| 1. |
- Gaudenzi, Rocco, et al.
(author)
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Transport mirages in single-molecule devices
- 2017
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In: Journal of Chemical Physics. - : AIP Publishing. - 1089-7690 .- 0021-9606. ; 146:9, s. 092330-
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Journal article (peer-reviewed)abstract
- Molecular systems can exhibit a complex, chemically tailorable inner structure which allows for targeting of specific mechanical, electronic, and optical properties. At the single-molecule level, two major complementary ways to explore these properties are molecular quantum-dot structures and scanning probes. This article outlines comprehensive principles of electron-transport spectroscopy relevant to both these approaches and presents a new, high-resolution experiment on a high-spin single-molecule junction exemplifying these principles. Such spectroscopy plays a key role in further advancing our understanding of molecular and atomic systems, in particular, the relaxation of their spin. In this joint experimental and theoretical analysis, particular focus is put on the crossover between the resonant regime [single-electron tunneling] and the off-resonant regime [inelastic electron (co)tunneling spectroscopy (IETS)]. We show that the interplay of these two processes leads to unexpected mirages of resonances not captured by either of the two pictures alone. Although this turns out to be important in a large fraction of the possible regimes of level positions and bias voltages, it has been given little attention in molecular transport studies. Combined with nonequilibrium IETS— four-electron pump-probe excitations—these mirages provide crucial information on the relaxation of spin excitations. Our encompassing physical picture is supported by a master-equation approach that goes beyond weak coupling. The present work encourages the development of a broader connection between the fields of molecular quantum-dot and scanning probe spectroscopy.
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| 2. |
- Ortmanns, Lara C., et al.
(author)
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Solution of master equations by fermionic-duality: Time-dependent charge and heat currents through an interacting quantum dot proximized by a superconductor
- 2023
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In: SciPost Physics. - 2542-4653. ; 14:5
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Journal article (peer-reviewed)abstract
- We analyze the time-dependent solution of master equations by exploiting fermionic duality, a dissipative symmetry applicable to a large class of open systems describing quantum transport. Whereas previous studies mostly exploited duality relations after partially solving the evolution equations, we here systematically exploit the invariance under the fermionic duality mapping from the very beginning when setting up these equations. Moreover, we extend the resulting simplifications -so far applied to the local state evolution- to non-local observables such as transport currents. We showcase the ex-ploitation of fermionic duality for a quantum dot with strong interaction -covering both the repulsive and attractive case- proximized by contact with a large-gap superconduc-tor which is weakly probed by charge and heat currents into a wide-band normal-metal electrode. We derive the complete time-dependent analytical solution of this problem involving non-equilibrium Cooper pair transport, Andreev bound states and strong in-teraction. Additionally exploiting detailed balance we show that even for this relatively complex problem the evolution towards the stationary state can be understood analyti-cally in terms of the stationary state of the system itself via its relation to the stationary state of a dual system with inverted Coulomb interaction, superconducting pairing and applied voltages.
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| 3. |
- Ortmanns, Lara Celine, 1990, et al.
(author)
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Transient transport spectroscopy of an interacting quantum dot proximized by a superconductor: Charge and heat currents after a switch
- 2023
-
In: Physical Review B. - 2469-9969 .- 2469-9950. ; 108:8
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Journal article (peer-reviewed)abstract
- We analyze the time evolution of a quantum dot which is proximized by a large-gap superconductor and weakly probed using the charge and heat currents into a wide-band metal electrode. We map out the full time dependence of these currents after initializing the system by a switch. We find that due to the proximity effect there are two simple yet distinct switching procedures which initialize a nonstationary mixture of the gate-voltage-dependent eigenstates of the proximized quantum dot. We find in particular that the ensuing time-dependent heat current is a sensitive two-particle probe of the interplay of strong Coulomb interaction and induced superconducting pairing. The pairing can lead to a suppression of charge and heat current decay which we analyze in detail. The analysis of the results makes crucial use of analytic formulas obtained using fermionic duality, a "dissipative symmetry"of master equations describing this class of open systems.
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| 4. |
- Placke, B. A., et al.
