Quantum oscillations in the magnetization and density of states of insulators

Abstract

The observation of 1 / B -periodic behavior in Kondo insulators and semiconductor quantum wells challenges the conventional wisdom that quantum oscillations (QOs) necessarily arise from Fermi surfaces in metals. We revisit recently proposed theories for this phenomenon, focusing on a minimal model of an insulator with a hybridization gap between two opposite-parity light and heavy mass bands with an inverted band structure. We show that there are characteristic differences between the QO frequencies in the magnetization and the low-energy density of states (LE-DOS) of these insulators, in marked contrast to metals where all observables exhibit oscillations at the same frequency. The magnetization oscillations arising from occupied Landau levels occur at the same frequency that would exist in the unhybridized case. The LE-DOS oscillations in a disorder-free system are dominated by gap-edge states and exhibit a beat pattern between two distinct frequencies at low temperature. Disorder-induced in-gap states lead to an additional contribution to the DOS at the unhybridized frequency. The temperature dependence of the amplitude and phase of the magnetization and DOS oscillations are also qualitatively different and show marked deviations from the Lifshitz–Kosevich form well known in metals. We also compute transport to ensure that we are probing a regime with insulating upturns in the direct current (DC) resistivity.

de Haas van Alphen oscillations in hybridization-gap insulators as a sudden change in the diamagnetic moment of Landau levels

“…The situation considered by Knolle and Cooper, somewhat generalized in subsequent treatments [3,[5][6][7][8], is as pictured in Fig. 1a.…”

“…The original Knolle and Cooper paper [3] does not suggest a physical origin for the oscillations: they emerge from the mathematics. Subsequent papers by these and other authors [5][6][7][8] simply state that the thermodynamic potential oscillates as Landau levels sequentially cross the region where the bands cross, although Pal [7] makes the enigmatic remark that, as B changes, the Landau levels "feel" the abrupt change in the slope of E(k) and "manifest as quantum oscillations". Moreoever, some papers that offer competing theories, e.g.…”

Quantum oscillations in an impurity-band Anderson insulator

“…The prevalence of these new classes of materials in modern physics makes it important to understand theories for their quantum oscillations. Recent theory has explored quantum oscillations in pristine band insulators [26][27][28][29][30][31], the roles of topological bands [21] and of impurity scattering [32,33], oscillations of the conductivity [34,35] and density of states [33], the effects of interactions [23,[36][37][38][39][40][41], and the consequences of quantum spin liquids [42] and of Kondo breakdown [43]. Experimental measurements of the above Kondo insulators also show other anomalous features.…”

Fluctuation-dominated quantum oscillations in excitonic insulators

“…the de Haas-van Alphen effect [13] -in the Kondo insulators SmB 6 [14][15][16][17] and YbB 12 [18][19][20] was particularly unexpected, since the presence of a Fermi surface was long believed to be a necessary condition to realize this effect [21,22]. Consequently, a large amount of theoretical work has gone into understanding how quantum oscillations (QOs) can manifest in insulators, some focused specifically on these Kondo systems [23][24][25][26][27][28][29][30][31][32], and others considering more general insulating systems [33][34][35][36][37][38][39][40][41][42][43][44][45], including excitonic insulators which will be our focus here.…”

“…Direct calculations show that even simple models of non-interacting band insulators can exhibit QOs [33][34][35][36][37][38][39][42][43][44][45]: provided the minimum band-gap traces out some closed area in reciprocal space the free energy contains an oscillatory component and therefore so do thermodynamic quantities like the magnetization. The resulting QOs have several properties that do not depend on specific details of the model.…”