Quantum design of Cooper quartets in a double quantum dot system coupled to ordinary superconducting leads is presented as a novel platform for the study of an elusive many-body state of matter, that is at the basis of the phenomenon of charge-4e superconductivity. A fundamentally novel, maximally correlated ground state, in the form of a superposition of vacuum |0⟩ and four-electron state |4e⟩, emerges as a narrow resonance and it is promoted by an attractive interdot interaction. A novel phenomenology in the dissipationless transport regime is elucidated, that yields typical flux quantization in units of h/4e and manifests in non-local multi-terminal coherence and in two-Cooper pair transport properties mediated by the quartet ground state. The results open the way to the exploration of correlation effects and non-local coherence in hybrid superconducting devices, parity-protected quantum computing schemes and more generally, the work poses the basis for the design and simulation of novel correlated states of matter starting from ordinary ingredients available in a quantum solid state lab.
Quantum design of Cooper quartets in a double quantum dot system coupled to ordinary superconducting leads is presented as a novel platform for the study of an elusive many-body state of matter, that is at the basis of the phenomenon of charge-4e superconductivity. A fundamentally novel, maximally correlated ground state, in the form of a superposition of vacuum |0⟩ and four-electron state |4e⟩, emerges as a narrow resonance and it is promoted by an attractive interdot interaction. A novel phenomenology in the dissipationless transport regime is elucidated, that yields typical flux quantization in units of h/4e and manifests in non-local multi-terminal coherence and in two-Cooper pair transport properties mediated by the quartet ground state. The results open the way to the exploration of correlation effects and non-local coherence in hybrid superconducting devices, parity-protected quantum computing schemes and more generally, the work poses the basis for the design and simulation of novel correlated states of matter starting from ordinary ingredients available in a quantum solid state lab.
Cooper quartets are aggregates of four electrons that generalize the concept of Cooper pairs, and their study can unfold unexplored perspectives in correlated matter and many-body physics. We propose a method to isolate them in a double-quantum-dot system coupled to conventional superconducting and normal leads. By driving the system out of equilibrium, we show that a resonance between the vacuum ∣0⟩ and the four-electron state ∣4e⟩ emerges in the high bias voltage regime, which involves a two-Cooper pair exchange process and is characterized by finite quartet correlations. We study the transport properties of the system and show that a peak in the Andreev current at high bias voltage has a width that scales with the magnitude of the quartet coupling Γ4e, which can be tuned by the phase of additional superconducting leads, yielding distinctive signatures. By further studying the current-current correlations and the Fano factor, we establish a regime characterized by equal auto- and cross-correlations, which we interpret as a definitive signature of fast coherent two-Cooper-pair oscillations between the dots and the superconducting leads. The proposed platform, experimentally accessible in a quantum solid-state laboratory, enables exploration of quartet correlations and multifermion-correlated states of matter.
The condensation of electron quartets, known as charge-4e superconductivity (SC), represents a novel quantum state of matter beyond the standard paradigm of Cooper pairing. However, concrete microscopic models realizing this phase in two dimensions remain a central challenge. Here, we introduce a non-engineered and sign-problem-free model, unambiguously demonstrating the emergence of a robust and high-temperature charge-4e SC phase using unbiased quantum Monte Carlo simulations. At zero temperature, the phase diagram reveals that charge-4e SC is the primary ground state in the strong-coupling regime. At finite temperature in the absence of charge-2e SC, we identify charge-4e SC through a Berezinskii-Kosterlitz-Thouless transition, marked by a universal jump in the superfluid stiffness consistent with a condensate of charge 4e. Remarkably, the transition temperature Tc increases nearly linearly with interaction strength, providing a robust mechanism for high-Tc quartet superconductivity. Furthermore, spectral analysis reveals a prominent pseudogap above Tc arising from strong phase fluctuations. Our results establish a canonical and numerically exact model system for charge-4e superconductivity, offering crucial guidance for its realization in experimental platforms such as moiré materials and ultracold atomic systems.
