arXiv subjects

Shu-Ichiro Suzuki

Publications and source records attributed to Shu-Ichiro Suzuki.

At least 19 recordsLinked to original sources

arXiv2024

Chirality Detection through Vortex Bound States in ($d+id'$)-Wave Superconductor

We present a method for detecting the chirality $χ$ of a ($d_{zx}+i χd_{yz}$)-wave superconductor through the analysis of the local density of states (LDOS) at the vortex core. Employing the quasiclassical Eilenberger theory, we examine the LDOS in a semi-infinite superconductor with a quantum vortex penetrating the surface perpendicularly. We show that $\mathrm{sgn}[χ]$ changes completely the LDOS at the core-surface intersection. Remarkably, the difference between LDOS for the $χ= 1$ and $χ= -1$ states becomes more prominent when the surface is dirtier, meaning that one does not need to pay close attention to the surface quality of the sample. The difference between these two states arises from the symmetry of the subdominant Cooper pairs induced at the core-surface intersection: whether the subdominant $s$-wave Cooper pairs are present or not. Due to the unique nature of this phenomenon in the ($d_{zx}+i χd_{yz}$)-wave superconductor, one can potentially demonstrate the realization of the ($d_{zx}+i χd_{yz}$)-wave superconductivity and determine its chirality by, for instance, through scanning tunnel spectroscopy experiments.

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arXiv2024

Chiral Current Inversion Induced by Flat-Band Andreev Bound States

We study the spontaneous chiral surface current circulating in a three-dimensional disk of a chiral superconductor (SC) utilizing the quasiclassical Eilenberger theory. We obtain spatial profiles of the chiral current for both a ($d_{zx} + i d_{yz}$)-wave and a ($p_{x} + i p_{y}$)-wave SCs (where the top and bottom surfaces of the disk are perpendicular to the $z$-axis). Whereas the chiral current for a ($p_{x} + i p_{y}$)-wave SC does not depend on $z$, a reversal of the chiral current takes place at the top and bottom surfaces in the case of a ($d_{zx} + i d_{yz}$)-wave SC. In this latter case, flat-band Andreev bound states appear at the top and bottom surfaces in addition to the chiral surface states at the lateral surface. The chiral current reversal is explained in terms of hybridization between the two types of Andreev bound states. As a result, the magnetic field around the disk differs drastically between the two cases.

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arXiv2023

Fulde-Ferrell-Larkin-Ovchinnikov state in a superconducting thin film attached to a ferromagnetic cluster

We study theoretically the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states appearing locally in a superconducting thin film with a small circular magnetic cluster. The pair potential, the pairing correlations, the free-energy density, and the quasiparticle density of states are calculated for several cluster sizes and the exchange potentials by solving the Eilenberger equation in two dimensions. The number of nodes in the pair potential increases with increasing the exchange potential and cluster size. The local FFLO states are stabilized by the superconducting condensate away from the magnetic cluster even though the free-energy density beneath the ferromagnet exceeds locally the normal-state value. The analysis of the pairing-correlation functions shows that the spatial variation of the spin-singlet $s$-wave pair potential generates $p$-wave Cooper pairs, and that odd-frequency Cooper pairs govern the inhomogeneous subgap spectra in the local density of states. We also discuss a way of detecting the local FFLO states based on the calculated quasiparticle density of states.

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arXiv2023

Supercurrent reversal in Zeeman-split Josephson junctions

We study theoretically the shape of the current-phase relation in a Josephson junction comprising the Zeeman-split superconductors (ZSs) and a normal metal (N). We show that at low temperatures the Josephson current in the ZS/N/ZS junctions exhibits an additional reversal in direction at a certain phase difference $φ_c \in (0, π)$. Calculating the spectral Josephson current, the band-splitting due to the Zeeman interaction is shown to cause the level crossing in the spectra of the Andreev bound states and the sign reversal in the Josephson current. Additionally, we propose an alternative method to electrically control the critical phase difference $φ_c$ by tuning the Rashba spin-orbit coupling, eliminating the need for manipulating magnetizations.

