Quantum Phase Transitions in Two-Dimensional Electron Systems Under Strong Magnetic Field.

Abstract Using several independent methods, we find that the metal-insulator transition occurs in the strongly-interacting two-valley two-dimensional electron system in ultra-high mobility SiGe/Si/SiGe quantum wells in zero magnetic field. The transition survives in this system in parallel magnetic fields strong enough to completely polarize the electrons’ spins, thus making the electron system “spinless.” In both cases, the resistivity on the metallic side near the transition increases with decreasing temperature, reaches a maximum at a temperature Tmax, and then decreases. The decrease reaches more than an order of magnitude in zero magnetic field. The value of Tmax in zero magnetic field is found to be close to the renormalized Fermi temperature. However, rather than increasing along with the Fermi temperature, the value Tmax decreases appreciably for spinless electrons in spin-polarizing magnetic fields. The observed behavior of Tmax cannot be described by existing theories. The results indicate the spin-related origin of the effect. At the same time, the low-temperature resistivity drop in both spin-unpolarized and spinless electron systems is described quantitatively by the dynamical mean-field theory.Abstract Using several independent methods, we find that the metal-insulator transition occurs in the strongly-interacting two-valley two-dimensional electron system in ultra-high mobility SiGe/Si/SiGe quantum wells in zero magnetic field. The transition survives in this system in parallel magnetic fields strong enough to completely polarize the electrons’ spins, thus making the electron system “spinless.” In both cases, the resistivity on the metallic side near the transition increases with decreasing temperature, reaches a maximum at a temperature Tmax, and then decreases. The decrease reaches more than an order of magnitude in zero magnetic field. The value of Tmax in zero magnetic field is found to be close to the renormalized Fermi temperature. However, rather than increasing along with the Fermi temperature, the value Tmax decreases appreciably for spinless electrons in spin-polarizing magnetic fields. The observed behavior of Tmax cannot be described by existing theories. The results indicate the spin-related origin of the effect. At the same time, the low-temperature resistivity drop in both spin-unpolarized and spinless electron systems is described quantitatively by the dynamical mean-field theory.

arXiv:2208.05356Journal of Experimental and Theoretical PhysicsOct 1, 20220 citations

Quantum phase transitions in magnetic systems

Omid Nohadani

Jan 1, 20140 citations

Resistivity of the insulating phase approaching the two-dimensional metal-insulator transition: The effect of spin polarization

Shiqi Li, Myriam P. Sarachik

The resistivities of the dilute, strongly interacting two-dimensional electron systems in the insulating phase of a silicon MOSFET are the same for unpolarized electrons in the absence of magnetic field and for electrons that are fully spin polarized by the presence of an in-plane magnetic field. In both cases the resistivity obeys Efros-Shklovskii variable range hopping $\ensuremath{\rho}(T)={\ensuremath{\rho}}_{0}\text{exp}[{({T}_{ES}/T)}^{1/2}]$, with ${T}_{ES}$ and $1/{\ensuremath{\rho}}_{0}$ mapping onto each other if one applies a shift of the critical density ${n}_{\text{c}}$ reported earlier. With and without magnetic field, the parameters ${T}_{ES}$ and $1/{\ensuremath{\rho}}_{0}={\ensuremath{\sigma}}_{0}$ exhibit scaling consistent with critical behavior approaching a metal-insulator transition.The resistivities of the dilute, strongly interacting two-dimensional electron systems in the insulating phase of a silicon MOSFET are the same for unpolarized electrons in the absence of magnetic field and for electrons that are fully spin polarized by the presence of an in-plane magnetic field. In both cases the resistivity obeys Efros-Shklovskii variable range hopping $\ensuremath{\rho}(T)={\ensuremath{\rho}}_{0}\text{exp}[{({T}_{ES}/T)}^{1/2}]$, with ${T}_{ES}$ and $1/{\ensuremath{\rho}}_{0}$ mapping onto each other if one applies a shift of the critical density ${n}_{\text{c}}$ reported earlier. With and without magnetic field, the parameters ${T}_{ES}$ and $1/{\ensuremath{\rho}}_{0}={\ensuremath{\sigma}}_{0}$ exhibit scaling consistent with critical behavior approaching a metal-insulator transition.

