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

Abstract

Motivated by recent experimental reports, we carry out a Fermi liquid many-body calculation of the interaction induced renormalization of the spin susceptibility and effective mass in realistic two dimensional (2D) electron systems as a function of carrier density using the leading-order 'ladder-bubble' expansion in the dynamically screened Coulomb interaction. Using realistic material parameters for various semiconductor-based 2D systems, we find reasonable quantitative agreement with recent experimental susceptibility and effective mass measurements. We point out a number of open questions regarding quantitative aspects of the comparison between theory and experiment in low-density 2D electron systems.

Contrast between spin and valley degrees of freedom

“…1 In particular, s ‫ء‬ and m ‫ء‬ are expected to be larger than the band values ͑ s,b and m b ͒ for large r s . [1][2][3][4][5][6][7] Enhancements of s ‫ء‬ and m ‫ء‬ at large r s are indeed observed in a number of different 2DESs. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] In addition to r s , the role of spin and valley degrees of freedom on s ‫ء‬ and m ‫ء‬ renormalization has been explored both experimentally 15,20,[22][23][24][25] and theoretically.…”

“…This unexpected result was subsequently explained by theoretical studies. 5,26,27 The valley susceptibility ͑ v ‫ء‬ ϰ E 2 ‫ء‬ m ‫ء‬ ͒ of AlAs 2DESs, defined as the rate of valley polarization with applied strain ͑in analogy to s ‫ء‬ which is defined as the rate of spin polarization with applied magnetic field͒, has also been measured 22 ͑E 2 ‫ء‬ is the conduction-band deformation potential͒. It was found that v ‫ء‬ depends on the spin subband occupation 28 in a similar way that s ‫ء‬ depends on the valley occupation.…”

“…[8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] In addition to r s , the role of spin and valley degrees of freedom on s ‫ء‬ and m ‫ء‬ renormalization has been explored both experimentally 15,20,[22][23][24][25] and theoretically. 5,6,26,27 Measurements of s ‫ء‬ in AlAs 2DESs, 20,22 e.g., revealed that s ‫ء‬ is smaller for a two-valley system than it is for a single-valley system. This unexpected result was subsequently explained by theoretical studies.…”

“…[3][4][5]18 Finite layer thickness softens the Coulomb interaction but cannot cause a difference between spin and valley degrees of freedom. In our measurements, we apply parallel magnetic field ͑B ʈ ͒ to fully spin polarize the 2DES or to tune the ͑Landau͒ energy levels.…”

Absence of Interlayer Tunnel Coupling of K -Valley Electrons in Bilayer MoS2

“…1 (c) shows the extracted m * for the three different samples. We obtain a density-averaged mass of m * ≈ 0.62 m e which does not show any obvious dependence neither on n nor on B [17,18].…”