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We investigate the topological properties of multiple exceptional points in non-Hermitian two-level systems, emphasizing vorticity as a topological invariant arising from complex energy structures. We categorize EP pairs as fundamental building blocks of larger EP assemblies, distinguishing two types: type-I pairs with opposite vorticities and type-II pairs with identical vorticities. By analyzing the branch cut formation in a two-dimensional parameter space, we reveal the distinct topological features of each EP pair type. Furthermore, we extend our analysis to configurations with multiple EPs, demonstrating the cumulative vorticity and topological implications. To illustrate these theoretical structures, we model complex energy bands within a two-dimensional photonic crystal composed of lossy materials, identifying various EP pairs and their branch cuts. These findings contribute to the understanding of topological characteristics in non-Hermitian systems., Comment: 8 pages, 6 figures

The Josephson diode effect (JDE), characterized by a unidirectional supercurrent across a Josephson junction, arises from non-reciprocal critical currents typically controlled by magnetic fields. In this study, we demonstrate JDE controlled by local electric fields, achieving complete polarity reversal through gate voltages on epitaxial Al-InAs Josephson junctions. Our observations reveal intricate effects of in-plane magnetic fields and gate voltages on the JDE. We develop a theoretical model that considers the coherent interplay between finite Cooper-pair momentum (fCPM) and anisotropic spin-orbit coupling (SOC), identifying that fCPM dominates JDE at low in-plane magnetic fields, while SOC governs its polarity reversal at high fields. This model aligns well with experimental data, illustrating precise electric control of JDE polarity through anisotropic SOC. These findings introduce a novel approach to controlling superconducting circuits, paving a route toward advanced applications in superconducting quantum devices., Comment: 42 pages, 19 figures, 1 table

Non-Hermitian systems have Riemann surface structures of complex eigenvalues that admit singularities known as exceptional points. Combining with geometric phases of eigenstates gives rise to unique properties of non-Hermitian systems, and their classifications have been studied recently. However, the physical realizations of classes of the classifications have been relatively limited because a small number of modes and exceptional points are involved. In this work, we show in microcavities that all five classes [J.-W. Ryu, et al., Commun. Phys. 7, 109 (2024)] of three modes can emerge with three exceptional points. In demonstrations, we identified various combinations of exceptional points within a two-dimensional parameter space of a single microcavity and defined five distinct encircling loops based on three selected exceptional points. According to the classification, these loops facilitate different mode exchanges and the acquisition of additional geometric phases during the adiabatic encircling of exceptional points. Our results provide a broad description of the geometric phases-associated topology induced by multiple exceptional points in realistic physical systems., Comment: 7 pages, 5 figures

The complex eigenenergies and non-orthogonal eigenstates of non-Hermitian systems exhibit unique topological phenomena that cannot appear in Hermitian systems. Representative examples are the non-Hermitian skin effect and exceptional points. In a two-dimensional parameter space, topological classifications of non-separable bands in multiband non-Hermitian systems can be established by invoking a permutation group, where the product of the permutation represents state exchange due to exceptional points in the space. We unveil in this work the role of pseudo-Hermitian lines in non-Hermitian topology for multiple bands. In particular, the non-separability of non-Hermitian multibands can be topologically non-trivial without exceptional points in two-dimensional space. As a physical illustration of the role of pseudo-Hermitian lines, we examine a multiband structure of a photonic crystal system with lossy materials. Our work builds on the fundamental and comprehensive understanding of non-Hermitian multiband systems and also offers versatile applications and realizations of non-Hermitian systems without the need to consider exceptional points., Comment: 11 pages, 12 figures

Open quantum systems provide a plethora of exotic topological phases of matter that has no Hermitian counterpart. Non-Hermitian skin effect, macroscopic collapse of bulk states to the boundary, has been extensively studied in various experimental platforms. However, it remains an open question whether such topological phases persist in the presence of many-body interactions. Notably, previous studies have shown that the Pauli exclusion principle suppresses the skin effect. In this study, we present a compelling counterexample by demonstrating the presence of the skin effect in doublon-holon excitations. While the ground state of the spin-half Hatano-Nelson model shows no skin effect, the doublon-holon pairs, as its collective excitations, display the many-body skin effect even in strong coupling limit. We rigorously establish the robustness of this effect by revealing a bulk-boundary correspondence mediated by the point gap topology within the many-body energy spectrum. Our findings underscore the existence of non-Hermitian topological phases in collective excitations of many-body interacting systems., Comment: 16 pages 8 figures

