arXiv subjects

Shun Tamura

Publications and source records attributed to Shun Tamura.

At least 19 recordsLinked to original sources

arXiv2024

Odd-frequency pairing due to Majorana and trivial Andreev bound states

Majorana and trivial Andreev bound states are predicted to appear in superconductor-semiconductor hybrid systems, but their identification is still a challenging task. Here we consider superconducting junctions with Rashba spin-orbit coupling and explore the signatures of Majorana and trivial Andreev bound states in the emergent superconducting correlations when the systems are subjected to an external Zeeman field. We first show that robust zero-energy Andreev bound states naturally appear due to confinement and helicity when the normal sector of the junction becomes helical. These Andreev states can evolve into Majorana states, developing alike oscillations around zero energy as a function of Zeeman field. Unlike Majorana states located at both ends, helical Andreev states are located at the interface. We then demonstrate that the emergent superconducting correlations are locally composed of even-frequency spin-singlet even-parity and odd-frequency spin-triplet even-parity pair amplitudes, which coexist due to the interplay of spin-orbit coupling, Zeeman field, and spatial translation invariance breaking. In the helical regime, trivial Andreev states enhance odd-frequency spin-triplet pairing, which decays in the superconductor and has a homogeneous long-range profile in the normal region. At zero frequency, however, odd-frequency spin-triplet pairing vanishes in the helical regime. In the topological phase, Majorana states enhance odd-frequency spin-triplet pairing, producing a long-range homogeneous leakage into the normal region. Interestingly, we discover that when Majorana states are truly zero-energy modes, odd-frequency pairing develops a divergent low-frequency profile, which we interpret as the unambiguous self-conjugated Majorana signature. Our results help understand Majorana and trivial Andreev states from a superconducting correlations perspective in Majorana devices.

cond-mat.supr-con↗

arXiv2024

Meissner effect in non-Hermitian superconductors

We study theoretically Meissner effect in non-Hermitian systems of BCS type, i.e., with an electron-electron interaction leading to the mean field description in a Cooper channel, via superfluid stiffness. We show that depending on the values of the mean fields, chemical potential, and temperature, we obtain paramagnetic or diamagnetic Meissner effect. Notably, positive real part of the product of mean fields guarantees diamagnetic Meissner effect in an $s$-wave 3D non-Hermitian superconductor. Once the mean fields are close to being anti-Hermitian, 2D $s$-, $p_x$-, and $d$-wave superconductors exhibit interesting behaviour, including negative superfluid stiffness giving paramagnetic Meissner effect for certain parameters. Negative superfluid stiffness indicates instability of this collective state.

cond-mat.supr-con↗

arXiv2024

Odd-frequency pairing of Bogoliubov quasiparticles in superconductor junction

We study a superconductor Josephson junction with a Bogoliubov Fermi surface, employing McMillan's Green's function technique. The low-energy degrees of freedom are described by spinless fermions (bogolons), where the characteristic feature appears as an odd-frequency pair potential. The differential equation of the Green's function is reduced to the eigenvalue problem of the non-Hermitian effective Hamiltonian. The physical quantities such as the density of states and pair amplitude are then extracted from the obtained Green's function. We find that the zero energy local density of states at the interface decreases as the relative phase of the Josephson junction increases. This decrease is accompanied by the generation of an even-frequency pair amplitude near the interface. We also clarify that the $\pi$-junction-like current phase relation is realized in terms of bogolons. In contrast to conventional $s$-wave superconductor junctions, where even-frequency pairs dominate in the bulk and odd-frequency pairs are generated near the interface, our findings illuminate the distinct behaviors of junctions with Bogoliubov Fermi surfaces. We further explore spatial dependences of these physical quantities systematically using quasiclassical Green's functions.

