Transport Out of Locally Broken Detailed Balance

Sánchez, Rafael

doi:10.1007/978-3-319-76599-0_3

Springer Proceedings in Mathematics &Amp; Statistics

2018

DOI: 10.1007/978-3-319-76599-0_3

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Transport Out of Locally Broken Detailed Balance

Rafael Sánchez

Abstract: Electrons move along potential or thermal gradients. In the presence of a global gradient, applied e.g. to the two terminals of a conductor, this induces electric charge and heat currents. They can also flow between two equilibrated terminals (at the same voltage and temperature) if detailed balance is broken in some part of the system. A minimal model involving two metallic islands in series is introduced whose internal potential and temperatures can be externally modulated. The conditions for a finite electr… Show more

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Cited by 2 publications

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References 72 publications

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“…This introduces crossed thermoelectric effects: the phonon bath behaves as a third terminal with which the electronic system exchanges heat (and of course, no charge). This heat exchange can be converted into a contribution of the charge current whose sign is defined by both mirror and electron-hole asymmetries 61,62 , even if ∆T = 0. This additional current can flow in the opposite direction as the backward current and eventually cancel it.…”

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Reversible thermal diode and energy harvester with a superconducting quantum interference single-electron transistor

Goury

Sánchez

2019

Applied Physics Letters

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The density of states of proximitized normal nanowires interrupting superconducting rings can be tuned by the magnetic flux piercing the loop. Using these as the contacts of a single-electron transistor allows to control the energetic mirror asymmetry of the conductor, this way introducing rectification properties. In particular, we show that the system works as a diode that rectifies both charge and heat currents and whose polarity can be reversed by the magnetic field and a gate voltage. We emphasize the role of dissipation at the island. The coupling to substrate phonons enhances the effect and furthermore introduces a channel for phase tunable conversion of heat exchanged with the environment into electrical current.Nanometric electronic devices demand on-chip components that are driven by temperature gradients or that manage thermal flows. Indeed, nanoscale conductors are interesting in this sense because of their intrinsic nonlinearities, strong spectral features and tunability 1,2 . However, progress in this direction has been slow due to difficulties in the precise experimental detection of heat currents. Only very recently, great advances have been achieved in various mesoscopic configurations [3][4][5][6][7][8] . They open the way to realize theoretical proposals of heat to current converters 9-17 , refrigerators 18-26 , thermal transistors 27,28 and diodes 29-32 , and valves 33 in the lab.A thermal rectifier is a system that responds to reversed temperature gradients with currents of different magnitude 34 . For it to work as a thermal diode, forward and backward flows must be of different orders of magnitude. In electronic systems, this is the case for two terminal mesoscopic junctions with strong non-linearities due to Coulomb interactions 29,[35][36][37][38] or coupled to an additional thermal bath with which it exchanges energy but no charge [39][40][41][42][43] . The performance of the device is then controlled by an external parameter, typically a gate voltage. A requirement is the absence of mirror symmetry, which can also be introduced in the spectral properties of the contacts [30][31][32]44,45 .At low temperatures, hybrid metallic-superconducting junctions are interesting candidates as one can make use of the properties of single-electron tunneling in strongly interacting islands 46 and of the energy filtering introduced by the gap of the superconducting contacts. Here we investigate a superconducting quantum interference single-electron transistor (SQUISET), sketched in Fig. 1(a). Similar setups have recently been proposed 47 and implemented 48 as single-particle sources and heat valves 49 . It consists on a normal metal island in the strong Coulomb blockade regime such that its occupation fluctuates between n=0,1 extra electrons. It can be controlled by the voltage V g of a plunger gate coupled to it via a capacitance C g . The island is tunnel-coupled to two short wires that close two respective superconducting rings serving as contacts. Due to the proximity effect, the wires acquire a min...

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“…The effect of having broken electron-hole symmetry (for n g = 1/2) and broken mirror symmetry (due to the superconducting gaps) breaks local detailed balance at both barriers, i.e. Γ + l p 0 = Γ − l p 1 62 . According to Eq.…”

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Reversible thermal diode and energy harvester with a superconducting quantum interference single-electron transistor

Goury

Sánchez

2019

Applied Physics Letters

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Correlation-induced refrigeration with superconducting single-electron transistors

Sánchez

2017

Applied Physics Letters

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A model of a superconducting tunnel junction which refrigerates a nearby metallic island without any particle exchange is presented. Heat extraction is mediated by charge fluctuations in the coupling capacitance of the two systems. The interplay of Coulomb interaction and the superconducting gap reduces the power consumption of the refrigerator. The island is predicted to be cooled from lattice temperatures of 200 mK down to close to 50 mK, for realistic parameters. The results emphasize the role of non-equilibrium correlations in bipartite mesoscopic conductors. This mechanism can be applied to create local temperature gradients in tunnel junction arrays or explore the role of interactions in the thermalization of non-equilibrium systems.Quantum coherent processes relevant to quantum information or quantum thermodynamics 1 are usually damaged by temperature. Solid state quantum simulators 2 or heat engines 3,4 have recently been proposed that operate at very low temperatures. Finding ways to cool nanoscale systems 5,6 , or introduce local temperature gradients well below 100 mK without injecting charge into them is hence a demanding task. This way they are minimally perturbed and not affected by Joule heating.Thermoelectric refrigeration is traditionally based on the Peltier effect. Driving a current through a conductor with broken electron-hole symmetry converts thermal excitations into transport. Mesoscopic refrigerators based on this effect make use of semiconductor quantum dots 7,8 , superconducting-insulator-normal metal (SIN) junctions 9-12 , or single-electron transistors (SET) 13,14 . Cooling mediated by the coupling to cavity photons has also been proposed in Josephson junctions 15-17 and implemented for the refrigeration of metallic islands [18][19][20][21][22] . Here an alternative approach is proposed based on the capacitive coupling of a two-terminal SINIS SET to the system to be cooled, see Fig. 1. We consider cooling of a single-electron box (SEB) 23,24 : a Coulomb blockade island which exchanges electrons with a third terminal. The extraction of energy is mediated by the Coulomb repulsion of electrons in different islands, J. The superconducting gap, ∆, acts as an energy filter: At subgap voltages, only transitions that take energy from from the capacitor contribute to transport. A normal metal SET would unavoidably emit Joule heat at all voltages into the island. The manipulation of electrical and thermal flows in capacitively coupled normal metal or semiconductor systems has been recently demonstrated, including effects such as quantum dot heat engines 25-32 , autonomous Maxwell's demon operations 33,34 , thermal rectifiers 35-37 , memristors 38 , or single-electron current switches 39-41 . The interplay of the two relevant energy scales, J and ∆, in the cooling mechanism is investigated. Subgap transport in the SET is assisted by the Coulomb interaction, hence increasing the voltage window where cooling takes place. Hot electrons in the SET island are thus pumped over the gap of the supercond...

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Transport Out of Locally Broken Detailed Balance

Cited by 2 publications

References 72 publications

Reversible thermal diode and energy harvester with a superconducting quantum interference single-electron transistor

Reversible thermal diode and energy harvester with a superconducting quantum interference single-electron transistor

Correlation-induced refrigeration with superconducting single-electron transistors

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