(author)
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Attractive and driven interactions in quantum dots: Mechanisms for geometric pumping
- 2018
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In: Physical Review B. - 2469-9969 .- 2469-9950. ; 98:8
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Journal article (peer-reviewed)abstract
- We analyze time-dependent transport through a quantum dot with electron-electron interaction that is statically tunable to both repulsive and attractive regimes, or even dynamically driven. Motivated by the recent experimental realization [A. Hamo, Nature (London) 535, 395 (2016)NATUAS0028-083610.1038/nature18639] of such a system in a static double quantum dot we compute the geometric pumping of charge in the limit of weak tunneling, high temperature, and slow driving. We analyze the responses for all possible pumping experiments or "driving protocols", each defined by choosing a pair of driving parameters (gate voltage, bias voltage, tunnel coupling, electron-electron interaction). We show that such responses for different experiments can be governed by a common, underlying pumping mechanism, which is characterized by a set of effective parameters. The latter are nontrivial combinations of the experimentally driven parameters and other static parameters. If two different pumping experiments result in the same modulation of the effective parameters, i.e., the underlying mechanism is the same, then their responses will also be the same. Interestingly, for static attractive interaction we find a nonzero pumping response despite the attractive Coulomb blockade that hinders stationary transport. Furthermore, we identify a unique pumping response whose underlying mechanism relies on the interaction to be one of the driving parameters: it cannot be obtained with other sets of driving parameters. Finally, although a single-dot model with orbital pseudospin describes most of the physics of the mentioned experimental setup, it is crucial to account for the additional (real-)spin degeneracy of the double dot and the associated electron-hole symmetry breaking. This is necessary because the pumping response is more sensitive than dc transport measurements and detects this difference through pronounced qualitative effects.
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| 5. |
- Pluecker, T., et al.
(author)
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Gauge freedom in observables and Landsberg's nonadiabatic geometric phase: Pumping spectroscopy of interacting open quantum systems
- 2017
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In: Physical Review B. - 2469-9969 .- 2469-9950. ; 95:15
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Journal article (peer-reviewed)abstract
- We set up a general density-operator approach to geometric steady-state pumping through slowly driven open quantum systems. This approach applies to strongly interacting systems that are weakly coupled to multiple reservoirs at high temperature, illustrated by an Anderson quantum dot. Pumping gives rise to a nonadiabatic geometric phase that can be described by a framework originally developed for classical dissipative systems by Landsberg. This geometric phase is accumulated by the transported observable (charge, spin, energy) and not by the quantum state. It thus differs radically from the adiabatic Berry-Simon phase, even when generalizing it to mixed states, following Sarandy and Lidar. As a key feature, our geometric formulation of pumping stays close to a direct physical intuition (i) by tying gauge transformations to calibration of the meter registering the transported observable and (ii) by deriving a geometric connection from a driving-frequency expansion of the current. Furthermore, our approach provides a systematic and efficient way to compute the geometric pumping of various observables, including charge, spin, energy, and heat. These insights seem to be generalizable beyond the present paper's working assumptions (e.g., Born-Markov limit) to more general open-system evolutions involving memory and strong-coupling effects due to low-temperature reservoirs as well. Our geometric curvature formula reveals a general experimental scheme for performing geometric transport spectroscopy that enhances standard nonlinear spectroscopies based on measurements for static parameters. We indicate measurement strategies for separating the useful geometric pumping contribution to transport from nongeometric effects. A large part of the paper is devoted to an explicit comparison with the Sinitsyn-Nemenmann full-counting-statistics (FCS) approach to geometric pumping, restricting attention to the first moments of the pumped observable. Covering all key aspects, gauge freedom, pumping connection, curvature, and gap condition, we argue that our approach is physically more transparent and, importantly, simpler for practical calculations. In particular, this comparison allows us to clarify how in the FCS approach an "adiabatic" approximation leads to a manifestly nonadiabatic result involving a finite retardation time of the response to parameter driving.
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| 6. |
- Schulenborg, Jens, 1988, et al.
(author)
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Duality for open fermion systems: Energy-dependent weak coupling and quantum master equations
- 2018
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In: Physical Review B. - 2469-9969 .- 2469-9950. ; 98:23
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Journal article (peer-reviewed)abstract
- Open fermion systems with energy-independent bilinear coupling to a fermionic environment have been shown to obey a general duality relation [J. Schulenborg, Phys. Rev. B 93, 081411 (2016)2469-995010.1103/PhysRevB.93.081411] which allows for a drastic simplification of time-evolution calculations. In the weak-coupling limit, such a system can be associated with a unique dual physical system in which all energies are inverted, in particular the internal interaction. This paper generalizes this fermionic duality in two ways: we allow for weak coupling with arbitrary energy dependence and describe both occupations and coherences coupled by a quantum master equation for the density operator. We also show that whenever generalized detailed balance holds (Kolmogorov criterion), the stationary probabilities for the dual system can be expressed explicitly in terms of the stationary recurrence times of the original system, even at large bias. We illustrate the generalized duality by a detailed analysis of the rate equation for a quantum dot with strong onsite Coulomb repulsion, going beyond the commonly assumed wide-band limit. We present predictions for (i) the decay rates for transient charge and heat currents after a gate-voltage quench and (ii) the thermoelectric linear-response coefficients in the stationary limit. We show that even for pronouncedly energy-dependent coupling, all nontrivial parameter dependence in these problems is entirely captured by just two well-understood stationary variables, the average charge of the system and of the dual system. Remarkably, it is the latter that often dictates the most striking features of the measurable quantities (e.g., positions of resonances), underscoring the importance of the dual system for understanding the actual one.
