Statistics of energy dissipation in a quantum dot operating in the cotunneling regime

Abstract

At Coulomb blockade valleys inelastic cotunneling processes generate particle-hole excitations in quantum dots (QDs), and lead to energy dissipation. We have analyzed the probability distribution function (PDF) of energy dissipated in a QD due to such processes during a given time interval. We obtained analytically the cumulant generating function, and extracted the average, variance and Fano factor. The latter diverges as T 3 /(eV ) 2 at bias eV smaller than the temperature T , and reaches the value 3eV /5 in the opposite limit. The PDF is further studied numerically. As expected, Crooks fluctuation relation is not fulfilled by the PDF. Our results can be verified experimentally utilizing transport measurements of charge.PACS numbers: 73.23. Hk, 73.63.Kv, 42.50.Lc Thermal properties of nano-structures are of profound importance, inasmuch as they are manifestations of the dynamics of the particle zoo inside them. The latter includes electrons, phonons, photons, and other (quasi)particles, depending on the system and its surrounding environment. At the same time, understanding thermal characteristics and gaining the ability to manipulate them will facilitate higher control over nanocircuits, which is at the heart of technological advances. Importantly, it may push forward the effort towards finding sustainable energy resources.As a consequence, recently there has been a growing interest in thermal aspects of nano-structures 1 . For instance, thermoelectricity in semiconductor nanostructures is investigated in Ref. [2]. The validity of the Wiedemann-Franz law in several mesoscopic systems is studied in Refs. [3]. The temperature of nano-structures is analyzed in Refs. [4]. Verification of the recently discovered non-equilibrium fluctuation relations 5 in the context of heat is reported in Refs. [6 and 7]. Energy relaxation in a quantum dot (QD), which is a pillar in the study of nano-electronic systems, is investigated in Ref. [8]. It was found there that half of the Jouleheating produced in transport is due to energy dissipation through the QD. Importantly, there are physical phenomena which are not fully accessible by charge related measurements. As an example we note the recently observed neutral modes in the fractional quantum Hall regime 9 , whose characterization may require thermometry 10 .Here we study the statistical properties of energy dissipated in a QD 11 tuned to be in a Coulomb blockade valley. In this regime sequential tunneling processes are mostly suppressed, and cotunneling processes play a leading role in transport. Cotunneling is a many-body coherent process, where electrons are transferred from one lead to another via a virtual (classically forbidden) state in the QD 12 . We are interested in the "inelastic" contribution, where a "trace" is left on the QD in the form of FIG. 1. Left: An equivalent circuit representing a quantum dot (QD) (the region bounded by the three capacitors c1, c2 and cg, marked by a blue rectangle) tunnel-coupled to two leads with potentials VL and VR. The energy le...

Distribution of waiting times between electron cotunneling events

“…5,11 Theoretical research into cotunneling has investigated its effect on transport in systems with inelastic scatterings, such as electron-electron and electron-phonon interactions. [12][13][14] Additional cotunneling research has focused on heat conductance, 15,16 transport in double quantum dots, 17,18 and inelastic cotunneling spectroscopy. 19,20 Recently multiple authors have studied the noise and full counting statistics (FCS) of cotunneling phenomena in an attempt to explore its effect on current fluctuations.…”

Full counting statistics and shot noise of cotunneling in quantum dots and single-molecule transistors

“…Such cotunneling spectroscopy is ideal for probing excited states and their lifetime in QDs, 35 molecules, [36][37][38][39] and graphene QDs. [40][41][42] Recently, the study of energy dissipation 43,44 and heat transport 45 in the cotunneling regime has gained interest. Experimentally, the shot noise in the cotunneling regime has been demonstrated to be super-Poissonian, [46][47][48][49][50][51] in agreement with theoretical predictions.…”