arXiv subjects

Satoshi Fujimoto

Publications and source records attributed to Satoshi Fujimoto.

At least 37 records · Page 2Linked to original sources

arXiv2023

Non-local spin correlation as a signature of Ising anyons trapped in vacancies of the Kitaev spin liquid

In the Kitaev chiral spin liquid, Ising anyons are realized as $Z_2$ fluxes binding Majorana zero modes, which, however, are thermal excitations with finite decay rates. On the other hand, a lattice vacancy traps a $Z_2$ flux even in the ground state, resulting in the stable realization of a Majorana zero mode in a vacancy. We demonstrate that spin-spin correlation functions between two vacancy sites exhibit long-range correlation arising from the fractionalized character of Majorana zero modes, in spite of the strong decay of bulk spin correlations. Remarkably, this non-local spin correlation does not decrease as the distance between two vacancy sites increases, signaling Majorana teleportation. Furthermore, we clarify that the non-local correlation can be detected electrically via the measurement of non-local conductance between two vacancy sites, which is straightforwardly utilized for the readout of Majorana qubits. These findings pave the way to the measurement-based quantum computation with Ising anyons trapped in vacancies of the Kitaev spin liquid.

cond-mat.str-el↗

arXiv2022

Matrix Product Renormalization Group: Potential Universal Quantum Many-Body Solver

The density matrix renormalization group (DMRG) is a celebrated tensor network algorithm, which computes the ground states of one-dimensional quantum many-body systems very efficiently. Here we propose an improved formulation of continuous tensor network algorithms, which we name a matrix product renormalization group (MPRG). MPRG is a universal quantum many-body solver, which potentially works at both zero and finite temperatures, in two and higher dimensions, and is even applicable to open quantum systems. Furthermore, MPRG does not rely on any variational principles and thus supports any kind of non-Hermitian systems in any dimension. As a demonstration, we present critical properties of the Yang-Lee edge singularity in one dimension as a representative non-Hermitian system.

cond-mat.str-el↗

arXiv2022

Engineering Yang-Lee anyons via Majorana bound states

We propose the platform of a Yang-Lee anyon system which is constructed from Majorana bound states in topological superconductors. Yang-Lee anyons, described by the non-unitary conformal field theory with the central charge $c=-22/5$, are non-unitary counterparts of Fibonacci anyons, obeying the same fusion rule, but exhibiting non-unitary non-Abelian braiding statistics. We consider a topological superconductor junction system coupled with dissipative electron baths, which realizes a non-Hermitian interacting Majorana system. Numerically estimating the central charge, we examine the condition that the non-Hermitian Majorana system can simulate the Ising spin model of the Yang-Lee edge singularity, and confirm that, by controlling model parameters in a feasible way, the Yang-Lee edge criticality is realized. On the basis of this scenario, we present the scheme for the fusion, measurement and braiding of Yang-Lee anyons in our proposed setup.

cond-mat.str-el↗

arXiv2022

Manipulation of Majorana Kramers Qubit and its Tolerance in Time-Reversal-Invariant Topological Superconductor

We investigate non-Abelian statistics of Majorana Kramers pairs (MKPs) in a network system of one-dimensional time-reversal invariant topological superconductors by using numerical simulations of braiding dynamics, and examine the tolerance against various perturbations which may cause decoherence of MKPs. We, first, consider effects of a magnetic field which breaks time-reversal symmetry. In contrast to a naive expectation, the non-Abelian braiding of MKPs is robust against applied magnetic fields provided that the initial and final states of a braiding process are invariant under the combination of a time reversal and a mirror reflection, even when intermediate states break the combined symmetry. Secondly, we investigate the stability of non-Abelian braidings in the case with gate-induced inhomogeneous potentials at junctions between superconducting nanowires, which generally generate a non-Majorana nearly zero-energy Andreeev bound state at the junctions. It is found that the non-Majorana nearly zero-energy states interfere with MKPs, resulting in the failure of non-Abelian braidings, when the length scale of the inhomogeneous potentials is comparable to the coherence length of the superconductors.

cond-mat.supr-con↗

arXiv2022

Intrinsic Anomalous Thermal Hall Effect in the Unconventional Superconductor UTe2