We derive symmetry-based conditions for tight-binding Hamiltonians with flatbands to have compact localized eigenstates occupying a single unit cell. The conditions are based on unitary operators commuting with the Hamiltonian and associated with local symmetries that guarantee compact localized states and a flatband. We illustrate the conditions for compact localized states and flatbands with simple Hamiltonians with given symmetries. We also apply these results to general cases such as the Hamiltonian with long-range hoppings and higher-dimensional Hamiltonian., Comment: 7 pages, 2 figures

Eigenstate coalescence in non-Hermitian systems is widely observed in diverse scientific domains encompassing optics and open quantum systems. Recent investigations have revealed that adiabatic encircling of exceptional points (EPs) leads to a nontrivial Berry phase in addition to an exchange of eigenstates. Based on these phenomena, we propose in this work an exhaustive classification framework for EPs in non-Hermitian physical systems. In contrast to previous classifications that only incorporate the eigenstate exchange effect, our proposed classification gives rise to finer $\mathbb{Z}_2$ classifications depending on the presence of a $\pi$ Berry phase after the encircling of the EPs. Moreover, by mapping arbitrary one-dimensional systems to the adiabatic encircling of EPs, we can classify one-dimensional non-Hermitian systems characterized by topological phase transitions involving EPs. Applying our exceptional classification to various one-dimensional models, such as the non-reciprocal Su--Schrieffer--Heeger (SSH) model, we exhibit the potential for enhancing the understanding of topological phases in non-Hermitian systems. Additionally, we address exceptional bulk-boundary correspondence and the emergence of distinct topological boundary modes in non-Hermitian systems., Comment: 8 pages, 4 figures

Layered ruthenates are a unique class of systems which manifests a variety of electronic and magnetic features emerged from competing energy scales. At the heart of such features lies the multi-orbital physics, especially, the orbital-selective behavior. Here, we propose that the SrRuO3-SrTiO3 heterostructure is a highly tunable platform to obtain the various emergent properties. Employing the density functional theory plus dynamical mean-field theory, we thoroughly investigate the orbital-dependent physics of the system and identify the competing magnetic fluctuations. We show that the epitaxial strain drives the system towards multi-orbital or orbital selective Mott phases from the Hund metal regime. At the same time, the two different types of static magnetism are stabilized, ferromagnetism and checkerboard antiferromagnetism, from the competition with the spin-density wave instability., Comment: 5 pages, 3 figures in the main text, Supplemental Material is included

In this study, we report the magnetic energy landscape of Sr2RuO4 employing the generalized Bloch approach within density functional theory. We identify the two dominant magnetic instabilities, ferromagnetic and spin-density-wave, together with other predominant instabilities. We show that epitaxial strain can change the overall magnetic tendency of the system, and tune the relative weight of the various magnetic instabilities in the system. Especially, the balance between spin-density wave and ferromagnetic instabilities can be controlled by the strain, and, eventually can lead to the new magnetic phases as well as superconducting phases with possibly altered pairing channels. Our findings are compared with previous theoretical models and experimental reports for the various magnetic features of the system and offer a first-principles explanation to them.

We propose a microscopic mechanism to resolve the long-standing puzzle of the insulator-to-metal transition in correlated electronic systems, most notably charge-density-wave (CDW) materials and Mott insulators, driven far-from-equilibrium by a DC electric field. By introducing a generic model of electrons coupled to an inelastic medium of phonons, we demonstrate that an electron avalanche can occur in the bulk limit of such insulators at arbitrarily small electric field. The quantum avalanche arises by the generation of a ladder of in-gap states, created by a multi-phonon emission process. Hot-phonons in the avalanche trigger a premature and partial collapse of the correlated gap. The details of the phonon spectrum dictate two-stage versus single-stage mechanisms which we associate with CDW and Mott resistive transitions, respectively. The electron and phonon temperatures, as well as the temperature dependence of the threshold fields, point to the quantum nature of this nonequilibrium phase transition.

We report an unprecedented quantum criticality crossover representing two different universal scaling behaviors in a Kitaev quantum magnetic material $\alpha$-RuCl$_3$. $\alpha$-RuCl$_3$ presents both a symmetry breaking antiferromagnetic order and a long-range entangled topological order of a quantum spin liquid, and thus could be a candidate system for a new universality class involving deconfined fractionalized excitations of the local Z$_2$ fluxes and itinerant Majorana fermions. Theoretical analyses on the inelastic neutron scattering and specific heat results demonstrate that Wilson-Fisher-Yukawa-type 'conventional' weak-coupling quantum criticality in high energy scales crosses over to heavy-fermion-type 'local' strong-coupling one in low energy scales. Our findings provide deep insight on how the quantum criticality evolves in fermion-boson coupled topological systems with different types of deconfined fermions., Comment: 14 pages, 11 figures

