Universal resistances of the quantum resistance–capacitance circuit

Abstract

We examine the concept of universal quantized resistance in the AC regime through the fully coherent quantum RC circuit comprising a cavity (dot) capacitively coupled to a gate and connected via a single spin-polarized channel to a reservoir lead. As a result of quantum effects such as the Coulomb interaction in the cavity and global phase coherence, we show that the charge relaxation resistance Rq is identical for weak and large transmissions and it changes from h/2e 2 to h/e 2 when the frequency (times ) exceeds the level spacing of the cavity; h is the Planck constant and e the electron charge. For large cavities, we formulate a correspondence between the charge relaxation resistance h/e 2 and the Korringa-Shiba relation of the Kondo model. Furthermore, we introduce a general class of models, for which the charge relaxation resistance is universal. Our results emphasize that the charge relaxation resistance is a key observable to understand the dynamics of strongly correlated systems.The Landauer-Büttiker formula for coherent DC transport lies at the heart of modern electronics 1,2,3 and embodies one of the most dramatic predictions of modern condensed-matter physics: the perfect quantization, in steps of e 2 /h, of the maximum electrical conductance in one-dimensional metallic channels. It is universal insofar as one may validly neglect the disruptive influences of inelastic scattering processes within the transport process. An elementary explanation of the quantization views the constriction as an electron wave guide which has a non-zero resistance even though there are no impurities, because of the reflections occurring when a small number of propagating modes in the wave guide is matched to a large number of modes in the reservoirs 4,5 . This conductance quantization has been observed in various systems such as quantum Hall states 6 , quantum point contacts 7,8 , carbon nanotubes 9,10 and the helical edge liquid of topological insulators 11 . In this manuscript, we thoroughly investigate the AC regime and show that the charge relaxation resistance may be universally quantized; while the quantized resistance in the DC case requires a perfectly transmitted channel 12,13 , the charge relaxation resistance remains quantized regardless of the mode transmission. More specifically, we consider the quantum RC circuit of Fig. 1 in the context of spin-polarized electrons. Theoretically, the study of AC coherent transport was pioneered in a scattering approach by Büttiker, Prêtre and Thomas 14 where a universal charge relaxation resistance of R q = h/2e 2 was predicted 15 for a single-mode resistor; the factor 1/2 is purely of quantum origin and must be distinguished from spin effects. Coulomb blockade effects 16,17 were ignored and later they have been partially included in an Hartree-Fock theory 18 . The quantum mesoscopic RC circuit has been successfully implemented in a two-dimensional electron gas and the charge relaxation resistance R q = h/2e 2 was measured 19,20 . Our work completes the proof of the univers...

Dynamics of energy transport and entropy production in ac-driven quantum electron systems

“…The latter type of interactions may, however, affect other more quantitative features such as the behavior of the instantaneous Joule law analyzed in Sec. VI C, since an electron-electron interaction is shown to affect the charge relaxation resistance R q at finite temperatures [52], for large cavities [53], and at finite magnetic fields [54]. Our results thus represent a significant advance toward a full understanding of dissipation and dynamics in quantum electron systems and might have important implications for nanoelectronics and quantum thermodynamics.…”

Cavity QED with hybrid nanocircuits: from atomic-like physics to condensed matter phenomena

“…Hence, it would be interesting to understand to which extent the universality of the charge relaxation resistance is robust to interactions [147][148][149][150][151] . There is not yet a full consensus on this question and the answer could depend on the regime of parameter considered.…”

Radio Frequency Charge Parity Meter

“…A number of novel phenomena have been studied in the high frequency response of mesoscopic systems, including a violation of Kirchhoff's laws at GHz frequencies [10][11][12][13][14][15]. In this regime, the electrical response can be characterized by a "mesoscopic admittance", Y (ω) = R −1 eff +iωC eff , where the effective resistance R eff and capacitance C eff are influenced by electronic tunneling and the density of states at the Fermi level [16].…”