cond-mat.supr-con↗

arXiv2024

Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors

Majorana zero modes have been shown to be the simplest quasiparticles exhibiting pure odd-frequency pairing, an effect that has so far been theoretically established in the static regime. In this work, we investigate the formation of Majorana modes and odd-frequency pairing in $p$-wave spin-polarized superconductors under a time-dependent drive. We first show that the driven system hosts multiple Majorana modes emerging at zero and $\pi$, whose formation can be controlled by an appropriate tuning of the drive frequency and chemical potential, in agreement with previous studies. Then we explore the induced pair correlations and find that odd-frequency spin-polarized $s$-wave pairing is broadly induced, acquiring large values in the presence of Majorana modes. We discover that, while odd-frequency pairing is proportional to $\sim1/\omega$ in the presence of Majorana zero modes, it is proportional to $\sim 1/(\omega-\pi\hbar/T)$ in the presence of Majorana $\pi$ modes, where $T$ is the periodicity of the drive. Furthermore, we find that the amount of odd-frequency pairing becomes larger when multiple Majorana modes appear but the overall divergent profile as a function of frequency remains. We also show that the divergent odd-frequency pairing is robust against scalar disorder. Notably, we establish a spectral bulk-boundary correspondence between the amount of boundary odd-$\omega$ pairing and the bulk topological invariants in driven chiral systems, which we show to be protected by chiral symmetry and is thus robust against disorder. Our work thus paves the way for understanding the emergent pair correlations in driven topological superconductors

cond-mat.supr-con↗

arXiv2024

Theory of Majorana zero modes in unconventional superconductors

Majorana fermions are spin-1/2 neutral particles that are their own antiparticles and were initially predicted by Ettore Majorana in particle physics but their observation still remains elusive. The concept of Majorana fermions has been borrowed into condensed matter physics, where, unlike particle physics, Majorana fermions emerge as zero-energy quasiparticles that can be engineered by combining electrons and holes and have therefore been coined Majorana zero modes. In this review, we provide a pedagogical explanation of the basic properties of Majorana zero modes in unconventional superconductors and their consequences in experimental observables, putting a special emphasis on the initial theoretical discoveries. In particular, we first show that Majorana zero modes are self-conjugated and emerge as a special type of zero energy surface Andreev bound states at the boundary of unconventional superconductors. We then explore Majorana zero modes in one-dimensional spin-polarized $p$-wave superconductors, where we address the formation of topological superconductivity and the physical realization in superconductor-semiconductor hybrids. In this part we highlight that Majorana quasiparticles appear as zero-energy edge states, exhibiting charge neutrality, spin-polarized, and spatial nonlocality as unique properties that can be already seen from their energies and wavefunctions. Next, we discuss analytically obtained Green's functions of $p$-wave superconductors and demonstrate that the emergence of Majorana zero modes is always accompanied by the formation of odd-frequency spin-triplet pairing as a unique result of the self-conjugate nature of Majorana zero modes. We finally address the signatures of Majorana zero modes in tunneling spectroscopy, including the anomalous proximity effect, and the phase-biased Josephson effect.

cond-mat.supr-con↗

arXiv2023

Equal contribution of even and odd frequency pairing to transport across normal metal-superconductor junctions

Odd-frequency pairing is an unconventional type of Cooper pairing in superconductors related to the frequency dependence of the corresponding anomalous Green function. We show by a combination of analytical and numerical methods that odd-frequency pairing is ubiquitously present in the current of Andreev-scattered particles across a junction formed by a normal metal (N) and a superconductor (S), even if the superconducting pairing is of conventional $s$-wave, spin singlet type. We carefully analyze the conductance of NS junctions with different pairing symmetries ($s$-wave, $p$-wave, $d$-wave). In all cases, we identify a generic equal balance of even and odd frequency pairing to the contributions related to Andreev reflection. This analysis shows in retrospect that the presence of odd-frequency pairing in electric currents across NS junctions is rather the rule, not the exception. This insight stems from an alternative approach of analyzing the transport problem of hybrid structures. It is based on the Kubo-Greenwood formula with direct access to symmetries of the anomalous Green functions characterizing the superconducting pairing. We expect that our predictions substantially enrich the interpretation of transport data across NS junctions in many material combinations.

