1 Switching between Mott-Hubbard and Hund physics in moir e quantum simulators Siheon Ryee1and Tim O. Wehling12

2025-04-30 0 0 6.25MB 25 页 10玖币
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Switching between Mott-Hubbard and Hund physics in moir´
e quantum simulators
Siheon Ryee1,∗and Tim O. Wehling1,2,∗
1I. Institute of Theoretical Physics, University of Hamburg, Notkestrasse 9, 22607 Hamburg, Germany
2The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany
∗Corresponding author. Email: sryee@physnet.uni-hamburg.de (S.R.); tim.wehling@physik.uni-hamburg.de (T.O.W.)
Abstract
Mott-Hubbard and Hund electron correlations have been realized thus far in separate classes of materials.
Here, we show that a single moir´
e homobilayer encompasses both kinds of physics in a controllable manner.
We develop a microscopic multiband model that we solve by dynamical mean-field theory to nonperturba-
tively address the local many-body correlations. We demonstrate how tuning with twist angle, dielectric
screening, and hole density allows us to switch between Mott-Hubbard and Hund correlated states in a
twisted WSe2bilayer. The underlying mechanism is based on controlling Coulomb-interaction-driven or-
bital polarization and the energetics of concomitant local singlet and triplet spin configurations. From a
comparison to recent experimental transport data, we find signatures of a filling-controlled transition from
a triplet charge-transfer insulator to a Hund-Mott metal. Our finding establishes twisted transition metal
dichalcogenides as a tunable platform for exotic phases of quantum matter emerging from large local spin
moments.
Keywords: moir´
e materials, strongly correlated electrons, Hund physics, Mott-Hubbard physics, charge-
transfer insulator, dynamical mean-field theory
arXiv:2210.13652v3 [cond-mat.str-el] 25 Jan 2023
2
Strong electron correlations in quantum materials are often associated with two different categories. In
single-orbital Mott-Hubbard systems [1, 2], strong correlations promoted by large onsite Coulomb repulsion
[3, 4] lead from Mott insulating to metallic and unconventional superconducting phases upon doping. In
contrast, distinct Hund correlations emerge in materials with almost degenerate multiple orbitals at low en-
ergies [5]. Prominent examples are iron-based superconductors and ruthenates [6–14]. Here, Hund coupling
Jinduces the formation of large local spin moments and impedes the quasiparticle coherence down to very
low temperatures [15–20]. Hund physics can also give rise to many intriguing broken-symmetry phases,
such as spin-triplet superconductivity [21–23], charge orders [24–26], and exciton condensates [27–29].
From a theoretical perspective, Mott-Hubbard and Hund physics arise, respectively, in the strong and
weak crystal-field limits of multiorbital Hamiltonians [5, 30]. Material-wise, however, Mott-Hubbard and
Hund correlated systems have appeared thus far as separate classes of compounds. This missing bridge
is related to chemical constraints on the tunability of “conventional” materials. In this respect, moir´
e het-
erostructures constitute a complementary domain of correlated electron physics [31].
In this work, twisted transition metal dichalcogenide (TMD) homobilayers are shown to host both Mott-
Hubbard and Hund physics. We demonstrate how Coulomb interactions facilitate the promotion of electrons
to higher energy moir´
e bands. As a consequence, multiorbital correlations can arise even in situations in
which moir´
e band theory suggests single-orbital physics. We combine a microscopic multiband contin-
uum model with dynamical mean-field theory (DMFT) [32] to demonstrate how twist angle (θ), dielectric
constant (), and hole density (n) (see Figure 1a) enable continuous switching between Mott-Hubbard and
Hund physics (Figure 1b) for the experimentally most relevant case of twisted WSe2(tWSe2) [33–38]. A
comparison to recent transport experiments [34] reveals a filling-controlled transition from a novel “triplet
charge-transfer insulator” to a strongly correlated Hund-Mott metal. The multiorbital spin correlations are
expected to control, both, excitonic physics and the emergence of magnetism and superconductivity in the
system.
We begin with the AA-stacked bilayer WSe2, where every W and Se atom in the top layer are located
on top of the same type of atom in the bottom layer. Twisting by a small angle θ(Figure 1a), a long-
wavelength moir´
e pattern with concomitant moir´
e Brillouin zone (mBZ) (see Figure 2a) emerges. Due
to the strong spin-valley locking, the topmost valence bands of each monolayer (schematically shown in
Figure 2b) exhibit solely spin-↑character in the Kvalley and spin-↓in the K0valley [39]. The top- and
bottom-layer valence bands hybridize in each valley through interlayer tunneling, which leads, by twisting
the two layers, to minibands at low energies.