We investigate the intrinsic anomalous thermal Hall effect as an effective probe of the order parameters of non-unitary pairing states of the putative spin-triplet superconductor UTe$_2$. We consider all symmetry-allowed non-unitary states under magnetic fields comprehensively, and calculate the anomalous Hall conductivity arising from time-reversal symmetry-breaking Weyl point nodes of the gap functions, assuming three types of Fermi surfaces; ellipsoid-shaped, cylinder-shaped, and ring-shaped ones, which are predicted by previous band calculations. We find the nonzero anomalous thermal Hall conductivity in the certain ratio of the two irreducible representations. The results may be utilized for future exploration of pairing states of UTe$_2$.

cond-mat.supr-con↗

arXiv2022

Thermodynamic signature of the $\mathrm{SU}(4)$ spin-orbital liquid and symmetry fractionalization from the Lieb-Schultz-Mattis theorem

The $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice is expected to host a quantum spin-orbital liquid at low temperature with an astonishing candidate material, $α$-ZrCl$_3$. We employed the canonical thermal pure quantum state method to investigate the finite-temperature phase of this model. Exploiting the full symmetry of $\mathrm{SU}(4)$, the calculation up to a 24-site cluster, which is equivalent to 48 sites in the spin-1/2 language, is possible. This state-of-the-art computation with large-scale parallelization enables us to capture the thermodynamic properties of the $\mathrm{SU}(4)$ Heisenberg model on the honeycomb lattice. In particular, the specific heat shows a characteristic peak-and-shoulder structure, which should be related to the nature of the low-temperature quantum spin-orbital liquid phase. We also discuss what can be concluded from the assumption that the ground state is gapped and symmetric in view of the generalized Lieb-Schultz-Mattis theorem.

cond-mat.str-el↗

arXiv2022

Anomalous acoustoelectric effect induced by clapping modes in chiral superconductors

Clapping modes, which are relative amplitude and phase modes between two chiral components of Cooper pairs, are bosonic collective modes inherent to chiral superconductors. These modes behave as long-lived bosons with masses smaller than the threshold energy, $2|Δ|$, for decay into unbound fermion pairs. Here, we clarify that the real/imaginary clapping modes in chiral superconductors directly couple to acoustic wave propagation when the weak particle-hole asymmetry of the normal state quasiparticle dispersion is taken into account. The clapping modes driven by an acoustic wave generate an alternating electric current, that is, the acoustoelectric effect in superconductors. Significantly, the clapping modes give rise to a transverse electric current. When the sound velocity is comparable to the Fermi velocity, as in heavy fermion compounds, the transverse current is resonantly enhanced at energy below the threshold for continuum excitations. This resonance provides a smoking-gun evidence of chiral superconductivity.

cond-mat.supr-con↗

arXiv2022

Spin-Nernst Effect in Time-Reversal-Invariant Topological Superconductors

We investigate the spin-Nernst effect in time-reversal invariant topological superconductors, and show that it provides a smoking-gun evidence for helical Cooper pairs. The spin-Nernst effect stems from asymmetric, in spin space, scattering of quasiparticles at nonmagnetic impurities, and generates a transverse spin current by the temperature gradient. Both the sign and the magnitude of the effect sensitively depend on the scattering phase shift at impurity sites. Therefore the spin-Nernst effect is uniquely suitable for identifying time-reversal invariant topological superconducting orders.

cond-mat.supr-con↗

arXiv2021

Quantum liquid crystals in the finite-field K$Γ$ model for $α$-RuCl$_3$

We study the extended Kitaev model called the K$Γ$ model, using a perturbative expansion combined with a well-controlled mean-field approximation and a cutting-edge exact diagonalization. In the phase diagram, we discover a nematic Kitaev spin liquid and a Kekulé Kitaev spin liquid. The former potentially explains the high-field nematic state with zero Chern number experimentally observed in $α$-RuCl$_3$, even for sufficiently small values of $Γ/|K|$. The latter has a Majorana zero mode in its $Z_3$ vortex core, which can be potentially controlled by the domain wall motion. This opens a possible application of the quantum liquid crystal phases in the K$Γ$ model to the topological quantum computation.

