Spin–valley phase diagram of the two-dimensional metal–insulator transition

Abstract

Using symmetry breaking strain to tune the valley occupation of a two-dimensional (2D) electron system in an AlAs quantum well, together with an applied in-plane magnetic field to tune the spin polarization, we independently control the system's valley and spin degrees of freedom and map out a spin-valley phase diagram for the 2D metal-insulator transition. The insulating phase occurs in the quadrant where the system is both spin-and valley-polarized. This observation establishes the equivalent roles of spin and valley degrees of freedom in the 2D metal-insulator transition.PACS numbers: 71.30.+h, 73.43.Qt, 73.50.Dn, The scaling theory of localization in two dimensions [1], which predicts an insulating phase for two-dimensional electron systems (2DESs) with arbitrarily weak disorder, was challenged by the observation of a metallic temperature dependence (dρ/dT > 0) of the resistivity, ρ, in low-disorder Si metal-oxide-semiconductor field-effect transistors (Si-MOSFETs) [2]. The associated metal-toinsulator transition (MIT) has subsequently become the subject of intense interest and controversy [3]. While behavior similar to that of Ref.[2] has now been reported for a wide variety of 2D carrier systems such as n-AlAs, 10], and p-Si/SiGe [11,12], the origin of the metallic state and its transition into the insulating phase remain major puzzles in solid state physics.Several experiments have demonstrated the important role of the spin degree of freedom in the MIT problem, either in systems with a strong spin-orbit interaction [10,13,14], or via the application of an external magnetic field to spin polarize the carriers [15,16,17,18,19]. The latter experiments have shown that a magnetic field applied parallel to the 2DES plane suppresses the metallic temperature dependence, ultimately driving the 2DES into the insulating regime as the 2DES is spin polarized. The relevance of multiple conduction-band valleys, on the other hand, is less known. Although it has been discussed theoretically that the occupation of multiple valleys may also be important [20,21], there has been no direct experimental demonstration. Here we show that the electrons' valley degree of freedom indeed plays a crucial role, analogous to that of spin. We study a 2DES, confined to an AlAs quantum well, in which we can independently tune both the spin and valley degrees of freedom. By studying the temperature dependence of ρ at various degrees of spin and valley polarization, we map out the metal-insulator phase diagram in this system at a constant density. The 2DES exhibits a metallic behavior when either the valley or spin are left fully unpolarized, and a minimum amount of both spin and valley polarization is required to enter the insulating phase.We performed experiments on 2DESs confined to modulation-doped, AlAs quantum wells of width 11 nm and 15 nm [22]. In these systems, the electrons occupy two conduction-band valleys of AlAs centered at the edges of the Brillouin zone along the [100] and [010] directions. We denote these valleys as X and Y...

Spontaneous Breaking of Time-Reversal Symmetry in Strongly Interacting Two-Dimensional Electron Layers in Silicon and Germanium

“…It is possible that because the UCF noise involves interference between two Feynman propagators, it is more likely to be affected by the localized spins than the WL correction which is determined by a single self intersecting propagator. Note that we have not discussed spatial inhomogeneity or clustering in the distribution of dopants which can lead to coexistence of localized and delocalized phases [14], impact of multiple valleys [39,40], or the inter-site Coulomb interaction [34,35,41] which are unlikely to affect the time reversal symmetry. In summary, magnetoconductivity and noise measurements reveal an unexpected spontaneous breaking of time reversal symmetry in 2D electron systems hosted in atomically confined Si:P and Ge:P crystals.…”

Valley-Polarized Interlayer Conduction of Anisotropic Dirac Fermions inSrMnBi2

“…In the so-called Dirac materials like graphene, two energy bands, corresponding to two equivalent sublattices, intersect linearly at different positions in the momentum space, providing multiple valley degeneracy. Since the valley degeneracy is balanced by crystal symmetry, producing a valley-selective current usually requires breaking crystal symmetry by, e.g., strain [1][2][3]. However, a recent study on a three-dimensional (3D) Dirac material, bismuth, demonstrated that a rotating magnetic field modulates the contribution of each valley to the conduction and also reveals the field-induced valley polarization [7][8][9].…”

“…Controlling the valley degree of freedom can be an effective way to modulate charge conduction and to induce intriguing phases [1][2][3][4][5][6][7][8][9][10]. In the so-called Dirac materials like graphene, two energy bands, corresponding to two equivalent sublattices, intersect linearly at different positions in the momentum space, providing multiple valley degeneracy.…”

An apparent metal-insulator transition in high-mobility two-dimensional InAs heterostructures

“…This apparent metal insulator transition (MIT) is marked by a "critical carrier density", n c which characterizes the crossover from the higherdensity metallic temperature dependence of the resistivity to the lower-density insulating temperature dependence. For n > n c , the system exhibits a metallic behavior (dρ/dT>0) while for n < n c , the resistivity increases with decreasing temperature and dρ/dT<0 in the insulating phase.In the past twenty years, MIT has been observed in a wide variety of 2D carrier systems such as n-Si MOSFETs [3], n-GaAs [5, 6], p-GaAs [7-9], n-Si/SiGe [10, 11], pSi/SiGe [12, 13] and n-AlAs [14,15]. In the current work we present the first experimental observation of 2D MIT in a narrow gap semiconductor, namely, 2D electrons confined in InAs quantum wells.…”

“…In the past twenty years, MIT has been observed in a wide variety of 2D carrier systems such as n-Si MOSFETs [3], n-GaAs [5, 6], p-GaAs [7-9], n-Si/SiGe [10, 11], pSi/SiGe [12, 13] and n-AlAs [14,15]. In the current work we present the first experimental observation of 2D MIT in a narrow gap semiconductor, namely, 2D electrons confined in InAs quantum wells.…”