A useful strategy to describe the noninteracting band structure associated with the long-wavelength
moir´
e potential is the continuum model [39–43]; see Supporting Information. Our moir´
e bands in Figure 2c
3
dielectric material
dielectric material
top gate
bottom gate
ab
doped
triplet CT ins.
weakly
correlated metal
Hund-Mott
metal (or ins.)
doped
Mott-Hubbard ins.
✓
✓,✏
n=1
n
E|2,1i=E|2,0i0
Figure 1. (a) Twisted TMD homobilayer surrounded by a dielectric material in the side view (top) and top view
(bottom). Voltages applied to the top and bottom gates control the hole density n. The emergent moir´
e superlattice
is illustrated by gray circles marking the AA stacked regions. (b) Nature of electron correlations depending on hole
density n, twist angle θ, and dielectric constant that effectively encodes screening processes affecting the magnitude
of Coulomb interactions.
are consistent with large-scale ab initio calculations at a nearby angle of θ= 5.08◦[34, 43]. We below
focus on θin a range of 3.5◦≤θ≤6.5◦, in light of recent experiments [34, 37]. At first glance, only the
topmost band seems to play a role for hole filling up to n'1.8; see dashed lines in Figure 2c. One of
our main conclusions, however, is that many-body interactions can significantly modify this picture, which
leads to multiorbital (or multiband) physics already at n= 1, contrary to the current belief.
To investigate the impact of electron correlations, we derive a lattice model for the two topmost moir´
e
bands. These bands resemble the parabolic top (bottom) layer states near k+(k−) and display an avoided
crossing in between them (schematically shown in Figure 2b). Using bonding-antibonding combinations of
top and bottom layer states we construct Wannier functions (Supporting Information), |eciησi, from the top-
most two bands. Here, idenotes the site, η∈ {1,2}the orbital, and σ∈ {↑,↓} the spin. The decomposition
of the two topmost bands into the Wannier orbitals in Figure 2c shows that the topmost (second) displays
predominantly |eci1σi(|eci2σi) character.
We now arrive at the two-orbital Hamiltonian H=Hk+PiHi
loc. We hereafter switch to the hole
representation by performing a particle-hole transformation: eciησ →d†
iησ.Hkis the kinetic term consisting
of inter-cell hopping amplitudes (see Supporting Information). Hi
loc contains all the nonnegligible local
terms acting at a site i:
Hi
loc =X
η
Uηniη↑niη↓+X
η<η0,σσ0
(U0−Jδσσ0)niησniη0σ0
+X
η6=η0
J(d†
iη↑d†
iη0↓diη↓diη0↑+d†
iη↑d†
iη↓diη0↓diη0↑) + X
η,σ ∆
2(−1)η−µniησ.
(1)
4
a
θ
top layer
bottom layer
b c max
min
|wi2(r)|2
min
dmax maxmin
e
Mott-Hubbard metal triplet CT insulator Hund-Mott metal
maxmin
f
-60
-40
-20
0
20
40
0 0.05 0.1 0.15 0.2 0.25
A() [arb. units]
Energy [meV]
orbital-1
orbital-2
-100
-80
-60
-40
-20
0
20
40
60
80
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
A() [arb. units]
Energy [meV]
orbital-1
orbital-2
-80
-60
-40
-20
0
20
40
60
80
0 0.02 0.04 0.06 0.08 0.1 0.12
A() [arb. units]
Energy [meV]
orbital-1
orbital-2
M
k+
k
A(!)
M
k+
k
A(!)
M
k+
k
A(!)
![meV]
![meV]
![meV]
![meV]
M
k+
k
M
k+
k
n=1
n= 1.8
k+
k
K
K0
K0
K
(✓= 3.8,✏= 16, n= 1)
(✓= 4.5,✏= 7, n= 1)
(✓= 4.5,✏= 7, n= 2)
Figure 2. (a) Brillouin zones of the top (red) and bottom (blue) layers along with the resulting mBZ (black). (b)
Upper: schematic band dispersion of the top (red) and bottom (blue) layer valence states whose valence band maxima
are located, respectively, at k+and k−points. Lower: schematic moir´
e bands resulting from the hybridization between
the top and bottom layer bands. (c) The band characters are represented by color intensity for orbital-1 (left panel;
η= 1) and orbital-2 (right panel; η= 2). The spin-↑band originating from the Kvalley and the spin-↓band from
K0are degenerate. The horizontal dashed lines indicate Fermi levels for two different hole fillings within a rigid-band
model. (d, e, f) Influence of many-body effects on excitation spectra as obtained from DMFT. The momentum-
dependent spectral functions A(k, ω)(color coded) and the local density of states A(ω)are shown for representative
examples of correlated regimes realized in tWSe2: (d) Mott-Hubbard metal, (e) triplet CT insulator, and (f) Hund-
Mott metal. The chemical potential is at ω= 0. White solid lines indicate the noninteracting continuum bands for the
same n.