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arXiv2023

Robustness of chiral surface current and subdominant $s$-wave Cooper pairs

The robustness of the chiral surface current of chiral superconductors against surface roughness is studied utilizing the quasiclassical Eilenberger theory. We consider the general chiral superconductors where the pair potential is given by the spherical harmonics $Y_l^m$ such that $(l,m)=(1, \pm1)$ state corresponds to an ($p_x \pm ip_y$)-wave superconductor. The self-consistent calculations demonstrate that the robustness of the chiral current is determined by whether subdominant $s$-wave Cooper pairs are induced by disorder. The induced $s$-wave pairs act as an effective pair potential. As a result, the spontaneous chiral current of ($p_x+ip_y$)- and ($d_{x^2-y^2}+id_{xy}$)-wave superconductors are robust against the roughness because the subdominant $s$-wave Cooper pairs are present.

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arXiv2023

Multiple Andreev reflections in two-dimensional Josephson junctions with broken time-reversal symmetry

Andreev bound states (ABS) occur in Josephson junctions when the total phase of the Andreev and normal reflections is a multiple of $2π$. In ballistic junctions with an applied voltage bias, a quasi-particle undergoes multiple Andreev reflections before entering the leads, resulting in peaks in the current-voltage $I(V)$ curve. Here we present a general model for Josephson junctions with spin-active interlayers i.e., magnetic or topological materials with broken time-reversal symmetry. We investigate how ABS change the peak positions and shape of $I(V)$, which becomes asymmetric for a single incident angle. We show how the angle-resolved $I(V)$ curve becomes a spectroscopic tool for the chirality and degeneracy of ABS.

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arXiv2022

Vortex supercurrent inversion by frequency-symmetry conversion of Cooper pairs

We theoretically demonstrate that the vortex supercurrent can be reversed by odd-frequency Cooper pairs accompanied by surface Andreev bound states. The surface of a three-dimensional superconductor pierced by a flux quantum is considered. We compare the vortex supercurrents near the surface of the spin-singlet $s$-wave and spin-triplet $p_z$-wave superconductors using quasiclassical Eilenberger theory, where the surface is perpendicular to the $z$ direction. We demonstrate that the vortex supercurrent near the surface of a $p_z$-wave superconductor is reversed compared to those far from the surface, whereas that of an $s$-wave superconductor is not. The splitting of the zero-energy states caused by the interference of the surface Andreev bound states and Caroli-de Gennes-Matricon modes is demonstrated.

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arXiv2022

An odd-frequency Cooper pair around a magnetic impurity

The Yu-Shiba-Rusinov (YSR) state appears as a bound state of a quasiparticle at a magnetic atom embedded in a superconductor. We discuss why the YSR state has energy below the superconducting gap and why the pair potential changes the sign at the magnetic atom. Although a magnetic atom in a superconductor has been considered as a pair breaker since 1960s, we propose an alternative physical picture to explain these reasons. We show that a magnetic atom converts a spin-singlet s-wave Cooper pair into an odd-frequency pair rather than breaking it. The odd-frequency pairing correlations always coexist with the quasiparticle states below the gap. The YSR state is an example of such a subgap quasiparticle state. The paramagnetic property of an odd-frequency pair explains the sign change of the pair potential at a magnetic atom and the decrease of superconducting transition temperature in the presence of many magnetic impurities.

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arXiv2022

Destruction of surface states of ($d_{zx}+id_{yz}$)-wave superconductor by surface roughness: application to Sr$_2$RuO$_4$

The fragility of the chiral surface current of ($d_{zx}+id_{yz}$)-wave superconductor, a potential candidate for Sr$_2$RuO$_4$, against surface roughness is demonstrated utilizing the quasiclassical Eilenberger theory. Comparing the chiral surface currents of ($d_{zx}+id_{yz}$)-wave and ($p_{x}+ip_{y}$)-wave pairings, we conclude the chiral current for ($d_{zx}+id_{yz}$)-wave SC is much more fragile than that for the ($p_x+ip_y$)-wave one. The difference can be understood in terms of the orbital symmetry of the odd-frequency Cooper pairs arising at the surface. Our results show the ($d_{zx}+id_{yz}$)-wave scenario can explain the null spontaneous magnetization in Sr$_2$RuO$_4$ experiments.

