arXiv subjects

Shun Tamura

Publications and source records attributed to Shun Tamura.

26 records · Page 2Linked to original sources

arXiv2019

Odd-Frequency Pairs in Chiral Symmetric Systems: Spectral Bulk-Boundary Correspondence and Topological Criticality

Odd-frequency Cooper pairs with chiral symmetry emerging at the edges of topological superconductors are a useful physical quantity for characterizing the topological properties of these materials. In this work, we show that the odd-frequency Cooper pair amplitudes can be expressed by a winding number extended to a nonzero frequency, which is called a `spectral bulk-boundary correspondence,' and can be evaluated from the spectral features of the bulk. The odd-frequency Cooper pair amplitudes are classified into two categories: the amplitudes in the first category have the singular functional form $\sim 1/z$ (where $z$ is a complex frequency) that reflects the presence of a topological surface Andreev bound state, whereas the amplitudes in the second category have the regular form $\sim z$ and are regarded as non-topological. We discuss the topological phase transition by using the coefficient in the latter category, which undergoes a power-law divergence at the topological phase transition point and is used to indicate the distance to the critical point. These concepts are established based on several concrete models, including a Rashba nanowire system that is promising for realizing Majorana fermions.

cond-mat.supr-con↗

arXiv2018

Inter-orbital topological superconductivity in spin-orbit coupled superconductors with inversion symmetry breaking

We study the superconducting state of multi-orbital spin-orbit coupled systems in the presence of an orbitally driven inversion asymmetry assuming that the inter-orbital attraction is the dominant pairing channel. Although the inversion symmetry is absent, we show that superconducting states that avoid mixing of spin-triplet and spin-singlet configurations are allowed, and remarkably, spin-triplet states that are topologically nontrivial can be stabilized in a large portion of the phase diagram. The orbital-dependent spin-triplet pairing generally leads to topological superconductivity with point nodes that are protected by a nonvanishing winding number. We demonstrate that the disclosed topological phase can exhibit Lifshitz-type transitions upon different driving mechanisms and interactions, e.g., by tuning the strength of the atomic spin-orbit and inversion asymmetry couplings or by varying the doping and the amplitude of order parameter. Such distinctive signatures of the nodal phase manifest through an extraordinary reconstruction of the low-energy excitation spectra both in the bulk and at the edge of the superconductor.

cond-mat.supr-con↗

arXiv2017

Current fluctuations in unconventional superconductor junctions with impurity scattering

The order parameter of bulk two-dimensional superconductors is classified as nodal, if it vanishes for a direction in momentum space, or gapful if it does not. Each class can be topologically nontrivial if Andreev bound states are formed at the edges of the superconductor. Non-magnetic impurities in the superconductor affect the formation of Andreev bound states and can drastically change the tunneling spectra for small voltages. Here, we investigate the mean current and its fluctuations for two-dimensional tunnel junctions between a normal-metal and unconventional superconductors by solving the quasi-classical Eilenberger equation self-consistently, including the presence of non-magnetic impurities in the superconductor. As the impurity strength increases, we find that superconductivity is suppressed for almost all order parameters since (i) at zero applied bias, the effective transferred charge calculated from the noise-current ratio tends to the electron charge $e$ and (ii) for finite bias, the current-voltage characteristics follows that of a normal state junction. There are notable exceptions to this trend. First, gapful nontrivial (chiral) superconductors are very robust against impurity scattering due to the linear dispersion relation of their surface Andreev bound states. Second, for nodal nontrivial superconductors, only p_x-wave pairing is almost immune to the presence of impurities due to the emergence of odd-frequency s-wave Cooper pairs near the interface. Owing to their anisotropic dependence on the wave vector, impurity scattering is an effective pair breaking mechanism for the rest of nodal superconductors. All these behaviors are neatly captured by the noise-current ratio, providing a useful guide to find experimental signatures for unconventional superconductivity.

cond-mat.supr-con↗

arXiv2017

Theory of surface Andreev bound states and tunneling spectroscopy in three-dimensional chiral superconductors

We study the surface Andreev bound states (SABSs) and quasiparticle tunneling spectroscopy of three-dimensional (3D) chiral superconductor by changing the surface (interface) misorientation angle of chiral superconductors. We obtain analytical formula of the energy dispersion of SABS for general pair potential when an original 4$\times$4 BdG Hamiltonian can be reduced to be two 2$\times$2 blocks. The resulting SABS for 3D chiral superconductors with pair potential given by $k_z(k_x + ik_y)^ν$ $(ν = 1, 2)$ has a complicated energy dispersion due to the coexistence of both point and line nodes. We focus on the tunneling spectroscopy of this pairing in the presence of applied magnetic field which induces Doppler shift of quasiparticle spectra. By contrast to previous known Doppler effect in unconventional superconductors, zero bias conductance dip can change into zero bias conductance peak by external magnetic field. We also study SABSs and tunneling spectroscopy for possible pairing symmetries of UPt$_3$ . For this purpose, we extend a standard formula of tunneling conductance of unconventional superconductor junctions in order to treat spin-triplet non-unitary pairings. The magneto tunneling spectroscopy, i.e., tunneling spectroscopy in the presence of magnetic field, can serve as a guide to determine the pairing symmetry of this material.

