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

Abstract

We report experimental evidence of a remarkable spontaneous time reversal symmetry breaking in two dimensional electron systems formed by atomically confined doping of phosphorus (P) atoms inside bulk crystalline silicon (Si) and germanium (Ge). Weak localization corrections to the conductivity and the universal conductance fluctuations were both found to decrease rapidly with decreasing doping in the Si:P and Ge:P δ−layers, suggesting an effect driven by Coulomb interactions. In-plane magnetotransport measurements indicate the presence of intrinsic local spin fluctuations at low doping, providing a microscopic mechanism for spontaneous lifting of the time reversal symmetry. Our experiments suggest the emergence of a new many-body quantum state when two dimensional electrons are confined to narrow half-filled impurity bands.Invariance to time reversal is among the most fundamental and robust symmetries of nonmagnetic quantum systems. Its violation often leads to new and exotic phenomena, particularly in two dimensions (2D), such as the quantized Hall conductance in semiconductor heterostructures [1], the quantum anomalous Hall effect in topological insulators [2] or the predicted chiral superconductivity in graphene [3]. The breaking of time reversal invariance is experimentally achieved either by an external magnetic field or intentional magnetic doping. Here we show that strong Coulomb interactions can also lift the time reversal symmetry in nonmagnetic 2D systems at zero magnetic field.While bulk P-doped Si and Ge have been extensively studied in the context of electron localization in three dimensions [4][5][6][7][8][9], confining the dopants to one or few atomic planes (δ−layers) of the host semiconductor has recently led to a new class of 2D electron system [10][11][12][13]. Electron transport in these atomically confined 2D layers occurs within a 2D impurity band where the effective Coulomb interaction is parameterized in terms of U/γ, with U being the Coulomb energy required to add an additional electron to a dopant site, and γ, the hopping integral between adjacent dopants. Since each dopant P atom contributes one valence electron, the impurity band is intrinsically 'half filled' (schematic in Fig. 1a), which reinforces the interaction effects due to the inbuilt electron-hole symmetry, and forms an ideal platform to explore the rich phenomenology of the 2D MottHubbard model, ranging from Mott metal-insulator transition (MIT) to novel spin excitations and magnetic ordering [14][15][16][17].In this Letter we show evidence of spontaneously broken time reversal symmetry in 2D Si:P and Ge:P δ-layers as the on-site effective Coulomb interaction is increased by decreasing the doping density of P atoms. Quantum transport and noise experiments indicate a strong suppression of quantum interference effects at low doping densities. We could attribute this to a spontaneous breaking of time reversal symmetry which manifest in an unambiguous suppression of universal conductance fluctuations (UCF) at zero magnetic fiel...

Dephasing rates for weak localization and universal conductance fluctuations in two dimensional Si:P and Ge:P δ-layers

“…1 and Ref. 42) and n T (∝ T ) is the density of active two level fluctuators373842. The observation of magneto-fingerprinting in and the temperature dependence of establishes the dominance of UCF in our devices.…”

“…However for the Si:P -layer, we were not able to extract for lower density devices since the UCF noise was suppressed at due to a spontaneous breakdown of time reversal symmetry in the strongly interacting regime as has been explained in Ref. 42. The inset of Fig.…”

“…However, we do not observe a full factor of two reduction in N G for Si-1 (it reduces to about 60–70% of the value at ). This happens due to a spontaneous breakdown of time reversal symmetry when the effective on-cite Coulomb interactions increase as has been elaborated in an earlier publication42. The -dependence of N G can be fitted with the theoretical crossover function to estimate the scattering rates relevant to UCF.…”

Bottom-up assembly of metallic germanium

“…The thickness h of the conducting 2D systems in the single and bi-layer samples can be extracted by fitting Δ σ WL ( ϑ ) in Fig. 2a,c to a generalized angle-dependent Hikami-Larkin-Nagaoka expression 20 21 (see Supplementary Section 3 for more details) that includes an additional dephasing rate due to the parallel magnetic field 22 23 . We obtain thicknesses of h = 1.49 ± 0.03 and 6.17 ± 0.05 nm for the single and bi-layer sample, respectively, in agreement with thicknesses of 1.41 ± 0.05 and 7.3 ± 0.2 nm obtained by atom probe tomography.…”

Mitigating valley-driven localization in atomically thin dopant chains in Si

“…However, in the context of low dimensional systems like P-donors arrays in Si, explicit inclusion of electron-electron correlations are known to affect the electronic behavior and may eventually dominate the transport behavior. 30 Nonetheless, the trends found here are expected to contribute to highly correlated chains, for which a detailed inclusion of the geometrical disorder and multi-valley effects may not be trivial.…”