We demonstrate general classifications of Riemann surface topology generated by multiple arbitrary-order exceptional points of quasi-stationary states. Our studies reveal all possible product permutations of holonomy matrices that describe a stroboscopic encircling of 2nd order exceptional points. The permutations turn out to be categorized into a finite number of classes according to the topological structures of the Riemann surfaces. We further show that the permutation classes can be derived from combinations of cyclic building blocks associated with higher-order exceptional points. Our results are verified by an effective non-Hermitian Hamiltonian founded on generic Jordan forms and then examined in physical systems of desymmetrized optical microcavities.

We investigate the role of generic scale invariance in a Mott transition from a U(1) spin-liquid insulator to a Landau Fermi-liquid metal, where there exist massless degrees of freedom in addition to quantum critical fluctuations. Here, the Mott quantum criticality is described by critical charge fluctuations, and additional gapless excitations are U(1) gauge-field fluctuations coupled to a spinon Fermi surface in the spin-liquid state, which turn out to play a central role in the Mott transition. An interesting feature of this problem is that the scaling dimension of effective leading local interactions between critical charge fluctuations differs from that of the coupling constant between U(1) gauge fields and matter-field fluctuations in the presence of a Fermi surface. As a result, there appear dangerously irrelevant operators, which can cause conceptual difficulty in the implementation of renormalization group (RG) transformations. Indeed, we find that the curvature term along the angular direction of the spinon Fermi surface is dangerously irrelevant at this spin-liquid Mott quantum criticality, responsible for divergence of the self-energy correction term in U(1) gauge-field fluctuations. Performing the RG analysis in the one-loop level based on the dimensional regularization method, we reveal that such extremely overdamped dynamics of U(1) gauge-field fluctuations, which originates from the emergent one-dimensional dynamics of spinons, does not cause any renormalization effects to the effective dynamics of both critical charge fluctuations and spinon excitations. However, it turns out that the coupling between U(1) gauge-field fluctuations and both matter-field excitations still persists at this Mott transition, which results in novel mean-field dynamics to explain the nature of the spin-liquid Mott quantum criticality.

We investigate a many-body localization transition based on a Boltzmann transport theory. Introducing weak localization corrections into a Boltzmann equation, Hershfield and Ambegaokar re-derived the Wolfle-Vollhardt self-consistent equation for the diffusion coefficient [Phys. Rev. B {\bf 34}, 2147 (1986)]. We generalize this Boltzmann equation framework, introducing electron-electron interactions into the Hershfield-Ambegaokar Boltzmann transport theory based on the study of Zala-Narozhny-Aleiner [Phys. Rev. B {\bf 64}, 214204 (2001)]. Here, not only Altshuler-Aronov corrections but also dephasing effects are taken into account. As a result, we obtain a self-consistent equation for the diffusion coefficient in terms of the disorder strength and temperature, which extends the Wolfle-Vollhardt self-consistent equation in the presence of electron correlations. Solving our self-consistent equation numerically, we find a many-body localization insulator-metal transition, where a metallic phase appears from dephasing effects dominantly instead of renormalization effects at high temperatures. Although this mechanism is consistent with that of recent seminal papers [Ann. Phys. (N. Y). {\bf 321}, 1126 (2006); Phys. Rev. Lett. {\bf 95}, 206603 (2005)], we find that our three-dimensional metal-insulator transition belongs to the first order transition, which differs from the Anderson metal-insulator transition described by the Wolfle-Vollhardt self-consistent theory. We speculate that a bimodal distribution function for the diffusion coefficient is responsible for this first order phase transition.

Resorting to a recently developed theoretical device called dimensional regularization for quantum criticality with a Fermi surface, we examine a metal-insulator quantum phase transition from a Landau's Fermi-liquid state to a U(1) spin-liquid phase with a spinon Fermi surface in two dimensions. Unfortunately, we fail to approach the spin-liquid Mott quantum critical point from the U(1) spin-liquid state within the dimensional regularization technique. Self-interactions between charge fluctuations called holons are not screened, which shows a run-away renormalization group flow, interpreted as holons remain gapped. This leads us to consider another fixed point, where the spinon Fermi surface can be destabilized across the Mott transition. Based on this conjecture, we reveal the nature of the spin-liquid Mott quantum critical point: Dimensional reduction to one dimension occurs for spin dynamics described by spinons. As a result, Landau damping for both spin and charge dynamics disappear in the vicinity of the Mott quantum critical point. When the flavor number of holons is over its critical value, an interacting fixed point appears to be identified with an inverted XY universality class, controlled within the dimensional regularization technique. On the other hand, a fluctuation-driven first order metal-insulator transition results when it is below the critical number. We propose that the destabilization of a spinon Fermi surface and the emergence of one-dimensional spin dynamics near the spin-liquid Mott quantum critical point can be checked out by spin susceptibility with a $2 k_{F}$ transfer momentum, where $k_{F}$ is a Fermi momentum in the U(1) spin-liquid state: The absence of Landau damping in U(1) gauge fluctuations gives rise to a divergent behavior at zero temperature while it vanishes in the presence of a spinon Fermi surface., Comment: Sign mistakes in previous RG equations were corrected. Physical aspects were rewritten