cond-mat.supr-con↗

arXiv2023

$\eta$-pairing on bipartite and non-bipartite lattices

The $\eta$-pairing is a type of Cooper pairing state in which the phase of the superconducting order parameter is aligned in a staggered manner, in contrast to the usual BCS superconductors with a spatially uniform phase. In this study, we search for a characteristic $\eta$-pairing state in a triangular lattice where a simple staggered alignment of the phase is not possible. As an example, we consider the attractive Hubbard model on both the square and triangular lattices under strong external Zeeman field. Using the mean-field approximation, we have identified several $\eta$-pairing states. Additionally, we have examined the electromagnetic stability of the pairing state by calculating the Meissner kernel. Odd-frequency pairing plays a crucial role in achieving diamagnetic response if the electrons experience a staggered superconducting phase during the propagation of current.

cond-mat.supr-con↗

arXiv2022

Surface State of Inter-orbital Pairing State in Sr$_2$RuO$_4$ Superconductor

We study the (001) surface state of a recently proposed $E_g$ symmetry inter-orbital-odd spin-triplet s-wave superconducting (SC) state in Sr$_2$RuO$_4$ (SRO). We confirm that this pair potential is transformed into a chiral $d$-wave pair potential and a pseudo-Zeeman field in the band basis for a low-energy range. Due to the chiral $d$-wave pair potential, the surface states appear near zero energy in the momentum range enclosed by the nodal lines of the chiral d-wave pair potential for each band at the (001) surface. Nevertheless, the pseudo-Zeeman field gives band splitting of the surface states, and its splitting energy is much smaller than the SC energy gap. The local density of states (LDOS) at the (001) surface of the SC state has a pronounced peak structure at zero energy due to the surface states near zero energy when the order of the resolution is lower than the splitting energy. This peak structure is robust under perturbations, such as an orbital Rashba coupling or an $E_u$ SC pair potential at the surface.

cond-mat.str-el↗

arXiv2022

Odd-frequency pairs and anomalous proximity effect in nematic and chiral states of superconducting topological insulators

We investigate emergent odd-frequency pairs and proximity effect in nematic and chiral states of superconducting topological insulators (STIs), such as $M_x$Bi$_2$Se$_3$ ($M=$ Cu, Sr, Nb). The interplay of superconducting gap symmetry, the orbital degrees of freedom, and strong spin-orbit interaction generates a variety of odd-frequency pairs in the bulk and surface of STIs. The nematic and chiral states are the prototypes of topological superconductors with and without time-reversal symmetry, respectively. We find that the Fermi surface evolution from a closed spheroidal to an open cylindrical shape gives rise to the evolution of the emergent odd-frequency pairs and surface Andreev bound states (SABSs). In addition, spin polarization of odd-frequency pairs and SABSs stems from the non-unitary pairing in the chiral state. These evolution and spin polarization of odd-frequency pairs and SABSs can be captured by tunnel conductance spectroscopy. Furthermore, we study the anomalous proximity effect in various irreducible representations of STIs. The anomalous proximity effect is originally predicted in spin-triplet superconductor junctions without spin-orbit interaction; Odd-frequency spin-triplet $s$-wave pairs penetrate into diffusive normal metals (DN) and induce a pronounced zero-energy peak of the local density of states in the DN region. Here we demonstrate that contrary to the well-known results, the anomalous proximity effect in STIs is not immune to nonmagnetic impurities. The fragility is attributed to the fact that the proximitized odd-frequency even-parity pairs are admixtures of $s$-wave and non-$s$-wave pairs due to strong spin-orbit interaction inherent to the parent materials.

cond-mat.supr-con↗

arXiv2022

Generation of polarized spin-triplet Cooper pairings by magnetic barriers in superconducting junctions

