Microscopic origin of collective exponentially small resistance states

Abstract

The formation of "zero" (exponentially small) resistance states (ESRS) in high mobility two-dimensional electron systems (2DES) in a static magnetic field B and subjected to strong microwave (MW) radiation has attracted great theoretical interest. These states appear to be associated with a new kind of energy gap _. Here I show that the energy gap _ is explained by a microscopic quantum model that involves the Prime Number Theorem, hitherto reserved for only mathematical contexts. The model also contains the zeroes of the zeta function, and explains the physical origin of the Riemann hypothesis.Two experimental groups have discovered giant magnetoresistance oscillations associated with low-field cyclotron resonance in samples previously used to study quantum Hall effects. In very high mobility samples the minima of these oscillations correspond to exponentially small resistance [1][2][3] . There are many suggested analogies to explain this entirely unexpected phenomenon [1][2][3][4][5][6][7][8][9] . Photon-assisted formation of collective tunneling states between initial and final states involving multiquantum well (MQW) geometries is well known 10 . Theories predicted 11 dynamic localization and absolute negative conductance due to coherent tunneling in semiconductor superlattices subjected to ac electric fields nearly 20 years before a similar effect associated with sequential incoherent tunneling was observed 12. Many examples of this phenomenon are now

Radiation-induced oscillatory magnetoresistance in a tilted magnetic field inGaAs∕AlxGa1−xAsMani1 2005Phys. Rev. B875460View full textAdd to dashboardCite

“…[7,8,9,10,11,12,13,14,15,16,17,18] At the present, the observed radiation-induced resistance oscillations are generally attributed to a field dependent scattering at impurities and/or a steady state change in the electronic distribution function, as a result of photoexcitation. [7,9,11,12,13,14,15] It turns out that in both of these theoretical scenarios, the amplitude of the magnetoresistance oscillations can increase with the radiation intensity, in analogy to the experimental observations.…”

Theory of microwave-induced zero-resistance states in two-dimensional electron systems

“…Among the proposed ideas are the so called "displacement" model [34][35][36][39][40][41]44 , originally proposed in Refs. 68,69 for a different physical situation, the microwave induced dynamical symmetry breaking 37 , the "inelastic" model 6,47,51,58,59 , nonparabolicity effects 45 , the photon assisted quantum tunneling 36 , phase transitions caused by electron pairing due to the exciton exchange 1 and a quantum model that involves the prime number theorem 38 . The "displacement" model suggests, for example, that microwaves assist the impurity and phonon scattering which leads to the spatially indirect transitions between the Landau levels N and N ′ = N + k, k = 1, 2, 3, .…”

“…Then we substitute (39) and (36) into (38), average the resulting expression over time and after some algebraic transformations finally get the ponderomotive force in the conventional form F pm (x 0 ) = −∂U pm (x 0 )/∂x 0 with the potential (25).…”

Radiation-induced oscillatory Hall effect in high-mobilityGaAs/AlxMani1, Narayanamurti2, Klitzing3 et al. 2004Phys. Rev. B13391241View full textAdd to dashboardCite

“…[3,4] These striking features have motivated substantial theoretical interest in this phenomenon. [5,6,7,8,9,10] It is well known from experimental studies of transport that changes in the diagonal conductivity, σ xx , such as those induced by the radiation in this context, can produce small corrections, in the strong field limit, in the Hall resistivity, ρ xy , via the tensor relation ρ xy = σ xy /(σ 2 xx +σ 2 xy ). [11].…”

“…These features seem to provide new experimental insight into this remarkable phenomenon. [3,4,5,6,7,8,9,10,12,13,15] …”