Exchange Intervalley Scattering And Magnetic Phase Diagram Of Transition Metal Dichalcogenide Monolayers

We analyze magnetic phases of monolayers of transition metal dichalcogenides that are two-valley materials with electron-electron interactions. The exchange inter-valley scattering makes two-valley systems less stable to the spin fluctuations but more stable to the valley fluctuations. We predict a first order ferromagnetic phase transition governed by the non-analytic and negative cubic term in the free energy that results in a large spontaneous spin magnetization. Finite spin-orbit interaction leads to the out-of-plane Ising order of the ferromagnetic phase. Our theoretical prediction is consistent with the recent experiment on electron-doped monolayers of MoS$_2$ reported by Roch $\textit{et al.}$ [1]. The proposed first order phase transition can also be tested by measuring the linear magnetic field dependence of the spin susceptibility in the paramagnetic phase which is a direct consequence of the non-analyticity of the free energy.Comment: 9 pages, 6 figure

Magnetic phase transitions in two-dimensional two-valley semiconductors with in-plane magnetic field

A two-dimensional electron gas (2DEG) in two-valley semiconductors has two discrete degrees of freedom given by the spin and valley quantum numbers. We analyze the zero-temperature magnetic instabilities of two-valley semiconductors with SOI, in-plane magnetic field, and electron-electron interaction. The interplay of an applied in-plane magnetic field and the SOI results in non-collinear spin quantization in different valleys. Together with the exchange intervalley interaction this results in a rich phase diagram containing four non-trivial magnetic phases. The negative non-analytic cubic correction to the free energy, which is always present in an interacting 2DEG, is responsible for first order phase transitions. Here, we show that non-zero ground state values of the order parameters can cut this cubic non-analyticity and drive certain magnetic phase transitions second order. We also find two tri-critical points at zero temperature which together with the line of second order phase transitions constitute the quantum critical sector of the phase diagram. The phase transitions can be tuned externally by electrostatic gates or by the in-plane magnetic field

Instability of the ferromagnetic quantum critical point and symmetry of the ferromagnetic ground state in two-dimensional and three-dimensional electron gases with arbitrary spin-orbit splitting

It is well known that in the absence of the spin-orbit (SO) splitting the zero-temperature ferromagnetic phase transition in two-dimensional (2D) and three-dimensional (3D) electron gas is discontinuous (first order). The physical reason for this effect lies in the infrared catastrophe brought by the long-range particle-hole fluctuations near the Fermi surface. It is widely believed that a finite SO splitting is able to regularize this infrared catastrophe, and therefore, to stabilize the ferromagnetic quantum critical point. In contrast to this, we show that the infrared catastrophe persists at arbitrary SO splitting and the zero-temperature ferromagnetic phase transition in the itinerant 2D and 3D electron gas is always discontinuous. We also find that SO splitting reduces the symmetry of the ferromagnetic ground state down to the symmetry of the spin-orbit term. For example, Rashba SO splitting in 2D electron gas leads to the easy-plane symmetry of the ferromagnetic ground state. A combination of the Rashba SO splitting with the Dresselhaus term reduces the symmetry of the ferromagnetic ground state down to the in-plane Ising ferromagnet. The infrared catastrophe can be measured via the nonanalytic dependence of the spin susceptibility on magnetic field. This dependence is strongly anisotropic and follows the symmetry of SO splitting

Fermi Surface Resonance and Quantum Criticality in Strongly Interacting Fermi Gases

Fermions in the Fermi gas obey the Pauli exclusion principle restricting any two fermions from filling the same quantum state. Strong interaction between fermions can completely change the properties of the Fermi gas. In our theoretical study we find a new exotic quantum phase in strongly interacting Fermi gases constrained to a certain condition imposed on the Fermi surfaces which we call the Fermi surface resonance. The new phase is quantum critical which can be identified by the power-law frequency tail of the spectral density and divergent static susceptibilities. An especially striking feature of the new phase is the anomalous power-law temperature dependence of the dc resistivity that is similar to strange metals. The new quantum critical phase can be experimentally found in ordinary semiconductor heterostructures

Dimensional reduction of the Luttinger-Ward functional for spin-degenerate DD-dimensional electron gases

We consider an isotropic spin-degenerate interacting uniform $D$-dimensional electron gas (DDEG) with $D > 1$ within the Luttinger-Ward (LW) formalism. We derive the asymptotically exact semiclassical/infrared limit of the LW functional at large distances, $r \gg \lambda_F$, and large times, $\tau \gg 1/E_F$, where $\lambda_F$ and $E_F$ are the Fermi wavelength and the Fermi energy, respectively. The LW functional is represented by skeleton diagrams, each skeleton diagram consists of appropriately connected dressed fermion loops. First, we prove that every $D$-dimensional skeleton diagram consisting of a single fermion loop is reduced to a one-dimensional (1D) fermion loop with the same diagrammatic structure, which justifies the name dimensional reduction. This statement, combined with the fermion loop cancellation theorem (FLCT), agrees with results of multidimensional bosonization. Here we show that the backscattering and the spectral curvature, both explicitly violate the FLCT and both are irrelevant for a 1DEG, become relevant at $D > 1$ and $D > 2$, respectively. The reason for this is a strong infrared divergence of the skeleton diagrams containing multiple fermion loops at $D > 1$. These diagrams, which are omitted within the multidimensional bosonization approaches, account for the non-collinear scattering processes. Thus, the dimensional reduction provides the framework to go beyond predictions of the multidimensional bosonization. A simple diagrammatic structure of the reduced LW functional is another advantage of our approach. The dimensional reduction technique is also applicable to the thermodynamic potential and various approximations, from perturbation theory to self-consistent approaches.Comment: 15 pages, 4 figure

Quantum phase transitions and cat states in cavity-coupled quantum dots

We study double quantum dots coupled to a quasistatic cavity mode with high mode-volume compression allowing for strong light-matter coupling. Besides the cavity-mediated interaction, electrons in different double quantum dots interact with each other via dipole-dipole (Coulomb) interaction. For attractive dipolar interaction, a cavity-induced ferroelectric quantum phase transition emerges leading to ordered dipole moments. Surprisingly, we find that the phase transition can be either continuous or discontinuous, depending on the ratio between the strengths of cavity-mediated and Coulomb interactions. We show that, in the strong coupling regime, both the ground and the first excited states of an array of double quantum dots are squeezed Schr\"{o}dinger cat states. Such states are actively discussed as high-fidelity qubits for quantum computing, and thus our proposal provides a platform for semiconductor implementation of such qubits. We also calculate gauge-invariant observables such as the net dipole moment, the optical conductivity, and the absorption spectrum beyond the semiclassical approximation

First-order magnetic phase-transition of mobile electrons in monolayer MoS2_2

Evidence is presented for a first-order magnetic phase transition in a gated two-dimensional semiconductor, monolayer-MoS$_2$. The phase boundary separates a spin-polarised (ferromagnetic) phase at low electron density and a paramagnetic phase at high electron density. Abrupt changes in the optical response signal an abrupt change in the magnetism. The magnetic order is thereby controlled via the voltage applied to the gate electrode of the device. Accompanying the change in magnetism is a large change in the electron effective mass