We investigate the proximity effect in an s-wave superconductor/ferromagnetic metal with a Rashba spin-orbit coupling/diffusive normal metal junction and an s-wave superconductor/noncollinear magnetic metal/diffusive normal metal junction. We show the generation of equal spin-triplet pairings in the diffusive normal metal due to spin-flip scattering in the intermediate magnetic regions. The emergence of the spin-triplet odd-frequency Cooper pairings can generate a zero-energy peak in the quasiparticle density of states in the diffusive normal metal.

cond-mat.supr-con↗

arXiv2021

Generalization of spectral bulk-boundary correspondence

The bulk-boundary correspondence in one dimension asserts that the physical quantities defined in the bulk and at the edge are connected, as well established in the argument for electric polarization. Recently, a spectral bulk-boundary correspondence (SBBC), an extended version of the conventional bulk-boundary correspondence to energy-dependent spectral functions, such as Green's functions, has been proposed in chiral symmetric systems, in which the chiral operator anticommutes with the Hamiltonian. In this study, we extend the SBBC to a system with impurity scattering and dynamical self-energies, regardless of the presence or absence of a gap in the energy spectrum. Moreover, the SBBC is observed to hold even in a system without chiral symmetry, which substantially generalizes its concept. The SBBC is demonstrated with concrete models, such as superconducting nanowires and a Su-Schrieffer-Heeger model. Its potential applications and certain remaining issues are also discussed.

cond-mat.mes-hall↗

arXiv2021

Thermoelectric detection of Andreev states in unconventional superconductors

We theoretically describe a thermoelectric effect that is entirely due to Andreev processes involving the formation of Cooper pairs through the coupling of electrons and holes. The Andreev thermoelectric effect can occur in ballistic ferromagnet-superconductor junctions with a dominant superconducting proximity effect on the ferromagnet, and it is very sensitive to surface states emerging in unconventional superconductors. We consider hybrid junctions in two and three dimensions to demonstrate that the thermoelectric current is always reversed in the presence of low-energy Andreev bound states at the superconductor surface. A microscopic analysis of the proximity-induced pairing reveals that the thermoelectric effect only arises if even and odd-frequency Cooper pairs coexist in mixed singlet and triplet states. Our results are an example of the richness of emergent phenomena in systems that combine magnetism and superconductivity, and they open a pathway for exploring exotic surface states in unconventional superconductors.

cond-mat.supr-con↗

arXiv2020

Impact of impurity scattering on odd-frequency spin-triplet pairing near the edge of the Kitaev chain

We study a Kitaev chain model, which is the simplest model of topological superconductors hosting Majorana fermion, appearing as a zero-energy state at the edge. We analytically calculate the Green's function of the semi-infinite Kitaev chain with a delta-function-type impurity potential within the quasi-classical regime to obtain the spatial dependence of the induced odd-frequency pairing. It is found that if the position of the impurity is not far from the edge, the spatial profile of the local density of states (LDOS) and the odd-frequency spin-triplet $s$-wave pair amplitude is tunable as a function of the strength of the impurity potential. Moreover, the zero-energy LDOS and low-frequency odd-frequency pair amplitude are found to have the same spatial dependence. The spatial profile of the zero-energy LDOS is analyzed based on the wave function of Majorana fermions.

cond-mat.mes-hall↗

arXiv2020

Anomalous Proximity Effect of Planer Topological Josephson Junctions

The anomalous proximity effect in dirty superconducting junctions is one of most striking phenomena highlighting the profound nature of Majorana bound states and odd-frequency Cooper pairs in topological superconductors. Motivated by the recent experimental realization of planar topological Josephson junctions, we describe the anomalous proximity effect in a superconductor/semiconductor hybrid, where an additional dirty normal-metal segment is extended from a topological Josephson junction. The topological phase transition in the topological Josephson junction is accompanied by a drastic change in the low-energy transport properties of the attached dirty normal-metal. The quantization of the zero-bias differential conductance, which appears only in the topologically nontrivial phase, is caused by the penetration of the Majorana bound states and odd-frequency Cooper pairs into a dirty normal-metal segment. As a consequence, we propose a practical experiment for observing the anomalous proximity effect.

