arXiv subjects

Peter Zalom

Publications and source records attributed to Peter Zalom.

13 recordsLinked to original sources

arXiv2026

Symmetry-Induced Weyl Nodes in Interacting Multi-Terminal Josephson Junctions

We show that an emergent geometric symmetry generates non-trivial topology in quantum-dot-based multi-terminal Josephson junctions. It confines same-spin Andreev bound state crossings to an analytic one-dimensional manifold of the synthetic Brillouin zone, where interdot coupling selects Weyl nodes of charge $\pm1$ in the singlet sector and doubly degenerate cones of charge $\pm2$ in the doublet sector, at gate-tunable locations. The mechanism yields a spectroscopic detection protocol and a design principle for fabricating devices with non-trivial topological signatures.

cond-mat.mes-hall↗

arXiv2025

Andreev bound state spectroscopy of a quantum-dot-based Aharonov-Bohm interferometer with superconducting terminals

We analytically and numerically investigate an Aharonov-Bohm interferometer with two superconducting terminals and a strongly correlated quantum dot in one arm. Through a rigorous derivation, we prove that this double-path interferometer is spectrally equivalent to a simpler system: an interacting quantum dot coupled to a non-interacting side-coupled proximitized mode and a semiconductor lead. This equivalence reveals a simple interpretation of the interferometer's behavior through the competition of a geometric factor $\chi$, a key parameter characterizing the anomalous part of the hybridization function, with the properties of the side-coupled mode. We identify the conditions for the formation of doublet chimney in the phase diagrams in more general setting. Moreover, we show how the obtained Andreev bound state spectra clearly indicate the presence of Josephson diode effect generated by interferometric phenomena.

cond-mat.mes-hall↗

arXiv2024

Double-quantum-dot Andreev molecules: Phase diagrams and critical evaluation of effective models

This work systematically investigates the phase diagram of a parallel double-quantum-dot Andreev molecule, where the two quantum dots are coupled to a common superconducting lead. Using the numerical renormalization group method, we map out the evolution of the ground state across a wide parameter space of level detunings, size of the superconducting gap, lead couplings, and inter-dot coupling strength. The intricate phase diagrams feature singlet, doublet, and a relatively uncommon triplet ground states, with the latter being a distinct signature of strong lead-mediated interactions between the quantum dots. We benchmark the applicability of simplified effective models, including the atomic limit and zero-bandwidth approximations, in capturing the complex behavior of this parallel configuration. Our analysis reveals severe limitations of these models, underscoring the necessity for maximal caution when extrapolating beyond their tested validity. In particular, all effective models except for the extended version of the zero-bandwidth approximation failed in reproducing the triplet ground state and made several false predictions. These findings provide crucial insights for interpreting experimental observations and designing superconducting devices based on quantum-dot architectures.

cond-mat.mes-hall↗

arXiv2023

Hidden symmetry in interacting-quantum-dot-based multi-terminal Josephson junctions

We study a multi-terminal Josephson junction based on an interacting quantum dot coupled to $n$ superconducting BCS leads. Using an Anderson type model of a local level with an arbitrary onsite Coulomb repulsion, we uncover its surprising equivalence with an effective two-terminal junction with symmetric couplings to appropriately phase-biased leads. Regardless of the strength of the Coulomb interaction, this hidden symmetry enables us to apply well-established numerical and theoretical tools for exact evaluation of various physical quantities, and imposes strict relations among them. Focusing on three-terminal devices, we then demonstrate several phenomena such as the existence of the finite energy band crossings, superconducting transistor and diode effects, as well as current phase relation modulation.

cond-mat.mes-hall↗

arXiv2023

Rigorous Wilsonian Renormalization Group for impurity models with a spectral gap

The Anderson impurity model (AIM) has long served as a cornerstone in the study of correlated electron systems. While numerical renormalization group (RG) offers great flexibility for metallic reservoirs, it becomes impossible in an unbiased way when a spectral gap $\Delta$ opens up in the tunneling density of states. The only known exception is provided by the superconducting bath. In this paper, we lift these limitations by a novel numerical RG procedure that employs a discretization of the gapped tunneling densities of states into patches which accumulate at the gap edges. This reveals an unusual double scaling which is a shared behavior by the superconducting and the scalar gapped AIMs. Moreover, it requires a special iterative diagonalization procedure with an alternating scheme for discarding states only every second iteration. The discretization and the diagonalization scheme form together, what we refer to as, the log-gap numerical RG. It is successfully applied to the superconducting and to the scalar gapped AIM. Consequently, it reveals that both models belong to the same RG equivalence class which manifests physically in common singlet-doublet quantum phase transitions accompanied by in-gap bound states of given parities. While superconducting AIM is mainly used for benchmarking of the log-gap numerical RG, we also rigorously confirm the phenomenon of in-gap states escaping into the continuum, which was recently indirectly considered in Ref. [1]. The gapped AIM is then tackled in a first ever exact numerical RG approach and confirms quantitatively assertions based on models with auxiliary metallic leads [2-5]. Moreover, it reveals that calculations performed in Refs. [6-8] are of strictly approximate nature.