cond-mat.mes-hall↗

arXiv2016

Staggered Flux State in Two-Dimensional Hubbard Models

The stability and other properties of a staggered flux (SF) state or a correlated d-density wave state are studied for the Hubbard (t-t'-U) model on extended square lattices, as a low-lying state that competes with the d(x2-y2)-wave superconductivity (d-SC) and possibly causes the pseudogap phenomena in underdoped high-Tc cuprates and organic kappa-BEDT-TTF salts. In calculations, a variational Monte Carlo method is used. In the trial wave function, a configuration-dependent phase factor, which is vital to treat a current-carrying state for a large U/t, is introduced in addition to ordinary correlation factors. Varying U/t, t'/t, and the doping rate (delta) systematically, we show that the SF state becomes more stable than the normal state (projected Fermi sea) for a strongly correlated (U/t\gtrsim 5) and underdoped (delta\lesssim 0.16) area. The decrease in energy is sizable, particularly in the area where Mott physics prevails and the circular current (order parameter) is strongly suppressed. These features are consistent with those for the t-J model. The effect of the frustration t'/t plays a crucial role in preserving charge homogeneity and appropriately describing the behavior of hole- and electron-doped cuprates and kappa-BEDT-TTF salts. We argue that the SF state does not coexist with d-SC and is not a `normal state' from which d-SC arises. We also show that a spin current (flux or nematic) state is never stabilized in the same regime.

cond-mat.str-el↗

arXiv2015

Drude and Superconducting Weights and Mott Transitions in Variation Theory

Drude weight ($D$) is a useful measure to distinguish a metal from an insulator. However, $D$ has not been justifiably estimated by the variation theory for long, since Millis and Coppersmith [Phys. Rev. B 43 (1991) 13770] pointed out that a variational wave function $Ψ_Q$, which includes the key ingredient (doublon-holon binding effect) for a Mott transition, yields a positive $D$ (namely metallic) even in the Mott-insulating regime. We argue that, to obtain a correct $D$, an imaginary part must exist in the wave function. By introducing a configuration-dependent phase factor ${\cal P}_θ$ to $Ψ_Q$, Mott transitions are successfully represented by $D$ ($D=0$ for $U>U_{\rm c}$) for a normal and $d$-wave pairing states; thereby, the problem of Millis and Coppersmith is settled. Generally, ${\cal P}_θ$ plays a pivotal role in describing current-carrying states in regimes of Mott physics. On the other hand, we show using a perturbation theory, the one-body (mean-field) part of the wave function should be complex for band insulators such as antiferromagnetic states in hypercubic lattices.

cond-mat.str-el↗

arXiv2014

Variational Approach to Localization Length for Two-Dimensional Hubbard Model

As a measure to ascertain whether a system is metallic or insulating, localization length $λ_N$, which represents the spread of electron distribution, can be a useful quantity, especially for approaching a metal-insulator transition from the insulator side. We try to calculate $λ_N$ using a variational Monte Carlo method for normal (paramagnetic), superconducting and antiferromagnetic states in the square-lattice Hubbard model. It is found that the behavior of $λ_N$ is consistent with what is expected from other quantities, and gives information complementary to another measure, the Drude weight.

cond-mat.str-el↗

arXiv2012

Variational Monte Carlo Study of Spin-Gapped Normal State and BCS-BEC Crossover in Two-Dimensional Attractive Hubbard Model

We study properties of normal, superconducting (SC) and CDW states for an attractive Hubbard model on the square lattice, using a variational Monte Carlo method. In trial wave functions, we introduce an interspinon binding factor, indispensable to induce a spin-gap transition in the normal state, in addition to the onsite attractive and intersite repulsive factors. It is found that, in the normal state, as the interaction strength $|U|/t$ increases, a first-order spin-gap transition arises at $|U_{\rm c}|\sim W$ ($W$: band width) from a Fermi liquid to a spin-gapped state, which is conductive through hopping of doublons. In the SC state, we confirm by analysis of various quantities that the mechanism of superconductivity undergoes a smooth crossover at around $|U_{\ma{co}}|\sim |U_{\rm c}|$ from a BCS type to a Bose-Einstein condensation (BEC) type, as $|U|/t$ increases. For $|U|<|U_{\ma{co}}|$, quantities such as the condensation energy, a SC correlation function and the condensate fraction of onsite pairs exhibit behavior of $\sim \exp(-t/|U|)$, as expected from the BCS theory. For $|U|>|U_{\ma{co}}|$, quantities such as the energy gain in the SC transition and superfluid stiffness, which is related to the cost of phase coherence, behave as $\sim t^2/|U|\propto T_{\rm c}$, as expected in a bosonic scheme. In this regime, the SC transition is induced by a gain in kinetic energy, in contrast with the BCS theory. We refer to the relevance to the pseudogap in cuprate superconductors.

cond-mat.str-el↗