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| 7. |
- Schulenborg, Jens, 1988, et al.
(author)
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Fermion-parity duality and energy relaxation in interacting open systems
- 2016
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In: Physical Review B. - 2469-9969 .- 2469-9950. ; 93:8, s. 081411-
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Journal article (peer-reviewed)abstract
- We study the transient heat current out of a confined electron system into a weakly coupled electrode in response to a voltage switch. We show that the decay of the Coulomb interaction energy for this repulsive system exhibits signatures of electron-electron attraction, and is governed by an interaction-independent rate. This can only be understood from a general duality that relates the non-unitary evolution of a quantum system to that of a dual model with inverted energies. Deriving from the fermion-parity superselection postulate, this duality applies to a large class of open systems.
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| 8. |
- Schulenborg, Jens, 1988, et al.
(author)
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Thermoelectrics of Interacting Nanosystems -- Exploiting Superselection Instead of Time-Reversal Symmetry
- 2017
-
In: Entropy. - : MDPI AG. - 1099-4300. ; 19:12
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Journal article (peer-reviewed)abstract
- Thermoelectric transport is traditionally analyzed using relations imposed by time-reversal symmetry, ranging from Onsager’s results to fluctuation relations in counting statistics. In this paper, we show that a recently discovered duality relation for fermionic systems—deriving from the fundamental fermion-parity superselection principle of quantum many-particle systems—provides new insights into thermoelectric transport. Using a master equation, we analyze the stationary charge and heat currents through a weakly coupled, but strongly interacting single-level quantum dot subject to electrical and thermal bias. In linear transport, the fermion-parity duality shows that features of thermoelectric response coefficients are actually dominated by the average and fluctuations of the charge in a dual quantum dot system, governed by attractive instead of repulsive electron-electron interaction. In the nonlinear regime, the duality furthermore relates most transport coefficients to much better understood equilibrium quantities. Finally, we naturally identify the fermion-parity as the part of the Coulomb interaction relevant for both the linear and nonlinear Fourier heat. Altogether, our findings hence reveal that next to time-reversal, the duality imposes equally important symmetry restrictions on thermoelectric transport. As such, it is also expected to simplify computations and clarify the physical understanding for more complex systems than the simplest relevant interacting nanostructure model studied here.
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| 9. |
- Schulenborg, Jens, 1988, et al.
(author)
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Thermovoltage in quantum dots with attractive interaction
- 2020
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In: Applied Physics Letters. - : AIP Publishing. - 0003-6951 .- 1077-3118. ; 116:24
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Journal article (peer-reviewed)abstract
- We study the linear and nonlinear thermovoltage of a quantum dot with effective attractive electron-electron interaction and weak, energy-dependent tunnel coupling to electronic contacts. Remarkably, we find that the thermovoltage shows signatures of repulsive interaction, which can be rationalized. These thermovoltage characteristics are robust against large potential and temperature differences well into the nonlinear regime, which we expect can be demonstrated in current state-of-the-art experiments. Furthermore, under nonlinear operation, we find extended regions of large power production at efficiencies on the order of the Curzon-Ahlborn bound interrupted only by a characteristic sharp dip.
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| 10. |
- Vanherck, Joren, 1993, et al.
(author)
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Relaxation of quantum dots in a magnetic field at finite bias - charge, spin and heat currents
- 2017
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In: Physica Status Solidi (B): Basic Research. - : Wiley. - 1521-3951 .- 0370-1972. ; 254:3
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Journal article (peer-reviewed)abstract
- We perform a detailed study of the effect of finite bias and magnetic field on the tunneling-induced decay of the state of a quantum dot by applying a recently discovered general duality [PRB 93, 81411 (2016)]. This duality provides deep physical insight into the decay dynamics of electronic open quantum systems with strong Coulomb interaction. It associates the amplitudes of decay eigenmodes of the actual system to the eigenmodes of a so-called dual system with attractive interaction. Thereby, it predicts many surprising features in the transient transport and its dependence on experimental control parameters: the attractive interaction of the dual model shows up as sharp features in the amplitudes of measurable time-dependent currents through the actual repulsive system. In particular, for interacting quantum dots, the time-dependent heat current exhibits a decay mode that dissipates the interaction energy and that is tied to the fermion parity of the system. We show that its decay amplitude has an unexpected gate-voltage dependence that is robust up to sizable bias voltages and then bifurcates, reflecting that the Coulomb blockade is lifted in the dual system. Furthermore, combining our duality relation with the known Iche-duality, we derive new symmetry properties of the decay rates as a function of magnetic field and gate voltage. Finally, we quantify charge- and spin-mode mixing due to the magnetic field using a single mixing parameter.
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