Resorting to the Schwinger-boson representation for the description of a localized magnetic-impurity state, we develop an RG-improved (renormalization group) perturbation theory for the Kondo effect. This Schwinger-boson based RG-improved perturbation theory covers the whole temperature range from a decoupled local moment state to a local Fermi-liquid state through the crossover temperature regime, shown from the specific heat and spin susceptibility of the magnetic impurity. The Schwinger-boson based RG-improved perturbation theory makes the strong coupling fixed point at IR (infrared) accessible from the gaussian one at UV (ultraviolet) within the perturbation framework, regarded to be complementary to the Schwinger-boson based NCA (non-crossing approximation) self-consistent theory [Phys. Rev. Lett. {\bf 96}, 016601 (2006)]. The existence of the perturbatively accessible strong coupling fixed point implies the nature on the statistics of spinons, not determined by hands but chosen by the nature of strongly coupled systems.

Introducing both Berry curvature and chiral anomaly into Landau's Fermi-liquid theory, we construct a topological Fermi-liquid theory, applicable to interacting Weyl metals in the absence of time reversal symmetry. Following the Landau's Fermi-liquid theory, we obtain an effective free-energy functional in terms of the density field of chiral fermions. The density field of chiral fermions is determined by a self-consistent equation, minimizing the effective free-energy functional with respect to the order-parameter field. Beyond these thermodynamic properties, we construct Boltzmann transport theory to encode both the Berry curvature and the chiral anomaly in the presence of forward scattering of a Fermi-liquid state, essential for understanding dynamic correlations in interacting Weyl metals. This generalizes the Boltzmann transport theory for the Landau's Fermi-liquid state in the respect of incorporating the topological structure and extends that for noninteracting Weyl metals in the sense of introducing the forward scattering. Finally, we justify this topological Fermi-liquid theory, generalizing the first-quantization description for noninteracting Weyl metals into the second-quantization representation for interacting Weyl metals. First, we derive a topological Fermi-gas theory, integrating over high-energy electronic degrees of freedom deep inside a pair of chiral Fermi surfaces. As a result, we reproduce a topological Drude model with both the Berry curvature and the chiral anomaly. Second, we take into account interactions between such low-energy chiral fermions on the pair of chiral Fermi surfaces. We perform the renormalization group analysis, and find that only forward scattering turns out to be marginal above possible superconducting transition temperatures, justifying the topological Fermi-liquid theory of interacting Weyl metals with time reversal symmetry breaking.

We report magnetoresistance data in magnetic semiconductor multilayers, which exhibit a clear step-wise behavior as a function of external field. We attribute this highly non-trivial step-wise behavior to next-nearest-neighbor interlayer exchange coupling. Our microscopic calculation suggests that this next-nearest-neighbor coupling can be as large as 24% of the nearest-neighbor coupling. It is argued that such unusually long-range interaction is made possible by the quasi-one-dimensional nature of the system and by the long Fermi wavelength characteristic of magnetic semiconductors.

We investigate the dependence of perpendicular and parallel spin transfer torque (STT) and tunneling magnetoresistance (TMR) on the insulator barrier energy in the magnetic tunnel junction (MTJ). We employed single orbit tight binding model combined with the Keldysh non-equilibrium Green's function method in order to calculate the perpendicular and parallel STT, and TMR in MTJ with the finite bias voltages. The dependences of STT and TMR on the insulator barrier energy are calculated for the semi-infinite half metallic ferromagnetic electrodes. We find that perfect linear relation between the parallel STT and the tunneling current for the wide range of the insulator barrier energy. Furthermore, the TMR also depends on the insulator barrier energy, which contradicts to the Julliere's simple model.

This paper has been withdrawn by the author due to a serious errors in the calculations., Comment: This paper has been withdrawn