niησ =d†
iησdiησ is the hole number operator. µis the chemical potential that determines the hole filling
and is experimentally controllable via gate voltage (see Figure 1a). Uηand U0are intra- and inter-orbital
Coulomb repulsions, respectively. Jis the Hund exchange coupling. The real-space shape of the Wannier
functions leads to an unusual hierarchy of Coulomb terms: U1> U0> U2> J. The values of Uη,
U0, and Jare tunable via twist angle and dielectric screening, where the latter approximately modifies the
Coulomb potential vc(r,r0) = e2/(|r−r0|)(see Supporting Information for further analysis). ∆(∆>0)
is the local energy-level splitting between the two orbitals and plays the role of a crystal field. To address
nonperturbatively the effects of the local many-body interactions, we solve the model using DMFT [44]
(see Supporting Information). For hole fillings smaller than n= 1 (n=Piησhniησi/Nswhere Nsis the
5
number of lattice sites), the low-energy physics is essentially captured by a single-orbital model. We thus
focus on a range of 1≤n≤2.
We first discuss how interactions affect the electron/hole excitation spectra. Central observables are the
momentum-dependent spectral function A(k, ω)and the local density of states A(ω), which can be mea-
sured by photoemission or scanning tunneling spectroscopies, respectively. Figures 2d–f presents A(k, ω)
and A(ω)of three different correlated states. Many-body interactions significantly modify the excitation
spectra compared to the noninteracting cases. Specifically, incoherent upper Hubbard bands (located far
above ω= 0) stemming from orbital-1 are clearly visible in all of the three cases. Lower Hubbard bands
(located below ω= 0) also form, but they are smeared over wider energy ranges due to the hybridization
with the relatively coherent states of orbital-2 (η= 2) character.
Looking into the spectra in more detail reveals distinct features in each regime. In the Mott-Hubbard
case (Figure 2d), low-energy charge excitations involve almost exclusively orbital-1. We also find that a
flatter dispersion (i.e., enhanced quasiparticle mass) emerges near ω= 0 compared to the noninteracting
one due to a large band-renormalization promoted by Mott-Hubbard physics. Hubbard models based solely
on orbital-1 can describe this case, as was done and reported previously [45–50].
For a smaller (i.e., weaker dielectric screening), however, the single-orbital description breaks down.
In Figure 2e, a pronounced charge gap emerges at one-hole filling, which demonstrates a phase transition to
a correlated insulator by many-body interactions. The nature of this insulating phase is clearly distinct from
what is expected from single-orbital Mott-Hubbard physics. Namely, the lowest-energy charge excitations
involve both orbital characters on the hole side. As a consequence, doped holes will occupy both orbitals.
Upon further hole doping (energies below ω' −20 meV), almost all the holes should go into orbital-2;
see the orbital-2 weight pronounced in A(ω)near ω' −40 meV. This type of insulator is reminiscent of
charge-transfer (CT) insulators [51]. Importantly, however, due to the Jin the system, two holes distributed
over both orbitals in a site should favor a local triplet, as opposed to the singlet realized in many typical CT
insulators like cuprates [52]. We, thus, call this phase a “triplet CT insulator”.
Heavy hole doping the triplet CT insulator up to n= 2 (Figure 2f) gives rise to a metal with strong mass
enhancement and with broad incoherent excitations up to about ±80 meV. Here, both orbitals contribute
again to the low-energy spectral weight. Since both orbitals are almost equally occupied in this regime, J
plays a crucial role in promoting strong correlations, which will be analyzed further below.
To pinpoint the microscopic origin of the distinct correlations revealed by the spectral functions, we look
at the eigenstates and eigenvalues of Hi
loc in the two-hole subspace. Here, two types of lowest-energy states
are competing in energy: an orbital-polarized singlet |N= 2, S = 0i0(N: the number of holes, S: total
spin of Nholes) and triply degenerate states |2,1i, where each orbital is occupied by one hole and total
摘要：

1SwitchingbetweenMott-HubbardandHundphysicsinmoir´equantumsimulatorsSiheonRyee1;andTimO.Wehling1;2;1I.InstituteofTheoreticalPhysics,UniversityofHamburg,Notkestrasse9,22607Hamburg,Germany2TheHamburgCentreforUltrafastImaging,LuruperChaussee149,22761Hamburg,GermanyCorrespondingauthor.Email:sryee@phy...

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