Spin-Independent Origin of the Strongly Enhanced Effective Mass in a Dilute 2D Electron System

Abstract

We have accurately measured the effective mass in a dilute two-dimensional electron system in silicon by analyzing temperature dependence of the Shubnikov-de Haas oscillations in the lowtemperature limit. A sharp increase of the effective mass with decreasing electron density has been observed. Using tilted magnetic fields, we have found that the enhanced effective mass is independent of the degree of spin polarization, which points to a spin-independent origin of the mass enhancement and is in contradiction with existing theories.PACS numbers: 71.30.+h,73.40.Qv,71.18.+y The ground state of an ideal, strongly interacting two-dimensional (2D) electron system is predicted to be Wigner crystal [1]. The strength of the interactions is usually characterized by the ratio between the Coulomb energy and the Fermi energy, r s = E c /E F . Assuming that the effective electron mass is equal to the band mass, the interaction parameter r s in the single-valley case reduces to the Wigner-Seitz radius, 1/(πn s ) 1/2 a B and therefore increases as the electron density, n s , decreases (here a B is the Bohr radius in semiconductor). In the strongly-interacting limit, no analytical theory has been developed to date. According to numeric simulations [2], Wigner crystallization is expected in a very dilute regime, when r s reaches approximately 35. The refined numeric simulations [3] have predicted that prior to the crystallization, in the range of the interaction parameter 25 r s 35, the ground state of the system is a strongly correlated ferromagnetic Fermi liquid. At yet higher electron densities, at r s ∼ 1, the (weaklyinteracting) electron liquid is expected to be paramagnetic, with the effective mass, m, and Landé g factor renormalized by interactions. Enhancement of g and m within the Fermi liquid theory is due to spin exchange effects, with renormalization of the g factor being dominant compared to that of the effective mass [4]. In contrast, the dominant increase of m near the onset of Wigner crystallization follows from an alternative description of the strongly-interacting electron system beyond the Fermi liquid approach, which also predicts the renormalization of m to be strongly sensitive to the polarization of spins [5,6].In dilute silicon metal-oxide-semiconductor-fieldeffect-transistors (MOSFETs), a strong metallic temperature dependence of the resistance was observed a decade ago [7]. Although this anomaly was almost immediately attributed to strong electron-electron interactions, only after a strongly enhanced ratio of the spin and the cyclotron splittings was found at low n s [8] has it become clear that the system behaves well beyond the weakly interacting Fermi liquid. Later, it was reported that the magnetic field required to produce complete spin polarization, B c ∝ n s /gm, tends to vanish at a finite electron density ≈ 8 × 10 10 cm −2 [9, 10]. These findings point to a sharp increase of the spin susceptibility and possible ferromagnetic instability in dilute silicon MOSFETs. In very dilute GaAs/AlGaAs he...

Density-dependent spin susceptibility and effective mass in interacting quasi-two-dimensional electron systems

“…There is no need to invoke any non-Fermi liquid concepts to explain the recent experimental results on quasiparticle renormalization effects 3,4,5,6,7,8,9,10,11 . This work is supported by the NSF, the DARPA, the US-ONR, and the LPS.…”

“…There has been a number of experimental papers appearing in the recent literature reporting the lowtemperature ( 100mK) measurement of the susceptibility 3,4,5,6,7,8,9 and effective mass 10,11 in 2D electron systems as a function of carrier density in the r s ≈ 1 − 10 parameter range. Although some aspects of the data in different experiments (and more importantly, the interpretation of the data) have been controversial -most especially on the issue of whether there is a spontaneous density-driven ferromagnetic spin polarization transition at low carrier densities in 2D systems -the experimental reports convincingly establish a strong enhancement in both the spin susceptibility and effective mass as a function of decreasing (increasing) carrier density n (interaction parameter r s ).…”

“…The 2D systems have the distinct advantage of the density being a tunable parameter so that the density dependence of the Fermi liquid renormalization can be studied directly. In this paper, we theoretically consider the density-dependent many-body renormalization of the 2D electronic spin susceptibility and effective mass, a subject of considerable recent experimental activity 3,4,5,6,7,8,9,10,11 in a number of different semiconductor heterostructures with confined 2D electron systems.…”

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

“…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. 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.…”

“…[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.…”