cond-mat.str-el↗

arXiv2023

Generalized atomic limit of a double quantum dot coupled to superconducting leads

We present an exactly solvable effective model of a double quantum dot coupled to superconducting leads. This model is a generalization of the well-known superconducting atomic limit approximation of the paradigmatic superconducting impurity Anderson model. However, in contrast to the standard atomic limit and other effective models, it gives quantitatively correct predictions for the quantum phase transition boundaries, subgap bound states as well as Josephson supercurrent in a broad range of parameters including experimentally relevant regimes. The model allows fast and reliable parameter scans important for the preparation and analysis of experiments which are otherwise inaccessible by more precise but computational heavy methods such as quantum Monte Carlo or the numerical renormalization group. The scans also allowed us to identify and investigate new previously unnoticed phase diagram regimes. We provide a thorough analysis of the strengths and limitations of the effective model and benchmark its predictions against numerical renormalization group results.

cond-mat.mes-hall↗

arXiv2021

Unified theory of quantum phase transitions in quantum dots with gapped host bands

We present a unified theory of quantum phase transitions for half-filled quantum dots (QDs) coupled to gapped host bands. We augment the bands by additional weakly coupled metallic lead which allows us to analyze the system by using standard numerical renormalization group techniques. The ground state properties of the systems without the additional metallic lead are then extrapolated in a controlled way from the broadened subgap spectral functions. We show that a broad class of narrow-gap-semiconductor tunneling densities of states (TDOSs) support the existence of two distinct phases known from their superconducting counterpart. Namely, $0$ phase which is marked by the singlet ground state and the $\pi$ phase regime with the doublet ground state. To keep a close analogy with the superconducting case, we focus on the influence of particle-hole asymmetry of the TDOS of the subgap spectral features. Nevertheless, we also discus the possibility of inducing singlet-doublet quantum phase transitions in experimental setups by varying the filling of the QD. In addition, for gapped TDOS functions with smoothed gap edges, we demonstrate that all subgap peaks may leak out of the gap into the continuous part of the spectrum, an effect which has no counterpart in the superconducting Anderson model.

cond-mat.mes-hall↗

arXiv2021

Spectral and transport properties of a half-filled Anderson impurity coupled to phase-biased superconducting and metallic leads

We derive and apply a general scheme for mapping a setup consisting of a half-filled single level quantum dot coupled to one normal metallic and two superconducting phase-biased leads onto an ordinary half-filled single impurity Anderson model with single modified tunneling density of states. The theory allows for the otherwise unfeasible application of the standard numerical renormalization group and enables to obtain phase-dependent local spectral properties as well as phase-dependent induced pairing and Josephson current. The resulting transport properties match well with the numerically exact continuous-time hybridization-expansion quantum Monte Carlo. For weakly coupled normal electrode, the spectral properties can be interpreted in terms of normal-electrode-broadened Andreev bound states with phase-dependent position analogous to the superconducting Anderson model, which coexist in the $π$-like phase with a Kondo peak whose phase-dependent Kondo temperature follows the form conjectured previously in Domański et al., Phys.~Rev.~B {\bf 95}, 045104 (2017)

cond-mat.mes-hall↗

arXiv2021

Tunable reentrant Kondo effect in quantum dots coupled to metal-superconducting hybrid reservoirs

We elaborate on the recently introduced concept of reentrant Kondo effect in quantum impurities/dots coupled to hybrid metal-semiconductor contacts [G.~Diniz {\em et al.}, Phys. Rev. B {\bf 101}, 125115 (2020)]. By noticing the equivalence of the originally suggested semiconducting arrangement to an analogous three-terminal quantum dot setup with a normal and two phase-biased superconducting leads introduced in our recent work [Phys. Rev. B {\bf 103}, 035419 (2021)], we put this effect into a new physical context, which enables us a fresh look on the problem. First, we identify the superconducting counterpart of the reentrant Kondo effect and, consequently, reveal its fragility with respect to an underlying doublet-singlet quantum phase transition induced by the particle-hole asymmetry of the reservoir densities of states. This is pertinent (even if previously unnoticed) also in the original as well as extended semiconducting setups, where it puts stringent conditions on the symmetry of the contact density of states. Furthermore, we analyze experimental feasibility of observing the reentrant Kondo effect in its superconducting realization concluding that even present day experiments might see the onset of the reentrant behavior, but fully developed Kondo features cannot be reached due to the required vast separation of energy/temperature scales.

