conductivity in the basal ab-plane shows a distinct strong anisotropy only when the pairing symmetry is an odd-parity spin-polarized triplet below the superconducting transition temperature (Tc). Such striking isotropy breaking below Tc is explicitly involved in Dirac formalism for superconductors, in which the spin-orbit coupling is essential. We classify possible gap functions based on the Dirac formalism and clarify an origin of the isotropy breaking.

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arXiv2012

Direct Numerical Demonstration of Sign-preserving Quasiparticle Interference via Impurity inside Vortex Core in Unconventional Superconductors

We perform large-scale numerical calculations self-consistently solving the Bogoliubov-de Gennes (BdG) equations in the magnetic field together with random impurities to directly demonstrate the typical quasi-particle interference (QPI) in the presence of vortices as observed by scanning tunneling microscopy/spectroscopy experiments in unconventional superconductors. The calculations reveal that vortex itself never works as a scatter causing the QPI pattern but vortex core containing impurity brings about the enhancement of the sign-preserving QPI peaks. Its origin is Andreev bound-states distorted by impurity, and all the measurement findings are consistently explained by the scenario based on the numerical results.

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