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arXiv2022

Quasiparticle spectrum in mesoscopic superconducting junctions with weak magnetization

We theoretically investigate the effects of the weak magnetization on the local density of states of mesoscopic proximity structures, where two superconducting terminals are attached to a side surface of the diffusive ferromagnet wire with a phase difference. When there is no phase difference, the local density of states is significantly modified by the magnetization in both spin-singlet $s$-wave and spin-triplet $p$-wave cases. When the phase difference is $π$, the local density of stets is less modified by the magnetization compared with the in-phase case because of the destructive interference of Cooper pairs.

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arXiv2021

Fingerprints of possible even-parity superconducting states in Sr$_2$RuO$_4$ detected by planar tunneling spectroscopy

After more than 25 years of research, three even-parity superconducting states -- the $d+id$-wave, $d+ig$-wave, and $s+id$-wave states -- have emerged as leading candidates for the superconducting states of Sr$_2$RuO$_4$. In the present work, we propose a tunneling spectroscopy experiment for distinguishing among these three superconducting states. The key component of our proposal is that we examine the conductance spectra of normal-metal/Sr$_2$RuO$_4$ junctions with various angles between the junction interface and the crystal axis of the Sr$_2$RuO$_4$. The angle dependence of the conductance spectra shows a unique pattern in each superconducting state, which can function as a fingerprint for verifying the pairing symmetry of Sr$_2$RuO$_4$.

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arXiv2021

Tunnelling conductance of $d+ip$-wave superconductor

We theoretically investigate the tunneling conductance of the $d+ip$-wave superconductor which is recently proposed to be realised at the (110) surface of a high-$T_c$ cuprate superconductor. Utilizing the quasiclassical Eilenberger theory, we obtain the self-consistent pair potentials and the differential conductance of the normal-metal/$d+ip$-wave superconductor junction. We demonstrate that the zero-bias peak of a $d$-wave superconductor is robust against the spin-triplet $p$-wave surface subdominant order even though it is fragile against the spin-singlet $s$-wave one. Comparing our numerical results and the experimental results, we conclude the spin-triplet $p$-wave surface subdominant order is feasible.

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arXiv2020

Anomalous inverse proximity effect in unconventional-superconductor junctions

We investigate the effects of Andreev bound states due to the unconventional pairing on the inverse proximity effect of ferromagnet/superconductor junctions. Utilizing quasiclassical Eilenberger theory, we obtain the magnetization penetrating into the superconductor. We show that in a wide parameter range the direction of the induced magnetization is determined by two factors: whether Andreev bound states are present at the junction interface and the sign of the spin-mixing angle. In particular, when Andreev bound states appear at the interface, the direction of the induced magnetization is opposite to that without Andreev bound states. We also clarify the conditions under which the inverted induced magnetization appears. Applying this novel effect helps distinguishing the pairing symmetry of a superconductor.

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arXiv2020

Identifying possible pairing states in Sr$_2$RuO$_4$ by tunneling spectroscopy

We examine the tunneling spectroscopy of three-dimensional normal-metal/Sr$_2$RuO$_4$ junctions as an experimental means to identify pairing symmetry in Sr$_2$RuO$_4$. In particular, we consider three different possible pairing states in Sr$_2$RuO$_4$: spin-singlet chiral $d$-wave, spin-triplet helical $p$-wave, and spin-nematic $f$-wave ones, all of which are consistent with recent nuclear-magnetic-resonance experiments [A. Pustogow et al., Nature 574, 72 (2019)]. The Blonder-Tinkham-Klapwijk theory is employed to calculate the tunneling conductance, and the cylindrical two-dimensional Fermi surface of Sr$_2$RuO$_4$ is properly taken into account as an anisotropic effective mass and a cutoff in the momentum integration. It is pointed out that the chiral $d$-wave pairing state is inconsistent with previous tunneling conductance experiments along the $c$-axis. We also find that the remaining candidates, the spin-triplet helical $p$-wave pairing state and the spin-nematic $f$-wave ones, can be distinguished from each other by the in-plane tunneling spectroscopy along the $a$- and $b$-axes.