cond-mat.mes-hall↗

arXiv2020

Magnetically-Tuned Kondo Effect in a Molecular Double Quantum Dot: Role of the Anisotropic Exchange

We investigate theoretically and experimentally the singlet-triplet Kondo effect induced by a magnetic field in a molecular junction. Temperature dependent conductance, $G(T)$, is calculated by the numerical renormalization group, showing a strong imprint of the relevant low energy scales, such as the Kondo temperature, exchange and singlet-triplet splitting. We demonstrate the stability of the singlet-triplet Kondo effect against weak spin anisotropy, modeled by an anisotropic exchange. Moderate spin anisotropy manifests itself by lowering the Kondo plateaus, causing the $G(T)$ to deviate from a standard temperature dependence, expected for a spin-half Kondo effect. We propose this scenario as an explanation for anomalous $G(T)$, measured in an organic diradical molecule coupled to gold contacts. We uncover certain new aspects of the singlet-triplet Kondo effect, such as coexistence of spin-polarization on the molecule with Kondo screening and non-perturbative parametric dependence of an effective magnetic field induced by the leads.

cond-mat.mes-hall↗

arXiv2019

Strongly correlated electrons: Analytic mean-field theories with two-particle self-consistency

A two-particle self-consistency is rarely part of mean-field theories. It is, however, essential for avoiding spurious critical transitions and unphysical behavior. We present a general scheme for constructing analytically controllable approximations with self-consistent equations for the two-particle vertices based on the parquet equations. We explain in detail how to reduce the full set of parquet equations not to miss quantum criticality in strong coupling. We further introduce a decoupling of convolutions of the dynamical variables in the Bethe-Salpeter equations to make them analytically solvable. We connect the self-energy with the two-particle vertices to satisfy the Ward identity and the Schwinger-Dyson equation. We discuss the role of the one-particle self-consistency in making the approximations reliable in the whole spectrum of the input parameters. We demonstrate the general construction on the simplest static approximation that we apply to the Kondo behavior of the single-impurity Anderson model.

cond-mat.str-el↗

arXiv2016

Helical turbulent Prandtl number in the $A$ model of passive advection: Two loop approximation

Using the field theoretic renormalization group technique in the two-loop approximation, turbulent Prandtl numbers are obtained in the general $A$ model of passive vector advected by fully developed turbulent velocity field with violation of spatial parity introduced via continuous parameter $ρ$ ranging from $ρ=0$ (no violation of spatial parity) to $|ρ|=1$ (maximum violation of spatial parity). In non-helical environments, we demonstrate that $A$ is restricted to $-1.723 \leq A \leq 2.800$ (rounded on the last presented digit) due to the constraints of two-loop calculations. When $ρ>0.749$ restrictions may be removed. Furthermore, three physically important cases $A \in \{-1, 0, 1\}$ are shown to lie deep within the allowed interval of $A$ for all values of $ρ$. For the model of linearized Navier-Stokes equations ($A = -1$) up to date unknown helical values of turbulent Prandtl number have been shown to equal $1$ regardless of parity violation. Furthermore, we have shown that interaction parameter $A$ exerts strong influence on advection diffusion processes in turbulent environments with broken spatial parity. In explicit, depending on actual value of $A$ turbulent Prandtl number may increase or decrease with $ρ$. By varying $A$ continuously we explain high stability of kinematic MHD model ($A=1$) against helical effects as a result of its closeness to $A = 0.912$ (rounded on the last presented digit) case where helical effects are completely suppressed. Contrary, for the physically important $A=0$ model we show that it lies deep within the interval of models where helical effects cause the turbulent Prandtl number to decrease with $|ρ|$. We thus identify internal structure of interactions given by parameter $A$, and not the vector character of the admixture itself to be the dominant factor influencing diffusion advection processes in the helical $A$ model.

cond-mat.stat-mech↗

arXiv2013

Spontaneous ferromagnetism in the spinor Bose gas with Rashba spin-orbit coupling

We show that in the two-component Bose gas with Rashba spin-orbit coupling an arbitrarily small attractive interaction between bosons with opposite spin induces spontaneous ferromagnetism below a finite critical temperature $T_c$. In the ferromagnetic phase the single-particle spectrum exhibits a unique minimum in momentum space in the direction of the magnetization. For sufficiently small temperatures below $T_c$ the bosons eventually condense into the unique state at the bottom of the spectrum, forming a ferromagnetic Bose-Einstein condensate.

cond-mat.quant-gas↗