arXiv:1607.07382Physical review. B./Physical review. BJan 11, 20176 citations

Quantum Phase Transitions in Two-Dimensional Electron

Systems Alexander Shashkin, Sergey Kravchenko

Alexander Shashkin Institute of Solid State Physics, Chernogolovka, Moscow District 142432, Russia Sergey Kravchenko Physics Department, Northeastern University, Boston, Massachusetts 02115, U.S.A. Two-dimensional (2D) electron systems are realized when the electrons are free to move in a plane but their motion perpendicular to the plane is quantized in a conﬁning potential well. Quantum phase transitions realized experimentally in such systems so far include metal-insulator transitions in perpendicular magnetic ﬁelds, metal-insulator transition in zero magnetic ﬁeld, and a possible transition to a Wigner crystal. The ﬁrst transition is governed by the externally controlled electron density or magnetic ﬁeld, while the other two are governed by the electron density. At low electron densities in 2D systems, the strongly-interacting limit is reached because the kinetic energy is overwhelmed by the energy of electron-electron interactions. The interaction strength is characterized by the ratio between the Coulomb energy and the Fermi energy, r∗s = Eee/EF . 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, rs = 1/(πns)1/2aB, and therefore increases as the electron density, ns, decreases (here aB is the Bohr radius in the semiconductor). Possible candidates for the ground state of the system include a Wigner crystal characterized by spatial and spin ordering [1], a ferromagnetic Fermi liquid with spontaneous spin ordering [2], a paramagnetic Fermi liquid [3], etc. In the strongly-interacting limit (rs 1), no analytical theory has been developed to date. According to numerical simulations [4], Wigner crystallization is expected in a very dilute regime, when rs reaches approximately 35. Reﬁned numerical simulations [5] have predicted that prior to the crystallization, in the range of the interaction parameter 25 ≤ rs ≤ 35, the ground state of the system is a strongly correlated ferromagnetic Fermi liquid. At higher electron densities, rs ∼ 1, the electron liquid is expected to be paramagnetic, with the eﬀective mass, m, and Lande´ g factor renormalized by interactions. Apart from the ferromagnetic Fermi liquid, other intermediate phases between the Wigner crystal and the paramagnetic Fermi liquid may also exist.Alexander Shashkin Institute of Solid State Physics, Chernogolovka, Moscow District 142432, Russia Sergey Kravchenko Physics Department, Northeastern University, Boston, Massachusetts 02115, U.S.A. Two-dimensional (2D) electron systems are realized when the electrons are free to move in a plane but their motion perpendicular to the plane is quantized in a conﬁning potential well. Quantum phase transitions realized experimentally in such systems so far include metal-insulator transitions in perpendicular magnetic ﬁelds, metal-insulator transition in zero magnetic ﬁeld, and a possible transition to a Wigner crystal. The ﬁrst transition is governed by the externally controlled electron density or magnetic ﬁeld, while the other two are governed by the electron density. At low electron densities in 2D systems, the strongly-interacting limit is reached because the kinetic energy is overwhelmed by the energy of electron-electron interactions. The interaction strength is characterized by the ratio between the Coulomb energy and the Fermi energy, r∗s = Eee/EF . 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, rs = 1/(πns)1/2aB, and therefore increases as the electron density, ns, decreases (here aB is the Bohr radius in the semiconductor). Possible candidates for the ground state of the system include a Wigner crystal characterized by spatial and spin ordering [1], a ferromagnetic Fermi liquid with spontaneous spin ordering [2], a paramagnetic Fermi liquid [3], etc. In the strongly-interacting limit (rs 1), no analytical theory has been developed to date. According to numerical simulations [4], Wigner crystallization is expected in a very dilute regime, when rs reaches approximately 35. Reﬁned numerical simulations [5] have predicted that prior to the crystallization, in the range of the interaction parameter 25 ≤ rs ≤ 35, the ground state of the system is a strongly correlated ferromagnetic Fermi liquid. At higher electron densities, rs ∼ 1, the electron liquid is expected to be paramagnetic, with the eﬀective mass, m, and Lande´ g factor renormalized by interactions. Apart from the ferromagnetic Fermi liquid, other intermediate phases between the Wigner crystal and the paramagnetic Fermi liquid may also exist.

CRC Press eBooksNov 2, 20101 citation

Quantum phase transitions of one-dimensional electron systems, 2

Hiromi Otsuka, 博巳大塚

Jan 1, 19990 citations

{T}_{ES}

and $1/{\ensuremath{\rho}}_{0}$ mapping onto each other if one applies a shift of the critical density

{n}_{\text{c}}

reported earlier. With and without magnetic field, the parameters

{T}_{ES}

and $1/{\ensuremath{\rho}}_{0}={\ensuremath{\sigma}}_{0}$ exhibit scaling consistent with critical behavior approaching a metal-insulator transition.