Heat rectification through single and coupled quantum dots

Abstract

We study heat rectification through quantum dots in the Coulomb blockade regime using a master equation approach. We consider both cases of two-terminal and four-terminal devices. In the two- terminal configuration, we analyze the case of a single quantum dot with either a doubly-degenerate level or two non-degenerate levels, and the case of a collection of N Coulomb-coupled quantum dots. In the sequential tunneling regime we analyze the behaviour of heat currents and rectification as functions of the position of the energy levels and of the temperature bias. In particular, we derive an upper bound for rectification in the closed-circuit setup with the doubly-degenerate level. We also prove the absence of a bound for the case of two non-degenerate levels and identify the ideal system parameters to achieve nearly perfect rectification. The second part of the paper deals with the effect of second-order cotunneling contributions, including both elastic and inelastic processes. In all cases we find that there exists ranges of values of parameters (such as the levels’ position) where rectification is enhanced by cotunneling. In particular, in the doubly-degenerate level case we find that cotunneling corrections can enhance rectification when they reduce the magnitude of the heat currents. For the four-terminal configuration, we analyze the non-local situation of two Coulomb- coupled quantum dots, each connected to two terminals: the temperature bias is applied to the two terminals connected to one quantum dot, while the heat currents of interest are the ones flowing in the other quantum dot. Remarkably, in this situation we find that non-local rectification can be perfect as a consequence of the fact that the heat currents vanish for properly tuned parameters.

Universal Behavior of the Coulomb-Coupled Fermionic Thermal Diode

“…Heat management devices have attracted recent interest in nanoscale systems; they prevent overheating due to heat flow in desired areas of electronic circuits [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ]. Following the theoretical proposal of a quantum dot thermal diode by Roukola and Ojanen [ 13 ], a number of studies have been carried out to achieve the rectification effect using simple quantum systems [ 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 30 ]. Yet, most of the works conducted to date rely on either temperature gradients of bosonic reservoirs or different coupling strengths between the system and the bath to break the inversion symmetry of the overall system [ 30 ].…”

“…Following the theoretical proposal of a quantum dot thermal diode by Roukola and Ojanen [ 13 ], a number of studies have been carried out to achieve the rectification effect using simple quantum systems [ 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 30 ]. Yet, most of the works conducted to date rely on either temperature gradients of bosonic reservoirs or different coupling strengths between the system and the bath to break the inversion symmetry of the overall system [ 30 ]. For example, Werlang et al [ 19 ] explored heat transport under the influence of strong coupling between two spins interacting with their respective bosonic baths.…”

“…Miranda et al [ 26 ] identified similar diode characteristics in the presence of different excitation frequencies between the coupled spins. Based on two- and four-terminal quantum dot setups, Tesser et al [ 30 ] recently explored the roles of level degeneracy and temperature bias. However, much less attention is paid to achieving the rectification effect by means of the statistical properties of the reservoir.…”

Universal behaviour of Coulomb coupled Fermionic thermal diode

“…Heat management devices has attracted recent interest in nanoscale systems to prevent overheating due to heat flow in desired areas of electronic circuits [1][2][3][4][5][6][7][8][9][10][11][12]. Following the theoretical proposal of a quantum dot thermal diode by Roukola and Ojanen [13], a number of studies are carried out in achieving rectification effect using simple quantum systems [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Yet, most of the works that have been done till now rely on either temperature gradient of bosonic reservoirs or different coupling strengths between the system and the bath to break the inversion symmetry of the overall system [30].…”

“…Based on a two and four terminal quantum dot setups, Tesser et.al. [30] recently explored the role of level degeneracy and temperature bias. However, much less attention is paid in achieving rectification effect by means of statistical properties of the reservoir.…”