cond-mat.supr-con↗

arXiv2020

Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model

The Su-Schrieffer-Heeger model describes fermions that hop on a one-dimensional chain with staggered hopping amplitude, where the unit cell contains two sites, or two sublattices. In this work we consider the Su-Schrieffer-Heeger model with superconducting pairing and show that the sublattice index acts as an additional quantum number in the classification of Cooper pairs, giving rise to inter- and intra-sublattice odd-frequency pair correlations in the bulk. Interestingly, this system behaves as a two band superconductor where the bulk odd-frequency correlations depend solely on the intrinsic staggering properties of the model. In general, odd-frequency correlations coexist with even-frequency correlations in both the trivial and topological phases, with comparable and even larger odd-frequency amplitudes at the topological phase transition points at low frequencies, due to the closing of the energy gap at these points. Furthermore, we also discuss how bulk odd-frequency amplitudes are correlated with pseudo-gaps in the density of states and also with a charge density wave that appears due to the chemical potential imbalance between sublattices.

cond-mat.mes-hall↗

arXiv2020

Odd-frequency pairing and proximity effect in Kitaev chain systems including topological critical point

In this paper, we investigate the relation between odd-frequency pairing and proximity effect in non-uniform Kitaev chain systems with a particular interest in the topological critical point. First, we correlate the odd-frequency pairing and Majorana fermion in a semi-infinite Kitaev chain, where we find that the spatial dependence of the odd-frequency pair amplitude coincides with that of the local density of states at low frequencies. Second, we demonstrate that, contrary to the standard view, the odd-frequency pair amplitude spreads into the bulk of a semi-infinite Kitaev chain at the topological critical point. Finally, we show that odd-frequency Cooper pairs cause the proximity effect in a normal metal/diffusive normal metal/ Kitaev chain junction even at the topological critical point. Our results hold relevance to the investigation of odd-frequency pairing and topological superconductivity in more complicated systems that involve Rashba nanowire with magnetic fields.

cond-mat.supr-con↗

arXiv2019

Spin-Orbital Hallmarks of Unconventional Superconductors Without Inversion Symmetry

The spin-orbital polarization of superconducting excitations in momentum space is shown to provide distinctive marks of unconventional pairing in the presence of inversion symmetry breaking.Taking the prototypical example of an electronic system with atomic spin-orbit and orbital-Rashba couplings, we provide a general description of the spin-orbital textures and their most striking changeover moving from the normal to the superconducting state. We find that the variation of the spin-texture is strongly imprinted by the combination of the misalignment of spin-triplet d-vector with the inversion asymmetry g-vector coupling and the occurrence of superconducting nodal excitations. Remarkably, the multi-orbital character of the superconducting state allows to unveil a unique type of topological transition for the spin-winding around the nodal points. This finding indicates the fundamental topological relation between chiral and spin-winding in nodal superconductors. By analogy between spin- and orbital-triplet pairing we point out how orbital polarization patterns can be also employed to assess the character of the superconducting state.

cond-mat.supr-con↗

arXiv2019

Theory of proximity effect in two-dimensional unconventional superconductor with Rashba spin-orbit interaction

We study the anomalous proximity effect in diffusive normal metal (DN)/unconventional superconductor junctions, where the local density of states (LDOS) in the DN has a zero-energy peak due to the penetration of the odd-frequency spin-triplet $s$-wave pairing. In this study, we consider a two-dimensional unconventional superconductor on the substrate in the presence of a Rashba spin-orbit coupling (RSOC) $λ$, where the Rashba vector is parallel to the $z$-direction. The anomalous proximity effect, originally predicted in spin-triplet $p$-wave superconductor junctions, is sensitive to the RSOC. It disappears with the increase of $λ$. On the other hand, the anomalous proximity effect can be switched on by the large $λ$ values in the spin-singlet $d_{xy}$-wave superconductor junctions. The resulting zero-energy LDOS and the magnitude of the odd-frequency spin-triplet $s$-wave pair amplitude increase with the increase of $λ$.

cond-mat.mes-hall↗