cond-mat.str-el↗

arXiv2021

Dissipationless Spin Current Generation in Kitaev's Chiral Spin Liquid

$α$-RuCl$_3$ is a promising candidate material for the Kitaev spin liquid state where the half quantization of the thermal Hall effect, suggesting a topological character, has been observed. However, its relation to the existence of chiral Majorana fermions, which is predicted from the theory of the Kitaev model, is still under debate. Here we propose a more direct signature of a chiral Majorana edge mode which emerges in a universal scaling of the Drude weight of the edge spin Seebeck effect in the Kitaev model. Moreover, the absence of backscatterings in the chiral edge mode results in the generation of a dissipationless spin current in spite of an extremely short spin correlation length close to a lattice constant in the bulk. This result is not only experimentally observable, but also opens a way towards spintronics application of Kitaev materials. In contrast to magnetically ordered systems, a Kitaev spin liquid state is stable even in the atomic scale and makes it possible to fabricate a highly integrated device with substantial efficiency to generate a spin current. This proposal for using $α$-RuCl$_3$ as a nano-scale device will pioneer Kitaev spintronics.

cond-mat.str-el↗

arXiv2021

Electric probe for the toric code phase in Kitaev materials through the hyperfine interaction

The Kitaev model is a remarkable spin model with gapped and gapless spin liquid phases, which are potentially realized in iridates and $α$-RuCl$_3$. In the recent experiment of $α$-RuCl$_3$, the signature of a nematic transition to the gapped toric code phase, which breaks the $C_3$ symmetry of the system, has been observed through the angle dependence of the heat capacity. We here propose a mechanism by which the nematic transition can be detected electrically. This is seemingly impossible because $J_\textrm{eff}=1/2$ spins do not have an electric quadrupole moment (EQM). However, in the second-order perturbation the virtual state with a nonzero EQM appears, which makes the nematic order parameter detectable by nuclear magnetic resonance and Mössbauer spectroscopy. The purely magnetic origin of EQM is different from conventional electronic nematic phases, allowing the direct detection of the realization of Kitaev's toric error-correction code.

cond-mat.str-el↗

arXiv2021

Topological Nematic Phase Transition in Kitaev Magnets Under Applied Magnetic Fields

We propose a scenario of realizing the toric code phase, which can be potentially utilized for fault-tolerant quantum computation, in candidate materials of Kitaev magnets. It is demonstrated that four-body interactions among Majorana fermions in the Kitaev spin liquid state, which are induced by applied magnetic fields as well as non-Kitaev-type exchange interactions, trigger a nematic phase transition of Majorana bonds without magnetic orders, accompanying the change of the Chern number from $\pm 1$ to zero. This gapful spin liquid state with zero Chern number is nothing but the toric code phase. Our result potentially explains the topological nematic transition recently observed in $α$-RuCl$_3$ via heat capacity measurements [O. Tanaka et al., arXiv:2007.06757].

cond-mat.str-el↗

arXiv2021

Paramagnetic effects of j-electron superconductivity and application to UTe2

The putative spin-triplet superconductor UTe2 has an Ising-like magnetic anisotropy, indicating the Cooper pair spins parallel to the easy-axis. However, the upper critical field for the hard-axis direction is much larger than that for the easy-axis, implying the strong suppression of the Pauli depairing effect even for the hard-axis direction. This observation is consistent with the recent NMR measurements which show the tiny decrease of the Knight shift below the transition temperature Tc for hard-axis magnetic fields. We clarify that these behaviors are naturally understood as a result of multi-orbital f -electron bands with total angular momentum j=5/2. Taking into account spin-orbit couplings for an orthorhombic structure, we demonstrate that for hard-axis magnetic fields, the decrease of the spin susceptibility below Tc and the Pauli depairing effect are strongly suppressed.

cond-mat.supr-con↗

arXiv2021

${\it Ab \ Initio}$ Simulation of Non-Abelian Braiding Statistics in Topological Superconductors