A phase of matter in which fermion quartets form a superconducting condensate, rather than the paradigmatic Cooper pairs, is a recurrent subject of experimental and theoretical studies. However, a comprehensive microscopic understanding of charge-4e superconductivity as a quantum phase is lacking. Here, we study a two-orbital tight-binding model with attractive Hubbard-type interactions. Such a model naturally provides the Bose-Einstein condensate as a limit for electron quartets and supports charge-4e superconductivity, as we show by mapping it to a spin-1/2 chain in this perturbative limit. Using density matrix renormalization group calculations for the one-dimensional case, we further establish that the ground state is indeed a superfluid phase of 4e charge carriers and that this phase can be stabilized well beyond the perturbative regime. Importantly, we demonstrate that 4e condensation dominates over 2e condensation even for nearly decoupled orbitals, which is a more likely scenario in electronic materials. Our model paves the way for both experimental and theoretical exploration of 4e superconductivity and provides a natural starting point for future studies beyond one dimension or more intricate 4e states.
We consider the subgap physics of a hybrid double-quantum dot Cooper-pair splitter with large single-level spacings, in the presence of tunneling between the dots and finite Coulomb intra- and interdot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized master-equation method, which easily yields currents, noise, and cross-correlators. In particular, for finite inter- and intradot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local and nonlocal tunneling processes between the superconductor and the dots. We examine the effect of interdot tunneling on the particle-hole symmetry of the currents with and without spin-orbit interaction. We show that spin-orbit interaction in combination with finite Coulomb energy opens the possibility to control the nonlocal entanglement and its symmetry (singlet/triplet). We demonstrate that the generation of nonlocal entanglement can be achieved even without any direct nonlocal coupling to the superconducting lead.
A direct charge-4e superconductor exhibits coherent four-electron order without condensation in any charge-2e pairing channel. We establish three complementary results. First, a particle-number-conserving Hamiltonian with electron hopping and two-body interactions moves bound quartets efficiently: for electron- and pair-hopping amplitudes t and K and local gap U0, virtual pair transfer produces quartet hopping at order K2/U0, whereas electron hopping alone contributes only at order t4/U03. Second, the microscopic theory identifies an exactly solvable parent Hamiltonian at the phase-separation boundary. Its ground state combines quartet off-diagonal long-range order and finite phase stiffness without pair condensation, while rigorous bounds establish quartet order beyond the parent in a family with explicit quartet transfer. Third, a single convergent strong-coupling expansion simultaneously controls quartet kinetics and thermodynamic stability and rules out condensation in every pair channel of the microscopic model. On bipartite hypercubic lattices at half quartet filling, it yields a parametrically controlled homogeneous phase for d≥2, with quartet order, a linear collective mode, and gapped charge-2e excitations. Virtual pair transfer thus enables a direct charge-4e superconducting ground state without pair condensation.
Recent experiments on Cooper pair splitters using superconductor-quantum dot hybrids have embarked on creating entanglement in the solid-state, by engineering the sub-gap processes in the superconducting region. Using the thermoelectric Cooper pair splitter setup [Nat. Comm., 12, 21, (2021)] as a prototype, we present a comprehensive analysis of the fundamental components of the observed transport signal, aiming to critically clarify the operating regimes and confirm the nonlocal and nonclassical nature of correlations arising from crossed Andreev processes. By making a nexus with quantum discord, we identify operating points of nonlocal quantum correlations in the CPS device—information that cannot be extracted from the transport signal alone. A notable consequence of our analysis is the finding that contact-induced level broadening of the quantum dot’s discrete energy spectrum, along with its hybridization with the superconducting segment, can lead to shifted resonances in the crossed Andreev process as well as a parity reversal in the thermoelectric current. Our work thereby provides detailed insights into the gate voltage control of the quantum correlations in superconducting-hybrid Cooper pair splitters, revealing new avenues for harnessing quantum correlations in solid-state systems.