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arXiv2019

Effects of the phase coherence on the local density of states in superconducting proximity structures

We theoretically study the local density of states in superconducting proximity structure where two superconducting terminals are attached to a side surface of a normal-metal wire. Using the quasiclassical Green's function method, the energy spectrum is obtained for both of spin-singlet $s$-wave and spin-triplet $p$-wave junctions. In both of the cases, the decay length of the proximity effect at the zero temperature is limited by a depairing effect due to inelastic scatterings. In addition to the depairing effect, in $p$-wave junctions, the decay length depends sensitively on the transparency at the junction interfaces, which is a unique property to odd-parity superconductors where the anomalous proximity effect occurs.

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arXiv2018

Local density of states in two-dimensional topological superconductors under a magnetic field: signature of an exterior Majorana bound state

We study quasiparticle states on a surface of a topological insulator (TI) with proximity-induced superconductivity under an external magnetic field. An applied magnetic field creates two Majorana bound states: a vortex Majorana state localized inside a vortex core and an exterior Majorana state localized along a circle centered at the vortex core. We calculate the spin-resolved local density of states (LDOS) and demonstrate that the shrinking of the radius of the exterior Majorana state, predicted in Ref. [R. S. Akzyanov et al., Phys. Rev. B 94, 125428 (2016)], under a strong magnetic field can be seen in LDOS without smeared out by non-zero-energy states. The spin-resolved LDOS further reveals that the spin of the exterior Majorana state is strongly polarized. Accordingly, the induced odd-frequency spin-triplet pairs are found to be spin-polarized as well. In order to detect the exterior Majorana states, however, the Fermi energy should be closed to the Dirac point to avoid contributions from continuum levels. We also study a different two-dimensional topological-superconducting system where a two-dimensional electron gas with the spin-orbit coupling is sandwiched between an s-wave superconductor and a ferromagnetic insulator. We show that the radius of an exterior Majorana state can be tuned by an applied magnetic field. However, on the contrary to the results at a TI surface, neither the exterior Majorana state nor the induced odd-frequency spin-triplet pairs are spin-polarized. We conclude that the spin-polarization of the Majorana state is attributed to the spin-polarized Landau level which is characteristic for systems with the Dirac-like dispersion.

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arXiv2016

Spontaneous edge current in a small chiral superconductor with a rough surface

We study theoretically the spontaneous edge current in a small chiral superconductor with surface roughness. We obtained self-consistent solutions of the pair potential and the vector potential by solving the quasiclassical Eilenberger equation and the Maxwell equation simultaneously. We then employed them to calculate numerically the spatial distribution of the chiral edge current in a small superconductor. The characteristic behavior of the spontaneous edge current depends strongly on the symmetries of the order parameters such as chiral $p$-, chiral $d$- and chiral $f$-wave pairing. The edge current is robust under the surface roughness in the chiral $p$- and chiral $d$-wave superconductors. In the chiral $d$-wave case, the surface roughness tends to flip the direction of the chiral current. On the other hand, the edge current in a chiral $f$-wave superconductor is fragile when there is surface roughness. We also discuss the temperature dependence of a spontaneous magnetization, which is a measurable value in standard experiments.

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arXiv2016

Quantization of Conductance Minimum and Index Theorem

We discuss the minimum value of the zero-bias differential conductance $G_{\textrm{min}}$ in a junction consisting of a normal metal and a nodal superconductor preserving time-reversal symmetry. Using the quasiclassical Green function method, we show that $G_{\textrm{min}}$ is quantized at $ (4e^2/h) N_{\mathrm{ZES}}$ in the limit of strong impurity scatterings in the normal metal. The integer $N_{\mathrm{ZES}}$ represents the number of perfect transmission channels through the junction. An analysis of the chiral symmetry of the Hamiltonian indicates that $N_{\mathrm{ZES}}$ corresponds to the Atiyah-Singer index in mathematics.

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