We numerically investigate non-Abelian braiding dynamics of vortices in two-dimensional topological superconductors, such as $s$-wave superconductors with Rashba spin-orbit coupling. Majorana zero modes (MZMs) hosted by the vortices constitute a topological qubit, which offers a fundamental building block of topological quantum computation. As the MZMs are protected by $\mathbb{Z}_2$ invariant, however, the Majorana qubit and quantum gate operations may be sensitive to intrinsic decoherence caused by quasiparticle interference. Numerically simulating the time-dependent Bogoliubov-de Gennes equation without assuming ${\it a \ priori}$ existence of MZMs, we examine quantum noises on the unitary operators of non-abelian braiding dynamics due to interactions with neighboring MZMs and other quasiparticle states. We demonstrate that after the interchange of two vortices, the lowest vortex-bound states accumulate the geometric phase $π/2$, and errors stemming from dynamical phases are negligibly small, irrespective of interactions of MZMs. Furthermore, we numerically simulate the braiding dynamics of four vortices in two-dimensional topological superconductors, and discuss an optimal braiding condition for realizing the high performance of non-Abelian statistics and quantum gates operations of Majorana-based qubits.

cond-mat.supr-con↗

arXiv2021

Spectrum collapse of disordered Dirac Landau levels as topological non-Hermitian physics

We investigate disorder effects on Landau levels in Dirac electron systems with the use of a non-Hermitian quasiparticle Hamiltonian formalism. This formalism reveals that spin-dependent scattering rates induce the spectrum collapse of Landau levels, i.e., the disappearance of the energy gaps between n-th and -n-th levels under a finite external magnetic field. The spectrum collapse occurs in both weak and strong magnetic field regimes, thus showing a reentrant behavior. Particularly, in the strong magnetic field regime, in contrast to naive expectation, the increase of a magnetic field stabilizes the spectrum collapse of Dirac Landau levels. Furthermore, it is revealed that the spectrum collapse is associated with the emergence of a vortex texture with a topological winding number of a complex energy spectrum of the non-Hermitian system.

cond-mat.mes-hall↗

arXiv2020

Topological piezoelectric effect and parity anomaly in nodal line semimetals

Lattice deformations act on the low-energy excitations of Dirac materials as effective axial vector fields. This allows to directly detect quantum anomalies of Dirac materials via the response to axial gauge fields. We investigate the parity anomaly in Dirac nodal line semimetals induced by lattice vibrations, and establish a topological piezoelectric effect; i.e., periodic lattice deformations generate topological Hall currents that are transverse to the deformation field. The currents induced by this piezoelectric effect are dissipationless and their magnitude is completely determined by the length of the nodal ring, leading to a semi-quantized transport coefficient. Our theoretical proposal can be experimentally realized in various nodal line semimetals, such as CaAgP and Ca$_{_3}$P${_2}$.

cond-mat.mes-hall↗

arXiv2020

Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state

We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with $Z_2$ gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the $Γ'$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction, and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\pm 1$ to an Abelian phase with the Chern number equal to $\pm 2$, in which the $Z_{2}$ vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $Γ$ term, only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.

cond-mat.str-el↗

arXiv2019

Chiral Higgs Mode in Nematic Superconductors

Nematic superconductivity with spontaneously broken rotation symmetry has recently been reported in doped topological insulators, $M_x$Bi$_2$Se$_3$ ($M$=Cu, Sr, Nb). Here we show that the electromagnetic (EM) response of these compounds provides a spectroscopy for bosonic excitations that reflect the pairing channel and the broken symmetries of the ground state. Using quasiclassical Keldysh theory, we find two characteristic bosonic modes in nematic superconductors: the nematicity mode and the chiral Higgs mode. The former corresponds to the vibrations of the nematic order parameter associated with broken crystal symmetry, while the latter represents the excitation of chiral Cooper pairs. The chiral Higgs mode softens at a critical doping, signaling a dynamical instability of the nematic state towards a new chiral ground state with broken time reversal and mirror symmetry. Evolution of the bosonic spectrum is directly captured by EM power absorption spectra. We also discuss contributions to the bosonic spectrum from sub-dominant pairing channels to the EM response.

cond-mat.supr-con↗