Spin-Independent Effective Mass in a Valley-Degenerate Electron System

Abstract

In a generic spin-polarized Fermi liquid, the masses of spin-up and spin-down electrons are expected to be different and to depend on the degree of polarization. This expectation is not confirmed by the experiments on two-dimensional heterostructures. We consider a model of an N -fold degenerate electron gas. It is shown that in the large-N limit, the mass is enhanced via a polaronic mechanism of emission/absorption of virtual plasmons. As plasmons are classical collective excitations, the resulting mass does not depend on N , and thus on polarization, to the leading order in 1/N . We evaluate the 1/N corrections and show that they are small even for N = 2.PACS numbers: 71.10.Ay, 71.18.+y, 71.10.Ca The observation of an apparent metal-insulator transition in high-mobility Si metal-oxide-semiconductor-fieldeffect-transistors (MOSFET's) [1] challenged the scaling theory of localization [2], which predicts that a twodimensional (2D) system undergoes only a continuous crossover between weak and strong localization regimes. Although there has been a substantial progress in understanding of transport and thermodynamic properties of MOSFET's and other heterostructures [3,4], the origin of the observed phenomena is still a subject of discussion. Although a conventional (dirty) Fermi-liquid (FL) theory [5,6] can account for many observed effects at least qualitatively and, in some cases, quantitatively, there is also a number of non-FL scenarios for the anomalous metallic state [7,8]. On the experimental side, the main argument for the FL-nature of the metallic state is the observation of quite conventional Shubnikov-de Haas (ShdH) oscillations [3,4], which implies an existence of well-defined quasiparticles albeit with the renormalized effective mass m * and spin susceptibility χ * s . The ShdH and magnetoresistance experiments show that at low densities both m * and χ * s are significantly enhanced compared to their band values [4] and, according to some studies [9,10], even diverge at the resistive transition point.Although none drastically non-FL features of the metallic state have been found in ShdH measurements as of now, there is one very intriguing observation which does seem to present a challenge for the FL theory, at least in its conventional formulation. Namely, in all studies when the spin and orbital degrees of freedom were controlled independently by applying a tilted magnetic field, the effective masses, m * ↑ and m * ↓ , and Dingle temperatures (impurity scattering rates), T D↑ and T D↓ , of spin-up and -down electrons, were found to be almost the same. Moreover, m * in MOSFETs [11,12] was found to be independent of the spin polarization, whereas T D was shown to depend on the polarization only weakly. In n-GaAs, the effective mass was found to depend on the parallel magnetic field [13]; however, this behavior was attributed to the coupling between the in-and out-ofplane degrees of freedom (Stern effect [14]), which is to be expected in systems with wider quantum wells. Given that the Stern effect is...

Effective mass and spin susceptibility of dilute two-dimensional holes in GaAs

“…In Fermi liquid theory, interacting particles can be treated as non-interacting quasi-particles with a renormalized effective mass (m * ) and spin susceptibility, χ * ∝ g * m * , where g * is the Lande g-factor. In the highly interacting, dilute regime (r s > ∼ 3), χ * and m * are typically enhanced compared to the band values and increase with increasing r s , as confirmed both theoretically [1][2][3][4][5][6][7][8] and experimentally. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] Besides r s , the spin and/or valley degrees of freedom also play an important role in the re-normalization of m * and χ * since they modify the exchange interaction.…”

“…[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] Besides r s , the spin and/or valley degrees of freedom also play an important role in the re-normalization of m * and χ * since they modify the exchange interaction. 5,6,17,[24][25][26][27] In particular, it was recently demonstrated that when a 2D electron system is fully spin and valley polarized, m * is suppressed compared to its band value. [24][25][26][27] This suppression was reproduced in subsequent, numerical theoretical work.…”

Probing electron interactions in a two-dimensional system by quantum magneto-oscillations

“…This is reminiscent of the predictions of the RPA model [16], according to which for the majority subband m * has to be smaller and T D to be lower due to better screening.…”

“…On the other hand, from intuitive expectations based on the RPA result [16,33], interactions within the minority subband should renormalize the effective mass stronger than in the majority one. In contrast to the latter expectations, earlier experiments [10,34] reported that the effective mass extracted from the amplitude of Shubnikov-de Haas (SdH) oscillations in Si-MOSFETs does not depend on the spin polarization to within 4%-5% accuracy.…”

Effective mass suppression in a ferromagnetic two-dimensional electron liquid

“…In the highly interacting dilute paramagnetic regime ͑3 Ͻ r s Ͻ 26͒, m ‫ء‬ is typically significantly enhanced compared to its band value m b and tends to increase with increasing r s . [4][5][6][7][8][9][10][11][12][13][14] A question of particular interest is the dependence of m ‫ء‬ on the 2D electrons' spin and valley degrees of freedom as these affect the exchange interaction. Recent measurements of m ‫ء‬ for 2D electrons confined to AlAs quantum wells ͑QWs͒ revealed that, when the 2DES is fully valley and spin polarized, m ‫ء‬ is suppressed down to values near or even slightly below m b .…”